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Essays on the effect of cognitive constraints on financial decision-making

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Essays on the effect of cognitive constraints on financial decision-making

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Content ESSAYS ON THE EFFECT OF COGNITIVE CONSTRAINTS ON FINANCIAL DECISION-MAKING by Constantin Charles A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (FINANCE AND BUSINESS ECONOMICS) May 2023 Copyright 2023 Constantin Charles Table of Contents List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Chapter 1: Memory and Trading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Empirical Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.1 Retail Investors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.2 Mutual Fund Managers . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4.1 Baseline Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4.2 Identifying Cueing Trades using Earnings Announcements . . . . . . 16 1.4.3 Similarity and Interference . . . . . . . . . . . . . . . . . . . . . . . . 16 1.4.4 Recency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.4.5 Contiguity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.5 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.5.1 Addressing Attention Spillover . . . . . . . . . . . . . . . . . . . . . . 23 1.5.2 Not a Relabeling of the Rank Effect . . . . . . . . . . . . . . . . . . . 26 1.5.3 Extremely Tight Fixed Effects . . . . . . . . . . . . . . . . . . . . . . 26 1.5.4 Alternative Weighting Functions . . . . . . . . . . . . . . . . . . . . . 30 1.6 Further Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 1.6.1 Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 1.6.2 Buying vs. Selling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 1.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Chapter 2: Memory Moves Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.2 Empirical Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.3.1 Full Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 ii 2.3.2 Pattern Firm Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.3.3 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.4.1 Baseline Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.4.2 Contiguity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.4.3 Recency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.4.4 Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.5 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.5.1 Reversals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.5.2 Surprise of the Cue . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.5.3 Large vs. Small Firms . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2.5.4 Trading Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 2.5.5 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 2.5.6 Alternative Explanations . . . . . . . . . . . . . . . . . . . . . . . . . 70 2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Chapter 3: Insensitive Investors (with C. Frydman and M. Kilic) . . . . . . . . . . . 74 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.2 Conceptual framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.2.1 Frictionless benchmark . . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.2.2 Insensitive actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.2.2.1 Compression towards a default valuation . . . . . . . . . . . 81 3.2.2.2 Implications for the risk-return relation . . . . . . . . . . . . 83 3.2.3 Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.3 Experiment 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.3.1 Experimental design . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.3.1.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . 87 3.3.1.2 Experimental procedures . . . . . . . . . . . . . . . . . . . . 90 3.3.2 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 3.3.2.1 Summary statistics . . . . . . . . . . . . . . . . . . . . . . . 91 3.3.2.2 Pricing results . . . . . . . . . . . . . . . . . . . . . . . . . 92 3.3.2.3 Subjective vs. objective expected returns . . . . . . . . . . . 95 3.3.2.4 Objectivity of beliefs and the transmission of beliefs to willingness to pay . . . . . . . . . . . . . . . . . . . . . . . . 97 3.4 Experiment 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 3.4.1 Experimental design . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 3.4.2 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 3.5.1 Implications for asset pricing models . . . . . . . . . . . . . . . . . . 106 3.5.2 Connections with the survey literature . . . . . . . . . . . . . . . . . 108 3.5.3 Sources of the weak transmission . . . . . . . . . . . . . . . . . . . . 109 3.5.4 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 iii 3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 G Chapter 1: Theoretical Framework . . . . . . . . . . . . . . . . . . . . . . . 121 H Chapter 1: Additional Tables . . . . . . . . . . . . . . . . . . . . . . . . . . 124 I Chapter 2: Additional Tables . . . . . . . . . . . . . . . . . . . . . . . . . . 129 J Chapter 3: Additional Figures . . . . . . . . . . . . . . . . . . . . . . . . . . 133 K Chapter 3: Derivations for the conceptual framework . . . . . . . . . . . . . 137 K.1 Gaussian signal extraction . . . . . . . . . . . . . . . . . . . . . . . . 137 K.2 Estimating x from willingness to pay and payoff expectations . . . . . 137 L Chapter 3: Expected cash flow and return effects . . . . . . . . . . . . . . . 138 M Chapter 3: Results using tail risk . . . . . . . . . . . . . . . . . . . . . . . . 139 N Chapter 3: Heterogeneity across subjects . . . . . . . . . . . . . . . . . . . . 141 O Chapter 3: Screenshots of the experiments . . . . . . . . . . . . . . . . . . . 142 O.1 Experiment 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 O.2 Experiment 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 iv List of Tables 1.1 : Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.2 : Baseline Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3 : Identifying Cueing Trades . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.4 : Similarity and Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.5 : Recency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.6 : Contiguity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.7 : Non-Adjacent Stock Pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.8 : Not a Relabeling of the Rank Effect . . . . . . . . . . . . . . . . . . . . . . 28 1.9 : Extremely Tight Fixed Effects . . . . . . . . . . . . . . . . . . . . . . . . . 29 1.10 : Alternative Weighting Functions . . . . . . . . . . . . . . . . . . . . . . . . 32 1.11 : Buying vs. Selling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.1 : Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.2 : Baseline Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.3 : Contiguity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.4 : Recency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2.5 : Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 2.6 : Reversals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.7 : Surprise of the Cue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 2.8 : Large vs. Small Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2.9 : Trading Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 2.10 : Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.1 : Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 3.2 : WTP, Subj. Exp. Payoffs, and Perc. Risk . . . . . . . . . . . . . . . . . . 92 v 3.3 : Subj. Exp. Returns, Subj. Exp. Payoffs, and Perc. Risk . . . . . . . . . . 95 3.4 : Transmission of Beliefs for Calibrated and Miscalibrated Subjects . . . . . 99 3.5 : Summary Statistics for Experiment 2 . . . . . . . . . . . . . . . . . . . . . 102 3.6 : WTP, Exp. Payoffs, and Perc. Risk in both Experiments . . . . . . . . . . 103 3.7 : Exp. Returns, Exp. Payoffs, and Perc. Risk in both Experiments . . . . . 104 3.8 : Linking Backwards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 3.9 : Memorability < 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 3.10 : Conditioning on Only One Trade . . . . . . . . . . . . . . . . . . . . . . . 126 3.11 : Recency with Additional Fixed Effects (1) . . . . . . . . . . . . . . . . . . 127 3.12 : Recency with Additional Fixed Effects (2) . . . . . . . . . . . . . . . . . . 128 3.13 : Baseline Results using only Largest Cue . . . . . . . . . . . . . . . . . . . 129 3.14 : Recency using only Largest Cue . . . . . . . . . . . . . . . . . . . . . . . . 130 3.15 : Interference using only Largest Cue . . . . . . . . . . . . . . . . . . . . . . 131 3.16 : Surprise of Largest Cue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 3.17 : Decomposition of Variation in WTP . . . . . . . . . . . . . . . . . . . . . . 138 3.18 : Subj. Expected Returns, Subj. Expected Payoffs, and Perceived Tail Risk . 139 3.19 : Decomposition of Variation: Subject and Time Fixed Effects . . . . . . . . 141 vi List of Figures 1.1 Baseline Results in the Raw Data . . . . . . . . . . . . . . . . . . . . . . . . 13 1.2 Heterogeneity in the Memory Effect . . . . . . . . . . . . . . . . . . . . . . . 33 2.1 Calendar Rotations: An Example . . . . . . . . . . . . . . . . . . . . . . . . 46 2.2 Contiguity Return Response (%) on the Day of a Memory Cue . . . . . . . . 55 2.3 Recency Return Response (%) on the Day of a Memory Cue . . . . . . . . . 58 2.4 Interference Return Response (%) on the Day of a Memory Cue . . . . . . . 61 3.1 The Impact of the Weak Transmission on the Risk-Return Relation . . . . . 85 3.2 WTP and Subj. Exp. Payoffs . . . . . . . . . . . . . . . . . . . . . . . . . . 93 3.3 Subjective Expected Returns and Perceived Risk . . . . . . . . . . . . . . . . 96 3.4 Subject-level Average Expected Payoff . . . . . . . . . . . . . . . . . . . . . 98 3.5 Expected Returns and Risk in Experiment 2 . . . . . . . . . . . . . . . . . . 105 3.6 Subjective Expected Payoffs and Perceived Risk . . . . . . . . . . . . . . . . 133 3.7 Departures from Bayesian Expectations and Perceived Risk . . . . . . . . . . 134 3.8 Bayesian Expected Returns and Perceived Risk . . . . . . . . . . . . . . . . 135 3.9 Subjective Expected Returns and Subjective Expected Payoffs . . . . . . . . 136 3.10 Subjective Expected Returns and Perceived Tail Risk . . . . . . . . . . . . . 140 3.11 Distribution in the good state . . . . . . . . . . . . . . . . . . . . . . . . . . 142 3.12 Distribution in the bad state . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 3.13 Dividend realization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 3.14 Overview of history of dividend realizations . . . . . . . . . . . . . . . . . . 143 3.15 Elicitation of payoff expectations . . . . . . . . . . . . . . . . . . . . . . . . 144 3.16 Elicitation of willingness to pay (after initiation) . . . . . . . . . . . . . . . . 145 3.17 Display of payoff distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 146 vii 3.18 Elicitation of willingness to pay (after initiation) . . . . . . . . . . . . . . . . 147 viii Abstract I show that cognitive constraints affect financial decision-making. First, I test the pre- dictions of human memory models in a high-stakes trading environment. Using alphabetical rankings of stocks from portfolio statements, I estimate plausibly random associations of adjacent stocks in an investor’s memory. When two stocks are associated in an investor’s memory, trading one stock cues the recall of the other, and increases the probability that the investor also trades the other stock. Second, I show that memory-induced attention can distort prices in financial markets. I exploit rigid earnings announcement schedules to identify which firms are associated in memory for many investors at the same time. Firms with randomly overlapping earnings announcements are associated in memory because they were experienced in the same context by many investors. Months later, when only one of the two firms announces earnings, this context is cued, and triggers the recall of the other, associated firm. On such days, I find that memory-induced attention leads to buying pres- sure in the associated firm’s stock. Third, in work with my co-authors, we show theoretically that the weak transmission of beliefs to actions induces a strong bias in basic asset pricing tests. We experimentally test this prediction and find that subjects exhibit an extremely weak transmission of beliefs to actions, which generates a negative risk-return relation. We argue that the weak transmission is due to cognitive noise and demonstrate that cognitive noise causally affects the risk-return relation. ix Chapter 1 Memory and Trading 1.1 Introduction An increasing body of empirical work documents that past experiences are important for determining financial decisions. Malmendier and Nagel (2011) show that investors who lived through the Great Depression are less likely to invest in the stock market later in life. In a similar context, experienced inflation has a disproportionate effect on expected inflation (Malmendier and Nagel (2016); Malmendier et al. (2021)). Motivated by this type of evidence, new theories of memory and economic choice – based on decades of experimental memory research – have emerged. Memory theories have broad applications in finance. For instance, they can can generate the experience effects mentioned above (Wachter and Kahana (2021)), they can generate overreaction to news (Da Silveira et al. (2020); Bordalo et al. (2022b)), they can shed light on investor behavior during financial crises (Wachter and Kahana (2021)), and they can explain asset pricing puzzles (Nagel and Xu (2022a)). However, despite their promise, empirical tests of these models in finance remain scarce. In this paper, I develop an empirical proxy for an investor’s memory that I use to conduct sharp tests of the growing class of memory models in finance. In doing so, I document a new fact about how individual investors and mutual fund managers behave. While similar tests have been run in the controlled laboratory over short timescales (Enke et al. (2022)), my empiricalapproachallowsmetoassesswhetherthesememorymodelsalsoprovidereasonable predictions over timescales of years and in a high-stakes trading environment. I find that 1 many of the properties of memory that have been embraced by the psychology literature for over a century (Kahana (2012)) also emerge in a database of individual investor trading decisions. I design my empirical tests by applying the theory of Bordalo et al. (2020), which builds on associative memory theory, to a setting of trading. The key idea of this theory is that a cue (e.g., a trade) triggers the recall of past trading experiences, especially those that are similar to the cue. The probability of recalling an experience is determined by two competing forces: similarity and interference. If the similarity between the cue and the experience is higher, the investor is more likely to recall the experience. However, if the cue is similar to many experiences in the investor’s memory, these other experiences interfere with recall and reduce the probability that the investor recalls the focal experience. I use the Barber and Odean (2000) data on the holdings and trades of retail investors to testwhethertradingdecisionsfollowthepredictionsofthistheoreticalframework. Guidedby the theory, I develop a measure – called Memorability jkit – that captures how strongly two stocks (j andk) are associated in investori’s memory on dayt. An increase in the similarity of two stocks increases Memorability jkit of the stock pair, while an increase in interference from other stocks decreasesMemorability jkit of the stock pair. Memorability jkit is the ratio of similarity to interference, and is bounded by 0 and 1. To construct Memorability jkit , I rely on an institutional feature that determines how investors receive information about their portfolio holdings. The investors in the Barber and Odean (2000) data receive monthly paper statements that display their portfolio holdings in alphabetical order. I use this alphabetical ranking to connect stocks that are adjacent on an investor’s monthly statement. My approach is inspired by classic experiments from the memory literature, in which participants study lists of random words. A striking finding is that adjacent words on the list are much more strongly associated in memory than any other two words on the list. The key idea behind my approach is that investors’ portfolio listings are very similar to the word lists in these experiments, allowing me to apply these insights to my institutional setting. To supplement the retail investor data and test for memory effects among professional investors, I also construct Memorability jkit for mutual 2 fund managers using the alphabetical ranking of the fund’s portfolio holdings. I source the quarterly holdings of mutual funds from Thomson Financial. By relying on alphabetical rankings,Memorability jkit is designed to capture associations that are orthogonal to stock fundamentals. The key assumption is that stock fundamentals are unrelated to the alphabetical ranking in an investor’s portfolio. Further, the associations are investor-specific: since alphabetical rankings differ across investors, the same two stocks may be associated for one investor but not for another. Finally, the associations may change over time, even for the same investor. Because the alphabetical ranking can change from one month to the next, two stocks might be associated at one point, but this association can fade away as time progresses. I compute Memorability jkit on a rolling basis using portfolio statements from the previous twelve months. With the memory associations captured byMemorability jkit , I can test whether memory associations affect trading behavior. To classify trades as memory-induced trades, I assume that recalling a stock increases the probability of trading the stock. Specifically, I assume that when an investor trades a stock, this trade (=the cue) brings back the memory of associated stocks. If the investor also trades an associated stock on the same day, I classify this second trade as a memory-induced trade. In my main tests, I regress a dummy variable indicating a memory-induced trade on Memorability jkit . I also include stock-pair fixed effects into this regression. By including stock-pair fixed effects, I fix two stocks, j andk, and leverage variation inMemorability jkit within and across investors. This approach holds stock fundamentals fixed and only varies Memorability jkit , which corresponds to a thought experiment in which I exogenously in- crease the memory association between two stocks to see how this affects the probability of a memory-induced trade. Using this specification, I find that a one-standard deviation increase in Memorability jkit increases the probability of a memory-induced trade by 4.82 percentage points. Put differ- ently, an increase in Memorability jkit from no memory association to full association leads to an increase in the trade probability of 13.40 percentage points. I find similar effects for the trades of mutual fund managers. In terms of magnitude, these effect sizes are comparable to the rank effect in Hartzmark (2015). 3 To better understand the mechanism behind my results, I zoom in on the different prop- erties of memory and test whether they drive individual trading decisions. These properties have decades of empirical support in the memory literature (Kahana (2012)). First, I test for the separate effects of similarity and interference. As expected, if the similarity between two stocks increases by one standard deviation, the probability of a memory-induced trade increases by about 5 percentage points. Crucially, interference from competing stock pairs reduces this effect, as predicted by theory. If interference increases by one standard devia- tion, the trade probability falls by about 3 percentage points. These results validate a key prediction of associative memory theory (Bordalo et al. (2020); Bordalo et al. (2022a)). Second, I test for the recency effect, i.e., whether recent experiences are easier to re- call than experiences from the distant past. Indeed, I find a stronger memory effect for associations estimated from recent monthly statements than for associations estimated from distant monthly statements. Third, I test for a characteristic pattern of memory, called the contiguity effect. This well-established effect refers to the finding that two items share a stronger association if they were experienced closer together. In line with this prediction, I find that the memory effect is weaker the further two stocks are positioned from each other in an alphabetically ranked portfolio. In sum, the memory-induced trades that I document are consistent with several sharp predictions of memory theory. Iprovideseveralrobustnessteststhathelpruleoutalternativetheories. First, Ishowthat the memory effect is not mechanically driven by portfolio size. I also show that stock-specific or stock-pair-specific information on the trading day cannot explain my results. Further, I show that my results are not a relabeling the rank effect (Hartzmark (2015)). Finally, I perform tests aimed at addressing concerns that my results might be driven by attention spillover rather than memory (Peng and Xiong (2006); Barber and Odean (2008); Hirshleifer et al. (2009); Da et al. (2011); An et al. (2022)). In these tests, I continue to find memory effects for stock pairs that were historically close to each other on a statement, but that are not close on the most recent portfolio statement. I contribute to the literature on experience effects, which has shown that life experiences have strong and persistent effects on financial decisions (Malmendier and Nagel (2011, 2016); Malmendier et al. (2011); Malmendier and Shen (2020); Malmendier et al. (2021)). My 4 results help uncover the mechanism behind these experience effects, since I design precise tests of memory theories that can generate such experience effects. Ialsocontributetothelargeliteratureoninvestorbehavior. Whilemuchofthisliterature has focused on retail investors (for an overview, see Barber and Odean (2013)), several studies also analyze trading behavior at the professional level (Wermers (1999); Griffin et al. (2003); Frazzini (2006); Jin and Scherbina (2011); Hartzmark (2015); Akepanidtaworn et al. (2021)). I add to this literature by showing that memory effects in trading are pervasive amongst both retail and institutional investors. Recent work has also incorporated memory into asset pricing (Bodoh-Creed (2020); Nagel and Xu (2022a)). My results lend support to this approach by providing evidence of memory effects in financial markets. More broadly, my findings relate to work that incorporates aspects of human memory into economic choice (Gilboa and Schmeidler (1995); Mullainathan (2002); Hirshleifer and Welch (2002); Bordalo et al. (2020); Wachter and Kahana (2021); Bordalo et al. (2022a)) and forecasting (Da Silveira et al. (2020); Afrouzi et al. (2022)). While the theoretical literature has pushed ahead in this area, empirical evidence of such memory effects remains scarce. To help fill this gap, two recent studies provide evidence from the experimental laboratory (Enke et al. (2022); Gödker et al. (2022)), while another study uses survey data (Colonnelli et al. (2021)). I test the models using trading decisions from high-stakes financial markets and support this growing body of theoretical work with evidence from the field. 1.2 Empirical Strategy In order to test whether the memory associations of stocks in an investor’s mind systemati- cally affect trading decisions, I need a measure that captures which stocks are associated in memory for each investor at each point in time. In the ideal experiment, I would randomly associate different stocks for different investors and then test whether these associations drive trading decisions. I approximate this ideal experiment by building on decades worth of theoretical and experimental work from the memory literature (Kahana (2012)), and discuss my approach in this section. In Appendix G, I also present a theoretical framework that illustrates the main forces of associative memory theory in a trading setting. 5 In associative memory theory, recall is driven by two competing forces: similarity and interference. To illustrate these forces, consider the following classic experiment from the memory literature. Participants study a list with N random words, which are provided sequentially from n = 1 to N. After the study phase, participants are asked to freely recall words from the list. A striking finding is that upon recalling any word with serial position n from the list, participants are much more likely to recall the word with serial position n + 1 compared to any other word from the list. In associative memory theory, these two words are encoded as similar in memory because they were experienced immediately after one another. As a result, cueing the word with serial position n triggers the recall of the word with serial position n + 1. However, recall is also affected by a second force: interference. If the cueing word is asso- ciated with many other words – e.g., because the participant studied several lists containing the cueing word – associations from these other lists can lead to interference in recall. That is, the participant might recall an associated word from one of the other lists instead of the word with serial position n + 1 from the focal word list. In my empirical strategy, I apply these insights to my institutional setting to estimate which stocks are associated in an investor’s memory. In estimating these associations, I rely on an important feature of my data set. Investors in my data set receive monthly paper statements that display their portfolio holdings in alphabetical order. The key idea behind my approach is that these portfolio listings are very similar to the word lists from the experiments described above. Further, the alphabetical rankings allow me to estimate associations that are orthogonal to stock fundamentals (I discuss this feature in more detail below). I estimate the similarity between two stocks as follows: S jkit = 12 X m=1 d jkim ·w m (1.1) Here,d jkim is a dummy variable that is equal to one if stockj immediately follows stock k on investori’s alphabetically ranked portfolio statement in month m. 1 As in the word list 1 I use forward-linking because humans generally read from top to bottom. In robustness tests, I link each stock to its predecessor in the ranking and find similar results. These results are displayed in Appendix Table 3.8. 6 experiments, adjacent stocks on a statement are experienced immediately after one another and should therefore be more strongly associated in memory than stocks that are located further away from each other. Thus, the dummy variable d jkim is a simple measure that is driven by the key forces of associative memory theory. To account for the role of recency in recall, the term w m is a weighting parameter that decayslinearlyfromthemostrecentportfoliostatementdowntozeroforportfoliostatements that are older than twelve months. 2 This weighting scheme is inspired by Malmendier and Nagel (2011), which shows that such a linear weighting scheme is a good approximation for the recency effect in the domain of experience effects in finance. 3 The weights sum up to one, bounding S jkit by zero and one. For each investor, I estimate S jkit on a rolling basis, using the monthly portfolios holdings from the previous twelve months. The measureS jkit is designed to capture associations that are orthogonal to stock funda- mentals by relying on the alphabetical rankings of tickers in investors’ monthly statements. The key assumption is that the alphabetical ranking in an investor’s portfolio is unrelated to stock fundamentals. It is worth noting that I do not need to assume that an individual stock’s ticker is unrelated to its fundamentals, since my measure is defined by the associa- tion of two stocks. Further, the associations are investor-specific: since alphabetical rankings differ across investors, the same two stocks may be associated for one investor but not for another. Finally, the associations may change over time, even for the same investor. Be- cause the alphabetical ranking can change from one month to the next, two stocks might be associated at one point, but this association can fade away as time progresses. Using this measure of similarity, I can construct the following composite measure: Memorability jkit ≡ S jkit P M x=1 S xkit (1.2) This measure captures the two key forces of associative memory theory. The term in the numerator is the pairwise similarity between stocks j and k. All else equal, if the similarity 2 The importance of recency in recall is well-documented in the memory literature. In the word list experiments described above, participants are generally most likely to recall words from the end of the list, since these are the words that they experienced most recently (Murdock Jr (1962)). 3 My results are robust to alternative weighting schemes. In Table 1.10, I show that I find similar results for (1) a weighting scheme that is calibrated to the data, and (2) if I omit the weighting scheme altogether. 7 betweenj andk is higher, the strength of the memory association betweenj andk increases. As a result, when cued with stock k, the investor is more likely to recall stock j. In contrast, the term in the denominator captures interference. Interference refers to the idea that the cue (here, stock k) might be similar to many stocks in the investor’s memory. These other stocks interfere with the recall of stock j. The denominator measures interference by summing the similarities between stock k and all M stocks in the memory database. If this sum is larger, interference is larger, and the probability of recalling stock j is lower. For expositional purposes, I label the combined measureMemorability jkit . This is the main measure in my empirical tests. To connect this measure to trading behavior, I make the following additional assumption: when an investor recalls a stock, he is more likely to trade the stock. Suppose that, as in the theoretical framework in Appendix G, there is a cue κ that contains stock k. Then, conditional on the cue κ, the probability of trading the associated stock j is an increasing function of Memorability jkit . I assume that the cue κ is a trade in stock k and that the function f is linear. This yields: P (Trade Stock j|Trade Stock k) it =α +β·Memorability jkit (1.3) I estimate this equation using the trades of a panel dataset of investors. In my empirical tests, I run the following regression, in whichj andk index stocks,i investors, andt trading days. I(Trade Stock j|Trade Stock k) it =α jk +β·Memorability jkit +ϵ jkit (1.4) In this regression, the dependent variable is a dummy variable that is equal to one if, conditionalontradingstockk, theinvestoralsotradestheassociatedstockj onthesameday. The independent variableMemorability jkit captures the strength of the memory association and is estimated using the investor’s portfolio holdings from the previous twelve months. While Memorability jkit is designed to be orthogonal to stock fundamentals, the ideal approach also holds stock fundamentals fixed and only varies Memorability jkit . This ap- proach addresses any concerns that the fundamentals of stocks could be correlated in ways 8 that are related to their alphabetical similarity (Jacobs and Hillert (2016)). To implement this approach, I fix two stocks, j andk, and leverage variation inMemorability jkit between those two stocks within and across investors. In the regression, this corresponds to including a stock-pair fixed effect α jk . This is the main specification that I estimate in my empirical analysis. 1.3 Data 1.3.1 Retail Investors I use data on the holdings and trades of retail investors, for the years 1991 to 1996, to calculate Memorability jkit and to identify memory-induced trades. These data are the same as in Barber and Odean (2000). The investors in this data set receive monthly paper statements containing their portfolio holdings. On the statements, the holdings are displayed in alphabetical order. I use this alphabetical ranking to construct Memorability jkit . I retain only common stocks, drop all trades with negative commissions, and match the data to CRSP for information on stock prices and tickers. The data specify the day on which an investor executed a trade, and I retain only days on which an investor traded at least two different stocks. I focus on these days since I require at least one trade to act as a cue, which brings back the memory of associated stocks. The other trade(s) allow me to identify memory-induced trades. 4 Finally, I retain only investors who trade on more than five distinct days in a year, to rule out the concern that my results are driven by investors who hold the same portfolio for an entire year and rebalance their portfolio once a year. This behavior could look like memory-induced trading since it would result in high Memorability jkit between adjacent stock pairs and in high joint trade probabilities. 4 In Appendix Table 3.10, I show that my results also hold when I include trading days on which an investor only traded one stock. These tests implicitly include a prediction task, namely predicting whether an investor will execute a second (potentially memory-induced) trade on the same day. Giglio et al. (2021a) show that it is difficult to predict when investors trade. Conditional on trading, however, investors trade according to their beliefs. Therefore, in my main tests, I abstract from predicting whether investors execute a second trade and instead focus on whether memory affects which stocks investor choose to trade, conditional on trading. 9 In Panel A of Table 1.1, I provide summary statistics for the sample of retail investors, which includes 11,164 distinct investors. For these investors, there are a total of 63,245 investor-days on which an investor sold at least two stocks. In my tests, however, the number of observations is generally larger than 63,245. This is because an observation in my setting is identified by a stock pair that is associated in an investor’s memory on a trading day, i.e., a stock pair that was adjacent at least once over the past twelve months. Thus, the number of observations on an investor-day is given by all pairs of associated stocks in the investor’s memory. 5 On average, investors in my sample hold 15 stocks in their portfolio (median: 9). The average probability of a memory-induced trade is 12%. When I break out memory-induced trades by buys and sells, I find that memory-induced sells are more likely than memory- induced buys. I explore this asymmetry in more detail in Table 1.11. Memorability jkit is bounded by zero and one, and has an average of 0.604. 