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Essays in empirical asset pricing

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Essays in empirical asset pricing

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Content Essays in Empirical Asset Pricing Haitao Mo A Dissertation Presented to the Faculty of the USC Graduate School University of Southern California in Candidacy of the Degree Doctor of Philosophy Adviser: Professor Wayne Ferson August 2013 c Copyright by Haitao Mo, 2013. All rights reserved. iii Abstract The literature on economic risk premiums has largely been based on ex post returns. In Chapter 1, I construct and assess implied ex ante economic risk premiums for a list of economic factors, which are driving forces in various asset pricing models, using direct expected returns estimates—i.e., the implied costs of capital (ICCs). For most economic factors, ICCs support significant nonzero average economic risk premiums which ex post returns fail to uncover since ex post returns are too volatile, implying that many economic factors are actually priced from an ex ante perspective. Second, implied ex ante factor risk premiums are a new and powerful predictor for future ex post returns of factor mimicking portfolios for most economic factors (e.g., value and size factors, default spread, inflation, the growth rate of labor income, and one-month T-bill real return), both in sample and out of sample. Analyses suggest that time-varying ex ante economic risk premiums are at least one major reason for the predictability of ICCs. In Chapter 2, I show that a stock return can be expressed as a sum of two components, which are a change in the stock’s fundamental value measured using tangible information such as accounting information and analysts’ forecasts, and a change in the deviation of the stock’s price from its fundamental value. I decompose the selectivity of mutual fund managers into their abilities to predict those two return components, and use the new decomposition to describe fund managers’ investment styles in a new way, reflecting their focuses on return components when investing. Average fund managers focus on price deviation information rather than fundamentals to guide their investments. Further, there is some significant evidence that these new styles can predict fund managers’ performance around announcements of new earnings or new analysts’ recommendations, and such performance predictability is at least partially driven by managers’ exploitation of the stock return predictability attributed to stocks’ fundamental value-price ratios proposed in Frankel & Lee (1998). iv Acknowledgements I would like to thank my dissertation advisor Wayne Ferson for his constant guidance, support, and inspiration throughout my study in the PhD program in finance. I am very grateful to the support and encouragement from my dissertation committee members Chris Jones, Oguzhan Ozbas, Peter Radchenko, and David Solomon. I appreciate many discussions I have had with other faculty members and Ph.D. students at USC. I benefit from the financial support from USC Marshall School of Business Department of Finance and Business Economics. v Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix 1 Implied Economic Risk Premiums 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Research Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 The Construction of Firm-level Implied Costs of Capital . . . . . . . . . . . 7 The Construction of Factor Risk Premiums . . . . . . . . . . . . . . . . . . . 9 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Average Economic Risk Premiums . . . . . . . . . . . . . . . . . . . . . . . . 14 Predicting Ex Post Economic Risk Premiums . . . . . . . . . . . . . . . . . 17 Several Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Biases in Analysts’ Earnings Forecasts . . . . . . . . . . . . . . . . . . . . . 24 Errors In Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Errors in Estimates of Factor Betas . . . . . . . . . . . . . . . . . . . . . . . 32 Robustness: Terminal Period, E/P, or Forecasted E/P . . . . . . . . . . . . . 33 Multiple Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Conclusions and Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Appendix: The Bootstrapping Procedure . . . . . . . . . . . . . . . . . . . . . . . 35 2 FundamentalValues,PriceDeviations,andtheSkillsofMutualFundMan- agers 62 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 A Model for Stock Return Decomposition . . . . . . . . . . . . . . . . . . . . . . 66 Model Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 vi Decomposing Fund Performance: New Styles . . . . . . . . . . . . . . . . . . . . . 69 The Analysis of Individual Funds . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Event Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Further Explorations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 vii List of Tables 1.1 Summary Statistics of Implied Economic Risk Premiums and Other Predictors 37 1.2 Average Economic Risk Premiums . . . . . . . . . . . . . . . . . . . . . . . . 38 1.3 Standard Deviations of Economic Risk Premiums . . . . . . . . . . . . . . . 39 1.4 Ex-post vs Ex-ante Risk Premium Differences For Duration Portfolios . . . . 40 1.5 In-sample Risk Premium Predictability Of ICCs (Traded Factor Case) . . . . 41 1.5 – Continued . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 1.6 In-sample Risk Premium Predictability Of ICCs (Nontraded Factor Case) . . 43 1.6 – Continued . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 1.6 – Continued . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 1.7 Out-of-sample Risk Premium Predictability Of ICCs . . . . . . . . . . . . . 46 1.8 Regressions for the Model-based Earnings Forecasts . . . . . . . . . . . . . . 47 1.9 In-sample Predictability of Mechanical-ICCs (Traded Factor Case) . . . . . . 48 1.9 – Continued . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 1.10 In-sample Predictability of Mechanical-ICCs (Nontraded Factor Case) . . . . 50 1.10 – Continued . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 1.10 – Continued . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 1.11 The Horse Race Between Two Versions of ICCs (Traded Factor Case) . . . . 53 1.11 – Continued . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 1.12 The Horse Race Between Two Versions of ICCs (Nontraded Factor Case) . . 