6 1.3.2 Mutual Fund Managers I also construct these variables for mutual fund managers using data on funds’ quarterly holdings for years 2000 to 2014. I create this sample by merging data on open-end US equity funds contained in the mutual fund database of the Center for Research in Security Prices (CRSP) with data on their quarterly holdings from Thomson Financial. As in Lou (2012), I impose several restrictions to ensure satisfactory data quality. First, I exclude all funds that report an investment objective code indicating “international,” “municipal bonds,” “bond & preferred,”or“metals”inThomsonFinancial. Second, Irequiretheaggregatevalueofequity holdings of a fund-quarter in Thomson Financial to be within the range of 75% and 120% of the fund’s total net assets reported in Thomson Financial. Third, total net assets reported in Thomson Financial for a fund-quarter may not differ by more than a factor of two from 5 Notice that I am not double counting stock pairs in my sample. This is because I associate stocks only in the forward direction, resulting in a clear one-directional relationship from cueing to cued stock. In Table 3.8, I show similar results when I associate stock pairs in the backward direction. 6 There are several observations withMemorability jkit equal to one. This happens when the cueing stock was associated with only one stock over the past twelve months. For these stock pairs, the numerator and denominator of Memorability jkit are identical, resulting in Memorability jkit equal to one. In Appendix Table 3.9, I show that these observations are not driving my results. In these tests, I drop all observations with Memorability jkit equal to one and find similar results. 10 Table 1.1: Summary Statistics Panel A: Retail Investors Mean p25 p50 p75 Std. Dev. Min Max N #Stocks in portfolio 15 5 9 16 29 1 632 63,245 Memory-induced trade (dummy) 0.120 0.000 0.000 0.000 0.325 0.000 1.000 175,081 Memory-induced buy (dummy) 0.031 0.000 0.000 0.000 0.172 0.000 1.000 175,081 Memory-induced sell (dummy) 0.089 0.000 0.000 0.000 0.285 0.000 1.000 175,081 Memorability 0.604 0.267 0.588 1.000 0.356 0.013 1.000 175,081 Panel B: Mutual Funds Mean p25 p50 p75 Std. Dev. Min Max N #Stocks in portfolio 99 45 68 104 130 2 3,670 54,715 Memory-induced trade (dummy) 0.192 0.000 0.000 0.000 0.394 0.000 1.000 727,507 Memory-induced buy (dummy) 0.084 0.000 0.000 0.000 0.277 0.000 1.000 727,507 Memory-induced sell (dummy) 0.109 0.000 0.000 0.000 0.311 0.000 1.000 727,507 Memorability 0.683 0.400 0.714 1.000 0.325 0.100 1.000 727,507 Notes: This table contains summary statistics of the two samples used in the empirical analysis. Panel A describes the sample of retail investors and Panel B describes the sample of mutual funds. A given stock may be associated with multiple stocks in the investor’s or fund manager’s memory, resulting in the large number of observations for memory variables. A memory-induced trade is defined at the investor-day-stock-pair level (Panel A) or the fund-quarter-stock-pair level (Panel B) and is a dummy variable that is equal to one if conditional on a trade in one stock of the stock pair (=the cueing stock), the investor (fund manager) also trades the other stock of the stock pair on the same day (in the same quarter). Memorability measures how strongly two stocks of a stock pair are associated in memory. It is bounded by zero (no association) and one (full association). those reported in the CRSP mutual fund database. Fourth, I exclude all fund-quarters with total net assets of less than $1 million in either the Thomson Financial or the CRSP mutual fund database. For the remaining observations, I cross-check each individual stock holding with data from the CRSP daily stock file as of the holding’s reporting date. Specifically, I require that the split-adjusted share price and the number of shares outstanding reported in Thomson Financial do not differ by more than 30% from those reported in the CRSP daily stock file. Finally, shares held by a single fund may not exceed the total number of shares outstanding in the CRSP daily stock file. Using the resulting sample, I calculate Memorability jkit and identify memory-induced trades in analogy to the sample of retail investors. Due to differences between the two data sets, I make several minor adjustments. In contrast to the retail investor data, I cannot observe how fund managers display their holdings internally. Thus, I construct 11 Memorability jkit for fund managers assuming that managers display their holdings alpha- betically. Second, to match the reporting frequency, I weight observations using linearly decaying quarterly weights when constructing Memorability jkit . Third, I define a trade as a change in the number of (split-adjusted) shares from the previous report. To reduce mea- surement error in identifying trades (e.g., due to small differences in the number of shares across reports), I retain only trades that are at least 0.5% of total net assets. 7 This restric- tion also allows me to focus on meaningful trades. Finally, I pool all trades that occurred in a quarter, since I cannot observe the exact day on which a mutual fund manager executed a trade. In Panel B of Table 1.1, I provide summary statistics for this sample, which includes 3,443 distinct funds. On average, funds hold 99 stocks (median: 68). An appealing aspect of these large portfolios is that I can estimate many memory associations for each fund. The average probability of a memory-induced trade is 19.2% and Memorability jkit is 0.683 on average. These figures are similar to those of the retail investor data. 1.4 Results 1.4.1 Baseline Results Tovisualizetherelationshipbetweenmemoryandtradingintherawdata,Figure1.1presents a binned scatterplot in whichMemorability jkit is on the horizontal axis, and the probability of a memory-induced trade is on the vertical axis. Panel A displays this result for retail investors and Panel B for mutual funds. Both figures show that as the strength of the as- sociation between two stocks increases, the probability of a memory-induced trade increases as well. In Table 1.2, I test for this relationship more rigorously by estimating regression 1.4. In this regression, a dummy indicating a memory-induced trade is the dependent vari- able and Memorability jkit is the explanatory variable. All specifications include stock-pair fixed effects α j,k . By holding fixed two stocks, these fixed effects address concerns that the fundamentals of stocks could be correlated in ways that are related to their alphabetical similarity. 7 My results are robust to using higher or lower cutoffs. 12 Figure 1.1. Baseline Results in the Raw Data (a) Panel A: Retail Investors 0 .05 .1 .15 .2 Probability of Trade 0 .2 .4 .6 .8 1 Memorability (b) Panel B: Mutual Funds 0 .1 .2 .3 .4 Probability of Trade 0 .2 .4 .6 .8 1 Memorability Notes: These figures show binned scatterplots of the probability of a memory-induced trade against Mem- orability. Memorability captures memory associations between stock pairs that are built up over the past twelve months (Panel A) or past four quarters (Panel B). The probability of a memory-induced trade is the probability that a trade in one stock of the pair (the cueing stock) triggers the recall and trade of the other stock of the pair on the same day (Panel A) or in the same quarter (Panel B). Both graphs include a linear fit. 13 Table 1.2: Baseline Results Panel A: Retail Investors Dependent variable: Memory-induced trade (dummy) (1) (2) (3) Memorability 0.134*** 0.132*** 0.124*** (0.004) (0.004) (0.005) Stock-pair FE yes yes yes Day FE yes Investor x Day FE yes Observations 175,081 175,081 138,522 R-squared 0.300 0.313 0.596 Panel B: Mutual Funds Dependent variable: Memory-induced trade (dummy) (1) (2) (3) Memorability 0.192*** 0.192*** 0.179*** (0.004) (0.004) (0.003) Stock-pair FE yes yes yes Quarter FE yes Fund x Quarter FE yes Observations 727,507 727,507 726,518 R-squared 0.232 0.232 0.384 Notes: This table presents results from regressions of a dummy variable indicating a memory-induced trade on Memorability. Across columns, various fixed effects are added to the regression. These fixed effects can result in singleton observations, which are dropped during the estimation. Standard errors are clustered by stock pair, investor, and trading day (Panel A) or stock pair, fund, and quarter (Panel B) and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 14 In the first column of Panel A, the coefficient on Memorability jkit implies that increasing Memorability jkit by one standard deviation increases the probability of a memory-induced tradeby4.77percentagepoints. Further,anincreaseinMemorability jkit fromnoassociation to full association increases the trade probability by 13.40 percentage points. In terms of economic magnitude, this effect is comparable to the rank effect in Hartzmark (2015). Inthesecondcolumn, Iaddatradingdayfixedeffecttoaddresstheconcernthatthetrad- ingdecisionmightbedrivenbytheday(e.g., aJanuaryeffect). Inthethirdcolumn, Iinclude investor x day fixed effects, which control for unobservable (potentially time-varying) char- acteristics of investors – such as sophistication and wealth – that might affect the propensity to engage in memory-induced trading. These fixed effects also address the potential concern that my results might be picking up mechanical effects due to differences in portfolio size. Such mechanical effects might occur if investors are more likely to trade a stock when they hold a smaller number of stocks in their portfolio. Further, since two stocks are more likely to be alphabetically adjacent in a smaller portfolio, there might mechanically be a posi- tive relationship between Memorability jkit and the conditional probability of a stock being traded. However, since the size of an investor’s portfolio is fixed on a trading day, investor x day fixed effects address this concern by allowing me to estimate the memory effect within fixed portfolio sizes. The magnitude of the coefficient is very similar even with these additional fixed effects. Across specifications, as the fixed effects become tighter, the number of observations drops since I remove singleton observations. The standard errors in all retail investor regressions are clustered by stock pair, investor, and trading date. In Panel B of Table 1.2, I display similar results for mutual funds. The effect size is similar to that of retail investors. For instance, in the first column, a one standard deviation increase in Memorability jkit corresponds to an increase in the probability of a memory- induced trade of 6.24 percentage points. The standard errors in all mutual fund regressions are clustered by stock pair, fund, and quarter. 15 1.4.2 Identifying Cueing Trades using Earnings Announcements One shortcoming of the previous tests is that I cannot distinguish the order in which an investor trades stocks on a given day. In the data, I only observe all the trades that an investor executed on a trading day. In the ideal experiment, I could also observe the order of trades and identify which trades act as cues for the recall of associated stocks. Ideally, I could also identify which of these cueing trades are exogenous. In this section, I try to identify such cueing trades by looking at trades that were likely triggered by an annual earnings announcement. When an investor trades a stock within three days of its annual earnings announcement, I classify it as a cueing trade. I use these cueing trades to estimate whether the investor is more likely to also trade a stock that did not have an annual earnings announcement, if the two stocks are associated in memory. I display the results of this test in Panel A of Table 1.3. Despite the small sample size, I find very similar memory effects. In Panel B of Table 1.3, I repeat the analysis for mutual funds. Due to data limitations, I cannot identify the precise day on which a mutual fund traded a stock. Therefore, I classify a trade as a cueing trade if the stock had its annual earnings announcement in a quarter. As before, I use these cueing trades to estimate whether the fund manager is more likely to also trade a stock that did not have its annual earnings announcement in that quarter, if the two stocks are associated in memory. Again, I find memory effects that are very similar to the effects estimated using all trades. 1.4.3 Similarity and Interference In the following tests, I probe the different properties of memory separately, to understand how they shape trading decisions. First, I test for the effects of similarity and interference separately. The importance of both similarity and interference for recall is a robust finding in laboratory experiments (Kahana (2012); Enke et al. (2022); Bordalo et al. (2022a)). As outlined in Section 1.2, Memorability jkit is comprised of both components: the numerator captures the similarity of a stock pair, while the denominator captures interference from 16 Table 1.3: Identifying Cueing Trades Panel A: Retail Investors Dependent variable: Memory-induced trade (dummy) (1) (2) (3) Memorability 0.105*** 0.111*** 0.122** (0.014) (0.016) (0.053) Stock-pair FE yes yes yes Day FE yes Investor x Day FE yes Observations 3,194 3,018 533 R-squared 0.015 0.177 0.521 Panel B: Mutual Funds Dependent variable: Memory-induced trade (dummy) (1) (2) (3) Memorability 0.211*** 0.210*** 0.195*** (0.007) (0.007) (0.007) Stock-pair FE yes yes yes Quarter FE yes Fund x Quarter FE yes Observations 74,121 74,121 54,717 R-squared 0.033 0.035 0.282 Notes: This table replicates the baseline regressions for a specific subset of stock-pairs. In Panel A, only stocks that were traded on the day of their annual earnings announcement or in the two calendar days after the announcement are included as cueing trades. Stocks that are classified as memory-induced trades cannot have had an annual earnings announcement on any of those days. In Panel B, only stocks that were traded in the quarter of their annual earnings announcement are included as cueing trades. Stocks that are classified as memory-induced trades cannot have had an annual earnings announcement in that quarter. Across columns, various fixed effects are added to the regression. These fixed effects can result in singleton observations, which are dropped during the estimation. Standard errors are clustered by stock pair, investor, and trading day (Panel A) or stock pair, fund, and quarter (Panel B) and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 17 other stock pairs. These two forces have opposing effects on the recall probability: higher similarity increases recall, while higher interference reduces recall. In Table 1.4, I include the numerator (similarity) and the denominator (interference) of Memorability jkit separately as independent variables into my baseline regressions. I expect a positive coefficient on similarity and a negative coefficient on interference. This is precisely whatIfind. Thus, thememoryeffectcapturedbymycompositemeasure Memorability jkit is the result of two competing forces: similarity increases the effect, while interference reduces the effect. In terms of economic magnitude, using the estimates from the first column, increasing similarity by one standard deviation (one std. dev. = 0.28) increases the trade probability by about 5 percentage points for retail investors. In contrast, increasing interference by one standard deviation (one std. dev. = 0.32) reduces the trade probability by about 3 percentage points for retail investors. These effect sizes are very similar for mutual funds: a one standard deviation increase in similarity leads to a 6 percentage point increase in the trade probability, while a one standard deviation increase in interference leads to a 4 percentage point reduction. Overall, the results in Table 1.4 provide strong evidence for the driving forces of associa- tive memory models, which help to distinguish my findings from alternative explanations. The negative effect of interference is a particularly distinctive pattern of associative memory theory. 1.4.4 Recency Next, I test for the recency effect, which posits that investors are more likely to recall stocks that they experienced recently. The role of recency is well established in the memory literature (Kahana (2012)) and its importance for financial decisions has been demonstrated in several studies (e.g., Malmendier and Nagel (2011); Nagel and Xu (2022a)). To test for the recency effect, I include dummies for each of the past twelve months, indicating whether two stocks were associated in a given month. 8 The goal of this approach 8 These dummies are the dummy variables d jkim that I use to construct the similarity measure S jkit described in Section 1.2. 18 Table 1.4: Similarity and Interference Panel A: Retail Investors Dependent variable: Memory-induced trade (dummy) (1) (2) (3) Similarity 0.177*** 0.175*** 0.148*** (0.005) (0.005) (0.007) Interference -0.100*** -0.097*** -0.109*** (0.005) (0.005) (0.009) Stock-pair FE yes yes yes Day FE yes Investor x Day FE yes Observations 175,081 175,081 138,522 R-squared 0.299 0.312 0.596 Panel B: Mutual Funds Dependent variable: Memory-induced trade (dummy) (1) (2) (3) Similarity 0.215*** 0.215*** 0.199*** (0.006) (0.006) (0.004) Interference -0.184*** -0.182*** -0.146*** (0.008) (0.008) (0.004) Stock-pair FE yes yes yes Quarter FE yes Fund x Quarter FE yes Observations 727,507 727,507 726,518 R-squared 0.231 0.232 0.382 Notes: This table presents results from regressions of a dummy variable indicating a memory-induced trade on Similarity and Interference, which are the numerator and denominator of Memorability, respectively. Across columns, various fixed effects are added to the regression. These fixed effects can result in singleton observations, which are dropped during the estimation. Standard errors are clustered by stock pair, investor, and trading day (Panel A) or stock pair, fund, and quarter (Panel B) and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 19 is to unveil the degree of recency by estimating the weighting function over the past twelve months directly. This test is akin to the weighting function in Malmendier and Nagel (2011), except that I do not need to impose the functional form assumptions of Malmendier and Nagel (2011). The prediction is that the magnitude of the coefficients drops off as the dummies move further into the past. I present the results in the first column of Table 1.5. 9 As expected, the loading on the most recent dummy is the strongest. Moving further into the past, the magnitude of the coefficients drops off sharply. Indeed, for retail investors (Panel A), the influence of previous statementsdisappearsataboutthreemonthsintothepast. Theresultsaresimilarformutual funds (Panel B), with the most recent association being the most important. In contrast to the retail investors, loadings on the dummies that are furthest in the past remain slightly positive and significant. One shortcoming of including all dummies simultaneously into the regression is that this approach might overstate the effect drop-off, since the portfolio holdings of investors are sticky. This stickiness creates autocorrelation in the dummies and, when all dummies are included simultaneously, the lag-1 dummy dominates. Therefore, as an alternative approach, I run separate regressions – one for each lag – in which I ensure that all previous lags are jointly equal to zero. For instance, to estimate the coefficient on lag-2, I run a regression with observations for which lag-1 is equal to zero. I run these types of regressions for all lags and display the results in the remaining columns of Table 1.5. 10 In this alternative approach, the drop-off after the first month remains sharp, but the effect fades way more gradually with time. For retail investors, associations going back up to five months continue to have a significant effect. Overall, the sharp drop off in the coefficients is a characteristic feature of memory and reminiscent of findings from classic memory experiments (e.g., Murdock Jr (1962)). In these experiments, participants study a list of random words. After the study phase, they are 9 The results presented in Table 1.5 control for stock-pair fixed effects. In Appendix Tables 3.11 and 3.12, I present similar results when I additionally control for day fixed effects and investor x day fixed effects. 10 I cannot run such a regression for lag-12. The reason is that I restrict my sample to a rolling window of 12 months to identify associated stocks. Thus, if I jointly set the dummies for lags 1 through 11 equal to zero, the dummy for lag-12 must mechanically be equal to one. As a result, there is no remaining variation to estimate the coefficient on lag-12. 20 Table 1.5: Recency Panel A: Retail investors Dependent variable: Memory-induced trade (dummy) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) Lag 1 (dummy) 0.120*** (0.003) Lag 2 (dummy) 0.014*** 0.023*** (0.003) (0.003) Lag 3 (dummy) 0.001 0.011*** 0.017*** (0.003) (0.003) (0.004) Lag 4 (dummy) 0.004 0.008* 0.011** 0.013** (0.003) (0.004) (0.005) (0.005) Lag 5 (dummy) -0.001 0.005* 0.005 0.007* 0.012*** (0.003) (0.003) (0.003) (0.004) (0.004) Lag 6 (dummy) 0.001 0.000 0.002 0.003 0.003 0.006 (0.003) (0.003) (0.003) (0.003) (0.003) (0.004) Lag 7 (dummy) -0.001 0.003 0.003 0.003 0.005 0.005 0.002 (0.003) (0.003) (0.003) (0.003) (0.003) (0.004) (0.005) Lag 8 (dummy) -0.001 -0.002 -0.001 -0.000 0.002 0.003 0.003 0.005 (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) (0.004) (0.005) Lag 9 (dummy) -0.001 0.001 0.002 0.004 0.003 0.004 0.003 -0.002 -0.002 (0.003) (0.003) (0.003) (0.003) (0.004) (0.004) (0.004) (0.004) (0.006) Lag 10 (dummy) 0.004 0.009*** 0.010*** 0.011*** 0.010*** 0.010*** 0.010*** 0.010** 0.012*** 0.015** (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) (0.004) (0.004) (0.004) (0.006) Lag 11 (dummy) -0.003 -0.002 -0.002 -0.002 0.001 0.004 0.005 0.003 0.000 0.003 -0.006 (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) (0.004) (0.005) (0.006) (0.009) Lag 12 (dummy) -0.001 -0.003 -0.001 -0.001 -0.000 0.002 0.000 0.001 0.003 0.005 -0.001 (0.003) (0.003) (0.003) (0.003) (0.004) (0.004) (0.005) (0.005) (0.006) (0.008) (0.012) Stock-pair FE yes yes yes yes yes yes yes yes yes yes yes Observations 175,081 84,718 67,368 53,976 43,364 34,520 26,950 20,243 14,513 9,558 5,287 R-squared 0.314 0.320 0.331 0.338 0.344 0.351 0.353 0.356 0.376 0.392 0.448 Panel B: Mutual funds Dependent variable: Memory-induced trade (dummy) (1) (2) (3) Lag 1 (dummy) 0.154*** (0.003) Lag 2 (dummy) -0.009** 0.004** (0.004) (0.002) Lag 3 (dummy) 0.018*** 0.006*** 0.008*** (0.003) (0.002) (0.002) Lag 4 (dummy) 0.015*** 0.001 0.001 (0.002) (0.002) (0.002) Stock-pair FE yes yes yes Observations 727,507 209,573 124,337 R-squared 0.238 0.309 0.325 Notes: This table presents results from regressions of a dummy variable indicating a memory-induced trade on a set of dummy variables indicating if a stock pair was associated in a given month (Panel A) or quarter (Panel B). Across columns, an increasing number of lags is omitted with the restriction that the dummy variables of all omitted lags are jointly equal to zero. All regressions include stock-pair fixed effects. These fixed effects can result in singleton observations, which are dropped during the estimation. Standard errors are clustered by stock pair, investor, and trading day (Panel A) or stock pair, fund, and quarter (Panel B) and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 21 asked to freely recall words from the list. The general finding is that participants have excellent recall of the last few words, but the recall probability drops off sharply for earlier words. 1.4.5 Contiguity In this section, I test another property of memory: the “law of contiguity”. This law states that two items are more strongly associated in memory if they were experienced closer to one another. The intuition of contiguity can be illustrated with the word list experiments described in Section 1.2. In these experiments, upon recalling any word with serial positionn fromthelist, participantsaremostlikelytorecallthewordwithserialpositionn+1. Further, therecallprobabilityofaworddecreasesmonotonicallyastheword’sserialpositionincreases relative to the cueing word with serial position n. According to the law of contiguity, the words with serial position n and n + 1 share the strongest association because they were experienced immediately after one another. However, the words with serial positions n and n+2 also share a memory association, albeit a weaker one. The further the distance in their respective serial positions, the weaker the memory association between two words. I apply this intuition to my setting by arguing that two stocks with ranking positions n and n + 1 on an investor’s portfolio statement should share a stronger memory association than two stocks with ranking positions n and n + 2. To test this prediction empirically, I construct additional flavors of Memorability jkit that capture these increasingly weaker memoryassociations. Specifically,eachflavor Memorability ∆( d) jkit isconstructedbyconnecting a stock with ranking position n to a stock with ranking position n +d. Thus, d = 1 yields baseline Memorability jkit . As d increases, the flavors capture increasingly weaker memory associations. In Table 1.6, I regress the dummy variable indicating a memory-induced trade on the different flavors of Memorability ∆( d) jkit . Notice that the number of observations in these re- gressions is much larger than in my baseline tests. This is because an observation in my setting is identified by a stock pair that is associated in an investor’s memory on a trading day. In my baseline tests, I only consider associations of stocks with d = 1. However, in 22 Table 1.6, I consider many more associations which are captured by the additional flavors, resulting in many more observations. As expected, the memory effect becomes weaker as the distance d between two stocks in the ranking increases. Indeed, the effect fades away almost monotonically, both for retail investors (Panel A) and mutual funds (Panel B). The specifications in the third column are particularly useful since they estimate this effect within an investor-day (Panel A) or a fund-quarter (Panel B). That is, conditional on trading stock k, the same investor is more likely to trade stockj if that stock was historically closer to stockk on the previous portfolio statements. These results are fully consistent with the law of contiguity. 1.5 Robustness In the previous section, I have presented evidence for memory effects in trading and shown that the different properties of memory affect trading decisions as predicted by associative memory theory. In the tests that follow, I show the robustness of these results and address several alternative explanations. 1.5.1 Addressing Attention Spillover An important concern is that my results might capture attention effects (Peng and Xiong (2006); Barber and Odean (2008); Hirshleifer et al. (2009); Da et al. (2011); Jiang et al. (2022); An et al. (2022)). For instance, if two stocks were historically adjacent on an in- vestor’s portfolio – and therefore associated in memory – they might still be adjacent on the day of the trade. Thus, when an investor trades a stock, he might also see the adja- cent stock, and decide to trade this stock as well. In this case, my findings would pick up attention-induced trades rather than memory-induced trades. To help address this concern, I perform the following test. I focus only on stocks that were adjacent on an investor’s statement at some point in the previous twelve months – and are therefore associated in the investor’s memory – but that are not adjacent on the day of the trade. 11 In Table 1.7, I re-run the regressions for these types of stock pairs. The first 11 This test is also helpful in ruling out any theory positing that investors simply trade adjacent stocks. 23 Table 1.6: Contiguity Panel A: Retail Investors Dependent variable: Memory-induced trade (dummy) (1) (2) (3) Memorability ∆(1) 0.172*** 0.172*** 0.117*** (0.003) (0.003) (0.003) Memorability ∆(2) 0.133*** 0.132*** 0.107*** (0.003) (0.003) (0.003) Memorability ∆(3) 0.111*** 0.110*** 0.099*** (0.003) (0.003) (0.003) Memorability ∆(4) 0.092*** 0.091*** 0.088*** (0.003) (0.003) (0.003) Memorability ∆(5) 0.082*** 0.081*** 0.084*** (0.003) (0.003) (0.003) Memorability ∆(6) 0.071*** 0.069*** 0.078*** (0.003) (0.003) (0.003) Memorability ∆(7) 0.066*** 0.065*** 0.073*** (0.004) (0.003) (0.003) Memorability ∆(8) 0.060*** 0.059*** 0.070*** (0.004) (0.003) (0.003) Memorability ∆(9) 0.062*** 0.060*** 0.075*** (0.004) (0.004) (0.004) Memorability ∆(10) 0.061*** 0.059*** 0.076*** (0.006) (0.005) (0.004) Stock-pair FE yes yes yes Day FE yes Investor x Day FE yes Observations 890,068 890,068 876,204 R-squared 0.257 0.271 0.424 24 Panel B: Mutual Funds Dependent variable: Memory-induced trade (dummy) (1) (2) (3) Memorability ∆(1) 0.291*** 0.291*** 0.232*** (0.005) (0.005) (0.004) Memorability ∆(2) 0.263*** 0.264*** 0.220*** (0.005) (0.005) (0.004) Memorability ∆(3) 0.243*** 0.243*** 0.210*** (0.004) (0.004) (0.003) Memorability ∆(4) 0.225*** 0.225*** 0.202*** (0.004) (0.004) (0.003) Memorability ∆(5) 0.209*** 0.209*** 0.195*** (0.004) (0.004) (0.003) Memorability ∆(6) 0.196*** 0.196*** 0.189*** (0.004) (0.004) (0.003) Memorability ∆(7) 0.183*** 0.183*** 0.183*** (0.004) (0.004) (0.003) Memorability ∆(8) 0.175*** 0.175*** 0.182*** (0.004) (0.004) (0.003) Memorability ∆(9) 0.172*** 0.172*** 0.186*** (0.004) (0.004) (0.003) Memorability ∆(10) 0.177*** 0.177*** 0.199*** (0.005) (0.005) (0.004) Stock-pair FE yes yes yes Quarter FE yes Fund x Quarter FE yes Observations 6,422,474 6,422,474 6,422,462 R-squared 0.215 0.215 0.334 Notes: This table presents results from regressions of a dummy variable indicating a memory-induced trade on different flavors of Memorability. Each flavor of Memorability ∆( d) is constructed by connecting a stock with ranking position n to a stock with ranking position n +d. Across columns, various fixed effects are added to the regression. These fixed effects can result in singleton observations, which are dropped during the estimation. Standard errors are clustered by stock pair, investor, and trading day (Panel A) or stock pair, fund, and quarter (Panel B) and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 25 three columns restrict the sample to stock pairs with a ranking distance > 1 on the day of the trade, the middle three columns focus on stock pairs with a ranking distance > 3, and the last three columns on stock pairs with a ranking distance > 5. As the restrictions become more binding, the sample sizes drop accordingly. Panel A of Table 1.7 presents results using the sample of retail investors. I continue to find strong memory effects, but the coefficients are somewhat smaller compared to the baseline results in Table 1.2. Panel B presents the results for mutual funds and also shows memory effects that are similar to the baseline results, albeit slightly weaker. These results suggest that attention does play a role in my setting, but they also show that attention is unlikely to explain the entire observed effect. 1.5.2 Not a Relabeling of the Rank Effect Another concern is that my results might be a relabeling of the rank effect (Hartzmark (2015)). The rank effect is the tendency of investors to sell extremely ranked stocks in their portfolio. Hartzmark (2015) shows that this effect extends to stocks that are first or last in alphabetical rankings. Thus, if investors jointly trade stocks that are very high or low in the alphabetical ranking, such behavior could explain why Memorability jkit is correlated with the probability of a memory-induced trade. To address this concern, in Table 1.8, I test for memory effects by focusing only on stocks in the middle section of an investor’s (Panel A) or a fund manager’s (Panel B) alphabetical ranking. The coefficient on Memorability jkit decreases in magnitude but remains statistically significant, suggesting that my results are not simply a relabeling of the rank effect. 1.5.3 Extremely Tight Fixed Effects In Table 1.9, I re-estimate the baseline regressions from Table 1.2 with additional fixed effects and various interactions of stock-pair fixed effects. While these additional fixed effects are useful in addressing several alternative explanations by controlling for potential omitted variables, they reduce the sample size substantially. In the first column, I augment my 26 Table 1.7: Non-Adjacent Stock Pairs Panel A: Retail Investors Dependent variable: Memory-induced trade (dummy) Sample: Ranking difference >1 Ranking difference >3 Ranking difference >5 (1) (2) (3) (4) (5) (6) (7) (8) (9) Memorability 0.091*** 0.091*** 0.104*** 0.074*** 0.075*** 0.069*** 0.073*** 0.076*** 0.052*** (0.005) (0.005) (0.010) (0.007) (0.007) (0.014) (0.008) (0.009) (0.017) Stock-pair FE yes yes yes yes yes yes yes yes yes Day FE yes yes yes Investor x Day FE yes yes yes Observations 62,912 62,912 39,512 36,538 36,538 21,871 29,201 29,201 17,337 R-squared 0.333 0.359 0.654 0.352 0.393 0.676 0.364 0.413 0.685 Panel B: Mutual Funds Dependent variable: Memory-induced trade (dummy) Sample: Ranking difference >1 Ranking difference >3 Ranking difference >5 (1) (2) (3) (4) (5) (6) (7) (8) (9) Memorability 0.181*** 0.181*** 0.175*** 0.165*** 0.165*** 0.163*** 0.155*** 0.155*** 0.156*** (0.004) (0.004) (0.004) (0.004) (0.004) (0.004) (0.004) (0.004) (0.005) Stock-pair FE yes yes yes yes yes yes yes yes yes Quarter FE yes yes yes Fund x Quarter FE yes yes yes Observations 479,219 479,219 474,121 284,643 284,643 275,825 184,748 184,748 175,694 R-squared 0.244 0.245 0.405 0.255 0.256 0.423 0.265 0.266 0.437 Notes: This table presents results from regressions of a dummy variable indicating a memory-induced trade on Memorability. Only stock pairs that are not adjacent in the ranking on the trading day are retained. In Columns (1) - (3) the ranking difference must be larger than 1, in Columns (4) - (6) it must be larger than 3, and in Columns (7) - (9) it must be larger than 5. Across columns, various fixed effects are added to the regression. These fixed effects can result in singleton observations, which are dropped during the estimation. Standard errors are clustered by stock pair, investor, and trading day (Panel A) or stock pair, fund, and quarter (Panel B) and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 27 Table 1.8: Not a Relabeling of the Rank Effect Panel A: Retail Investors Dependent variable: Memory-induced trade (dummy) (1) (2) (3) Memorability 0.096*** 0.096*** 0.102*** (0.005) (0.005) (0.007) Stock-pair FE yes yes yes Day FE yes Investor x Day FE yes Observations 76,967 76,967 62,931 R-squared 0.303 0.331 0.582 Panel B: Mutual Funds Dependent variable: Memory-induced trade (dummy) (1) (2) (3) Memorability 0.134*** 0.134*** 0.136*** (0.005) (0.005) (0.005) Stock-pair FE yes yes yes Quarter FE yes Fund x Quarter FE yes Observations 281,911 281,911 280,333 R-squared 0.235 0.236 0.404 Notes: This table presents results from regressions of a dummy variable indicating a memory-induced trade on Memorability. In Panel A, only retail investor portfolios with at least seven stocks are retained and the first two and last two stocks in alphabetical ranking are dropped. In Panel B, only mutual fund portfolios with at least fifty stocks are retained and the first twenty and last twenty stocks in alphabetical ranking are dropped. Across columns, various fixed effects are added to the regression. These fixed effects can result in singleton observations, which are dropped during the estimation. Standard errors are clustered by stock pair, investor, and trading day (Panel A) or stock pair, fund, and quarter (Panel B) and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 28 Table 1.9: Extremely Tight Fixed Effects Panel A: Retail Investors Dependent variable: Memory-induced trade (dummy) (1) (2) (3) Memorability 0.109*** 0.123*** 0.108*** (0.020) (0.006) (0.020) Stock-pair FE yes Stock x Day FE yes Stock-pair x Investor FE yes Stock-pair x Day FE yes Observations 11,731 119,824 10,024 R-squared 0.789 0.432 0.743 Panel B: Mutual Funds Dependent variable: Memory-induced trade (dummy) (1) (2) (3) Memorability 0.185*** 0.154*** 0.188*** (0.004) (0.004) (0.005) Stock-pair FE yes Stock x Quarter FE yes Stock-pair x Fund FE yes Stock-pair x Quarter FE yes Observations 648,206 465,702 405,097 R-squared 0.401 0.502 0.411 Notes: This table presents results from regressions of a dummy variable indicating a memory-induced trade on Memorability. Across columns, various fixed effects are added to the regression. These fixed effects can result in singleton observations, which are dropped during the estimation. Standard errors are clustered by stock pair, investor, and trading day (Panel A) or stock pair, fund, and quarter (Panel B) and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 29 baseline regression with stock-day fixed effects, which control for stock-specific information on the trading day that might drive the decision to trade. In the second column, I interact the stock-pair fixed effects with investor fixed effects. In this specification, the coefficient on Memorability jkit is estimated using only variation for the same stock pair and same investor across different days. This effectively estimates the memory effect within-investor as, over time, a given stock pair becomes more or less associated in memory. Finally, in the third column, I interact the stock-pair fixed effects with day fixed effects. In this specification, I estimate the coefficient using only variation in the memory strength acrossinvestorsforthesamestockpaironthesameday. Thisapproachaddressestheconcern that stock-pair-specific information on the trading day might drive trading behavior. In all specifications, the results are similar to the baseline estimates from Table 1.2. The specifications in the second and third column are also helpful in determining whether the results are driven by variation within or across investors. By isolating each type of variation, these results show that the effect is driven both by time series and cross-sectional variation. 1.5.4 Alternative Weighting Functions IntheconstructionofmymainmeasureMemorability jkit , Iusealinearlydecayingweighting function to allocate a higher weight to more recent than to more distant experiences. While this approach is motivated by the results in Malmendier and Nagel (2011), this weighting function is arguably somewhat ad hoc. In this section, I show that my results are not sensitive to this particular weighting function. In the first three columns of Table 1.10, I show that I find similar, albeit somewhat weaker results when I omit the weighting function altogether. This shows that my results are not driven by the weighting. However, by allocating equal weight to distant experiences (which should have a weaker effect on recall according to memory theory), the effect becomes predictably somewhat weaker. Asanalternativeapproach, Icalibratetheweightingfunctiontothedata. Todoso, Itake the coefficients on each lag from the 11 regressions displayed in Table 1.5 and use them as weights. I make two minor adjustments: first, I set the weight for lag-12 equal to zero. I also 30 set the weights for negative coefficients (lags 9 and 11) equal to zero. In the remaining three columns of Table 1.10, I present the results when I use these calibrated weights. Overall, the strength of the memory effect is very similar to the baseline effects presented in Table 1.2. These findings are in line with the observation in Malmendier and Nagel (2011) that a linear weighting function is a good approximation for the effect of recency in financial decisions. 1.6 Further Exploration This section explores two extensions of the baseline results. I show that the propensity to execute memory-induced trades is heterogeneous across investors and discuss the asymmetry in memory-induced buying and selling decisions. 1.6.1 Heterogeneity In this section, I estimate the memory effect for each investor and fund manager individually, which allows me to back out the distribution of effect sizes in my sample. Specifically, I regress the dummy variable indicating a memory-induced trade onMemorability jkit for each investorandfundmanagerseparately, andplotahistogramoftheresultingMemorability jkit coefficients in Figure 1.2. I retain only investors and fund managers with at least 100 observations to ensure that there is enough variation to estimate the coefficient. For both retail investor and fund managers, the bulk of the estimates is positive, showing that the results are not driven by a few outliers with extreme memory effects. Further, both distributions are positively skewed, suggesting that both groups include individuals who are particularly prone to memory-induced trading. 1.6.2 Buying vs. Selling In all of my tests so far, I have pooled buys and sells, and focused on trading decisions as a whole. Here, I separate buying from selling decisions to see whether the memory effect operates more strongly in either domain. On the one hand, memory theory is silent on whether the effect should be stronger for buying or selling decisions. On the other hand, 31 Table 1.10: Alternative Weighting Functions Panel A: Retail Investors Dependent variable: Memory-induced trade (dummy) (1) (2) (3) (4) (5) (6) Memorability (unweighted) 0.117*** 0.116*** 0.095*** (0.004) (0.004) (0.006) Memorability (calibrated) 0.149*** 0.147*** 0.152*** (0.004) (0.004) (0.005) Stock-pair FE yes yes yes yes yes yes Day FE yes yes Investor x Day FE yes yes Observations 175,081 175,081 138,522 171,568 171,568 136,301 R-squared 0.296 0.310 0.594 0.309 0.322 0.604 Panel B: Mutual funds Dependent variable: Memory-induced trade (dummy) (1) (2) (3) (4) (5) (6) Memorability (unweighted) 0.166*** 0.166*** 0.143*** (0.004) (0.004) (0.003) Memorability (calibrated) 0.154*** 0.154*** 0.143*** (0.002) (0.002) (0.002) Stock-pair FE yes yes yes yes yes yes Quarter FE yes yes Fund x Quarter FE yes yes Observations 727,507 727,507 726,518 726,948 726,948 725,951 R-squared 0.225 0.225 0.377 0.237 0.237 0.389 Notes: This table presents results from regressions of a dummy variable indicating a memory-induced trade on flavors of Memorability that are constructed using different weighting functions. In Columns (1) - (3), Memorability is constructed without a weighting function. In Columns (4) - (6), Memorability is constructed usingweightsthatarecalibratedtothedatabasedonthecoefficientsfromTable1.5. Acrosscolumns, various fixed effects are added to the regression. These fixed effects can result in singleton observations, which are dropped during the estimation. Standard errors are clustered by stock pair, investor, and trading day (Panel A) or stock pair, fund, and quarter (Panel B) and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 32 Figure 1.2. Heterogeneity in the Memory Effect (a) Panel A: Retail Investors 0 2 4 6 8 Density -.1 0 .1 .2 .3 .4 Memorability Coef. (b) Panel B: Mutual Funds 0 1 2 3 4 Density -.1 0 .1 .2 .3 .4 .5 .6 Memorability Coef. Notes: ThesefiguresshowdensitiesoftheMemorabilitycoefficient, estimatedforeachinvestor(PanelA)and each fund manager (Panel B) separately. Only investors and fund managers with at least 100 observations are retained in the sample. The coefficient estimates are winsorized at the 1% and 99% level. The figures include a kernel density estimate. 33 Table 1.11: Buying vs. Selling Panel A: Retail Investors Dependent variable: Memory-induced buy (dummy) Memory-induced sell (dummy) (1) (2) (3) (4) (5) (6) Memorability 0.020*** 0.019*** 0.006** 0.114*** 0.113*** 0.118*** (0.002) (0.002) (0.003) (0.003) (0.003) (0.005) Stock-pair FE yes yes yes yes yes yes Day FE yes yes Investor x Day FE yes yes Observations 175,081 175,081 138,522 175,081 175,081 138,522 R-squared 0.249 0.261 0.540 0.280 0.297 0.603 Panel B: Mutual Funds Dependent variable: Memory-induced buy (dummy) Memory-induced sell (dummy) (1) (2) (3) (4) (5) (6) Memorability 0.082*** 0.081*** 0.061*** 0.111*** 0.111*** 0.118*** (0.003) (0.003) (0.002) (0.003) (0.003) (0.003) Stock-pair FE yes yes yes yes yes yes Quarter FE yes yes Fund x Quarter FE yes yes Observations 727,507 727,507 726,518 727,507 727,507 726,518 R-squared 0.175 0.176 0.369 0.168 0.170 0.366 Notes: This table presents results from regressions of a dummy variable indicating a memory-induced buy (firstthreecolumns)oramemory-inducedsell(lastthreecolumns)onMemorability. Acrosscolumns, various fixed effects are added to the regression. These fixed effects can result in singleton observations, which are dropped during the estimation. Standard errors are clustered by stock pair, investor, and trading day (Panel A) or stock pair, fund, and quarter (Panel B) and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 34 recent research has shown that investors – even sophisticated investors – tend to make larger errors on the selling side than the buying side (Akepanidtaworn et al. (2021)). To the extent that memory-induced trades are “errors”, the memory effect might be stronger on the selling side. In Table 1.11, I replicate my baseline regressions using dummies that break out the trading decision as a buy (first three columns) or a sell (last three columns). I find that the memory effect operates in both domains, but that it is stronger for selling decisions. This is consistent with the finding in Akepanidtaworn et al. (2021) that selling decisions are more behavioral than buying decisions. 35 1.7 Conclusion Economists are increasingly incorporating aspects of human memory into theoretical models of economic and financial decision-making. These models offer the promise of explaining a variety of empirical facts and puzzles in financial markets. So far, however, tests of these models are confined to the experimental laboratory. My paper contributes to this growing literature by providing theory-driven, micro-level evidence of memory effects in a financial setting outside of the experimental laboratory. I use the alphabetical rankings of stocks in investors’ portfolio statements to estimate which stocks are associated in memory and find that these associations drive trading deci- sions. When I test for the different properties of memory, I find that they affect trading behavior as predicted by associative memory theory. The memory effect increases with the similarity between two stocks but decreases if interference in recall is higher. Further, associ- ations that were encoded recently have a stronger effect than associations that were encoded further in the past. I also find that the memory effect fades away if two stocks were listed further from each other during the encoding of a memory association. In my tests, a trade in one stock acts as the cue for the recall of associated stocks. How- ever, investors are surely exposed to many more cues, and the different effects of those cues could be tested empirically. For instance, news events, social interactions, or advertisements could all plausibly act as cues for the recall of associated memories. The type of empiri- cal tests I conduct here could be used as a template for testing these broader predictions of associative memory theory. Another important direction for future research is to test whether the memory effects I document at the individual level are strong enough to impact market outcomes. I explore this possibility in Charles (2022) and find evidence that a similar memory mechanism appears strong enough to distort prices in financial markets, but further tests in different contexts are surely needed. 36 Chapter 2 Memory Moves Markets 2.1 Introduction There is a large literature in finance analyzing the role of attention in financial markets (see Barberetal.(2019)foranoverview). Thisliteraturehasuncoveredvarioussourcesofinvestor attention, including media coverage, abnormal trading volume, extreme stock returns, and the display of information (e.g., Barber and Odean (2008); Hartzmark (2015)). 1 A unifying theme of these sources is that they are external sources of attention. By contrast, there might also be internal sources of attention – like memory associations inside an investor’s mind – that systematically direct attention. So far, however, there is little evidence of internally-generated attention in financial markets. Onepossiblereasonforthisdearthofevidenceisthatresearchershavelackedformal models of, and empirical proxies for, these internal sources. Fortunately, recent advances in memory theory provide the necessary structure to analyze memory recall as a source of internally-generated attention (Bordalo et al. (2020); Wachter and Kahana (2021)). Memory models formalize which items will be associated in an investor’s memory and therefore allow for targeted tests of memory-induced attention in financial markets. Put differently, memory 1 Further external sources of attention identified in the literature include: ownership of an asset (Hartz- mark et al. (2021)), earnings announcements (Hartzmark and Shue (2018); Hirshleifer et al. (2009); Schmidt (2019)), extraordinary events (Chen et al. (2019); Seasholes and Wu (2007)), advertisement (Lou (2014)), information display (Barber et al. (2021); Frydman and Wang (2020); An et al. (2022)), social media (Jiang et al. (2022)), and days of the week (DellaVigna and Pollet (2009)). 37 models allow me to test for a different type of investor attention than has previously been investigated. In this paper, I test whether an event that increases attention to one firm also channels attention to another firm if the two firms are associated in investors’ memory. My tests build on the strong existing evidence showing that individual investors are net buyers of attention-grabbing stocks, to the point where they can create positive price pressure (Barber and Odean (2008); Da et al. (2011)). Motivated by this evidence, I test and confirm the hypothesis that memory-induced attention creates buying pressure, and show that it leads to positive abnormal returns for memory-associated firms. The two key empirical challenges in testing this hypothesis are (1) estimating which firms are associated in investors’ memory and (2) identifying memory associations that are orthogonal to firm fundamentals. In addressing these challenges, I am guided by the model of Bordalo et al. (2020), which builds heavily on associative memory theory (Kahana (2012)). In associative memory theory, recall is shaped by two competing forces: similarity and interference. To see how these forces operate, assume that Coca-Cola announces earnings on day t. When an investor is cued by this event, she recalls past experiences that are similar to the cue. For instance, the investor might recall IBM, because IBM announced earnings on the same day as Coca-Cola in the previous quarter, and the two firms were both covered in the news on that day. In the terminology of the model, these two firms are encoded as more similar in memory, because they were experienced in a similar context by the investor in the previous quarter. In contrast, if many other firms announced earnings on the same day as Coca-Cola and IBM in the previous quarter, the investor may recall one of these other firms instead of IBM. Thus, the memories of these other firms interfere with the recall of IBM on day t. My hypothesis is simple. When Coca-Cola announces earnings on day t, this event naturally attracts attention to Coca-Cola itself. But since IBM and Coca-Cola are associated in memory, some attention might also be directed to IBM, even though IBM does not announce earnings on day t. Thus, I hypothesize that Coca-Cola’s earnings announcement 38 (the cue) creates memory-induced attention to IBM, leading to buying pressure in IBM’s stock on day t. 2 In my empirical tests, I follow the logic of this example and estimate which firms are associated in investors’ memory using overlaps of earnings announcements in previous quar- ters. In my main specification, I regress the return of firm j on day t (IBM) on a dummy variable that is equal to one if at least one firm that announced earnings on the same day as firm j in the previous quarter (Coca-Cola) announces earnings on day t. In all my tests, I ensure that firm j does not have an own earnings announcement within [t− 3, t + 3], to avoid confounding effects from a firm’s own earnings announcement. Further, I only retain firm pairs that operate in very different industries, using the text-based industries of Hoberg and Phillips (2010, 2016). Ifindthatamemorycueleadstoadailyabnormalreturnof3–5basispointsforthecued firm. In annual terms, this corresponds to an abnormal return of 7.5 – 12.5%. Risk-based return movements are unlikely to explain these results since I use characteristic-adjusted returns as in Daniel et al. (1997). In terms of magnitude, this effect size is on par with the earnings announcement premium (Frazzini and Lamont (2007); Barber et al. (2013)). It is also possible to construct a trading strategy that takes advantage of predictable memory cues and generates a daily alpha of 8.7 basis points. My empirical strategy is designed to capture memory associations that are orthogonal to firm fundamentals, by exploiting the fact that most firms follow rigid schedules for their earnings announcements (Hartzmark and Shue (2018); Noh et al. (2021)). For instance, Coca-Cola typically announces earnings on the third Tuesday, Wednesday, or Thursday of the first month of a calendar quarter, while IBM typically announces on the 18th or 19th of the first month of a calendar quarter. These rigid schedules result in overlaps for some quarterly earnings announcements but not for others, depending on how the calendar shakes out in each quarter. Nevertheless, one may be concerned that not all firms follow rigid schedules or that some firms strategically advance or delay their earnings announcement depending on the earnings they plan to report (Penman (1987); Bagnoli et al. (2002); Johnson and So (2018)). To 2 In a related study, Charles (2021) uses microdata to show that such a cue increases the probability that an individual investor trades the stock of IBM. 39 directly address these concerns, I replicate all my results using only earnings announcements that were exogenously shifted by calendar rotations (Noh et al. (2021)). These are announce- ments of firms that follow a strict pattern in their announcement timing for several years in a row and do not deviate from this pattern by even a single day. Examples of patterns that firms follow are to always announce on the first Thursday of a month, or to always announce on the fifth Thursday after the fiscal period end. 3 For such “Pattern firms”, the day-of-week on which a calendar month begins determines the date of their earnings an- nouncement. Crucially, the day-of-week on which a calendar month begins rotates from year to year, shifting the dates of earnings announcements, and creating exogenous overlaps of earnings announcements for Pattern firms. All my results are very similar for the subsample of Pattern firms. As a deeper test of the mechanism, I next examine how the psychological properties of memory modulate the strength of the effect. First, I test for contiguity in the memory effect. The intuition of contiguity can be best illustrated with an example. Recall that in the opening example Coca-Cola and IBM announced earnings on the same day last quarter, but this quarter they do not. Assume further that last quarter Apple announced earnings one day after Coca-Cola announced. Because Coca-Cola and Apple announced with a gap of one day in the previous quarter, they share a weaker memory association than Coca- Cola and IBM (who announced on the same day). Applying this intuition to my setting, I test whether an earnings announcement of Coca-Cola on day t results in a weaker return response for Apple than for IBM, since the memory association between Coca-Cola and Apple is weaker. I find strong evidence in favor of this prediction. The memory effect drops sharply if memories were encoded with a timing gap of just one day, which is consistent with the differing contexts during the encoding of the memory association. These tests also help alleviate concerns that my results are driven by similar firms an- nouncing at similar times during an earnings season. The identifying assumption in these tests is that amongst a set of firms announcing close in time to each other (e.g., late in the quarter), firms that announce on the same day are not systematically different from firms that announce with a gap of one day. This assumption is likely satisfied, especially for the 3 Such patterns are sometimes explicitly required by the firms’ bylaws (Noh et al. (2021)). 40 set of Pattern firms whose earnings announcement dates are shifted by exogenous calendar rotations. Second, I test whether recent experiences have a stronger effect than distant experiences, a classic prediction of memory models. Indeed, I find a stronger effect if memory associations were encoded in more recent quarters, and I find that the effect fades away with increasing quarterly lags. In addition to validating a key prediction of memory theory, this finding is helpful in further attenuating concerns that my results are driven by attention to fun- damentally related firms. If my results were purely driven by the fact that fundamentally related firms are more likely to announce quarterly earnings on the same day, the coefficients on each quarterly lag should be approximately similar in magnitude. However, I observe a systematic decay in the effect, consistent with a memory channel. Finally, I test whether interference weakens the documented effect. As discussed in the introductory example, if many firms announced earnings together with Coca-Cola and IBM, this should weaken the memory association between these two firms. Inherent in this line of reasoning is the assumption that there is strong attentional interaction between firms that have earnings announcements on the same day. In support of this key premise, Hirshleifer et al. (2009) find that attention to one firm reduces attention to another firm on earnings announcement days. This finding adds plausibility to the idea that during the encoding of memory traces, earnings announcements by other firms distract from the encoding of an associative memory trace between Coca-Cola and IBM. When I test for interference directly, I find that memory associations that were encoded on days with many earnings announcements lead to weaker effects than associations that were encoded on days with few earnings announcements. These findings provide evidence of interference effects, a signature prediction of associative memory theory. In additional tests, I find that the documented effect quickly reverses, a finding that is helpful in further addressing the concern that my results might be affected by fundamental relationships between firms. I also explore whether the earnings surprise of the cueing firm (Coca-Cola) predicts the return response of the cued firm (IBM). If my results were driven by information spillover from the cueing firm’s earnings announcement, this might manifest itself in a systematic relationship between the earnings surprise and the return response. 41 For instance, more positive surprises might lead to higher returns and more negative sur- prises might lead to lower returns (Thomas and Zhang (2008)). In contrast, if the earnings announcement purely acts as a memory cue that directs attention, the earnings surprise is unlikely to play an important role for the strength of the effect. Consistent with the latter, I do not find any relationship between the surprise of the cueing firm and the return response of the cued firm. I discuss further alternative explanations in Section 2.5.6. My paper contributes to the large literature in finance that studies the role of limited attention in financial markets (e.g., Barber and Odean (2008); Hirshleifer et al. (2009); Da et al. (2011)). Memory theory offers one explanation for why investors allocate their attention to certain firms: when cued with an event, investors retrieve associated firms from memory, and subsequently allocate more attention to these firms. This memory-induced attention can be strong enough to distort the stock prices of these firms. A related strand of the literature documents that recurring firm events are associated with predictably high returns (Hartzmark and Solomon (2018)). In contrast to most studies in this literature, I do not focus on firms’ own returns following a recurring event. Rather, I show that recurring firm events, such as earnings announcements, can serve as cues that trigger the recall of associated memories. Through these memory associations, events at the cueing firm can affect the returns of associated firms. Myresultsalsoprovideastrongempiricaljustificationforincorporatingaspectsofhuman memory into economic models, an approach taken by a growing theoretical literature (Gilboa and Schmeidler (1995); Mullainathan (2002); Hirshleifer and Welch (2002); Bordalo et al. (2020); Wachter and Kahana (2021); Bordalo et al. (2022a); Da Silveira et al. (2020); Bodoh- Creed (2020); Nagel and Xu (2022a)). My paper differs from previous empirical tests of memory models, as these tests largely focus on individual decision-making (e.g., Enke et al. (2022); Gödker et al. (2022); Colonnelli etal.(2021); Goetzmannetal.(2022)). Inarelatedstudy, Charles(2021)showsthatmemory associations affect the trading behavior of individual investors. In contrast, the current study shows that memory effects can be powerful enough to affect asset prices. 42 2.2 Empirical Strategy My goal is to identify exogenous associations of firms in investors’ memory. In the ideal ex- periment, I would randomly associate firms in investors’ memory, for example by randomly exposing investors to different firms on different days. The resulting joint experience of two firms would create an association of those firms in investors’ memory. I aim to approxi- mate this ideal experiment using overlaps of firms’ quarterly earnings announcements. I use earnings announcements as building blocks for estimating memory associations, since these announcements naturally draw attention to announcing firms. In addition, there is evidence of attentional interaction between firms that announce on the same day (Hirshleifer et al. (2009)). I consider two firms as associated in memory if they announced earnings on the same day in any of the previous four fiscal quarters. This approach has the benefit of being simple while capturing the main forces of associative memory theory (Kahana (2012); Bordalo et al. (2020)). For instance, by focusing on associations that were encoded in the previous quarter vs. a more distant quarter, I can test for the effect of recency in recall (Murdock Jr (1962); Chang et al. (2017)). Similarly, by comparing associations that were encoded on days with many announcing firms vs. on days with few announcing firms, I can test for the effect of interference in recall (Kahana (2012); Bordalo et al. (2020); Bordalo et al. (2022a)). My empirical approach builds on the fact that many firms follow rigid rules for their earningsannouncementtiming(HartzmarkandShue(2018); Nohetal.(2021)). Forinstance, some firms follow the rule to announce on the kth day-of-week of a calendar month (e.g., third Thursday), while other firms announce on the kth day in a calendar month (e.g., the 18thday). Theserulesresultinoverlapsforsomeearningsannouncementsbutnotforothers, depending on how the calendar shakes out in each month. In my baseline tests, I estimate regressions of the following type: return j,t =α +β·cue j,t +γ t +u j,t (2.1) wherereturn j,t is firm j’s characteristic-adjusted return on dayt,cue j,t is a dummy variable that is equal to one if at least one firm that announced earnings on the same day as firm j 43 in any of the previous four fiscal quarters announces earnings on day t, andγ t is a day fixed effect. The coefficient β captures the effect of a memory cue for firm j on dayt. My hypothesis is that such a cue creates memory-induced attention and leads to buying pressure. Therefore, I hypothesize thatβ is positive. When estimating this specification, I ensure that firm j does not have an own earnings announcement within [t− 3, t + 3] to avoid confounding effects from a firm’s own earnings announcement. I cluster standard errors in all regressions by firm and day. I also frequently focus on associations that were encoded in the previous quarter, since these associations are likely strongest and therefore easiest to recall. In these tests, I estimate regressions of the following type: return j,t =α +β·cue j,t,q−1 +γ t +u j,t (2.2) In this specification, cue j,t,q−1 is a dummy variable that is equal to one if at least one firm that announced earnings on the same day as firm j in the previous quarter announces earningsondayt. Thesubscript"q−1"referstothefactthattheseassociationswereencoded in the previous quarter. A natural worry with this approach is that firms with overlapping earnings announce- ments might be fundamentally more related than firms without overlapping earnings an- nouncements. In this case, cue j,t (and cue j,t,q−1 ) could pick up fundamental relationships. Indeed, firms do announce earnings in clusters and their schedules are known to be correlated across industries and other firm characteristics. For instance, firms in the same industry tend to announce close in time to each other in a quarter. For this reason, in all my tests I ex- clude all firm-pairs that are in the same TNIC-2 industry (Hoberg and Phillips (2010, 2016)). However, while helpful, this does not address cross-industry relationships or endogenous tim- ing of earnings announcements. There is a large literature showing that firms strategically advance or delay their earnings announcements depending on the news they plan to report (Penman (1987); Bagnoli et al. (2002); Johnson and So (2018)). Firms that announce early in the quarter generally announce good news, while firms that announce late in the quarter 44 generally announce bad news. As a result, the set of firms that announce early in a quarter is systematically different from the set of firms that announce late in a quarter. Given these challenges, in further tests I strengthen the identification by exploiting only variation that results from firms announcing on the same day vs. with a gap of one day. The identifying assumption in these tests is that amongst a set of firms announcing close in time to each other (e.g., late in the quarter), firms that announce on the same day are not systematically different from firms that announce with a gap of one day. For instance, con- sider a firm with bad earnings news. In order to look relatively better, this firm might prefer to announce among firms with even worse news. As a result, the firm might strategically reschedule its earnings announcement to a time later in the quarter, in order to announce amongst the set of firms that generally announce bad news. But it would be hard for the firm to reschedule its announcement to the precise day on which firms with even worse news are announcing. The reason is that even for firms with bad news, it is hard to predict how bad the news of other firms is (Hartzmark and Shue (2018)). Therefore, it is plausible that amongst the set of firms that announce late in the quarter, firms that announce on the same day are not systematically different than firms that announce with a gap of one day. This is the variation that I am exploiting in these tests, which I implement by estimating the following regression: return j,t =α +β 1 ·cue ∆( −2) j,t,q−1 +β 2 ·cue ∆( −1) j,t,q−1 +β 3 ·cue ∆(0) j,t,q−1 +β 4 ·cue ∆(+1) j,t,q−1 +β 5 ·cue ∆(+2) j,t,q−1 +γ t +u j,t (2.3) In this regression, cue ∆( k) j,t,q−1 is a dummy variable that is equal to one if at least one firm that announced earnings k days after firm j in the previous quarter announces earnings on day t. For instance, cue ∆(+1) j,t,q−1 is a dummy variable that is equal to one if at least one firm that announced earnings one day after firm j in the previous quarter announces earnings on day t. Similarly, cue ∆( −1) j,t,q−1 is a dummy variable that is equal to one if at least one firm that announced earnings one day before firm j in the previous quarter announces earnings on dayt. Finally,cue ∆(0) j,t,q−1 is a dummy variable that is equal to one if at least one firm that announced earnings on the same day as firm j in the previous quarter announces earnings 45 on day t (i.e., this dummy variable corresponds to the main dummy variable in Equation (2.2)). By comparingβ 3 toβ 2 andβ 4 , I can gauge whether a cue has a stronger effect if the memory association was encoded when both firms announced on the same day vs. with a gap of one day. Figure 2.1. Calendar Rotations: An Example Sun Mon Tue Wed Thu Fri Sat 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 Sun Mon Tue Wed Thu Fri Sat 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 June, July, August 2013 June, July, August 2014 Fiscal quarter-end (June 30th) A and B announce Fiscal quarter-end (June 30th) B announces A announces However, given the large set of factors that could potentially affect earnings announce- ment timing, there may be endogenous factors that affect even the decision to announce on the same day vs. with a gap of one day. To directly address these concerns, I repeat my analysis for the subsample of earnings announcement dates that were exogenously shifted by calendar rotations (Noh et al. (2021)). As an illustration of how this works, consider two 46 firms, A and B, whose fiscal quarters end on June 30th. 4 Further, assume that both firms are “Pattern firms”, i.e., they both follow a strict quarter-specific pattern in their earnings announcement timing and have not deviated from this pattern by even one day for at least three years. Specifically, Firm A always announces on the first Thursday in August and Firm B always announces on the fifth Thursday since the end of the fiscal quarter. As shown in Figure 2.1, the month of August began on a Thursday in 2013, but on a Friday in 2014. As a result, both firms announced on August 1st in 2013. However, in 2014, Firm A announced on August 7th and Firm B announced on July 31st. This is how calendar rotations – changes in the day-of-week on which a calendar month begins – create plausibly random overlaps of earnings announcements for Pattern firms. All my results hold in the subsample of Pattern firms. 2.3 Data 2.3.1 Full Sample Thefullsamplespansyears1995to2020andconsistsofallfirm-dayswithoutanownearnings announcement within +/- 3 trading days. Throughout the paper, the term “days” always refers to trading days. I use data from I/B/E/S to identify quarterly earnings announcement dates. Since my empirical strategy relies on identifying overlaps of earnings announcements, it is crucial that the earnings announcement dates are measured without error. I therefore follow DellaVigna and Pollet (2009) and use only data from 1995 onwards, since the accuracy of the earnings date is near perfect after December 1994. I match I/B/E/S data with CRSP for information on stock returns and with Compustat for firm-specific accounting information. I calculate characteristic-adjusted returns as in Daniel et al. (1997) and Hartzmark and Shue (2018). Specifically, I triple-sort stocks into quintiles of size, book-to-market, and momentum, and then match each individual stock to one of the resulting 125 portfolios. If I cannot match a stock to one of the portfolios due to missing data in one of the sorting variables, I drop it. The characteristic-adjusted return on day t is the stock’s raw return 4 This example is adapted from Noh et al. (2021). 47 on day t minus the value-weighted return of the portfolio on day t. I use portfolio stocks’ market capitalization from day t− 3 as the weights in this calculation. In all my tests, the term “returns” refers to these characteristic-adjusted returns. I winsorize all variables at the 1st and the 99th percentile. Onsomefirm-days,cueingeventsoccur,whichIcapturewithasimpledummyvariable. A cueingeventforfirm j ondaytoccursifatleastonefirmthatannouncedearningsonthesame day as firm j in any of the previous four fiscal quarters announces earnings on day t. I require cueing firms to be in a different industry than firm j to avoid picking up within-industry information spillovers. I use the text-based network industry classifications of Hoberg and Phillips (2010, 2016) to ensure that the two firms operate in dissimilar industries. 5 Further, similar to Hartzmark and Shue (2018), I require cueing firms to have a market capitalization (measured on dayt−3) that is above the NYSE’s 90th percentile of market capitalization in that month. I do so to focus on large and salient cues, but my results also hold for different cutoffs, which I show later in the paper. Of the 16,474 distinct firms in my sample, 10,023 firms (60.84%) have at least one cueing event. On firm-days with a cueing event, I also calculate the earnings surprise of the cueing firm(s). In calculating the surprise, I follow Hartzmark and Shue (2018) and identify each analyst’s most recent forecast in I/B/E/S, and then take the median of all analyst forecasts made between 2 and 15 days prior to the earnings announcement. Then, I calculate the differencebetweentheactualearningsannouncedbythecueingfirmandthemedianearnings forecast and scale this difference by the share price of the firm from three trading days prior to the announcement. If there are multiple cueing firms that announce earnings on day t, I calculate the equally-weighted as well as the value-weighted average surprise of the cueing firms, using each cueing firm’s market capitalization three days prior to the announcement as value weights. 5 This classification is more flexible than standard classifications (e.g., SIC or NAICS), as it changes over time and allows each firm to have a unique set of competitors. I use the broader TNIC-2 industries provided by the authors, which are calibrated to be as granular as two-digit SIC codes. Specifically, 4.5% of randomly drawn firms are deemed to be peers according to this classification. 48 2.3.2 Pattern Firm Sample I also construct a second sample, which I label “Pattern firm sample”. This sample is constructed near-identically to the full sample and consists of all firm-days without an own earnings announcement within +/- 3 trading days. I also apply all the other filters described above, such as the exclusion of firm-pairs that operate in the same TNIC-2 industry. The key difference of the Pattern firm sample vis-à-vis the full sample is that cueing events are estimated using only the earnings announcement dates of Pattern firms. I calculate cueing events for the Pattern firm sample using data provided by Noh et al. (2021). 6 Since this data is available for years 2005 – 2019, I restrict the Pattern firm sample to these years. I focus on the threshold3 dataset provided by the authors, which classifies a firm as a Pattern firm if it followed a strict quarter-specific pattern in its earnings an- nouncement timing for three years or more. I cross-check the earnings announcement dates in the threshold3 dataset with those in my dataset and drop any discrepancies (less than 1% of observations). In the Pattern firm sample, a cueing event for Pattern firm j on day t occurs if at least one Pattern firm that announced earnings on the same day as Pattern firm j in any of the previous four fiscal quarters announces earnings on day t. That is, in this sample, only Pattern firms can be cueing or cued firms. Note, however, that this sample also contains non-Pattern firms, since the sample contains all firm-days without an earnings announcement within +/- 3 days. It is just that non-Pattern firms cannot be cueing or cued firms in this sample. As a result, of the 9,244 distinct firms in the Pattern firm sample, only 3,963 firms (42.87%) have at least one cueing event. 2.3.3 Summary Statistics Table 2.1 presents summary statistics for the full sample in Panel A and for the Pattern firm sample in Panel B. In both samples, returns in excess of the characteristic-matched portfolio are slightly negative. This is because both samples systematically exclude days with an own earnings announcement, and therefore systematically exclude the earnings announcement premium (Frazzini and Lamont (2007); Barber et al. (2013)). 6 Available here. 49 In the full sample (Panel A), there is a cueing event on 5.22% of days. This captures cues from memory associations that were encoded in any of the previous four fiscal quarters. However, in many tests, I focus on memory associations that were encoded in the previous quarter, since these are likely strongest and easiest to recall. The dummy variable Cue q−1 captures cueing events from such associations and shows that on 1.79% of days, there is a cueing event from a memory association that was encoded in the previous quarter. The subscript "q− 1" refers to the fact that these associations were encoded in the previous quarter. While there is only one cue on the median day with a cueing event, there are also days with multiple cues. On such days, I calculate the earnings surprise of the cue as either the equally-weighted or value-weighted average surprise of the cueing firms. Earnings surprises are typically close to zero. The Pattern firm sample (Panel B) looks very similar. The main difference is that cueing events are much less frequent, since they are calculated using only overlaps of earnings announcements of Pattern firms. In the Pattern firm sample, there is a cueing event on 0.66% of days and 0.21% of cueing events are from associations that were encoded in the previous quarter. 2.4 Results 2.4.1 Baseline Results In my first test, I estimate Equation (2.1) for the full sample and regress the return of firm j on day t on a dummy variable that is equal to one if there is a cueing event for firm j on day t. This dummy variable is equal to one if at least one firm that announced earnings on the same day as firm j in any of the previous four fiscal quarters announces earnings on day t. The first column in Panel A of Table 2.2 shows that the coefficient on this dummy variable is positive and highly significant. In terms of magnitude, the estimate implies that such a cue leads to a daily abnormal return of 2.3 basis points, which corresponds to 5.8% in annual terms. In the second column, I augment this regression with day fixed effects. These fixed effects account for the possibility that my results might be driven by days on which big 50 Table 2.1: Summary Statistics Panel A: Full Sample Mean p25 p50 p75 Std. Dev. Min Max N Return (%) -0.0168 -1.3331 -0.0801 1.1828 3.2857 -10.9855 12.8454 31,392,090 Cue (dummy) 0.0522 0.0000 0.0000 0.0000 0.2225 0.0000 1.0000 31,392,090 Cue q−1 (dummy) 0.0179 0.0000 0.0000 0.0000 0.1325 0.0000 1.0000 31,392,090 Number of cues 2.2170 1 1 2 2.4032 1 35 1,639,021 Surprise of cue (EW) 0.0008 0.0001 0.0005 0.0011 0.0024 -0.0087 0.0156 1,639,021 Surprise of cue (VW) 0.0007 0.0001 0.0004 0.0011 0.0022 -0.0081 0.0142 1,639,021 Panel B: Pattern Firm Sample Mean p25 p50 p75 Std. Dev. Min Max N Return (%) -0.0145 -1.1239 -0.0522 1.0218 2.7287 -10.9855 12.8454 15,773,961 Cue (dummy) 0.0066 0.0000 0.0000 0.0000 0.0809 0.0000 1.0000 15,773,961 Cue q−1 (dummy) 0.0021 0.0000 0.0000 0.0000 0.0456 0.0000 1.0000 15,773,961 Number of cues 1.8256 1 1 2 1.7427 1 19 103,809 Surprise of cue (EW) 0.0007 0.0000 0.0005 0.0012 0.0017 -0.0052 0.0082 103,809 Surprise of cue (VW) 0.0007 0.0000 0.0005 0.0013 0.0016 -0.0050 0.0082 103,809 Notes: This table contains summary statistics of the two samples used in the empirical analysis. Panel A contains the full sample, which covers years 1995-2020. Panel B contains the Pattern firm sample, which covers years 2005-2019. Return is the raw return of a stock on day t minus the value-weighted return of a portfolio of stocks matched on size, book-to-market, and momentum. Cue is a dummy equal to one if at least one firm that announced earnings on the same day as firm j in any of the previous four fiscal quarters announces earnings on day t. Cue q−1 is a similar dummy but focuses on firms that announced on the same day as firm j in the previous quarter. Number of cues is the number of cueing firms announcing on days with Cue equal to one. Surprise is the earnings surprise of the cueing firm(s) announcing on days with Cue equal to one. On days with multiple cues, I calculate both the equally-weighted (EW) and value-weighted (VW) earnings surprise. and famous firms announce (Chen et al. (2022)), but the effect is virtually identical when controlling for day fixed effects. In the third column, I estimate Equation (2.2), which is similar but focuses on cueing events from associations that were encoded in the previous quarter. The idea behind this test is that recent associations might be easier to recall, potentially leading to stronger effects (although such associations are also captured by the catchall dummy in the first two columns). 7 Indeed, the coefficient is slightly larger and implies that such a cue leads to a daily abnormal return of 3 basis points, which annualizes to 7.5%. Controlling for day fixed effects in the fourth column also does not affect the size or significance of this coefficient. In the fifth and sixth columns, I break out the effect separately for days with one cue, two cues, and three or more cues. The effect tends to become stronger as the number of cues increases, 7 I explore the role of recency in recall in more detail in Table 2.4. 51 Table 2.2: Baseline Results Panel A: Full Sample Dependent variable: Return on day t (%) (1) (2) (3) (4) (5) (6) Cue (dummy) 0.023*** 0.021*** (0.005) (0.006) Cue q−1 (dummy) 0.030*** 0.029*** (0.007) (0.008) Single Cue (dummy) 0.022*** 0.021*** (0.005) (0.006) Two Cues (dummy) 0.018** 0.014 (0.007) (0.009) Three or More Cues (dummy) 0.028*** 0.026** (0.009) (0.011) Day FE no yes no yes no yes Observations 31,392,090 31,392,090 31,392,090 31,392,090 31,392,090 31,392,090 R-squared 0.000 0.003 0.000 0.003 0.000 0.003 Panel B: Pattern Firm Sample Dependent variable: Return on day t (%) (1) (2) (3) (4) (5) (6) Cue (dummy) 0.038*** 0.027** (0.011) (0.013) Cue q−1 (dummy) 0.062*** 0.053*** (0.015) (0.018) Single Cue (dummy) 0.035*** 0.023* (0.011) (0.013) Two Cues (dummy) 0.077*** 0.056** (0.023) (0.026) Three or More Cues (dummy) 0.014 0.018 (0.024) (0.028) Day FE no yes no yes no yes Observations 15,773,961 15,773,961 15,773,961 15,773,961 15,773,961 15,773,961 R-squared 0.000 0.004 0.000 0.004 0.000 0.004 Notes: This table presents results from regressions of the return on day t on different measures of memory cues. Return on day t is the raw return of a stock minus the value-weighted return of a portfolio of stocks matched on size, book-to-market, and momentum. In the first two columns, the independent variable is the dummy variable Cue, which is equal to one if at least one firm that announced earnings on the same day as firm j in any of the previous four fiscal quarters announces earnings on day t. In the next two columns, the independent variable is Cue q−1 , which is a similar dummy but focuses on firms that announced on the same day as firm j in the previous quarter. In the last two columns, the independent variables are dummies that indicate the number of cueing firms on days with Cue equal to one. Columns (2), (4), and (6) also include day fixed effects. Panel A shows results for the full sample and Panel B for the Pattern firm sample. Standard errors are clustered by firm and trading day and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 52 which is plausible, since a larger number of cues is more likely to direct memory-induced attention to the cued firm. 8 In Panel B, I replicate these results for the Pattern firm sample. In the first column of Panel B, I find that the effect of a cue is similar, and indeed slightly stronger, in this sample. A cueing event leads to a daily abnormal return of 3.8 basis points, which annualizes to 9.5%. When I test for the equality of coefficients across samples, I find that the difference is not significant ( p = 0.117). In the second column, in which I account for day fixed effects, the coefficient slightly diminishes in magnitude and is even more similar to the corresponding coefficient in the full sample. In the third and fourth columns I again focus on cues from associations that were encoded in the previous quarter. The effect size is slightly larger for these cues, again suggesting that these associations might be stronger and easier to recall. Finally, in the fifth and sixth columns, I find that days with two cues tend to lead to stronger effects than days with a single cue. However, the coefficient on the dummy indicating three or more cues is small and insignificant in this sample, which might be driven by the fact that it is very rare for this many cues to occur in the Pattern firm sample. The Pattern firm sample provides a powerful setting in which to test robustness of my results, since the cues in this sample are driven by plausibly exogenous calendar rotations. However, one downside of this setting is that it favors identification at the expense of gener- alizability (Noh et al. (2021)). Given this, it is reassuring that the effect sizes are similar in both samples, suggesting that the documented effects hold for a broad set of firms. Overall, the results Table 2.2 support the hypothesis that internally-generated attention can lead to buying pressure in memory-associated stocks. 2.4.2 Contiguity In this next set of tests, I estimate Equation (2.3) from Section (2.2). These tests serve a dual purpose: first, they tighten the identification; second, they allow me to explore an important property of memory, called the “law of contiguity”. This law states that two items share a stronger association in memory if they were experienced closer in time together (Kahana 8 In the Appendix, I show that I find similar results when I focus only on cueing events from the largest firm that had an overlapping earnings announcement with firm j in any of the previous four quarters. 53 (2012)). The intuition of contiguity, and how I test for it in my setting, can be illustrated bestwiththeintroductoryexample. Recallthatlastquarter, Coca-ColaandIBMannounced earnings on the same day. Now, also assume that last quarter Apple announced one day after Coca-Cola. According to the law of contiguity, Coca-Cola and Apple should share a weaker association than Coca-Cola and IBM. Therefore, in the tests that follow, I compare whether an earnings announcement of Coca-Cola on day t results in a weaker return response for Apple than for IBM, since the association between Coca-Cola and Apple is weaker than the association between Coca-Cola and IBM. To implement these tests, I estimate Equation (2.3), which includes several dummy vari- ables that capture different types of cues. For instance, cue ∆( −1) j,t,q−1 is equal to one if at least one firm that announced earnings one day before firm j in the previous quarter announces earnings on day t. Thus, this dummy variable captures the return response of Apple if Coca-Cola announces earnings on day t. Similarly, cue ∆(0) j,t,q−1 is equal to one if at least one firm that announced earnings on the same day as firm j in the previous quarter announces earnings on day t (i.e., this is the standard dummy that I use in most specifications). This dummy captures the return response of IBM if Coca-Cola announces earnings on day t. Table 2.3 presents the results from these regressions and Figure 2.2 plots the coefficients together with their corresponding 95% confidence intervals. The effect is strongest and most significant for associations that were encoded on the same day, and it drops of sharply for associations that were encoded with a gap of just one day. These results are fully consistent with the law of contiguity and show that memory associations are stronger if they were encoded in a more similar context. In addition to providing support for an important property of memory, these tests also helpalleviateconcernsthatmyresultsaredrivenbysimilarfirmsannouncingatsimilartimes during an earnings season. As discussed in Section (2.2), these tests exploit variation from firms announcing on the same day vs. with a gap of one day in the previous quarter. Thus, the identifying assumption in these tests is that amongst a set of firms announcing close in time to each other (e.g., late in the quarter), firms that announce on the same day are not systematically different from firms that announce with a gap of one day. This assumption is 54 Figure 2.2. Contiguity Return Response (%) on the Day of a Memory Cue (a) Panel A: Full Sample -.01 0 .01 .02 .03 .04 Effect Size -2 -1 0 +1 +2 Timing Gap (in days) when Memory is Encoded (b) Panel B: Pattern Firm Sample -.05 0 .05 .1 Effect Size -2 -1 0 +1 +2 Timing Gap (in days) when Memory is Encoded Notes: This figure plots the coefficient estimates from Table 2.3 along with 95% confidence intervals. Panel A shows results for the full sample and Panel B for the Pattern firm sample. 55 Table 2.3: Contiguity Dependent variable: Return on day t (%) Sample: Full Pattern Firm (1) (2) Cue ∆( −2) q−1 (dummy) 0.000 -0.019 (0.006) (0.018) Cue ∆( −1) q−1 (dummy) 0.003 0.009 (0.005) (0.015) Cue ∆(0) q−1 (dummy) 0.023*** 0.051*** (0.006) (0.016) Cue ∆(+1) q−1 (dummy) 0.008 0.013 (0.006) (0.017) Cue ∆(+2) q−1 (dummy) 0.013** 0.014 (0.006) (0.016) Day FE yes yes Observations 31,392,090 15,773,961 R-squared 0.003 0.004 Notes: This table presents results from regressions of the return on day t on dummy variables that capture different types of cues. The dummies are all of the type cue ∆( k) j,t,q−1 and are equal to one if at least one firm that announced earningsk days after firm j in the previous quarter announces earnings on dayt. Column (1) shows results for the full sample and column (2) for the Pattern firm sample. Both columns also include day fixed effects. Standard errors are clustered by firm and trading day and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 56 likely satisfied, especially for the set of Pattern firms, whose earnings announcement dates are shifted by exogenous calendar rotations. 2.4.3 Recency Perhaps the best-known property of human memory is that recent experiences are easier to recall than distant experiences, a property which I explore in the tests that follow. To do so, I augment Equation (2.2) with dummies for each of the previous four quarters, indicating cueing events from memory associations that were encoded in the respective quarter. These dummies allow me to back out the recency slope non-parametrically. The first column in Panel A of Table 2.4 shows that when I estimate this specification for the full sample, the effect is strongest for the most recent quarter and fades away with further lags. This finding provides direct evidence that recently encoded memory associations have stronger effects. In Figure 2.3, I also show this effect graphically. Each dot in the figure is a coefficient estimate from the regression and the bars show corresponding 95% confidence intervals. The figure shows a clear systematic decay in the effect. Not only is this result consistent with a long psychology literature on memory, but also with the findings in Chang et al. (2017), which shows that investors tend to overweight the most recent quarter. In the second through fifth column of Table 2.4, I also estimate separate regressions, each with a dummy variable for a different quarterly lag. These separate regressions further address the worry that my results are picking up fundamental relationships. A possible interpretation of the full regression presented in the first column is that each quarterly lag proxies for fundamentally related firms, but the prior quarter is the best proxy. Under this interpretation, when included separately, each dummy should be a strong predictor on its own, getting a bit noisier with further lags. In contrast, under a memory channel, the coefficients from the separate regressions should look similar to those from the full regression and also show a systematic decay. This is precisely what I find. In Panel B, I replicate these results in the Pattern firm sample. Here, too, I find that the coefficient on the previous quarter is strongest and that the effect becomes weaker as the lag increases. The drop off from the first to the second lag is even sharper in this sample than in the full sample. In sum, the results in Table 2.4 not only validate a key prediction 57 Figure 2.3. Recency Return Response (%) on the Day of a Memory Cue (a) Panel A: Full Sample 0 .01 .02 .03 .04 Effect Size -4 -3 -2 -1 Quarter that Memory is Encoded (b) Panel B: Pattern Firm Sample -.05 0 .05 .1 Effect Size -4 -3 -2 -1 Quarter that Memory is Encoded Notes: This figure plots the coefficient estimates from the first column of Table 2.4 along with 95% confidence intervals. Panel A shows results for the full sample and Panel B for the Pattern firm sample. 58 Table 2.4: Recency Panel A: Full Sample Dependent variable: Return on day t (%) (1) (2) (3) (4) (5) Cue q−1 (dummy) 0.021*** 0.029*** (0.007) (0.008) Cue q−2 (dummy) 0.013** 0.022*** (0.006) (0.007) Cue q−3 (dummy) 0.008 0.018*** (0.006) (0.007) Cue q−4 (dummy) 0.015** 0.022*** (0.008) (0.008) Day FE yes yes yes yes yes Observations 31,392,090 31,392,090 31,392,090 31,392,090 31,392,090 R-squared 0.003 0.003 0.003 0.003 0.003 Panel B: Pattern Firm Sample Dependent variable: Return on day t (%) (1) (2) (3) (4) (5) Cue q−1 (dummy) 0.046*** 0.053*** (0.017) (0.018) Cue q−2 (dummy) 0.012 0.025 (0.016) (0.018) Cue q−3 (dummy) 0.024 0.032* (0.017) (0.019) Cue q−4 (dummy) -0.012 -0.001 (0.022) (0.023) Day FE yes yes yes yes yes Observations 15,773,961 15,773,961 15,773,961 15,773,961 15,773,961 R-squared 0.004 0.004 0.004 0.004 0.004 Notes: This table presents results from regressions of the return on dayt on memory cues that were encoded in different quarters. The independent variables are dummy variables for each of the previous four fiscal quarters, and are equal to one if at least one firm that announced earnings on the same day as firm j in that quarter announces earnings on day t. Column (1) includes all dummies simultaneously and the remaining columns each include only one dummy at a time. All columns include day fixed effects. Panel A shows results for the full sample and Panel B for the Pattern firm sample. Standard errors are clustered by firm and trading day and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 59 of memory theory, but also help attenuate concerns that my results are driven by attention to fundamentally related firms. 2.4.4 Interference I next turn to tests that explore whether interference dampens the documented effect. The intuition is straightforward. If a memory association between Coca-Cola and IBM was encoded on a day that many other firms also announced earnings, the strength of this association should be weaker. The reason is that on such days, investors not only encode associationsbetweenCoca-ColaandIBM,butalsoassociationsbetweenCoca-Colaandthese other firms. As a result, when cued with an earnings announcement by Coca-Cola on day t, investors might not recall IBM, but one of these other firms instead. Put differently, the memories of these other firms interfere with the recall of IBM. Thus, I hypothesize that the return response of IBM is weaker if interference is higher. Applying this intuition to my setting, I classify associations as having “low interference” if they were encoded on days that the number of other firms announcing was below the median. Conversely, I classify associations as having “high interference” if the number of firms announcing on the same day was above the median. I calculate the median cutoff for each year separately to account for time-varying trends in the number of firms announcing. In Table 2.5, I show that the effect is stronger for cues from associations with low in- terference. In the full sample, the effect is almost 50% larger if interference is low. In the Pattern firm sample, the effect is more than double if interference is low. Figure 2.4 also visualizes this result as a coefficient plot with 95% confidence intervals. 2.5 Robustness 2.5.1 Reversals Since memory-induced buying pressure carries no new information, prices should eventually revert to their fundamental values. In contrast, if my results were driven by fundamental relationships, thereshouldbenosystematicreversal. Totestforthesepossibilities, Iexamine 60 Figure 2.4. Interference Return Response (%) on the Day of a Memory Cue (a) Panel A: Full Sample 0 .01 .02 .03 .04 .05 Effect Size Low High Interference (b) Panel B: Pattern Firm Sample -.05 0 .05 .1 .15 Effect Size Low High Interference Notes: This figure plots the coefficient estimates from Table 2.5 along with 95% confidence intervals. Panel A shows results for the full sample and Panel B for the Pattern firm sample. 61 Table 2.5: Interference Dependent variable: Return on day t (%) Sample: Full Pattern Firm (1) (2) Cue q−1 x Low Interference 0.034*** 0.071*** (0.009) (0.022) Cue q−1 x High Interference 0.024** 0.031 (0.011) (0.027) Day FE yes yes Observations 31,392,090 15,773,961 R-squared 0.003 0.004 Notes: This table presents results from regressions of the return on dayt on memory cues that were encoded with low and high interference. Cue q−1 x Low Interference is equal to one if at least one firm that announced earnings on the same day as firm j in the previous quarter announces earnings on day t, and if the number of firms announcing on that day in the previous quarter was below the median. Cue q−1 x High Interference is defined equivalently, except that the number of firms announcing on that day in the previous quarter was above the median. Column (1) shows results for the full sample and column (2) for the Pattern firm sample. Both columns also include day fixed effects. Standard errors are clustered by firm and trading day and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 62 Table 2.6: Reversals Panel A: Full Sample Return window: [t] [t + 1] [t + 2] [t, t + 1] [t, t + 2] (1) (2) (3) (4) (5) Cue q−1 (dummy) 0.035** -0.037*** -0.001 -0.001 -0.006 (0.015) (0.014) (0.015) (0.021) (0.025) Day FE yes yes yes yes yes Observations 28,180,614 28,163,550 28,146,559 28,163,550 28,147,444 R-squared 0.004 0.004 0.004 0.004 0.004 Panel B: Pattern Firm Sample Return window: [t] [t + 1] [t + 2] [t, t + 1] [t, t + 2] (1) (2) (3) (4) (5) Cue q−1 (dummy) 0.083*** -0.046 0.044 0.031 0.075 (0.032) (0.030) (0.028) (0.045) (0.053) Day FE yes yes yes yes yes Observations 14,215,217 14,209,807 14,204,430 14,209,807 14,204,847 R-squared 0.005 0.005 0.005 0.005 0.004 Notes: This table presents results from regressions of the return for various return windows on Cue q−1 . The return windows are indicated in the column headers. The sample excludes firm-days with an additional cue on day t + 1 or t + 2. All firm-days within [ t− 10, t + 10] of an own earnings announcement of firm j are excluded from the sample. All columns include day fixed effects. Panel A shows results for the full sample and Panel B for the Pattern firm sample. Standard errors are clustered by firm and trading day and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. the effect for return windows that extend beyond day t in Table 2.6. When testing for reversal, it is important to ensure that no new cues occur in the return window that is being analyzed, since these new cues would confound the effect of the reversal. Therefore, in these tests I exclude all observations for which there is an additional cue on day t + 1 or t + 2. Further, since the return windows extend beyond day t, it is important to ensure that the returns in these windows are not affected by (the anticipation of) an own earnings announcement. To err on the conservative side in these tests, I extend my baseline window and exclude all days within [t− 10, t + 10] of an own earnings announcement. Panel A presents the results for the full sample. In the first column of Table 2.6, I reproduce the main effect for this restricted sample. The coefficient on Cue q−1 is very similar 63 to the baseline effect in Table 2.2. The second column shows that there is full reversal of the effect on day t+1, and the remaining columns show that there is no significant effect for return windows that extend beyond day t. Panel B presents similar results for the Pattern firm sample. In this sample, there is partial reversal on day t + 1, but the effects are not as clearcut. However, eveninthissample, Icannotdetectasignificanteffectforreturnwindows that extend beyond day t. Taken together, these results suggest that the mispricing due to memory-induced buying pressure is quickly corrected by the market. 2.5.2 Surprise of the Cue In this next set of tests, I explore whether the earnings surprise of the cueing firm predicts the return response of the cued firm. These tests are designed to address the potential con- cern that my results might be driven by information spillover from the cueing firm’s earnings announcement. Such spillovers might manifest themselves in a systematic relationship be- tween the earnings surprise of the cueing firm and the return response of the cued firm. For instance, more positive surprises might lead to higher returns and more negative sur- prises might lead to lower returns (Thomas and Zhang (2008)). In contrast, if the earnings announcement purely acts as a memory cue that directs attention, the earnings surprise is unlikely to play an important role for the strength of the effect. In Table 2.7, I regress the return of firm j on day t on the earnings surprise of the cueing firm. I also test whether the effect varies along the distribution of the cueing firms’ earnings surprise, to account for potential non-linear relationships. The sample in these tests is restricted to days with a cueing event, since these are the only days on which an earnings surprise of cueing firms can be calculated. On days with multiple cues, I calculate either the equally-weighted average (first and second column) or the value-weighted average (third and fourth column) of the cueing firms’ earnings surprise. Panel A presents the results of these tests for the full sample, and Panel B for the Pattern firm sample. 64 Table 2.7: Surprise of the Cue Panel A: Full Sample Dependent variable: Return on day t (%) Surprise: EW VW (1) (2) (3) (4) Surprise -2.304 -2.715 (2.101) (2.105) Surprise Quintile 2 (dummy) 0.002 0.015 (0.013) (0.014) Surprise Quintile 3 (dummy) 0.030** 0.030** (0.014) (0.014) Surprise Quintile 4 (dummy) 0.023 0.015 (0.014) (0.014) Surprise Quintile 5 (dummy) 0.024 0.015 (0.016) (0.015) Day FE yes yes yes yes Observations 1,639,021 1,639,021 1,639,021 1,639,021 R-squared 0.006 0.006 0.006 0.006 65 Panel B: Pattern Firm Sample Dependent variable: Return on day t (%) Surprise: EW VW (1) (2) (3) (4) Surprise -10.786 -10.006 (10.520) (9.539) Surprise Quintile 2 (dummy) -0.010 -0.001 (0.039) (0.037) Surprise Quintile 3 (dummy) 0.022 0.032 (0.041) (0.037) Surprise Quintile 4 (dummy) -0.009 -0.006 (0.042) (0.037) Surprise Quintile 5 (dummy) -0.021 -0.061 (0.047) (0.047) Day FE yes yes yes yes Observations 103,784 103,784 103,784 103,784 R-squared 0.021 0.021 0.021 0.021 Notes: This table presents results from regressions of the return on day t on the earnings surprise of the cueing firm(s). The sample is restricted to days with a cue. Surprise is the difference between the actual earnings announced by the cueing firm and the median analyst earnings forecast, scaled by the share price of the firm from three trading days prior to the announcement. If there are multiple cues on day t, columns (1) and (2) use the equally-weighted average surprise, and columns (3) and (4) use the value-weighted average surprise. Columns (1) and (3) include the surprise directly as an independent variable, while columns (2) and (4) include dummy variables that indicate the second through fifth quintile of the surprise distribution. Panel A presents results for the full sample and Panel B for the Pattern firm sample. All columns include day fixed effects. These fixed effects can result in singleton observations, which are dropped during the estimation (specifically, 25 observations in Panel B). Standard errors are clustered by firm and trading day and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. I find that the surprise of cueing firms does not have predictive power for the return response of the cued firm, neither in the full sample nor in the Pattern firm sample. While at first blush the coefficients in the first and third column might appear economically large, this magnitude is driven by the fact that the earnings surprise variable has a tiny standard deviation (see Table 2.1). For instance, the coefficient in the first column of Panel A implies that a one standard deviation increase in the earnings surprise of the cueing firm would decrease the return response of the cued firm by half a basis point. The small economic magnitudes of the earnings surprise coefficients are also apparent in the non-parametric 66 estimations in the second and fourth column. Taken together, these findings help address the concern that my results might be picking up information spillovers from cueing to cued firms. In contrast, these results are wholly consistent with a memory-based explanation, in which a cueing firm’s earnings announcement simply directs attention to the memory- associated firm, regardless of the sign or magnitude of the earnings surprise. 2.5.3 Large vs. Small Firms I also explore whether the documented effect is stronger for large or small firms. On the one hand, conditional on a cue, large firms might come easier to mind. On the other hand, large firms have more liquid stocks, making buying pressure less likely to occur. To test for these possibilities, I split the sample along median firm size, using the market capitalization from t− 3, and show the effects separately for large and small firms, both in the full sample and in the Pattern firm sample. Table 2.8 presents the results. I find that the effect is driven mostly by small firms. However, particularly in the Pattern firm sample, the effect can also be documented for large firms. Table 2.8: Large vs. Small Firms Dependent variable: Return on day t (%) Sample: Full Pattern firm Firm size: Small Large Small Large (1) (2) (3) (4) Cue q−1 (dummy) 0.054*** 0.010* 0.106*** 0.028** (0.014) (0.006) (0.039) (0.014) Day FE yes yes yes yes Observations 15,696,043 15,696,047 7,886,980 7,886,981 R-squared 0.008 0.002 0.010 0.001 Notes: This table splits the sample along the median market capitalization of firm j fromt−3 and presents results from regressions of the return on day t on Cue q−1 . Columns (1) and (2) show results for the full sample and columns (3) and (4) for the Pattern firm sample. All columns include day fixed effects. Standard errors are clustered by firm and trading day and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 67 2.5.4 Trading Strategy Since earnings announcements are usually scheduled at least a week ahead of time (Boulland and Dessaint (2017)), it is possible to construct a trading strategy that takes advantage of the buying pressure caused by memory-induced attention. This intentionally simple trading strategy is a daily long-short strategy that is held on day t. The strategy goes long stocks for which Cue q−1 is equal to one and it goes short stocks for which Cue q−1 is equal to zero. The long and short leg of the strategy are value-weighted portfolios using the market capitalization of each stock on day t− 3. I use small firms (market capitalization from t− 3 is below the median) to form these portfolios, since these firms drive most of the effect (see Table 2.8). To account for the potential role of risk factors, I regress the time series of daily returns generated by this trading strategy on the market, size, value, momentum, and short-term reversal factors, which are sourced from the Kenneth French Data Library. Table 2.9 shows that the strategy yields a daily alpha of 8.7 basis points, which is significant at the 5% level. This daily alpha would correspond to an annual abnormal return of about 22% if the trading strategy could be implemented every trading day. However, the trading strategy can only be implemented if there is a cueing event (i.e., an earnings announcement) and if there are stocks that fall into the long and short leg of the strategy. In my sample, the strategy can be implemented on an average of 110 trading days per year. Thus, the strategy generates an annual abnormal return of about 9.5%. Whether this strategy continues to yield positive abnormal returns after accounting for transaction costs depends on the size and nature of these costs, which likely differ across investors. However, the purpose of illustrating this trading strategy is not to identify the highest possible alpha, but rather to show that the main result holds in a different spec- ification, with a different risk adjustment. To this end, Table 2.9 shows that while there are loadings on the factors, these loadings are economically small and do not wash out the positive and significant alpha. Thus, a risk-based explanation is unlikely to explain the re- sults. Overall, these results highlight the robustness of my findings using calendar-time asset pricing methods. 68 Table 2.9: Trading Strategy Dependent variable: Return on day t (%) (1) Alpha [%] 0.087** (0.039) Mkt 0.124*** (0.034) SMB 0.323*** (0.060) HML 0.061 (0.060) Momentum -0.115*** (0.043) ST Reversal -0.003 (0.044) Observations 2,753 R-squared 0.023 Notes: This table presents results from a regression of daily trading strategy returns on the daily market, size, value, momentum, and short-term reversal factors, which are sourced from the Kenneth French Data Library. The daily trading strategy returns are the daily returns of a long-short strategy. The long leg of the strategy consists of a value-weighted portfolio of stocks with Cue q−1 equal to one, and the short leg of the strategy consists of a value-weighted portfolio of stocks with Cue q−1 equal to zero. The weights in these portfolios are the market capitalization of each stock on day t− 3. These portfolios are formed using firms whose market capitalization from t− 3 is below the median. Standard errors are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 69 2.5.5 Robustness In my tests so far, I focus on large and salient cues by requiring each cueing firm to have a market capitalization that is above the NYSE’s 90th percentile of market capitalization. Here, I show that these results are robust to using the 85th and 95th percentile as cutoffs. In Table 2.10, I rerun my main regressions using these different cutoffs. Panel A shows the results for the full sample while Panel B shows the results for the Pattern firm sample. Overall, my results are robust to using different size cutoffs. Inmymain tests, I ensurethatfirm j doesnot have anownearningsannouncementinthe window [t−3,t+3] to avoid confounding effects from a firm’s own earnings announcement. However, this window is somewhat ad hoc. Therefore, in Table 2.10, I explore the robustness of my results for different windows. Specifically, I replicate my main results using samples in which I ensure that there is no own earnings announcement in [t− 1, t + 1] and in [t− 5, t + 5]. Panel A presents the results for the full sample and Panel B presents results for the Pattern firm sample. For both alternative windows, I find very similar results as with the baseline window. An open question is whether my results reflect investors’ memory, or whether they reflect analysts’ memory. For instance, assume that an analyst follows Coca-Cola and IBM, and has historically experienced both firms. If Coca-Cola announces earnings on day t, the analyst will likely recall IBM, and might decide to update his forecast for IBM. In this scenario, the stock price reaction of IBM on day t might be a side-effect of the forecast update of the analyst. In order to rule out this scenario, I exclude all firm-pairs that have any overlap in analyst following in the days t− 45 to t. Using this restricted sample, I rerun my main regressions and present the results in the fifth column of Table 2.10. The coefficient estimates are virtually unchanged relative to the main results in Table 2.2 and support the hypothesis that it is investors’ memory, rather than analysts’ memory, that is driving my results. 2.5.6 Alternative Explanations My results strongly support the hypothesis that memory-induced attention leads to buying pressure. In several tests aimed at the mechanism, I find support for key predictions of 70 Table 2.10: Robustness Panel A: Full Sample Dep. var.: Return on day t (%) Sample: Cue above Cue above No own EA in No Analyst 85th pctile 95th pctile [t− 1, t + 1] [t− 5, t + 5] Overlap (1) (2) (3) (4) (5) Cue q−1 0.026*** 0.027*** 0.028*** 0.029*** 0.029*** (0.008) (0.009) (0.008) (0.009) (0.008) Day FE yes yes yes yes yes Observations 31,392,090 31,392,090 32,000,990 30,781,708 31,392,090 R-squared 0.003 0.003 0.003 0.003 0.003 Panel B: Pattern Firm Sample Dep. var.: Return on day t (%) Sample: Cue above Cue above No own EA in No Analyst 85th pctile 95th pctile [t− 1, t + 1] [t− 5, t + 5] Overlap (1) (2) (3) (4) (5) Cue q−1 0.053*** 0.046** 0.047*** 0.054*** 0.053*** (0.016) (0.022) (0.017) (0.019) (0.018) Day FE yes yes yes yes yes Observations 15,773,961 15,773,961 16,111,016 15,435,974 15,773,961 R-squared 0.004 0.004 0.004 0.004 0.004 Notes: This table presents results from regressions of the return on day t on Cue q−1 . Column (1) only uses cueing firms that have a market capitalization (measured on day t−3) above the NYSE’s 85th percentile of market capitalization in that month, and column (2) uses only cueing firms that have a market capitalization (measured on day t− 3) above the NYSE’s 95th percentile of market capitalization in that month. Column (3) drops all firm-days within [ t−1,t+1] of an own earnings announcement of firm j, and column (4) drops all firm-days within [ t−5,t+5] of an own earnings announcement. Column (5) only includes cues from firms that have no overlap in analyst following with firm j in [t− 45, t]. All columns include day fixed effects. Panel A shows results for the full sample and Panel B for the Pattern firm sample. Standard errors are clustered by firm and trading day and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 71 associative memory theory. Specifically, I find that if two firms historically announced with a timing gap between their earnings announcements, they share a weaker memory association. Further, I find that associations that were encoded in recent quarters have a stronger effect than associations that were encoded in more distant quarters. And finally, the effect weakens if there were more distracting earnings announcements by other firms during the encoding of a memory association between two firms. These distracting events lead to interference in recall on the day of the cue. Here, I discuss two alternative explanations for these results. The first possibility is that the results could be driven by fundamental relationships between cueing and cued firms, and/or information spillover from the cueing firm’s earnings announcement. However, my tests are designed to rule out these possibilities. First, I find that there is a sharp discontinuity in the effect if two firms announced with a gap of just one day, making it unlikely that the effect is driven by similar firms announcing during similar times in an earnings season. Second, I find that the earnings surprise of the cueing firm has no predictive power for the return response of the cued firm. And third, I replicate all my results in the sample of Pattern firms, whose earnings announcement dates are exogenously shifted by calendar rotations. The second possibility is that the results are not driven by investors’ memories, but instead by some form of external information archive that mimics the properties of mem- ory. To organize the discussion, recall the introductory example where Coca-Cola and IBM announced earnings on the same day last quarter, but this quarter they do not. This alter- native explanation posits that when Coca-Cola announces earnings this quarter, investors rediscover IBM, for example by reading an archived newspaper article from last quarter, in which both Coca-Cola and IBM are covered. While this explanation might plausibly explain the baseline results, it must also explain the results from the mechanism tests. Specifically, it must explain: 1. Why there is such a sharp discontinuity in the effect if two firms announced with a gap of just one day. If investors access historically archived newspaper articles, they might plausibly discover firms that announced one day before or after the cueing firm, since these firms could be covered in the same articles as well. 72 2. Why interference dampens the effect. If anything, we might expect more newspaper articles to be written on days with many earnings announcements. Thus, investors should be more likely to discover a firm if it announced on a busy day. Thus, for this explanation to work, information must be archived and accessed in very particular ways. Furthermore, to have aggregate effects, many investors must be using the same (or very similarly organized) archives. Associative memory provides one such archive, one with clear predictions from decades of experimental work. While it is difficult to fully rule out the alternative explanation of some external archive, associative memory provides a very parsimonious explanation. 2.6 Conclusion In this paper, I provide evidence of memory effects in financial markets. I show that memory- induced attention creates buying pressure in the cued firm’s stock. In tests aimed at the mechanism, I show that the documented effect varies with the strength of the underlying memory association. Memories that were encoded on the same day have a much stronger effectthanmemoriesthatwereencodedwithatimegap. Further,Ifindthatrecentlyencoded memories have the strongest effect, and that the effect fades away with time. Finally, the documented effect is stronger if there are fewer interfering events during the encoding of a memory association. Mostexistingtestsofhumanmemoryareconductedattheindividual-level. Severalrecent studies focus on how memory constraints affect beliefs and individual decision-making (e.g., Charles (2021); Enke et al. (2022); Gödker et al. (2022)). In contrast, my setting allows me to show that the constraints of human memory can aggregate and affect asset prices. My results also provide evidence consistent with the idea that internally-generated attention can have effects on financial markets. This suggests that there is a whole class of internal attention sources, a class that is distinct from the external sources that have previously been investigated. In other words, the set of attention sources that is relevant for financial decision-making is potentially much larger than previously thought. Future research may flesh out these internal sources in more detail and test their effects on financial markets. 73 Chapter 3 Insensitive Investors (with C. Frydman and M. Kilic) 3.1 Introduction Economists have spent the past several years using surveys to document facts about in- vestors’ expectations of stock returns. A clear fact that emerges from this literature is that the subjective expected returns that investors report on surveys systematically depart from objective expected returns (Greenwood and Shleifer (2014), Adam and Nagel (2022), Nagel and Xu (2022c)). This fact rejects standard rational expectations models and has motivated a new class of asset pricing theories aimed at matching both subjective expectations and realized returns (e.g., Barberis et al. (2015), Hirshleifer et al. (2015), Barberis et al. (2018), Bordalo et al. (2019), Jin and Sui (2022), Nagel and Xu (2022b)). These models formal- ize the subjective expectation formation process in a psychologically grounded manner, but retain the standard assumption that investors fully act on their subjective expectations. In a parallel strand of research, several authors have highlighted a puzzling disconnect between measured subjective beliefs and investor actions. Using data from a sample of wealthy retail investors, Giglio et al. (2021a) document that the sensitivity of equity portfolio shares to subjective return expectations is an order of magnitude weaker than predicted by standard frictionless models. This weak transmission of beliefs to actions appears to be a robust phenomenon that is observed in a variety of other settings (Amromin and Sharpe (2014), Drerup et al. (2017), Ameriks et al. (2020), Liu and Palmer (2021), Beutel and Weber (2022)). Even in times of a market crash, when investors arguably pay a lot of attention to the stock market, actions remain too insensitive to subjective beliefs (Giglio et al. (2021b)). 74 Inthispaper, weanalyzeandexperimentallytesthowtheweaktransmissionofsubjective beliefs to actions affects the basic building blocks of asset pricing. In the theoretical part of the paper, we show that failing to account for a weak transmission of beliefs to actions can fundamentally alter the interpretation of the risk-return relationship. Our main theoretical result is that inference from regressions of subjective expected returns on perceived risk is severely biased when investors do not fully transmit their beliefs into actions. Intuitively, when an investor raises her subjective expected payoff, the weak transmission dampens her associated increase in willingness to pay. The larger increase in expected payoff compared to willingness to pay leads to an increase in the subjective expected return. The weak transmission therefore induces a positive correlation between expected returns and expected payoffs. Thus, if the econometrician runs a univariate regression of subjective expected return on perceived risk, there will be an omitted variable bias when subjective expected payoff correlates with perceived risk. If the link between beliefs and actions is weak enough, the measured risk-return relation can become negative. Importantly, controlling for the omitted expected payoff variable will restore the positive risk-return relation. We test our theoretical predictions across two controlled experiments. We design our first experiment (Experiment 1) to provide three main advantages that complement data from surveys. First, we exogenously set the payoff process and control the subject’s information set; we can then make quantitative statements about how subjective expected returns differ from objective (statistical) expected returns. Second, we incentivize subjects to price a one-period dividend strip in a partial equilibrium setting. For each subject, we elicit both their full distribution of beliefs about next period’s stochastic dividend and their willingness to pay (WTP) for the dividend. The partial equilibrium aspect allows us to study the relationship between expectations and valuations at the subject level, without requiring the subject to be the marginal investor. Third, we back out the implied subjective expected return from valuations and expectations. This method circumvents common concerns in the survey literature about respondents not understanding what is meant by “expected returns” (Cochrane (2011), Cochrane (2017)). We first test for the weak transmission of subjective payoff expectations to WTP, which is a necessary assumption for our theoretical predictions. In a frictionless model, a one unit 75 increase in a subject’s expected payoff generates a one unit increase in her WTP. Our ex- perimental data strongly depart from this frictionless benchmark: we find that a one unit increase in expected payoff leads to only a 63% increase in WTP. Importantly, our experi- mental design shuts down all institutional frictions that can plausibly explain the disconnect between beliefs and actions in the field – such as costly portfolio monitoring, capital gains taxes, default retirement contributions, and leverage and short-selling constraints. More- over, because we ask subjects for their WTP and beliefs on the same experimental screen, beliefs should be readily accessible which arguably tilts the scales away from finding the weak transmission effect. After establishing the weak pass-through of beliefs to WTP in our experimental setting, we turn to testing our main predictions about the risk-return relation. When estimating a simple regression of measured subjective expected returns on perceived risk, we find a strong negative relationship. This result is striking given that the average subject in our experimentisriskaverse. Ourconceptualframeworkprovidesanexplanationforthenegative relationship between expected returns and perceived risk. By omitting the expected payoff from the regression, there is a severe downward bias in the risk-return relation. Importantly, when we add expected payoff to the regression, the risk-return relation flips sign to become positive. This result suggests that it is important to account for the weak transmission, especially in simple regressions of returns on risk. Given the absence of any institutional frictions in our experiment, we argue that a psy- chological explanation is responsible for the observed weak transmission of beliefs to WTP. We interpret the weak transmission through the lens of a new agenda in behavioral eco- nomics which argues that the decision-making process is subject to inherent cognitive noise (see Woodford (2020) for a review). The noise arises in the investor’s mind due to cognitive constraints, and it increases with the complexity of the task at hand. Crucially, the noise leads to systematic decision biases: the investor is aware of this noise, and consequently shades her decision toward a “default value” that does not vary with the specific problem at hand (Enke and Graeber (2021)). For example, when coming up with the valuation for an asset, an investor will naturally lean on her beliefs about future payoffs. But she may be uncertain about how to arrive at 76 an appropriate valuation given these beliefs and her risk appetite. As such, she selects a valuation that is somewhere between the one dictated by her stated beliefs and a default valuation. The compression of actions towards a default may be interpreted as a rule of thumb, but it can also be microfounded by Bayesian updating in the presence of cognitive noise (Gabaix (2019)). For our purposes, the important implication of cognitive noise is that shading of valuations towards a cognitive default immediately dampens the transmission of stated beliefs to WTP. In our second experiment (Experiment 2), we manipulate the level of cognitive noise to assess its impact on the degree of weak transmission and the risk-return relationship. To do so, we draw on the finding from Enke and Graeber (2021) that subjects report higher levels of cognitive uncertainty when decisions are more complex. We argue that it is more complex to price an asset based on subjective beliefs that are learned from past dividends compared to objective beliefs that are endowed. We therefore manipulate cognitive noise by varying whether beliefs are subjective or objective, but we hold constant the beliefs themselves. We implement the cognitive noise manipulation through a novel design feature. We endow subjects in Experiment 2 with the beliefs reported by subjects from Experiment 1. Specifically, each subject in Experiment 2 is endowed with an objective payoff distribution, and we generate this payoff distribution from the subjective beliefs of a randomly matched partner in Experiment 1. To help convey the critical design aspect, suppose that after observing a sequence of dividends, a subject from Experiment 1 reports a distribution of beliefs denoted by b 1 (and her associated WTP given these beliefs). In Experiment 2, there is no learning and we instead endow the subject with beliefsb 1 and ask her to price the asset conditional on these objective beliefs. Our manipulation is grounded in the hypothesis that cognitive noise is larger in settings where additional cognitive operations are needed, such as learning from past data and forming subjective beliefs. By comparing the sensitivity of WTP to beliefs across experiments, we can assess the causal effect of cognitive noise. We find that endowing subjects with objective beliefs leads to a striking difference in pricing behavior: for every unit increase in expected payoff, subjects in Experiment 2 in- crease their WTP by 87%, compared to 63% in Experiment 1. Because we hold beliefs constant across experiments, our interpretation is that cognitive noise causally decreases the 77 sensitivity of actions to beliefs. Moreover, to our knowledge, this is the first piece of evi- dence indicating that valuation is substantially less sensitive to subjective beliefs compared to objective beliefs. 1 We then test how the greater pass-through of beliefs to actions affects the risk-return relation. It is worth emphasizing that any change in the risk-return relation that we find acrossexperimentsmustbeduetotheincreasedtransmissionsinceweholdconstantallother parameters. As predicted by our theory, we find that the slope of the measured risk-return relation increases significantly compared to Experiment 1. The increased pass-through from beliefs to actions is so much stronger in Experiment 2 that it flips the sign and restores a positive risk-return relation – even without controlling for expected payoff. Our results suggest that cognitive noise is a key source of the disconnect between beliefs and actions. Because the noise arises inside the investor’s mind, it is distinct from classical measurement error in surveys. If measurement error was solely responsible for the weak transmission, we would not expect any change in transmission strength across our two ex- periments, yet we find a substantial difference. The distinction between the two mechanisms is important because cognitive noise and measurement error will have different effects on aggregation, as behavior with cognitive noise depends heavily on a default value which can differ across investors (Liu and Palmer (2021)). Overall, our experimental findings provide important guidance for the role of subjec- tive expectations data in asset pricing. Brunnermeier et al. (2021) point to the need for more research on the interaction between beliefs and actions to better understand the role of expectations data for asset pricing. Our work highlights that the weak transmission of reported beliefs to valuations can arise in a simple environment that is insulated from in- stitutional frictions, and it can generate a wedge between subjective and objective expected returns. Relatedly, Nagel and Xu (2022c) document a systematic difference between the cyclical behavior of subjective and objective expected returns; our framework suggests that 1 Our finding is similar to, but distinct from, the experimental result in Hartzmark et al. (2021) where subjects react more strongly to information about goods that they own compared to those that they do not own. In Hartzmark et al. (2021), the endowment of an asset is randomly varied across treatments. In our setting, it is the endowment of beliefs that varies across treatments, and we find that WTP reacts more strongly when beliefs are endowed rather than learned. 78 weak transmission may be one potential explanation for this pattern in the data. While sur- vey data is clearly valuable for unveiling differences in subjective and objective expectations, our work suggests caution in quantitative modeling approaches that assume agents fully act on their beliefs. At the same time, adding a weak transmission channel to existing models may provide an opportunity to further improve quantitative fits. We also contribute to a burgeoning literature studying the weak transmission of beliefs to actions in the field. In a related paper, Liu and Palmer (2021) find that the beliefs investors report on surveys do not contain all the information used in actual investment decisions. Respondents who are less confident in their beliefs tend to rely on factors – such as past returns – to a greater extent in their decision making. Our results are wholly consistent with these effects, but we additionally provide causal evidence in a controlled setting. Beutel and Weber (2022) also study the causal effects of survey beliefs on portfolio choices. One important advantage of our design is that we match the exogenous distribution of beliefs in Experiment2totheendogenouslyformeddistributionofbeliefsinExperiment1. Thisdesign feature enables us to show that the objectivity of beliefs causally affects asset valuations (by comparing behavior across our two experiments). In a related paper, Andries et al. (2022) conduct an experimental study in which they vary the signal informativeness about future returns. When subjects perceive the signal to be less informative, allocations underreact more severely to beliefs. To the extent that subjects in our experiment perceive subjective beliefs to be less informative than objective beliefs, our results are consistent with those of Andries et al. (2022). Finally, Barberis and Jin (2022) develop a model of investor behavior based on rein- forcement learning and argue that it can explain a variety of facts about financial markets, including the disconnect between beliefs and portfolios. Their explanation relies on a “model free” system of decision-making, which is disconnected from the “model based” system that generates the beliefs reported by investors. While the psychology is quite different across models, cognitive noise and reinforcement learning both provide a foundation for the belief- action disconnect that arises from the investor’s decision process, rather than from external factors such as measurement error or institutional constraints. 79 Therestofthispaperisorganizedasfollows. Section3.2presentsaconceptualframework that illustrates the impact of the weak transmission of beliefs to WTP on the risk-return relation. Sections 3.3 and 3.4 present the results from Experiment 1 and Experiment 2, respectively. Section 3.5 discusses how our results relate to field evidence and broader im- plications for asset pricing. Section 3.6 concludes with directions for future work. 3.2 Conceptual framework We start by stating the relationship between beliefs and WTP under the frictionless bench- mark. We then introduce our key assumption of cognitive noise, and derive its implications for pricing and the measurement of the risk-return relation. 3.2.1 Frictionless benchmark Suppose that an agent can invest in an asset which delivers a stochastic payoff D t at each time t. The agent forms beliefs about the payoff’s conditional distribution, where the mean of this subjective distribution is given by E ∗ t [D t+1 ]. After forming expectations, and before the payoff D t+1 is realized, the agent decides what priceP t she is willing to pay for a claim on D t+1 . 2 The agent’s subjective expected return is therefore given byE ∗ t [R t+1 ] =E ∗ t [D t+1 ]/P t . We can rewrite this identity as r t =d t −p t , (3.1) wherer t = logE ∗ t [R t+1 ],d t = logE ∗ t [D t+1 ], andp t = logP t . Unless otherwise noted, through- out the rest of this section we use WTP, expected returns, and expected payoffs in logs which will simplify the predictions that we derive here and test in the next section. The expected return r t is equivalent to the discount rate that the agent applies to the payoff d t , in order to generate her WTP, p t . This equivalence is easily seen by rearranging 2 One can think of such an asset as a dividend strip. The one-period nature of the asset simplifies the expectation formation process that subjects in our experiment engage in and is sufficient to convey our main conceptual insight. 80 (3.1) intop t =d t −r t . We assume that the agent discounts the expected payoff based on her perceived riskiness of the payoff and her risk preference represented by r t =γλ t , (3.2) where γ is the price of risk (e.g., risk aversion) and λ t is the quantity of risk implied by the agent’s subjective beliefs about d t (e.g., conditional volatility). 3 Hence, the expected return r t represents compensation for risk which is a common notion in asset pricing for undiversifiable risks. 4 If the econometrician has data on the investor’s subjective distribution of D t+1 and her WTP, p t , then it is straightforward to implement tests of the relation between risk and expected return shown in (3.2). That is, the econometrician can measurer t as the difference between expected payoff and WTP as in (3.1). The econometrician can then regress the measured r t on λ t , where the latter is also computed based on the investor’s subjective distribution of D t+1 . For any risk averse agent, there is a positive relationship between risk and expected return, and the strength of this relationship is governed by the investor’s risk aversion. 3.2.2 Insensitive actions 3.2.2.1 Compression towards a default valuation We have so far maintained the standard assumption that the investor values the asset by assessingtheexpectedpayoff(fromhersubjectivebeliefs)andthenapplyingadiscountbased on perceived risk. In particular, her beliefs “pass through” to her WTP in a 1-1 fashion, such that a one unit increase in her subjective expected payoff generates a one unit increase in the price she is willing to pay, controlling for perceived risk. Here we relax this assumption and consider a friction in the transmission of the agent’s reported beliefs to her actions. The 3 We assume that the time increment is short enough such that the riskless rate is zero and the discount rate only represents an instantaneous risk premium. We interpret this assumption as the agent perceiving the stochastic payoff as an instantaneous gamble with no necessity for time discounting, which will be the case in our experimental design. 4 For instance, Cochrane (2011) considers “discount rate” and “expected return” to be equivalent in his discussion of time variation in discount rates. 81 friction is motivated by a recent agenda in behavioral economics which argues that cognitive noisecorruptsthedecision-makingprocessandleadstosystematicbiases(Woodford(2020)). In particular, define the agent’s true valuation of the asset at time t as p ∗ t =d t −γλ t , where d t and λ t are the agent’s reported expected payoff and perceived risk, respectively. The variable p ∗ t is the benchmark price that is predicted by a frictionless model: it is the price the agent arrives at when she has no uncertainty about her beliefs, her risk aversion, or how to optimally combine these components. Our key assumption is that cognitive noise prevents the agent from accessing this frictionless valuation due to cognitive and attentional constraints (Gabaix (2019), Enke and Graeber (2021)). Instead, she only has access to a noisy cognitive signal p 0 t =p ∗ t +ϵ t =d t −γλ t +ϵ t , where ϵ t is drawn from N(0,σ 2 ϵ ). The investor herself generates the noisy cognitive signal when she is deliberating about what her true valuation is. In our setting, cognitive noise may be interpreted as difficulty with the process of valuing the asset conditional on beliefs, but it can also reflect uncertainty about valuation inputs such as beliefs or risk aversion. The agent exhibits less cognitive noise as she becomes more certain about her expectations. Yet, even when she is completely certain about her expectations, noise still arises in the decision process that transforms precise expectations to actions. Following Gabaix (2019) and Enke and Graeber (2021) we adopt a Bayesian perspective whereby the agent has a prior over what her true valuation is: p ∗ t is drawn from a normal distributionN(¯ p,σ 2 p ). Here ¯ p is a “cognitive default” which represents the average valuation in a similar class of problems. It is the valuation she would choose before drawing her noisy cognitive signal. The agent then combines her prior and signal to come up with the posterior mean, which is the WTP that she reports: p t = (1−x)¯ p +xp 0 t = (1−x)¯ p +xd t −xγλ t +xϵ t (3.3) wherex =σ 2 p /(σ 2 p +σ 2 ϵ ) is the weight she attaches to her noisy signal relative to the cognitive default. See Appendix K.1 for a derivation. Importantly, a one unit increase ind t now leads to an increase in p t by only x units. 82 To help illuminate the mapping between our framework and applications, consider an investor who is assessing her valuation for the aggregate stock market. If good fundamental news is released about the market, then the investor updates her beliefs about future cash flows, which corresponds to an increase in d t in our framework. But it may be very difficult for the investor to figure out exactly how much this shift in cash flow expectations should shift her WTP for the stock market. We model this friction as the additive noise term, ϵ t . The investor is aware of this difficulty, and when coming up with her WTP, she therefore leans on a default price, which could be yesterday’s price or some weighted average price from the recent past. The default is very likely to depend on an investor’s past experience with the asset, and thus can differ across investors (Liu and Palmer (2021)). The default price is represented by ¯ p in our framework. If enough investors behave in this manner, then the price of the stock market will adjust in the right direction, but not by enough. It is important to point out that Equation (3.3) implies that WTP will also sluggishly respond to perceived risk. In other words, the weak transmission of beliefs to valuation is not confined to the first moment of the subjective payoff distribution, but also operates over our assumed measure of perceived risk. This is a testable prediction that we will take to our experimental data later in the paper. We emphasize that while cognitive noise readily generates a stickiness in actions, in gen- eral, there are other factors that can also lead to an insensitivity between reported beliefs and actions. For example, in the field, default contribution rates or capital gains taxes may lead investors to act less aggressively than is dictated by their beliefs alone. Alternative be- havioral models based on inattention or memory constraints may also drive a wedge between reported beliefs and actions. In what follows, the key assumption we rely on is encoded in Equation (3.3): agents underreact to their reported beliefs. The microfoundation based on cognitive noise helps us structure the predictions for our experiment, but the implications we now present apply more generally in the presence of alternative frictions. 3.2.2.2 Implications for the risk-return relation The weak transmission of beliefs to WTP has important implications for the risk-return relation. The economic interpretation of the measured subjective expected returnr t =d t −p t 83 changes in the case of weak transmission of beliefs to WTP. Plugging WTP from (3.3) into the expected return in (3.1), we obtain r t =−(1−x)¯ p + (1−x)d t +xγλ t −xϵ t . (3.4) The measured subjective expected return with x< 1 no longer depends only on the risk premium γλ t but also on the belief d t . In the case of weak transmission, the subjective expected return based on the agent’s reported beliefs differs from her risk-based discount rate. This difference becomes larger as the transmission becomes weaker (i.e., as x→ 0). Intuitively, when the reported payoff expectationd t increases andp t does not fully respond to the increase, the asset price becomes relatively “cheaper”. This leads to a higher subjective expected return. Conversely, when an investor lowers her reported expectation, she prices the asset lower, but not as low as under the frictionless benchmark. Thus, the weak transmission induces a positive correlation between expected payoffs and expected returns. In the frictionless case, equation (3.4) becomes r =γλ t , and the expected return again corresponds to the risk premium only. Equation (3.4) implies that the weak transmission of beliefs to actions gives rise to an omittedvariablebiasintestsoftherisk-returnrelation. Inparticular, supposethatperceived risk λ t and payoff expectation d t are correlated and have an affine relation given by: d t =α +βλ t +η t , (3.5) where α and β are constants and η t represents variation in d t that is orthogonal to λ t . Plugging (3.5) into (3.4), we obtain r t =−(1−x)¯ p + (1−x)α + [(1−x)β +xγ]λ t + (1−x)η t −xϵ t , =−(1−x)¯ p + (1−x)α +   (1−x)β− (1−x)γ | {z } bias +γ   λ t + (1−x)η t −xϵ t (3.6) Hence, a univariate regression ofr onλ generates a coefficient on risk equal to (1−x)β− (1−x)γ +γ. The term (1−x)β− (1−x)γ represents the omitted variable bias, which can 84 Figure 3.1. The Impact of the Weak Transmission on the Risk-Return Relation 4.5 4.6 4.7 4.8 4.4 4.5 4.6 4.7 4.8 x = 1.00 x = 0.82 x = 0.78 x = 0.61 0 10 20 30 40 0 0.02 0.04 0.06 0.08 Notes: The figure illustrates numerical examples for different values of x. Panel A plots p against d using equation (3.3). Panel B plots r against λ using equation (3.6) where λ-d pairs are based on equation (3.5) with η = 0. The parameter values are ¯ p = 4.72,γ = 0.0019,β =−0.0068,α = 4.88. have a substantial effect on the estimated risk-return relationship. The strength of the bias depends on the degree of the weak transmission (x), the loading of expected payoff on risk (β), and the price of risk (γ). The coefficient on risk will be biased downward when the following conditions are met: (i) there is weak transmission (0<x< 1) (ii) there is a negative correlation between expected payoff and risk ( β< 0), and (iii) the price of risk is positive (γ> 0). For instance, suppose the asset moves between two states: a bad state with low expected payoffs and high risk, and a good state with high payoffs and low risk (as will be the case in our experimental design). When the asset enters the bad state, the expected return r t increases because risk (λ t ) is higher (andγ is positive by assumption). But this effect is offset by the negative term [(1−x)β− (1−x)γ], which creates the downward bias in estimation. Fixing β and γ, the downward bias becomes more severe as the transmission becomes weaker (x→ 0). 85 Figure 3.1 illustrates the consequences of the weak transmission on the risk-return rela- tion. To create this figure, we fix the price of risk γ, the default value ¯ p, and the parameters which govern the relation between payoff and risk (α,β). The only parameter we vary is x, which captures the strength of the transmission of beliefs to WTP. 5 When x = 1 (blue solid line), the reported belief, d, is transmitted 1-1 into the WTP: p is therefore equal to d discounted by the risk premium, γλ. However, as x decreases, p become less responsive to d (Panel A). Crucially, the slope of the risk-return relation also decreases as x decreases, despite holding constant the price and quantity of risk (Panel B). Equation (3.6) implies that there is a threshold value for x (equal to β β−γ ) for which risk and return will exhibit zero correlation (red dotted line). For any value ofx less than this threshold, the risk-return relation flips sign and becomes negative (e.g., the purple dash-dotted line). 3.2.3 Predictions Here we summarize the main implications of our conceptual framework and develop two testable predictions that we take to the experimental data. Our first prediction is on the measured risk-return relation in the presence of weak transmission. Prediction 1. If (i) the transmission of beliefs to willingness to pay is weak and (ii) payoff expectations and risk are negatively correlated, then regressing expected return on risk will lead to a downward biased coefficient on risk. The coefficient on risk increases if the payoff expectation is included as a control in the regression. Because the amount of bias in the risk-return relation depends on the parameter x, it follows from our conceptual framework that manipulating x will systematically affect the risk-return relation. Because one source of weak transmission can be cognitive noise, we predict that manipulating cognitive noise will systematically affect the risk-return relation. Prediction 2. If payoff expectations and risk are negatively correlated, then exogenously decreasing cognitive noise will (i) strengthen the sensitivity of WTP to payoff expectations, 5 To create Figure 1, we pick parameter values based on our experimental results. In particular, γ is based on the coefficient on λ t in a regression of p t on d t and λ t , and (α,β) are based on a regression of d t on λ t . We set the value of ¯ p to the mean log payoff expectation. 86 (ii) strengthen the sensitivity of WTP to perceived risk, and (iii) increase the coefficient on risk in a regression of expected returns on risk. In the next section, we test these predictions in an experimental setting. 3.3 Experiment 1 3.3.1 Experimental design 3.3.1.1 Experimental setup The goal of our experiment is to cleanly test for the weak transmission of beliefs to WTP and its implications for the risk-return relation. Importantly, our design shuts down several factors that Giglio et al. (2021a) suggest can generate a low sensitivity of portfolios to beliefs in the field, such as capital gains taxes, default options in retirement plans, and costly portfolio monitoring. Additionally, and in contrast to standard survey methodologies, we incentivize the elicitation of beliefs and expected returns. We also infer the expected return from a subject’s (i) WTP for the asset and (ii) reported beliefs about the asset payoff. In our design there is a stock that pays a dividend, D t , in each of 30 periods. There are five possible values for the dividend: {$60,$85,$115,$135,$150}. This five point distribution of payoffs is similar to the distribution of returns that Giglio et al. (2021a) use to elicit beliefs from their survey respondents. 6 The conditional distribution of D t is governed by a two-state Markov chain. We denote the state in periodt bys t , which can take on one of two values, either good or bad. In the bad state, the distribution of dividends is given by: Pr(D t |s t =bad)≡ ($60,0.15;$85,0.30;$115,0.40;$135,0.10;$150,0.05) (3.7) In the good state, the distribution of dividends is given by: Pr(D t |s t =good)≡ ($60,0.05;$85,0.10;$115,0.40;$135,0.30;$150,0.15). (3.8) 6 Giglio et al. (2021a) elicit a distribution over five different ranges of returns, whereas we elicit a distri- bution over five different values of the dividend. 87 The distribution in thegood state has a higher mean and lower volatility, compared with the dividend distribution in thebad state. We initialize the state in period 1 to be eithergood or bad with equal probability: Pr(s 1 =good) = 50%. The states are persistent: the probability of remaining in the same state from one period to the next is 80%. Therefore, with 20% probability, the state switches in each period. Subjects are given all the above information about the model of dividends; however, they do not observe the identity of the state in each period. As such, subjects face a learning problem in which they can use data on past dividends to infer the probability that the current state is good. We choose the above stochastic process for two main reasons. First, the Markov chain induces substantial time series variation in the expected dividend. Moreover, the two-state switching process guarantees that the variation does not decline over time (as would be the case in, say, a model where the probability of switching from one state to the other is zero). Second, the switching process induces a negative time series correlation between the conditional expectation and volatility of the payoff. This negative correlation is important because it is one of the necessary conditions for Prediction 1 to obtain. 7 To ease comparability of behavior across subjects, we use the same realized sequence of thirty dividends for all subjects. In 8 randomly chosen periods, we elicit a subject’s full distribution of expectations about next period’s dividend. In the remaining 22 periods, we do not elicit any expectations, and subjects simply observe the realized dividend. 8 Specifically, we ask subjects for the probability that they attach to each of the five possible dividend outcomes. The ordering of the buckets (i.e., lowest to highest or highest to lowest) is randomized across subjects, and we ensure that the probabilities add up to 100%. We also ask subjects to report the price they are willing to pay for the right to receive next period’s dividend,D t+1 . These two elicitations enable us to test the relation between subjective payoff expectations and WTP as well as how the subjective payoff distribution differs from the objective distribution. 7 The predictions in our conceptual framework rest on the assumption that the subjective expected payoff d t and the perceived risk λ t are negatively correlated (i.e., that β < 0). By definition, it is impossible to impose this correlation on subjective beliefs. However, we can increase the chance of observing such a correlation by imposing a negative correlation for a Bayesian agent. In Section 3.3.2 we confirm that the subjective expected payoff and perceived risk are indeed negatively correlated. 8 We elicit beliefs in the same 8 (randomly chosen) periods for all subjects. See Internet Appendix O for screenshots of the experiment. 88 Importantly, we incentivize the expectations question and the WTP question. When we elicit a subject’s distribution of beliefs about next period’s dividend, we pay subjects based on their accuracy relative to how a Bayesian agent would respond. To see how a Bayesian agent would respond, we derive the probability that the state is bad, conditional on all past dividends. We denote this probability as q t = Pr(s t =bad|D t ,D t−1 ,...,D 1 ). Conditional on q t , the distribution of dividends can be computed using the distributions in good and bad states depicted in equations (3.7) and (3.8). Because the stochastic process is Markovian, we can rewrite the expression for q t as a function of the current period’s realized dividend and the prior belief: q t (q t−1 ,D t ) = Pr(D t |s t =bad)Pr(s t =bad|q t−1 ) Pr(D t |s t =bad)Pr(s t =bad|q t−1 ) + Pr(D t |s t =good)Pr(s t =good|q t−1 ) = Pr(D t |s t =bad)(0.8q t−1 + 0.2(1−q t−1 )) Pr(D t |s t =bad)(0.8q t−1 + 0.2(1−q t−1 )) + Pr(D t |s t =good)(0.2q t−1 + 0.8(1−q t−1 )) , (3.9) where the expressions Pr(D t |s t =bad) and Pr(D t |s t =good) are defined in equations (3.7) and (3.8) (Frydman et al. (2014)). Given the probability that the stock is in the bad state, the expected dividend is just a weighted average of the expected dividend in each of the two states: E[D t |q t ] =q t E[D t |s t =bad] + (1−q t )E[D t |s t =good]. Similarly, the probability of each dividend outcome is a weighted average of the probability of that outcome in each of the two states. For example, for a $60 dividend, Pr(D t = $60|q t ) =q t Pr(D t = $60|s t = bad) + (1−q t )Pr(D t = $60|s t =good). The calculations above establish the Bayesian benchmark, which we use to incentivize subjects when they report their beliefs. In particular, we randomly pick one of the eight periods in which we elicit the distribution of beliefs and the WTP, and then pay subjects based on either the distribution question or the WTP question. If the distribution question is randomly chosen, then we randomly select one of the outcomes of the distribution and pay subjects a $3 bonus if their elicited probability estimate is within one percentage point of the objective probability of that outcome. For each percentage point that subjects deviate from the Bayesian prediction, we subtract 3 cents. 89 If instead the WTP question is randomly chosen, we implement a Becker-DeGroot- Marschak (BDM) mechanism, which is designed so that it is in the subject’s best interest to report their true WTP. To implement the mechanism, we endow the subject with $210 in experimental wealth, which can be used to purchase the right to next period’s dividend. After the subject reports their WTP for next period’s dividend, we draw a random price between $60 and $150. If the price that we draw is equal to or smaller than the WTP, the subject purchases the one period asset at the randomly drawn price. If the number is larger than the stated WTP, the subject does not purchase the asset. Subjects receive their remaining experimental wealth after any profits or losses from purchasing the asset. Each dollar in the experiment converts to $0.01. Thus, subjects can receive a bonus of up to $3 for the WTP question. While it may be difficult for subjects to implement the Bayesian updating rule in (3.9), our tests do not rely on subjects’ ability to accurately compute q t . Importantly, our con- ceptual framework in Section 3.2 does not depend on whether beliefs depart from Bayesian rationality. Indeed, the implications from Section 3.2 are based on reported beliefs, which are inherently subjective. At the same time, the Bayesian benchmark is useful not only for eliciting incentive-compatible beliefs, but also to study any systematic differences between objective and subjective beliefs. The wedge between subjective and objective beliefs will turn out to be an an important predictor for the weak transmission across subjects. 3.3.1.2 Experimental procedures We recruit 300 subjects from the online data collection platform, Prolific. The sample size and exclusion criteria are pre-registered on Aspredicted.org. 9 Subjects received $2 for completing the experiment, in addition to their bonus payment. The average completion time of the experiment was approximately 13 minutes, and the average earnings were $4.39, including the $2 participation fee. 9 See https://aspredicted.org/6Z4_RLQ for the pre-registration document. After analyzing the data, the emphasis of our analysis changed to the weak transmission of beliefs to actions. We believe that including the initial pre-registration here is important for transparency, particularly about sample size and exclusion criteria. See Appendix M for additional pre-registered analyses. Our analyses in Experiment 1 provide crucial motivation for the design of Experiment 2, which we also pre-register; details are provided in Section 3.4. 90 3.3.2 Experimental results 3.3.2.1 Summary statistics Our experiment with 300 subjects produces a panel dataset with 2,400 total observations (8 elicitations per subject). Table 3.1 provides summary statistics of the dataset where E ∗ denotes expectations under subjects’ reported beliefs and E b denotes the Bayesian expecta- tion. Because all subjects face the same sequence of payoffs (dividends), the time series of the Bayesian distribution is identical across subjects. Table 3.1: Summary Statistics Mean p25 p50 p75 SD Min Max Subjective expected payoff E ∗ [D] 112.60 105.5 113.00 120.50 12.04 65.00 150.00 Deviation from Bayesian E ∗ [D]/E b [D] 1.01 0.96 1.02 1.08 0.10 0.59 1.32 Willingness to pay P 95.15 80.00 95.70 110.00 20.88 60.00 150.00 Subjective expected return E ∗ [R]=E ∗ [D]/P 1.23 1.04 1.19 1.38 0.27 0.52 2.23 Perceived volatility Vol ∗ [D] 23.64 21.36 24.81 27.22 6.05 0.00 39.69 Bayesian volatility Vol b [D] 25.37 24.70 25.73 26.02 0.84 23.96 26.07 Notes: This table presents summary statistics for the main variables in our sample. The sample consists of 300 subjects, each elicited at 8 elicitation periods, yielding 2,400 observations. E ∗ [D] is the subjective expected payoff, defined as the mean of a subject’s reported dividend distribution. E b [D] is the Bayesian expected payoff, defined as the mean of the Bayesian dividend distribution. P is the subject’s reported willingness to pay for next period’s dividend. Perceived volatility, Vol ∗ [D], is the volatility of a subject’s reported dividend distribution. Bayesian volatility, Vol b [D], is the volatility of the Bayesian distribution. Table 3.1 reveals that subjects are quite accurate about the expected payoff on average, but there are sizeable deviations from the Bayesian benchmark. The average deviation from the Bayesian expectation, which we compute as E ∗ [D]/E b [D], is 1.01, where a value of 1.00 corresponds to no deviation from Bayesian expectations. The prices that subjects are willing to pay are, on average, lower than expected payoffs, which is consistent with risk aversion among our subjects. Thus, on average, subjective expected returns are greater than 1. Because we elicit subjects’ beliefs about the entire payoff distribution, we can measure perceived risk as the volatility of the elicited distribution. While the average and median perceived volatility are close to the Bayesian benchmark, perceived risk exhibits a lot more variation. 91 For all subsequent empirical analyses, we transform WTP and expectations to logs in order to be consistent with the conceptual framework in Section 3.2. In particular,p denotes logP, d denotes logE ∗ [D], λ denotes Vol ∗ [D], and r denotes logE ∗ [R]. In addition, most of our analyses in the following sections focus on the within-subject time series relation between variables. Appendix N shows that there is also significant time-invariant variation in beliefs and WTP across subjects, a finding that is consistent with the field evidence in Giglio et al. (2021a). 3.3.2.2 Pricing results We begin by testing the underlying assumption of our theory from Section 3.2, namely, the existence of weak transmission of beliefs to actions. Because our theory is about pricing and beliefs at the individual level, we allow for heterogeneity in parameters across subjects when conducting our empirical tests. We assume that the default WTP (¯ p), price of risk (γ), degree of weak transmission (x), and the loading of payoff expectations on perceived risk ( β) are fixed within subjects – but can vary across subjects. In particular, all of our empirical results are based on mixed effects regressions with random slopes and a random intercept. Table 3.2: WTP, Subj. Exp. Payoffs, and Perc. Risk p (1) (2) d 0.634 ∗∗∗ 0.610 ∗∗∗ (0.049) (0.050) λ −0.195 ∗∗∗ (0.073) Observations 2,400 2,400 Notes: This table presents results from mixed effects regressions of WTP ( p) on subjective expected payoffs (d) and perceived volatility (λ). These regressions include a random effect for d and λ, as well as for the intercept. Standard errors are clustered at the subject level and displayed in parentheses below the coefficient estimates. The coefficients and standard errors for λ are multiplied by 100. ∗ , ∗∗ , and ∗∗∗ indicate statistical significance at the 10%, 5%, and 1% levels, respectively. Column 1 of Table 3.2 reports that the sensitivity of WTP to payoff expectations is 0.634, which is significantly below one. Figure 3.2 illustrates this result by showing that the best 92 Figure 3.2. WTP and Subj. Exp. Payoffs 4.2 4.4 4.6 4.8 5 Log WTP, p 4.4 4.6 4.8 5 Log payoff expectation, d Notes: This figure is a binned scatter plot of willingness to pay ( p) and subjective expected payoffs ( d) controlling for subject fixed effects. The sample size is 2,400 and the number of subjects is 300. The upper line is the 45-degree line. fitting line is much shallower than the 45-degree line. Of course, our univariate regression of p t ond t has an omitted variable, namely, risk. In Appendix K.2, we show that the omission ofλ t biases the estimate ofx upward whenever (i) the price of risk is positive (e.g., subjects are risk averse) and (ii) the correlation between payoff expectations d t and perceived riskλ t is negative. 10 It follows that our underreaction result is robust to alternative measures of perceived risk besides volatility, since omitting the appropriate measure of risk will lead to an upward bias in the sensitivity of WTP to expected payoff. We show in Column 2 that the responsiveness of WTP to beliefs remains significantly below one after controlling for our assumed measure of risk, namely, conditional volatility. The specification in Column (2) also confirms that subjects demand compensation for risk ( γ> 0), as they are willing to pay less when risk is higher, holding the payoff expectation constant. 10 By design, the correlation between payoff expectations and volatility is negative for a Bayesian investor. Figure 3.6 demonstrates that this negative correlation is also present in the subjective beliefs data. 93 Having established that x< 1, which is a necessary assumption for our predictions, we now turn to testing Prediction 1. Recall that this prediction states that ifx< 1 and if payoff expectations and risk are negatively correlated, then regressing expected return on risk will lead to a downward biased coefficient on risk. Specifically, Equation (3.6) shows that the slope coefficient from regressing expected return on risk is given by (1−x)β− (1−x)γ +γ, where (1−x)β−(1−x)γ is the omitted variable bias. We have already shown thatx< 1 and β< 0, which implies there should be a downward bias in the estimated risk-return relation. If this bias is strong enough, it can flip the sign of the relationship from positive to negative. Our data reveal that the bias is substantial: Column 1 of Table 3.3 shows that there is a negative relationship between expected return and risk. Figure 3.3 illustrates the negative correlation. 11 This result may initially appear puzzling in light of our earlier finding that subjects exhibit a lower valuation for the asset as perceived risk increases (Column 2 of Table 3.2). Ourconceptualframeworkresolvesthepuzzlebyshowingthatthenegativerelationship is caused by an omitted variable problem, which derives from the weak transmission of beliefs to WTP. It is worth spelling out the intuition in more detail for how the econometrician can detect a negative risk-return relationship among a population of risk averse subjects. The reason is that when a risk averse subject’s beliefs are not fully transmitted into her WTP, the measured subjective expected return r t =d t −p t no longer depends only on the risk premium; it also depends on the payoff expectation, as illustrated in equation (3.4). In other words, the subjective expected return based on reported beliefs is no longer equal to the more economically meaningful discount rate that represents risk compensation. Importantly, we can restore the positive risk-return relation by controlling for payoff expectations in a regression of expected return on risk. Column 2 of Table 3.3 shows that the sign of the coefficient on risk flips from negative to positive when adding a control for subjects’ reported expected payoffs. In sum, our results are consistent with Prediction 1. We have thus shown that even when subjects are risk averse, the weak transmission of beliefstoWTPcancreatetheillusionthatriskpremiaimpliedbysubjectiveexpectedreturns are declining in risk. This phenomenon arises because subjective expected returns no longer 11 Appendix M shows that the risk-return relationship remains qualitatively unchanged when using the subjective probability for the lowest possible payoff ($60) as the perceived risk measure. 94 Table 3.3: Subj. Exp. Returns, Subj. Exp. Payoffs, and Perc. Risk r (1) (2) d 0.390 ∗∗∗ (0.050) λ −0.173 ∗∗ 0.195 ∗∗∗ (0.078) (0.073) Observations 2,400 2,400 Notes: This table presents results from mixed effects regressions of subjective expected returns ( r) on subjective expected payoffs ( d) and perceived volatility (λ). These regressions include a random effect for d and λ, as well as for the intercept. Standard errors are clustered at the subject level and displayed in parentheses below the coefficient estimates. The coefficients and standard errors for λ are multiplied by 100. ∗ , ∗∗ , and ∗∗∗ indicate statistical significance at the 10%, 5%, and 1% levels, respectively. represent only the discount rate which rises in bad times, but also the payoff expectation which declines in bad times. If the latter force dominates – which can occur with sufficient cognitive noise – the subjective expected returns will become procyclical, which is wholly consistent with our data. 3.3.2.3 Subjective vs. objective expected returns So far we have focused on analyzing the link between subjective expected returns and per- ceived risk. What do our results imply for the link between objective expected returns and risk? What would an econometrician who observes WTP and expectations from realized payoffs infer from our data? To investigate these questions we first define the objective expected return as r b t =d b t −p t = (d t −p t ) | {z } r t −(d t −d b t ). (3.10) where d b is the log Bayesian expectation of the payoff. An econometrician can compute d b , like we did, using the sequence of payoff realizations. Combining the subject’s WTP with the Bayesian payoff expectation gives us r b . The Bayesian expected return is conceptually 95 Figure 3.3. Subjective Expected Returns and Perceived Risk .1 .15 .2 .25 Log expected return, r 10 20 30 40 Volatility, λ Notes: This figure is a binned scatter plot of the subjective expected return ( r) and perceived risk (λ) controlling for subject fixed effects. The sample size is 2,400 and the number of subjects is 300. similar to measures of objective expected returns in asset pricing computed using predictive regressions or Bayesian estimation. Equation (3.10) shows that the difference between the objective and subjective expected returns, r and r b , is driven by the departures of subjective payoff expectations from the Bayesian benchmark, namely, the difference between d and d b . This immediately implies that the difference in the sensitivity of the objective and subjective expected return to risk depends on the relation between d−d b and risk. In Appendix Figure 3.7, we show that d−d b is steeply declining in perceived risk with a coefficient of -0.0056 ( p< 0.01). While the departure is centered around zero, subjects are too pessimistic in times of high perceived volatility and too optimistic in times of low perceived volatility. This suggests an overall overreaction in expectation formation. The strong relationship between d−d b and risk also suggests that objective expected returns have a higher sensitivity to perceived risk compared to their subjective counterparts. 96 The reason is that objective expected returns can be rewritten as subjective expected re- turns minus d−d b (see Equation (3.10)). Since the term d−d b strongly varies with risk, objective expected returns are especially sensitive to risk. Indeed, the coefficient of objective expected returns on risk is 0.005 (p< 0.01), which is larger in magnitude than the coeffi- cient of subjective expected returns on risk shown in Column 1 of Table 3.3. Perhaps more strikingly, the coefficient for objective expected returns is positive (see Appendix Figure 3.8 for a visualization). Therefore, an econometrician using predicted payoffs to form objective expected returns would identify a completely different risk-return relation compared to the one using elicited subjective expected returns and risk. Theintuitionbehindthisstarkcontrastcanbesummarizedasfollows. Inourexperiment, when subjects perceive high volatility, they generally also expect a low payoff (one can think of this as subjects perceiving the state to be bad). In these situations, subjects lower their WTP both due to lower expected payoffs and higher discounts (Table 3.2). These effects are jointly stronger than the decline in the objective payoff expectation. Another way to interpret this result is that WTP fluctuates more strongly than Bayesian payoff expectations, despite the weak transmission of beliefs to WTP. As a result, the objective expected return increases with risk. These experimental results are qualitatively consistent with Nagel and Xu (2022c), who document countercyclical objective expected returns across several asset classes, but a lack of cyclicality in subjective expected returns. To summarize, our controlled experimental setting generates data in which objective expected returns are higher and subjective expected returns are lower in bad times. The behavior of subjective expected returns is grounded in the weak transmission of beliefs to WTP. The differential sensitivity of objective vs. subjective expected returns to risk is driven by the systematic departures of subjective expectations from the Bayesian benchmark. 3.3.2.4 Objectivity of beliefs and the transmission of beliefs to willingness to pay Earlier we highlighted that one advantage of our conceptual framework is that all empirical tests can be conducted regardless of whether beliefs are rational, where rational beliefs are 97 defined as the beliefs of a Bayesian learner. Here, we test whether subjects whose subjective beliefs are closer to the objective Bayesian beliefs also act on their beliefs more aggressively. Figure 3.4. Subject-level Average Expected Payoff 0 .05 .1 Density 90 100 110 120 130 Average E*[D] Notes: This figureplots the histogram andkernel density of the average expected payoff E ∗ [D] at the subject- level. Each observation is the average expected payoff of a subject across the eight elicitations. The vertical red line corresponds to the average objective (Bayesian) expectation. The sample size is 300. Referring back to our summary statistics in Table 3.1, one salient fact is that the average deviation of subjective payoff expectations from Bayesian expectations is small. This can be seen more clearly in Figure 3.4, which plots a histogram and kernel density of subject- level average expectations. The density is roughly centered at the true mean, but there is substantial heterogeneity. A large number of subjects are pessimists who expect payoffs below the objective expectation; there are also many subjects who are optimists and expect payoffs above the objective expectation. We now examine, for each subject, whether the transmission of beliefs to WTP depends on how far their beliefs are from the objective benchmark. We conjecture that subjects whose beliefs are better calibrated will also be more confident in their beliefs. Given past work demonstrating that more confident investors exhibit a stronger sensitivity to beliefs, we hypothesize that subjects with better calibrated beliefs are more sensitive to these beliefs 98 in their pricing (Giglio et al. (2021a)). We emphasize that precise control of the dividend process is key to conducting a test of this hypothesis. It would be difficult to implement such a test in the field where neither the investor nor the econometrician has access to the true data generating process of dividends. To begin, for each subject we compute a measure of how well calibrated their beliefs are using the absolute error summed across the eight elicitation periods. In particular, for each subject s, we compute: calibration error s = P 8 t=1 |d st −d b t | where d s is the subjective payoff for subjects andd b is the Bayesian expectation. The median calibration error across all 300 subjects is 0.552. We define those subjects who are below the median – and thus exhibit beliefs that are relatively close to the objective benchmark – as calibrated. Those subjects who are above the median are defined as miscalibrated. Table 3.4: Transmission of Beliefs for Calibrated and Miscalibrated Subjects Sample: Calibrated Miscalibrated Difference p (1) (2) (1) - (2) d 1.068 ∗∗∗ 0.506 ∗∗∗ 0.562 ∗∗∗ (0.075) (0.054) (0.092) Observations 1,200 1,200 2,400 Notes: This table presents results from mixed effects regressions of willingness to pay ( p) on subjective expected payoffs ( d) separately for calibrated (first column) and miscalibrated (second column) subjects. The difference in coefficients is reported in the third column. These regressions include a random effect for d as well as for the intercept. Standard errors are clustered at the subject level and displayed in parentheses below the coefficient estimates. ∗ , ∗∗ , and ∗∗∗ indicate statistical significance at the 10%, 5%, and 1% levels, respectively. We then estimate the sensitivity of WTP to beliefs for each of the two subsamples. The first column of Table 3.4 shows that for the calibrated subsample, the coefficient of WTP on expected payoff is almost exactly 1. By contrast, in the second column we see that the coefficient magnitude is cut in half for the miscalibrated subsample. The third column shows that the difference is indeed statistically significant at the 1% level. Thus, our results are consistent with the conjecture that subjects who form beliefs that are closer to the objective benchmark also transmit these beliefs to their WTP in a stronger fashion. We emphasize 99 that the results in Table 3.4 only provide correlational evidence that beliefs closer to the objective benchmark are transmitted more strongly into prices. In the next section, we discuss an experiment that provides a causal test. 3.4 Experiment 2 In this section, we exogenously manipulate cognitive noise and measure the impact on the transmission of beliefs to WTP. In particular, we test whether we can increase the transmis- sion strength to the extent that the measured risk-return relationship becomes positive. 3.4.1 Experimental design Recall that in Experiment 1, subjects face a learning problem in which realized dividends can be used to form Bayesian beliefs about the next period dividend. While subjects are endowed with all information about the data generating process, implementing the optimal Bayesian updating scheme is complex. Thus, subjects may be cognitively uncertain about their own expectations, and we hypothesize that this cognitive uncertainty dampens the transmission of beliefs to WTP. In order to test this hypothesis, we conduct a second experiment in which we endow subjects with objective beliefs about the next period dividend. Subjects do not need to learn because we explicitly provide them with the true payoff distribution. Our manipula- tion is meant to reduce cognitive noise which, in turn, should increase the strength of the transmission of beliefs to WTP. Perhaps the most natural experimental design would involve simply endowing subjects with the Bayesian beliefs from Experiment 1. An issue however, is that the WTP elicited in such a design would be based on beliefs that differ from the subjective beliefs reported by subjects in Experiment 1. Any difference in behavior could thus be due to differences in beliefs, rather than a difference in the objectivity of those beliefs. Thus, we would not be able to identify cognitive noise as a channel through which WTP becomes more responsive to beliefs. 100 To sidestep this concern, we design an experiment in which we recruit a new set of 300 subjects, and each subject is uniquely matched to a subject from Experiment 1. The new subject in Experiment 2 inherits the beliefs reported by her matched partner. That is, the subjectivebeliefsreportedbythesubjectinExperiment1becometheobjectivebeliefsforthe subject in Experiment 2. Subjects in Experiment 2 are not told anything about the source of such beliefs, or even about the existence of Experiment 1. Instead, we incentivize subjects from Experiment 2 to report their WTP for an asset that pays a dividend according to the objective distribution that we present them. We provide screenshots of this experiment in Internet Appendix O. The design allow us to test Prediction 2: reducing cognitive noise will strengthen the transmission of beliefs to WTP and, as a result, increase the coefficient on risk in a regression of expected returns on risk. Importantly, any change we detect across experiments in the estimated risk-return relationship must be due to a difference in the strength of transmission of beliefs to WTP. To see this, recall that the sensitivity of expected return to risk is given by (1−x)β− (1−x)γ +γ (from equation 3.6), and the only value in this expression that varies across our two experiments isx. Why? The value ofβ, which captures the correlation between expected payoff and volatility, does not vary across experiments because we impose the beliefs that subjects report from Experiment 1 on those subjects in Experiment 2. The value of γ also remains unchanged across experiments: γ represents the risk aversion of our subjects, and we randomly draw subjects from the same population in each experiment. Taken together, any change in the estimated risk-return relationship across experiments can be attributed to the reduction in cognitive noise. As in Experiment 1, subjects in Experiment 2 are incentivized using the BDM mechanism and one of the questions is randomly chosen to be paid. Note that subjects in Experiment 2 thereforeansweronly8questions(comparedwith16inExperiment1). Tokeeptheincentives per question constant across experiments, we cut the bonus incentive in Experiment 2 in half compared with Experiment 1. This is important because larger incentives could lead to lower cognitive noise in Experiment 2, and we want to hold incentives constant across experiments. 101 As in Experiment 1, we recruit subjects from Prolific and pre-registered the experiment on Aspredicted.org. 12 Subjects received $2 for completing the experiment, in addition their bonus payment. The average completion time of the experiment was 6 minutes, and the average earnings were $3.06 including the $2 participation fee. 3.4.2 Experimental results Experiment 2 delivers a panel dataset with 2,400 observations that consist of eight distinct WTPs, elicited from each of the 300 subjects. Table 3.5 reports summary statistics from the dataset. Because we endow subjects with beliefs, we focus here only on the elicited WTP and the implied expected returns. We observe similar average WTP and expected returns across the two experiments, though both variables exhibit slightly greater dispersion in Experiment 2 compared to Experiment 1. Table 3.5: Summary Statistics for Experiment 2 Mean p25 p50 p75 SD Min Max N Willingness to pay P 97.00 79.80 99.90 115.00 23.22 60.00 150.00 2,400 Expected return E ∗ [R]=E ∗ [D]/P 1.22 1.00 1.14 1.40 0.30 0.48 2.36 2,400 Notes: This table presents summary statistics for the variables in Experiment 2 that are different from Experiment 1. The sample consists of 300 subjects, each elicited for 8 payoff distributions, yielding 2,400 observations. P is the subject’s reported willingness to pay for next period’s dividend. E ∗ [R] is the expected return using the mean of the dividend distribution and the subject’s willingness to pay. We first test whether our experimental manipulation indeed strengthens the transmission of beliefs to WTP. Column 1 in Table 3.6 presents results from regressions of WTP on payoff expectation using data from both experiments, where “Exp2” is a dummy variable that equals one if and only if the observation is from Experiment 2. Consistent with our Prediction 2, the transmission of beliefs to WTP is causally strengthened when we endow subjects with beliefs, thereby eliminating the need for subjects to learn in order to arrive at a belief. Among subjects in Experiment 2, the coefficient on d is 0.877 (= 0.634 + 0.243), which is significantly higher than 0.634 in Experiment 1. The intercept of the regression is 12 For pre-registration details, see: https://aspredicted.org/NWL_YML 102 lower in Experiment 2 because the higher loading on payoff expectations captures a larger fraction of the level of the WTP. Table 3.6: WTP, Exp. Payoffs, and Perc. Risk in both Experiments p (1) (2) d 0.634 ∗∗∗ 0.610 ∗∗∗ (0.049) (0.050) d x Exp2 0.243 ∗∗∗ 0.207 ∗∗∗ (0.064) (0.066) λ −0.188 ∗∗∗ (0.073) λ x Exp2 −0.221 ∗ (0.121) Exp2 −1.134 ∗∗∗ −0.910 ∗∗∗ (0.302) (0.322) Observations 4,800 4,800 Notes: This table presents results from mixed effects regressions of willingness to pay ( p) on expected payoffs (d) and perceived volatility (λ), combining data from Experiments 1 and 2. These regressions include a random effect for d and λ, as well as for the intercept. Standard errors are clustered at the subject level and displayed in parentheses below the coefficient estimates. The coefficients and standard errors for λ are multiplied by 100. ∗ , ∗∗ , and ∗∗∗ indicate statistical significance at the 10%, 5%, and 1% levels, respectively. The stronger transmission of payoff expectations to WTP remains significant after con- trolling for risk as shown in Column 2 of Table 3.6. The coefficient on d significantly increases from 0.610 in Experiment 1 to 0.817 in Experiment 2. These results suggest that cognitive noise from expectation formation explains about half of the underreaction of WTP to payoff expectations. In line with Prediction 2, decreasing cognitive noise also increases the reaction of WTP to risk perceptions. Column 2 of Table 3.6 shows that the negative loading on risk increases in magnitude when going from Experiment 1 to 2. The coefficient on risk more than doubles in magnitude, though the effect is only statistically significant at the 10% level (the large standard error here is due in part to the strong negative correlation between λ and d). It is important to note that the transmission from beliefs to actions is still not as strong as predicted by the frictionless benchmark; the coefficient on d remains significantly below 103 one in Experiment 2. Endowing subjects with objective beliefs clearly reduces cognitive noise, but it is not fully eliminated. In the discussion section, we speculate on other sources of cognitive noise that remain in our Experiment 2. Table 3.7: Exp. Returns, Exp. Payoffs, and Perc. Risk in both Experiments r (1) (2) d 0.390 ∗∗∗ (0.050) d x Exp2 −0.207 ∗∗∗ (0.066) λ −0.174 ∗∗ 0.188 ∗∗∗ (0.078) (0.073) λ x Exp2 0.418 ∗∗∗ 0.221 ∗ (0.121) (0.121) Exp2 −0.113 ∗∗∗ 0.910 ∗∗∗ (0.032) (0.322) Observations 4,800 4,800 Notes: This table presents results from mixed effects regressions of expected returns ( r) on expected payoffs (d) and perceived volatility (λ), combining data from Experiments 1 and 2. These regressions include a random effect for d and λ, as well as for the intercept. Standard errors are clustered at the subject level and displayed in parentheses below the coefficient estimates. The coefficients and standard errors for λ are multiplied by 100. ∗ , ∗∗ , and ∗∗∗ indicate statistical significance at the 10%, 5%, and 1% levels, respectively. We now turn to assessing the causal effect of cognitive noise on the risk-return relation- ship. Equation (3.6) shows that an increase in x mitigates the omitted variable bias in the univariate risk-return relation. Mitigating the omitted variable bias will increase the slope of the risk-return relation, and it can potentially restore a positive risk-return relation. Here we report results from estimating the risk-return relationship, which by design uses the same set of beliefs from Experiment 1. Column 1 of Table 3.7 shows that the loading on λ be- comes positive in Experiment 2, where subjects price the asset based on the objective payoff distribution. The fact that the sign of the relationship flips demonstrates that endowing subjects with objective beliefs – rather than having them form subjective expectations as in Experiment 1 – is associated with a substantial reduction in cognitive noise. We are able to make this inference because β and γ are held constant across experiments, and thus all 104 of the action must be through an increase in x, which we interpret as a reduction in cogni- tive noise. Figure 3.5 demonstrates the positive risk return relationship. It is worth noting that the relationship looks markedly different compared with the risk-return relation from Experiment 1 (displayed in Figure 3.3). Figure 3.5. Expected Returns and Risk in Experiment 2 Slope = 0.0025*** (0.0008) .1 .15 .2 .25 .3 Log expected return, r 10 20 30 40 Volatility, λ Notes: This figure is a binned scatter plot of expected returns ( r) and risk (λ) in Experiment 2 controlling for subject fixed effects. The sample size is 2,400 and the number of subjects is 300. Finally, recall that cognitive noise induces a positive correlation between expected payoffs and expected returns. Since we predict less cognitive noise in Experiment 2, the correlation between expected payoff and expected return should be attenuated towards zero. We find that this is indeed the case. In Column 2 of Table 3.7, we regress expected return on both expected payoff and risk, and find that the coefficient on expected payoff is significantly closer to zero in Experiment 2 compared to Experiment 1. In other words, the impact of payoff expectations on expected returns induced by the weak transmission becomes smaller in Experiment 2, which is consistent with equation (3.4). TosummarizethemainfindingfromExperiment2, weprovidecausalevidencethatWTP is substantially more responsive to beliefs when subjects price an asset based on objective 105 – rather than subjective – beliefs. The increased responsiveness is so large that it flips the sign of the risk-return relationship. Our results suggest that subjects rely much less on a cognitive default parameter when they are endowed with objective beliefs. 3.5 Discussion In this section, we discuss the implications of our results for the development of asset pricing models and we discuss connections with the broader literature on survey data. We also discuss in more detail the psychological source of weak transmission in our experiments and address limitations of our experimental approach. 3.5.1 Implications for asset pricing models Over the past few years several models have been proposed to quantitatively match both asset prices and survey expectations (e.g., Barberis et al. (2015), Hirshleifer et al. (2015), Jin and Sui (2022)). While these models formalize the subjective expectation formation process in a psychologically grounded manner, they retain the standard assumption that investors fully act on their subjective beliefs. Our focus in this paper takes expectations as given, and examines how these expectations propagate into actions. One key finding that emerges from our experiments is that the transmission of beliefs to actions is far from 1-to-1. We believe that this result should motivate future theoretical work to explicitly incorporate weak transmission into the investor’s decision process, in order to potentially improve quantitative fits to the data. 13 An obvious concern, however, is that injecting deviations from rationality in both ex- pectation formation and expectation transmission gives the modeler too much flexibility. Indeed, the number of non-rational expectations models is large enough, and adding an additional degree of freedom does not help the case for parsimony. However, there is an intriguing possibility that departures from rational expectations are connected to how these expectations propagate into actions. In Table 3.4 we show that subjects who state beliefs 13 For related work in macroeconomics, see Khaw et al. (2017) for a theoretical model that incorporates inattentive adjustment of actions. 106 closer to the rational benchmark are the same subjects whose valuations are more sensitive to these beliefs. While more empirical data is needed, our results suggest that the belief formation process can partially constrain the degree of weak transmission. 14 Our results also provide guidance for asset pricing models with learning and state un- certainty. In Experiment 1, we implement an imperfect information environment in which subjects receive noisy signals about the state in the form of realized dividends. Using these signals, subjects are incentivized to form subjective beliefs about the conditional distribution of payoffs. This imperfect information approach is common in the asset pricing literature. For instance, several models generate realistic asset price dynamics by relying on the fluctu- ations in beliefs that result from Bayesian learning about the stochastic state (e.g., Veronesi (1999), Johannes et al. (2016), Ghaderi et al. (2022)). Our results suggest that learning models in particular may benefit from incorporating the weak transmission of beliefs to actions. More broadly, our results suggest that the degree of weak transmission depends on whether investors have state uncertainty. Recall that in Experiment 1, subjects must learn from the payoff process, while in Experiment 2, we shut down the learning channel and en- dow subjects with beliefs. We find that when subjects are endowed with beliefs, their asset valuations are substantially more sensitive to the endowed beliefs. Because the beliefs are held constant across experiments, our results provide evidence that belief formation causally affects how investors act on those beliefs. Applying this intuition to the field, our Experiment 1 corresponds to a real-world envi- ronment in which investors form expectations about the stock market. For instance, at the beginning of the COVID-19 crisis in March 2020, investors formed a subjective assessment of how the stock market would behave going forward. Giglio et al. (2021b) show that investors updated their beliefs and became more pessimistic about the stock market in the short term. However, these investors did not adjust their portfolios nearly as much as frictionless asset pricing models would predict. This finding is consistent with the weak transmission of beliefs to actions, documented in our Experiment 1. In contrast, Experiment 2 constructs a counter- factual to Experiment 1 that is impossible to implement in the field. It allows us to test how 14 See also Andries et al. (2022), who show that experimental subjects are more likely to underreact in their investment decisions when forming extrapolative expectations compared to rational expectations. 107 investors would have responded if they were endowed with the objective payoff distribution. This is akin to asking how investors would have behaved in the COVID-19 crisis, if they were given an objective probability distribution of the short-run stock market performance. The results from Experiment 2 suggest that investors would have reacted more strongly to these (objective) beliefs and would have adjusted their portfolios more aggressively. Our paper is also related to a recent strand of literature that quantifies a demand system using portfolio holdings of different investors. One key finding from this literature is that investors’ asset demand is very inelastic compared to predictions from standard asset pricing models (Koijen and Yogo (2019)). The weak transmission due to cognitive noise, which is the foundation for the biased risk-return relationship in our work, may be helpful in explaining the inelasticity. Specifically, cognitive noise can provide a potential microfoundation for the observed low elasticity of demand for assets in response to expected return fluctuations (e.g., Haddad et al. (2021), Chaudhry (2022)). 3.5.2 Connections with the survey literature Our results also relate to the growing literature on survey data in finance. Recent work has examined the specific factors that investors say are important to their personal investment decisions (Bender et al. (2021), Chinco et al. (2021)). For example, beyond expected return and risk, Choi and Robertson (2020) find that investors report other factors such as time left until retirement as important determinants of their portfolio decisions. While we focus our analysis on the sensitivity to expected payoff and perceived risk, it is possible that investors may not act as aggressively on other factors that they state in surveys. Indeed, if cognitive noise is in part responsible for affecting an investor’s valuation of an asset conditional on risk and return, then it seems plausible that cognitive noise would also be present when investors use additional factors to arrive at asset valuations. The survey conducted by Giglio et al. (2021a) is similar to our experimental paradigm, in that we also collect data on beliefs and actions at the individual level. As in Giglio et al. (2021a), we regress actions on beliefs and find that the empirical link is weaker than predicted by frictionless models. However, an important difference between the two studies is that an action in our experiment is defined by a subject-specific WTP. In contrast, an 108 action in Giglio et al. (2021a) is defined by a portfolio allocation – in which all investors face the same market price. This distinction makes it difficult to directly compare the subjective expected returns that we infer from WTP and the subjective expected returns that Giglio et al. (2021a) directly elicit from Vanguard investors. It is also worth noting that, like us, Giglio et al. (2021a) find a negative relationship between expected returns and perceived risk. Our explanation for this pattern (at least in Experiment 1), is driven by a combination of cognitive noise and omitted variable bias. We caution that such a mechanism cannot be used to justify the negative relationship between between expected returns and perceived risk that Giglio et al. (2021a) document. This is because our results rely on time series variation in beliefs and actions within an individual. The results in Giglio et al. (2021a) rely on cross-sectional variation in beliefs and actions, where all investors face the same equilibrium asset price and form heteregeneous subjective return expectations conditional on that price. Thus, while the insensitivity between actions and beliefs demonstrated in both studies may derive from a common mechanism of cognitive noise, our data cannot speak directly to the pattern of subjective expected returns uncovered by Giglio et al. (2021a). Our results also connect with research on analyst forecast surveys. De La O and Myers (2021) show that analyst forecasts of cash flows explain almost all the variation in stock mar- ket valuations while return expectations play a much smaller role. In Appendix L, we show that payoff expectations explain a higher fraction of price variation under subjective beliefs compared with Bayesian beliefs in our experiment. Such a fact is qualitatively consistent with the pattern documented by De La O and Myers (2021) in the field. 3.5.3 Sources of the weak transmission In the field, there are several potential reasons for the weak transmission of beliefs to actions. For example, Giglio et al. (2021a) discuss heterogeneous frictions such as capital gains taxes, institutional settings of retirement plans, and infrequent trading. Our experiment rules out such institutional frictions by design, and allows us to identify the weak transmission as driven by a psychological friction. In Experiment 1, where subjects need to form subjective 109 beliefs, it is likely that some of the cognitive noise arises from uncertainty about expecta- tions, perhaps because subjects have difficulty implementing Bayes’ rule (Kuhnen (2015)), Ben-David et al. (2019)). But importantly, in Experiment 2, we show that shutting down uncertainty about beliefs still leads to weak transmission. We speculate that the noise in Experiment 2 arises primarily from integrating beliefs about payoffs with perceived risk to arrive at a valuation. 3.5.4 Limitations We have argued that the one period nature of the asset in our experiment is useful because it allows us to see how valuation relates to expectations in a simple setting. Indeed, we find clear evidence of a weak transmission of beliefs to actions, even when there is no need for subjects to form expectations over long horizons. Yet this simplicity also means that our analyses cannot speak directly to other previously documented facts about subjective expectations from the field. For example, one of the most salient facts from the survey literature is that investors extrapolate recent returns when forming expectations about future returns (Greenwood and Shleifer (2014), Barberis et al. (2015)). One reason we do not analyze this dimension of the data in our experiment is because the degree of extrapolation, and more generally, expectational errors, may depend on the horizon of the forecast (Giglio and Kelly (2018), Da et al. (2021), De Silva and Thesmar (2021)). One opportunity for future work is to enrich the experimental design we present here by having subjects price an asset that delivers a long stream of cash flows – rather than a one period dividend strip. For example, one could integrate into our design the experimental method from Afrouzi et al. (2021), which elicits expectations along the term structure. This would further enable testing of other important phenomena, including the dividend-price ratio and its ability to predict returns of long-duration assets such as aggregate equity. 110 3.6 Conclusion Survey data on subjective beliefs have recently opened up a vibrant area of research in asset pricing (Adam and Nagel (2022)). Subjective beliefs data offer the promise of disciplining models using the expectations that investors actually report, rather than the rational expec- tations that investors are typically assumed to hold. Our paper contributes to this agenda by exploring the implications of investors who do not fully act on their stated beliefs. We show theoretically that the weak transmission of beliefs to actions induces a substantial bias in even the most basic asset pricing tests. Our experimental data provide strong support for the prediction of a downward bias in the risk-return relation. Subjects in our experiment are indeed insensitive investors, and we find that expected returns systematically decline in perceived risk – despite the fact that the average subject is risk averse. Our framework also provides a recipe for restoring the positive risk-return relation: include expected payoff in the regression of expected returns on risk. In our data, adding this control flips the sign of the risk-return relation from negative to positive. Because our experiment shuts down institutional frictions by design, we identify the source of the weak transmission as a psychological friction. In particular, we interpret the weak sensitivity as arising from cognitive noise, and we find strong evidence that cognitive noise causally affects the risk-return relation. We interpret the noise as arising from a combination of uncertainty about expectations, uncertainty about perception of risk, and the cognitive process of integrating these quantities to arrive at an asset’s valuation. The fact that we document the weak transmission of beliefs to actions in a controlled experimental setting points to the idea that weak transmission may be a fundamental com- ponent of the investor’s decision process. As such, one natural path for future work is to incorporate this ingredient into existing asset pricing models and assess the change in quan- titative fit. Another path forward is to better understand the importance that institutional frictions play in generating weak transmission in the field. Because institutional frictions are shut down in our experiment, the bias may be even more substantial in tests using data from the field. 111 References Adam, Klaus, and Stefan Nagel, 2022, Expectations data in asset pricing, NBER Working paper. Afrouzi, Hassan, Spencer Yongwook Kwon, Augustin Landier, Yueran Ma, and David Thes- mar, 2021, Overreaction in expectations: Evidence and theory, SSRN Working paper. Afrouzi, Hassan, Spencer Yongwook Kwon, Augustin Landier, Yueran Ma, and David Thes- mar, 2022, Overreaction in expectations: Evidence and theory, Working paper. Akepanidtaworn, Klakow, Rick Di Mascio, Alex Imas, and Lawrence Schmidt, 2021, Sell- ing fast and buying slow: Heuristics and trading performance of institutional investors, Journal of Finance forthcoming. Ameriks, John, Gábor Kézdi, Minjoon Lee, and Matthew D Shapiro, 2020, Heterogeneity in expectations, risk tolerance, and household stock shares: The attenuation puzzle, Journal of Business & Economic Statistics 38, 633–646. Amromin, Gene, and Steven A Sharpe, 2014, From the horse’s mouth: Economic conditions and investor expectations of risk and return, Management Science 60, 845–866. An, Li, Xin Chen, Zhengwei Wang, and Jianfeng Yu, 2022, Attention spillover in asset pricing, Working Paper. Andries, Marianne, Milo Bianchi, Karen K Huynh, and Sébastien Pouget, 2022, Return pre- dictability, expectations, and investment: Experimental evidence, SSRN Working paper. Bagnoli, Mark, William Kross, and Susan G Watts, 2002, The information in management’s expected earnings report date: A day late, a penny short, Journal of Accounting Research 40, 1275–1296. Barber, Brad M, Emmanuel T De George, Reuven Lehavy, and Brett Trueman, 2013, The earnings announcement premium around the globe, Journal of Financial Economics 108, 118–138. Barber, Brad M, Xing Huang, Terrance Odean, and Christopher Schwarz, 2021, Attention induced trading and returns: Evidence from robinhood users, Journal of Finance forth- coming. 112 Barber, Brad M, Shengle Lin, and Terrance Odean, 2019, Mediating investor attention, Working paper. Barber, Brad M, and Terrance Odean, 2000, Trading is hazardous to your wealth: The common stock investment performance of individual investors, Journal of Finance 55, 773–806. Barber, Brad M, and Terrance Odean, 2008, All that glitters: The effect of attention and news on the buying behavior of individual and institutional investors, Review of Financial Studies 21, 785–818. Barber, Brad M, and Terrance Odean, 2013, The behavior of individual investors, in Hand- book of the Economics of Finance, volume 2, 1533–1570 (Elsevier). Barberis, Nicholas, Robin Greenwood, Lawrence Jin, and Andrei Shleifer, 2015, X-CAPM: An extrapolative capital asset pricing model, Journal of Financial Economics 115, 1–24. Barberis, Nicholas, Robin Greenwood, Lawrence Jin, and Andrei Shleifer, 2018, Extrapola- tion and bubbles, Journal of Financial Economics 129, 203–227. Barberis, Nicholas, and Lawrence Jin, 2022, Model-free and model-based learning as joint drivers of investor behavior, Working paper. Ben-David, Itzhak, Elyas Fermand, Camelia M Kuhnen, and Geng Li, 2019, Expectations uncertainty and household economic behavior, NBER Working paper. Bender, Svetlana, James J Choi, Danielle Dyson, and Adriana Z Robertson, 2021, Mil- lionaires speak: What drives their personal investment decisions?, Journal of Financial Economics forthcoming. Beutel, Johannes, and Michael Weber, 2022, Beliefs and portfolios: Causal evidence, SSRN Working paper. Bodoh-Creed, Aaron L, 2020, Mood, memory, and the evaluation of asset prices, Review of Finance 24, 227–262. Bordalo, Pedro, John J Conlon, Nicola Gennaioli, Spencer Y Kwon, and Andrei Shleifer, 2022a, Memory and probability, Quarterly Journal of Economics conditionally accepted. Bordalo, Pedro, Nicola Gennaioli, Rafael La Porta, and Andrei Shleifer, 2019, Diagnostic expectations and stock returns, Journal of Finance 74, 2839–2874. Bordalo, Pedro, Nicola Gennaioli, and Andrei Shleifer, 2020, Memory, attention, and choice, Quarterly Journal of Economics 135. Bordalo, Pedro, Nicola Gennaioli, and Andrei Shleifer, 2022b, Overreaction and diagnostic expectations in macroeconomics, Journal of Economic Perspectives 36, 223–44. 113 Boulland, Romain, and Olivier Dessaint, 2017, Announcing the announcement, Journal of Banking & Finance 82, 59–79. Brunnermeier,Markus,EmmanuelFarhi,RalphSJKoijen,ArvindKrishnamurthy,SydneyC Ludvigson, Hanno Lustig, Stefan Nagel, and Monika Piazzesi, 2021, Perspectives on the future of asset pricing, Review of Financial Studies 34, 2126–2160. Campbell, John Y, and Robert J Shiller, 1988, The dividend-price ratio and expectations of future dividends and discount factors, Review of Financial Studies 1, 195–228. Chang, Tom Y, Samuel M Hartzmark, David H Solomon, and Eugene F Soltes, 2017, Being surprised by the unsurprising: Earnings seasonality and stock returns, Review of Financial Studies 30, 281–323. Charles, Constantin, 2021, Memory and trading, Working paper. Charles, Constantin, 2022, Memory moves markets, Working paper. Chaudhry, Aditya, 2022, The causal impact of macroeconomic uncertainty on expected re- turns, SSRN Working paper. Chen, Ting, Zhenyu Gao, Jibao He, Wenxi Jiang, and Wei Xiong, 2019, Daily price limits and destructive market behavior, Journal of Econometrics 208, 249–264. Chen, Yixin, Randolph B Cohen, and Zixuan Kevin Wang, 2022, Famous firms, earnings clusters, and the stock market, Working Paper. Chinco, Alex, Samuel M Hartzmark, and Abigail B Sussman, 2021, A new test of risk factor relevance, Journal of Finance forthcoming. Choi, James J, and Adriana Z Robertson, 2020, What matters to individual investors? Evidence from the horse’s mouth, Journal of Finance 75, 1965–2020. Cochrane, John H, 2011, Presidential address: Discount rates, Journal of Finance 66, 1047– 1108. Cochrane, John H, 2017, Macro-finance, Review of Finance 21, 945–985. Colonnelli, Emanuele, Niels J Gormsen, and Timothy McQuade, 2021, Selfish corporations, Working paper. Da, Zhi, Joseph Engelberg, and Pengjie Gao, 2011, In search of attention, Journal of Finance 66, 1461–1499. Da, Zhi, Xing Huang, and Lawrence J Jin, 2021, Extrapolative beliefs in the cross-section: What can we learn from the crowds?, Journal of Financial Economics 140, 175–196. 114 Da Silveira, Rava Azeredo, Yeji Sung, and Michael Woodford, 2020, Optimally imprecise memory and biased forecasts, Working paper. Daniel, Kent, MarkGrinblatt, SheridanTitman, andRussWermers, 1997, Measuringmutual fund performance with characteristic-based benchmarks, Journal of Finance 52, 1035– 1058. DeLaO,Ricardo,andSeanMyers,2021,Subjectivecashflowanddiscountrateexpectations, Journal of Finance 76, 1339–1387. De Silva, Tim, and David Thesmar, 2021, Noise in expectations: Evidence from analyst forecasts, NBER Working paper. DellaVigna, Stefano, and Joshua M Pollet, 2009, Investor inattention and friday earnings announcements, Journal of Finance 64, 709–749. Drerup, Tilman, Benjamin Enke, and Hans-Martin Von Gaudecker, 2017, The precision of subjective data and the explanatory power of economic models, Journal of Econometrics 200, 378–389. Enke, Benjamin, and Thomas Graeber, 2021, Cognitive uncertainty, NBER Working paper. Enke, Benjamin, Frederik Schwerter, and Florian Zimmermann, 2022, Associative memory and belief formation, Working paper. Frazzini, Andrea, 2006, The disposition effect and underreaction to news, Journal of Finance 61, 2017–2046. Frazzini, Andrea, and Owen Lamont, 2007, The earnings announcement premium and trad- ing volume, Working paper. Frydman, Cary, Nicholas Barberis, Colin Camerer, Peter Bossaerts, and Antonio Rangel, 2014, Using neural data to test a theory of investor behavior: An application to realization utility, Journal of Finance 69, 907–946. Frydman, Cary, and Baolian Wang, 2020, The impact of salience on investor behavior: Evidence from a natural experiment, Journal of Finance 75, 229–276. Gabaix, Xavier, 2019, Behavioral inattention, in Handbook of Behavioral Economics: Appli- cations and Foundations 1, 261–343 (Elsevier). Ghaderi, Mohammad, Mete Kilic, and Sang Byung Seo, 2022, Learning, slowly unfolding disasters, and asset prices, Journal of Financial Economics 143, 527–549. Giglio, Stefano, and Bryan Kelly, 2018, Excess volatility: Beyond discount rates, Quarterly Journal of Economics 133, 71–127. 115 Giglio, Stefano, Matteo Maggiori, Johannes Stroebel, and Stephen Utkus, 2021a, Five facts about beliefs and portfolios, American Economic Review 111, 1481–1522. Giglio, Stefano, Matteo Maggiori, Johannes Stroebel, and Stephen Utkus, 2021b, The joint dynamics of investor beliefs and trading during the COVID-19 crash, Proceedings of the National Academy of Sciences 118. Gilboa, Itzhak, and David Schmeidler, 1995, Case-based decision theory, Quarterly Journal of Economics 110, 605–639. Gödker, Katrin, Peiran Jiao, and Paul Smeets, 2022, Investor memory, Working paper. Goetzmann, William N, Akiko Watanabe, and Masahiro Watanabe, 2022, Evidence on re- trieved context: How history matters, Working Paper. Greenwood, Robin, and Andrei Shleifer, 2014, Expectations of returns and expected returns, Review of Financial Studies 27, 714–746. Griffin, John M, Jeffrey H Harris, and Selim Topaloglu, 2003, The dynamics of institutional and individual trading, Journal of Finance 58, 2285–2320. Haddad, Valentin, Paul Huebner, and Erik Loualiche, 2021, How competitive is the stock market? Theory, evidencefromportfolios, andimplicationsfortheriseofpassiveinvesting, SSRN Working paper. Hartzmark, Samuel M, 2015, The worst, the best, ignoring all the rest: The rank effect and trading behavior, Review of Financial Studies 28, 1024–1059. Hartzmark, Samuel M, Samuel D Hirshman, and Alex Imas, 2021, Ownership, learning, and beliefs, Quarterly Journal of Economics 136, 1665–1717. Hartzmark, Samuel M, and Kelly Shue, 2018, A tough act to follow: Contrast effects in financial markets, Journal of Finance 73, 1567–1613. Hartzmark, Samuel M, and David H Solomon, 2018, Recurring firm events and predictable returns: The within-firm time series, Annual Review of Financial Economics 10, 499–517. Hirshleifer, David, Jun Li, and Jianfeng Yu, 2015, Asset pricing in production economies with extrapolative expectations, Journal of Monetary Economics 76, 87–106. Hirshleifer, David, Sonya Seongyeon Lim, and Siew Hong Teoh, 2009, Driven to distraction: Extraneous events and underreaction to earnings news, Journal of Finance 64, 2289–2325. Hirshleifer, David, and Ivo Welch, 2002, An economic approach to the psychology of change: Amnesia, inertia, and impulsiveness, Journal of Economics & Management Strategy 11, 379–421. 116 Hoberg, Gerard, and Gordon Phillips, 2010, Product market synergies and competition in mergers and acquisitions: A text-based analysis, Review of Financial Studies 23, 3773– 3811. Hoberg, Gerard, and Gordon Phillips, 2016, Text-based network industries and endogenous product differentiation, Journal of Political Economy 124, 1423–1465. Jacobs, Heiko, and Alexander Hillert, 2016, Alphabetic bias, investor recognition, and trad- ing behavior, Review of Finance 20, 693–723. Jiang, Lei, JinyuLiu, LinPeng, andBaolianWang, 2022, Investorattentionandassetpricing anomalies, Review of Finance 26, 563–593. Jin, Lawrence J, and Pengfei Sui, 2022, Asset pricing with return extrapolation, Journal of Financial Economics 145, 273–295. Jin, Li, andAnnaScherbina, 2011, Inheritinglosers, Review of Financial Studies 24, 786–820. Johannes, Michael, Lars A Lochstoer, and Yiqun Mou, 2016, Learning about consumption dynamics, Journal of Finance 71, 551–600. Johnson, TravisL,andEricCSo, 2018, Timewilltell: Informationinthetimingofscheduled earnings news, Journal of Financial and Quantitative Analysis 53, 2431–2464. Kahana, Michael J, 2012, Foundations of human memory (OUP USA). Khaw, Mel Win, Luminita Stevens, and Michael Woodford, 2017, Discrete adjustment to a changing environment: Experimental evidence, Journal of Monetary Economics 91, 88– 103. Koijen, Ralph SJ, and Motohiro Yogo, 2019, A demand system approach to asset pricing, Journal of Political Economy 127, 1475–1515. Kuhnen, Camelia M, 2015, Asymmetric learning from financial information, Journal of Fi- nance 70, 2029–2062. Liu, Haoyang, and Christopher Palmer, 2021, Are stated expectations actual beliefs? New evidence for the beliefs channel of investment demand, NBER Working paper. Lou, Dong, 2012, A flow-based explanation for return predictability, Review of Financial Studies 25, 3457–3489. Lou, Dong, 2014, Attracting investor attention through advertising, Review of Financial Studies 27, 1797–1829. Malmendier, Ulrike, and Stefan Nagel, 2011, Depression babies: do macroeconomic experi- ences affect risk taking?, Quarterly Journal of Economics 126, 373–416. 117 Malmendier, Ulrike, and Stefan Nagel, 2016, Learning from inflation experiences, Quarterly Journal of Economics 131, 53–87. Malmendier, Ulrike, Stefan Nagel, and Zhen Yan, 2021, The making of hawks and doves, Journal of Monetary Economics 117, 19–42. Malmendier, Ulrike, Geoffrey Tate, and Jon Yan, 2011, Overconfidence and early-life expe- riences: the effect of managerial traits on corporate financial policies, Journal of Finance 66, 1687–1733. Malmendier, Ulrike M, and Leslie Sheng Shen, 2020, Scarred consumption, Working paper. Mullainathan, Sendhil, 2002, Amemory-basedmodelofboundedrationality, Quarterly Jour- nal of Economics 117, 735–774. Murdock Jr, Bennet B, 1962, The serial position effect of free recall, Journal of Experimental Psychology 64, 482. Nagel, Stefan, and Zhengyang Xu, 2022a, Asset pricing with fading memory, Review of Financial Studies 35, 2190–2245. Nagel, Stefan, and Zhengyang Xu, 2022b, Asset pricing with fading memory, Review of Financial Studies 35, 2190–2245. Nagel, Stefan, and Zhengyang Xu, 2022c, Dynamics of subjective risk premia, NBER Work- ing paper. Noh, Suzie, Eric C So, and Rodrigo S Verdi, 2021, Calendar rotations: A new approach for studying the impact of timing using earnings announcements, Journal of Financial Economics 140, 865–893. Peng, Lin, and Wei Xiong, 2006, Investor attention, overconfidence and category learning, Journal of Financial Economics 80, 563–602. Penman, Stephen H, 1987, The distribution of earnings news over time and seasonalities in aggregate stock returns, Journal of Financial Economics 18, 199–228. Schmidt, Daniel, 2019, Distracted institutional investors, Journal of Financial and Quanti- tative Analysis 54, 2453–2491. Seasholes, Mark S, and Guojun Wu, 2007, Predictable behavior, profits, and attention, Journal of Empirical Finance 14, 590–610. Thomas, Jacob, and Frank Zhang, 2008, Overreaction to intra-industry information trans- fers?, Journal of Accounting Research 46, 909–940. 118 Veronesi, Pietro, 1999, Stock market overreactions to bad news in good times: A rational expectations equilibrium model, Review of Financial Studies 12, 975–1007. Wachter, Jessica A, and Michael J Kahana, 2021, A retrieved-context theory of financial decisions, Working paper. Wermers, Russ, 1999, Mutual fund herding and the impact on stock prices, Journal of Finance 54, 581–622. Woodford, Michael, 2020, Modeling imprecision in perception, valuation, and choice, Annual Review of Economics 12, 579–601. 119 Appendices 120 G Chapter 1: Theoretical Framework In the following, I provide a stylized theoretical framework of an investor’s memory that closely follows Bordalo et al. (2020), which builds on Kahana (2012). The framework is designed to be as simple as possible to illustrate the main properties of associative memory theory in a setting of trading. An investor’s memory is a “database” that contains experi- ences of past trading opportunities. I define an experience as a stock that was or could have been traded. There are a total of M experiences stored in the database. Each experience e j = (q j ,c j ) consists of hedonic attributes q of stock j and the context c in which the stock was experienced. The hedonic attributes include a stock’s ticker, price, past performance, industry, and so on. For simplicity, I narrowly define context as the monthly portfolio state- ment on which the investor experienced the stock. This context contains time, and therefore drifts slowly over time. A broader version of context could include the environmental fea- tures such as the location and the weather, or emotional features such as the mood of the investor, during the trading opportunity. Finally, as in Bordalo et al. (2020), I assume that both the hedonic attributes q and the context c are cardinal. Investors can encounter a cue κ = (q k ,c k ) that stimulates the recall of experiences from the memory database. For instance, if the investor trades a stock with hedonic attributes q k in context c k , that trade acts as a cue for the recall of past experiences. I make two assumptions about recall: first, recall is imperfect, meaning that investors are not always able to recall all their past experiences. Second, recall is tilted towards experiences that are similar to the cue. More similar experiences are more likely to be recalled. Following Bordalo et al. (2020), I define the similarity between an experience e j and a cue κ as the multiplicatively separable distance: S(e j ,κ) =S 1 (|q j −q k |)S 2 (|c j −c k |) (G.1) 121 This definition of similarity captures key characteristics of associative memory theory. First, similarity is higher if the experience and the cue have similar hedonic attributes q. 15 Second, similarity is higher if the experience and the cue share a similar context c. For instance, two stocks that are close to each other on a portfolio statement share a more similar context than two stocks that are far away from each other on the statement. Further, since context drifts slowly over time, today’s context is more similar to yesterday’s context than to last week’s context. Thus, all other things equal, a cue today is more similar to recent experiences than to distant experiences. This captures the role of recency in recall. The probability that the investor recalls experiencee j when faced with cueκ, depends on the similarity betweenκ ande j , as well as the similarity betweenκ and all other experiences stored in the memory database. Formally, the recall probability is given by the following expression: P (e j |κ) = S(e j ,κ) P M x=1 S(e x ,κ) (G.2) The left-hand side of this expression is the probability of recalling experience e j condi- tional on encountering cue κ. The right-hand side of the expression defines this probability as the ratio of two terms. The term in the numerator is the pairwise similarity of experience e j and cueκ. All other things equal, ife j andκ are more similar, the investor is more likely to recall e j . This captures the fact that more similar experiences are easier to recall. In contrast, the term in the denominator captures interference in recall. Interference refers to the idea that the cue might be similar to many experiences in the investor’s memory. These other experiences interfere with the recall of e j . The denominator measures interference by summing the similarities between κ and all M experiences in the memory database. If this sum is larger, interference is larger, and the probability of recalling e j is lower. In order to connect this recall probability to trading behavior, I make the following additional assumption: when an investor recalls an experience that contains a stock, he is 15 Inmyempiricalanalysis, Igenerallyabstractfromtheroleofsimilarhedonicattributesofstocksonrecall by including stock-pair or stock-pair x day fixed effects into all my regressions. This approach holds fixed the hedonic attributes of the cueing and cued stock. I do so to avoid conflating memory effects (potentially due to similar hedonic attributes) with fundamental relationships between stocks that could plausibly be driving trading decisions. 122 more likely to trade that stock. Suppose that the experience e j contains stock j. Then, the probability of trading stockj when encountering cueκ is a function of the recall probability: P (Trade Stock j|κ) =f(P (e j |κ)) (G.3) where ∂f ∂(P (e j |κ)) > 0 (G.4) Equation G.3 can be rewritten as: P (Trade Stock j|κ) =f( S(e j ,κ) P M x=1 S(e x ,κ) ) (G.5) 123 H Chapter 1: Additional Tables Table 3.8: Linking Backwards Panel A: Retail Investors Dependent variable: Memory-induced trade (dummy) (1) (2) (3) Memorability 0.141*** 0.139*** 0.136*** (0.004) (0.004) (0.006) Stock-pair FE yes yes yes Day FE yes Investor x Day FE yes Observations 175,495 175,495 138,781 R-squared 0.299 0.313 0.597 Panel B: Mutual Funds Dependent variable: Memory-induced trade (dummy) (1) (2) (3) Memorability 0.196*** 0.196*** 0.185*** (0.004) (0.004) (0.004) Stock-pair FE yes yes yes Quarter FE yes Fund x Quarter FE yes Observations 726,993 726,993 725,988 R-squared 0.232 0.233 0.383 Notes: This table presents results from regressions of a dummy variable indicating a memory-induced trade on a flavor of Memorability that estimates associations between stock pairs by connecting a stock at position n in the alphabetical ranking with a stock at position n− 1 in the ranking. Across columns, various fixed effects are added to the regression. These fixed effects can result in singleton observations, which are dropped during the estimation. Standard errors are clustered by stock pair, investor, and trading day (Panel A) or stock pair, fund, and quarter (Panel B) and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 124 Table 3.9: Memorability < 1 Panel A: Retail Investors Dependent variable: Memory-induced trade (dummy) (1) (2) (3) Memorability 0.130*** 0.128*** 0.104*** (0.006) (0.006) (0.007) Stock-pair FE yes yes yes Day FE yes Investor x Day FE yes Observations 106,568 106,568 96,284 R-squared 0.310 0.327 0.593 Panel B: Mutual Funds Dependent variable: Memory-induced trade (dummy) (1) (2) (3) Memorability 0.196*** 0.196*** 0.188*** (0.004) (0.004) (0.004) Stock-pair FE yes yes yes Quarter FE yes Fund x Quarter FE yes Observations 400,642 400,642 398,235 R-squared 0.253 0.253 0.381 Notes: This table presents results from regressions of a dummy variable indicating a memory-induced trade on Memorability. The sample only includes stock pairs with Memorability < 1. Across columns, various fixed effects are added to the regression. These fixed effects can result in singleton observations, which are dropped during the estimation. Standard errors are clustered by stock pair, investor, and trading day (Panel A) or stock pair, fund, and quarter (Panel B) and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 125 Table 3.10: Conditioning on Only One Trade Panel A: Retail Investors Dependent variable: Memory-induced trade (dummy) (1) (2) (3) Memorability 0.054*** 0.053*** 0.080*** (0.002) (0.002) (0.003) Stock-pair FE yes yes yes Day FE yes Investor x Day FE yes Observations 427,510 427,510 276,270 R-squared 0.227 0.234 0.594 Panel B: Mutual Funds Dependent variable: Memory-induced trade (dummy) (1) (2) (3) Memorability 0.190*** 0.190*** 0.179*** (0.004) (0.004) (0.003) Stock-pair FE yes yes yes Quarter FE yes Fund x Quarter FE yes Observations 734,171 734,171 729,127 R-squared 0.231 0.232 0.384 Observations 648,206 465,702 405,097 R-squared 0.401 0.502 0.411 Notes: Thistablepresentsresultsfromregressionsofadummyvariableindicatingamemory-inducedtradeon Memorability. The sample includes all days on which an investor traded at least one stock. Across columns, variousfixedeffectsareaddedtotheregression. Thesefixedeffectscanresultinsingletonobservations, which are dropped during the estimation. Standard errors are clustered by stock pair, investor, and trading day (Panel A) or stock pair, fund, and quarter (Panel B) and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 126 Table 3.11: Recency with Additional Fixed Effects (1) Panel A: Retail investors Dependent variable: Memory-induced trade (dummy) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) Lag 1 (dummy) 0.119*** (0.003) Lag 2 (dummy) 0.014*** 0.024*** (0.003) (0.003) Lag 3 (dummy) 0.001 0.010*** 0.015*** (0.003) (0.003) (0.004) Lag 4 (dummy) 0.004 0.007* 0.011** 0.012** (0.003) (0.004) (0.004) (0.005) Lag 5 (dummy) -0.001 0.005* 0.005 0.006* 0.013*** (0.003) (0.003) (0.003) (0.004) (0.004) Lag 6 (dummy) 0.001 0.000 0.002 0.003 0.004 0.006 (0.003) (0.003) (0.003) (0.003) (0.004) (0.004) Lag 7 (dummy) -0.002 0.003 0.003 0.002 0.004 0.004 0.004 (0.003) (0.003) (0.003) (0.003) (0.003) (0.004) (0.005) Lag 8 (dummy) -0.001 -0.001 -0.001 0.001 0.003 0.003 0.004 0.006 (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) (0.004) (0.005) Lag 9 (dummy) 0.000 0.002 0.002 0.004 0.004 0.005 0.003 0.000 0.003 (0.003) (0.003) (0.003) (0.003) (0.003) (0.004) (0.004) (0.004) (0.006) Lag 10 (dummy) 0.004 0.008*** 0.008*** 0.010*** 0.010*** 0.009*** 0.010*** 0.010** 0.015*** 0.021*** (0.003) (0.003) (0.003) (0.003) (0.003) (0.004) (0.004) (0.004) (0.005) (0.006) Lag 11 (dummy) -0.002 -0.002 -0.002 -0.002 0.000 0.003 0.004 0.002 -0.002 0.002 -0.004 (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) (0.004) (0.004) (0.005) (0.006) (0.011) Lag 12 (dummy) -0.000 -0.002 -0.000 0.001 0.001 0.003 0.002 0.001 0.006 0.008 0.012 (0.003) (0.003) (0.003) (0.004) (0.004) (0.004) (0.005) (0.005) (0.007) (0.008) (0.014) Stock-pair FE yes yes yes yes yes yes yes yes yes yes yes Day FE yes yes yes yes yes yes yes yes yes yes yes Observations 175,081 84,718 67,368 53,976 43,364 34,520 26,949 20,243 14,508 9,516 5,083 R-squared 0.326 0.340 0.356 0.368 0.377 0.391 0.401 0.419 0.459 0.509 0.621 Panel B: Mutual funds Dependent variable: Memory-induced trade (dummy) (1) (2) (3) Lag 1 (dummy) 0.154*** (0.003) Lag 2 (dummy) -0.008** 0.004** (0.004) (0.002) Lag 3 (dummy) 0.018*** 0.007*** 0.008*** (0.003) (0.002) (0.002) Lag 4 (dummy) 0.015*** 0.002 0.002 (0.002) (0.002) (0.002) Stock-pair FE yes yes yes Quarter FE yes yes yes Observations 727,507 209,573 124,337 R-squared 0.238 0.310 0.326 Notes: This table replicates Table 1.5 but additionally includes day fixed effects (Panel A) or quarter fixed effects (Panel B). 127 Table 3.12: Recency with Additional Fixed Effects (2) Panel A: Retail investors Dependent variable: Memory-induced trade (dummy) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) Lag 1 (dummy) 0.117*** (0.004) Lag 2 (dummy) 0.019*** 0.028*** (0.003) (0.006) Lag 3 (dummy) 0.002 0.005 0.007 (0.003) (0.005) (0.007) Lag 4 (dummy) 0.003 0.009 0.013* 0.023** (0.003) (0.006) (0.007) (0.010) Lag 5 (dummy) -0.001 0.003 0.001 0.006 0.013 (0.003) (0.004) (0.005) (0.006) (0.008) Lag 6 (dummy) 0.000 0.002 0.006 0.010** 0.001 0.005 (0.003) (0.004) (0.004) (0.005) (0.006) (0.009) Lag 7 (dummy) 0.001 0.001 -0.001 0.001 0.001 -0.000 0.006 (0.003) (0.004) (0.004) (0.005) (0.005) (0.007) (0.012) Lag 8 (dummy) 0.002 -0.001 -0.002 0.002 0.002 0.001 -0.002 -0.020* (0.003) (0.004) (0.004) (0.005) (0.005) (0.006) (0.009) (0.012) Lag 9 (dummy) -0.003 -0.004 -0.005 -0.000 -0.004 -0.011* -0.006 -0.019* -0.053** (0.003) (0.004) (0.004) (0.004) (0.005) (0.006) (0.008) (0.010) (0.024) Lag 10 (dummy) 0.006* 0.013*** 0.016*** 0.020*** 0.017*** 0.018** 0.021** 0.008 -0.012 0.134 (0.003) (0.004) (0.005) (0.005) (0.006) (0.007) (0.009) (0.011) (0.016) (0.087) Lag 11 (dummy) 0.000 -0.003 -0.001 -0.001 -0.003 -0.004 -0.003 -0.008 -0.018 0.059 -0.198 (0.004) (0.005) (0.005) (0.006) (0.005) (0.006) (0.008) (0.010) (0.014) (0.046) (0.241) Lag 12 (dummy) -0.002 -0.005 -0.001 0.006 -0.000 -0.003 -0.003 0.001 0.009 0.016 -0.198 (0.004) (0.005) (0.006) (0.008) (0.008) (0.009) (0.011) (0.013) (0.016) (0.028) (0.241) Stock-pair FE yes yes yes yes yes yes yes yes yes yes yes Day FE yes yes yes yes yes yes yes yes yes yes yes Investor x Day FE yes yes yes yes yes yes yes yes yes yes yes Observations 138,522 56,280 42,139 31,404 23,237 16,872 11,846 7,610 4,516 2,250 739 R-squared 0.604 0.632 0.659 0.674 0.697 0.716 0.738 0.759 0.790 0.805 0.791 Panel B: Mutual funds Dependent variable: Memory-induced trade (dummy) (1) (2) (3) Lag 1 (dummy) 0.141*** (0.002) Lag 2 (dummy) 0.004** 0.010*** (0.002) (0.002) Lag 3 (dummy) 0.006*** 0.003* 0.006*** (0.001) (0.002) (0.002) Lag 4 (dummy) 0.011*** -0.001 0.002 (0.001) (0.002) (0.003) Stock-pair FE yes yes yes Quarter FE yes yes yes Fund x Quarter FE yes yes yes Observations 726,518 197,971 110,088 R-squared 0.389 0.473 0.532 Notes: This table replicates Table 1.5 but additionally includes day and investor x day fixed effects (Panel A) or quarter and fund x quarter fixed effects (Panel B). 128 I Chapter 2: Additional Tables Table 3.13: Baseline Results using only Largest Cue Dependent variable: Return on day t (%) Sample: Full Pattern firm (1) (2) (3) (4) Cue q−1 of largest cue (dummy) 0.024*** 0.021** 0.061*** 0.053** (0.007) (0.008) (0.018) (0.021) Day FE no yes no yes Observations 31,392,090 31,392,090 15,773,961 15,773,961 R-squared 0.000 0.003 0.000 0.004 Notes: This table presents results from regressions of the return on day t on Cue q−1 of the largest cue. This dummy is equal to one if the largest firm that announced earnings on the same day as firm j in the previous fiscal quarter announces earnings on day t. Columns (1) and (2) show results for the full sample and columns (3) and (4) for the Pattern firm sample. Columns (2) and (4) also include day fixed effects. Standard errors are clustered by firm and trading day and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 129 Table 3.14: Recency using only Largest Cue Panel A: Full Sample Dependent variable: Return on day t (%) (1) (2) (3) (4) (5) Cue q−1 of largest cue (dummy) 0.018** 0.021** (0.008) (0.008) Cue q−2 of largest cue (dummy) 0.014* 0.017** (0.007) (0.007) Cue q−3 of largest cue (dummy) 0.008 0.012* (0.007) (0.007) Cue q−4 of largest cue (dummy) 0.018* 0.020** (0.009) (0.009) Day FE yes yes yes yes yes Observations 31,392,090 31,392,090 31,392,090 31,392,090 31,392,090 R-squared 0.003 0.003 0.003 0.003 0.003 Panel B: Pattern Firm Sample Dependent variable: Return on day t (%) (1) (2) (3) (4) (5) Cue q−1 of largest cue (dummy) 0.048** 0.053** (0.021) (0.021) Cue q−2 of largest cue (dummy) 0.010 0.020 (0.017) (0.018) Cue q−3 of largest cue (dummy) 0.035* 0.039** (0.019) (0.020) Cue q−4 of largest cue (dummy) -0.019 -0.013 (0.024) (0.024) Day FE yes yes yes yes yes Observations 15,773,961 15,773,961 15,773,961 15,773,961 15,773,961 R-squared 0.004 0.004 0.004 0.004 0.004 Notes: This table presents results from regressions of the return on dayt on memory cues that were encoded in different quarters. The independent variables are dummy variables for each of the previous four fiscal quarters, and are equal to one if the largest firm that announced earnings on the same day as firm j in that quarter announces earnings on day t. Column (1) includes all dummies simultaneously and the remaining columns each include only one dummy at a time. All columns include day fixed effects. Panel A shows results for the full sample and Panel B for the Pattern firm sample. Standard errors are clustered by firm and trading day and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 130 Table 3.15: Interference using only Largest Cue Dependent variable: Return on day t (%) Sample: Full Pattern Firm (1) (2) Cue q−1 x Low Interference 0.030*** 0.078*** (0.010) (0.024) Cue q−1 x High Interference 0.011 0.025 (0.013) (0.034) Day FE yes yes Observations 31,392,090 15,773,961 R-squared 0.003 0.004 Notes: This table presents results from regressions of the return on dayt on memory cues that were encoded with low and high interference. Cue q−1 x Low Interference is equal to one if the largest firm that announced earnings on the same day as firm j in the previous quarter announces earnings on day t, and if the number of firms announcing on that day in the previous quarter was below the median. Cue q−1 x High Interference is defined equivalently, except that the number of firms announcing on that day in the previous quarter was above the median. Column (1) shows results for the full sample and column (2) for the Pattern firm sample. Both columns also include day fixed effects. Standard errors are clustered by firm and trading day and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 131 Table 3.16: Surprise of Largest Cue Dependent variable: Return on day t (%) Sample: Full Pattern Firm (1) (2) (3) (4) Surprise 0.678 8.294 (3.157) (7.677) Surprise Quintile 2 (dummy) -0.004 -0.009 (0.020) (0.041) Surprise Quintile 3 (dummy) 0.002 0.079* (0.019) (0.042) Surprise Quintile 4 (dummy) -0.015 0.050 (0.019) (0.045) Surprise Quintile 5 (dummy) 0.002 0.005 (0.019) (0.046) Day FE yes yes yes yes Observations 821,168 821,168 77,970 77,970 R-squared 0.008 0.008 0.024 0.024 Notes: This table presents results from regressions of the return on day t on the earnings surprise of the largestcueingfirm. Thesampleisrestrictedtodayswithacuefromthelargestfirm. Surpriseisthedifference between the actual earnings announced by the cueing firm and the median analyst earnings forecast, scaled by the share price of the firm from three trading days prior to the announcement. Columns (1) and (3) include the surprise directly as an independent variable, while columns (2) and (4) include dummy variables that indicate the second through fifth quintile of the surprise distribution. Columns (1) and (2) present results for the full sample and columns (3) and (4) for the Pattern firm sample. All columns include day fixed effects. These fixed effects can result in singleton observations, which are dropped during the estimation (specifically, 1 observation in Panel A and 25 observations in Panel B). Standard errors are clustered by firm and trading day and are displayed in parentheses below the coefficients. *, **, and ***, indicate statistical significance at the 10%, 5%, and 1% level, respectively. 132 J Chapter 3: Additional Figures Here, we provide several additional figures that are referenced in the main body of the paper. Figure 3.6. Subjective Expected Payoffs and Perceived Risk Slope = -0.0067*** (0.0005) 4.6 4.65 4.7 4.75 4.8 4.85 Log payoff expectation, d 10 20 30 40 Volatility, λ Notes: This figure is a binned scatter plot of subjective expected payoffs ( d) and perceived volatility (λ) controlling for subject fixed effects. The reported slope results from a mixed effects regression of d on λ. The regression includes a random effect for λ as well as for the intercept. The standard error in parentheses is clustered at the subject level. The sample size is 2,400 and the number of subjects is 300. The data are from Experiment 1. 133 Figure 3.7. Departures from Bayesian Expectations and Perceived Risk Slope = -0.0056*** (0.0004) -.1 -.05 0 .05 .1 Departure from Bayesian expectation, d - d b 10 20 30 40 Volatility, λ Notes: This figure is a binned scatter plot of departures of subjective expected payoffs from the Bayesian benchmark (d−d b ) and perceived risk (λ) controlling for subject fixed effects. The reported slope results from a mixed effects regression of d−d b on λ. The regression includes a random effect for λ as well as for the intercept. The standard error in parentheses is clustered at the subject level. The sample size is 2,400 and the number of subjects is 300. The data are from Experiment 1. 134 Figure 3.8. Bayesian Expected Returns and Perceived Risk Slope = 0.0050*** (0.0008) .1 .15 .2 .25 .3 Log Bayesian expected return, r b 10 20 30 40 Volatility, λ Notes: This figure is a binnedscatter plot of Bayesian expected returns ( r b ) and perceived risk (λ) controlling for subject fixed effects. The reported slope results from a mixed effects regression of r b onλ. The regression includes a random effect for λ as well as for the intercept. The standard error in parentheses is clustered at the subject level. The sample size is 2,400 and the number of subjects is 300. The data are from Experiment 1. 135 Figure 3.9. Subjective Expected Returns and Subjective Expected Payoffs Slope = 0.37*** (0.05) -.1 0 .1 .2 .3 .4 Log expected return, r 4.4 4.6 4.8 5 Log payoff expectation, d Notes: This figure is a binned scatter plot of subjective expected returns ( r) and subjective expected payoffs (d) controlling for subject fixed effects. The reported slope results from a mixed effects regression of r ond. The regression includes a random effect for d as well as for the intercept. The standard error in parentheses is clustered at the subject level. The sample size is 2,400 and the number of subjects is 300. The data are from Experiment 1. 136 K Chapter3: Derivationsfortheconceptualframework K.1 Gaussian signal extraction We adapt the basic Bayesian signal extraction studied by Gabaix (2019) to our conceptual framework. Suppose that the agent’s objective is to minimize the squared distance between her true willingness to pay p ∗ and the willingness to pay p conditional on her noisy signal p 0 =p ∗ +ϵ, where ϵ is normally distributed with mean 0 and variance σ 2 ϵ : max p E[−1/2(p−p ∗ ) 2 |p o ]. (K.1) Hence the optimality condition isE[p−p ∗ |p o ] = 0. Becauseϵ has a zero mean, the prediction aboutp ∗ conditional on the signalp 0 isE[p ∗ |p o ] = (1−x)¯ p+xp o where the dampening factor is given by: x = σ 2 p σ 2 p +σ 2 ϵ . (K.2) As the variance of the noisy signal increases, the agent optimally puts more weight on the default ¯ p. K.2 Estimating x from willingness to pay and payoff expectations In the following, we show that the univariate relation between p and d results in a upward- biased estimate of x if payoff expectation d and perceived risk λ are negatively correlated. Rearranging equation (3.5) results in λ t =− α β + 1 β d t − 1 β η t , (K.3) which can be plugged into (3.3) to obtain p t = (1−x)¯ p + xγα β +x " 1− γ β # d t + xγ β η t . (K.4) As a result, the coefficient of p on d is x h 1− γ β i which is larger than x if γ> 0 and β< 0. 137 L Chapter 3: Expected cash flow and return effects We decompose the variation in WTP into expected payoff and expected return effects and report results in Table 3.17. This exercise is similar to the Campbell and Shiller (1988) decomposition of the price-dividend ratio into expected dividend growth and expected return effects. Table 3.17: Decomposition of Variation in WTP Bayesian Subjective d b 4% d 25% - r b 96% - r 75% Notes: This table shows the decomposition of variation in willingness to pay p into expected payoff and expected return effects using the identities p =d−r and p =d b −r b . The numbers represent cov(˜ q,p) var(p) where ˜ q is one ofd b ,d, -r b , and -r. The sample size is 2,400 and the number of subjects is 300. The data are from Experiment 1. 138 M Chapter 3: Results using tail risk In this section, we present the risk-return relationship in Experiment 1 using the subjective probability of the lowest payoff ($60) as the measure of perceived risk. This is a measure of tail risk and is similar to the measure of disaster risk in Giglio et al. (2021a). Table 3.18 and Figure 3.10 show that the results are similar to our main results from Table 3.3, in which we use volatility as the perceived risk measure. Table 3.18: Subj. Expected Returns, Subj. Expected Payoffs, and Perceived Tail Risk r (1) (2) d 0.401 ∗∗∗ (0.051) λ −0.210 ∗∗ 0.186 ∗∗∗ (0.047) (0.060) Observations 2,400 2,400 Notes: This table presents results from mixed effects regressions of subjective expected returns ( r) on subjective expected payoffs ( d) and the perceived probability of the lowest payoff ( λ). These regressions include a random effect for d andλ, as well as for the intercept. Standard errors are clustered at the subject level and displayed in parentheses below the coefficient estimates. The data are from Experiment 1. ∗ , ∗∗ , and ∗∗∗ indicate statistical significance at the 10%, 5%, and 1% levels, respectively. 139 Figure 3.10. Subjective Expected Returns and Perceived Tail Risk 0 .1 .2 .3 Log expected return, r -.2 0 .2 .4 .6 Disaster risk, λ Notes: This figure is a binned scatter plot of subjective expected returns ( r) and the perceived probability of the lowest payoff ( λ) controlling for subject fixed effects. The sample size is 2,400 and the number of subjects is 300. The data are from Experiment 1. 140 N Chapter 3: Heterogeneity across subjects Here, we analyze the sources of variation in the data from Experiment 1 and report the fractions of variation explained by time and subject fixed effects in Table 3.19. Consistent with the field evidence from Giglio et al. (2021a), fixed effects explain a large fraction of WTP, subjective return expectations, and perceived risk. Payoff expectations have a larger component driven by time rather than subject fixed effects. This result likely reflects the commonality in learning. Table 3.19: Decomposition of Variation: Subject and Time Fixed Effects Time FE Subject FE Both FE R 2 in % (1) (2) (3) d 24.8 8.1 36.2 p 6.1 65.6 71.7 r 0.6 68.3 68.8 λ 3.6 54.7 58.3 Observations 2,400 2,400 2,400 Notes: This table reports the R 2 s corresponding to the regressions of the variables displayed in the first column on time fixed effects, subject fixed effects, or both. The dependent variables are subjective expected payoffs ( d), willingness to pay (p), subjective expected returns (r), and perceived volatility (λ). The data are from Experiment 1. 141 O Chapter 3: Screenshots of the experiments O.1 Experiment 1 Subjects had full information of the dividend distribution in both states. The distributions were displayed to subjects before the first dividend realization and in each elicitation period. Figure 3.11. Distribution in the good state Figure 3.12. Distribution in the bad state 142 Below is a screenshot showing how dividend realizations were displayed to subjects in each period: Figure 3.13. Dividend realization After observing the dividend realizations over the course of several periods, subjects were asked to answer two questions. While answering these questions, they received an overview of the full history of dividend realizations: Figure 3.14. Overview of history of dividend realizations 143 Subjects were able to report the probability that they attached to each dividend outcome. The ordering of the buckets (i.e., highest to lowest or lowest to highest) was randomized across subjects. The probability of each bucket was restricted to [0%, 100%] and the sum of the five probabilities was required to add up to 100%. Subjects were able to input their willingness to pay using a slider. This slider had to be initiated by the subject by clicking on the slider. The screenshots below show how the slider appeared before and after initiation: Figure 3.15. Elicitation of payoff expectations 144 Figure 3.16. Elicitation of willingness to pay (after initiation) 145 O.2 Experiment 2 Subjects were shown the probability of each dividend outcome. The ordering of the buckets (i.e., highest to lowest or lowest to highest) was randomized across subjects. Subjects were able to input their willingness to pay using a slider. This slider had to be initiated by the subject by clicking on the slider. The screenshots below show how the slider appeared before and after initiation: Figure 3.17. Display of payoff distribution 146 Figure 3.18. Elicitation of willingness to pay (after initiation) 147

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Creator Charles, Constantin (author)

Core Title Essays on the effect of cognitive constraints on financial decision-making

School Marshall School of Business

Degree Doctor of Philosophy

Degree Program Finance

Degree Conferral Date 2023-05

Publication Date 03/06/2023

Defense Date 03/03/2023

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag cognitive constraints,cognitive noise,financial decision-making,Memory,OAI-PMH Harvest

Format theses (aat)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Frydman, Cary (committee chair), Hirshleifer, David (committee member), Korteweg, Arthur (committee member), Libgober, Jonathan (committee member), Parsons, Christopher (committee member)

Creator Email ccharles@marshall.usc.edu,ccharles@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC112764283

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