55 1.12 – Continued . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 1.12 – Continued . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 1.13 Correlations With Theoretical Drivers (Traded Factor Case) . . . . . . . . . 58 1.13 – Continued . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 1.14 Correlations With Theoretical Drivers (Nontraded Factor Case) . . . . . . . 60 1.14 – Continued . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 2.1 Performance Decomposition Of Average Mutual Funds . . . . . . . . . . . . 76 2.2 Fund Performance Predictability Of New Styles . . . . . . . . . . . . . . . . 77 viii 2.3 Predictability Of New Styles For Before-cost Fund Performance Around Events 78 2.3 – Continued . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 2.3 – Continued . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 2.3 – Continued . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 ix List of Figures IMPLIED ECONOMIC RISK PREMIUMS 1 Chapter 1 Implied Economic Risk Premiums Introduction In the center of asset pricing models lie various economic factors as market driving forces compensated with risk premiums. 1 For example, the Capital Asset Pricing Model (CAPM) highlights the market portfolio as the single driving factor while consumption growth plays a central role in consumption-based models. Although many studies, such as Chen et al. (1986), Ferson & Harvey (1991), Campbell (1996), and McElroy & Burmeister (1988), have empirically examined various economic factors in different asset pricing models, their important roles as predicted by the models still remain far from convincing, because previous evidence of average risk premiums associated with economic factors (i.e., economic risk premiums) has been disappointing, as pointed out by Balduzzi & Robotti (2010) and Shanken & Weinstein (2006). For example, estimates of average economic risk premiums are often insignificant, inconsistent across studies, and very sensitive to empirical choices such as test assets, sample periods, and estimation methods. Even the most basic economic risk premium, the market risk premium in CAPM, can be insignificantly different from zero (Fama & French (1992)). As illustrated in Chan et al. (1998), the general impression is that economic factors perform poorly when explaining asset returns. Why do previous studies result in disappointingly insignificant or fragile average economic risk premiums? One plausible reason is that previous studies all use ex post returns to estimate economic risk premiums. This approach can be problematic for both theoretical and empirical reasons. Theoretically, predictions about economic risk premiums are always ex ante, making it questionable to use ex post returns as measuring tools. 1 Starting from the Capital Asset Pricing Model (CAPM) of Sharpe (1964), Lintner (1965), and Black (1972), the literature has proposed various asset pricing models, such as Merton (1973)’s Intertemporal Capital Asset Pricing Model (ICAPM), Ross (1976)’s Arbitrage Pricing Theory (APT), consumption-based models dated back to Lucas (1978), and term structure models such as Cox et al. (1985). IMPLIED ECONOMIC RISK PREMIUMS 2 Empirically, although the sample means of ex post returns should be unbiased estimates of expected returns, ex post returns are notoriously noisy, leading to the fact that sample means are imprecise estimates of expected returns because of large standard errors (e.g., Fama & French (1997)). Further, sample means are subject to finite sample bias which means they can differ from expected returns by substantial amounts in finite samples (e.g., Elton (1999)). To avoid the drawbacks of using ex post returns and to improve the test power by fitting theoretical predictions more closely, in this study, I propose to use direct expected returns estimates—i.e., the implied costs of capital (ICCs)—to construct implied ex ante economic risk premiums, and assess average levels of economic risk premiums from an ex ante perspective (first research question). The ICC is the discount rate that sets the stock price equal to the discounted present value of analysts’ forecasts of future stock earnings. While a number of previous papers have used ICCs to proxy for expected stock returns, the focus is usually on individual stocks or the market portfolio. This paper breaks new ground by using ICCs to develop implied ex ante risk premiums for a range of economic factors. 2 I consider both traded and nontraded economic factors that act as driving forces in various asset pricing models, and construct their monthly ex post and implied ex ante risk premiums from January 1981 to December 2010, based on unit-beta factor mimicking portfolios (unit-beta version). For traded economic factors (e.g., the size factor) which are portfolios themselves, I also examine another version of factor risk premiums based on alternative mimicking portfolios that are determined by the market composition weights of factors (market-weight version). Conceptually, as ex ante measures, ICCs can mitigate excessive noise and finite sample biases induced by unexpected returns in ex post returns, and ICCs can fit theoretical predictions about ex ante factor risk premiums more closely, thus ICCs should have more power to uncover priced economic factors than ex post returns. Evidence supports this prediction. Average implied risk premiums for most economic factors, including two versions of risk premiums for three traded factors (market, size and value), are all reliably estimated with strong statistical significance, because implied economic risk premiums are much less volatile, leading to small standard errors and precise estimates. In contrast, ex post returns report statistically insignificant average risk premiums for most factors, including the three traded factors if I measure the unit-beta version of their risk premiums. Even if I examine the market-weight version of their risk premiums, the size factor is still not significantly priced. The evidence implies that from an ex ante perspective many economic factors are actually priced. The evidence hence resurrects the important role of 2 Applications of ICCs to asset pricing include Gordon & Gordon (1997), Pástor et al. (2008), Lee et al. (2009), Chava & Purnanandam (2010), and Li et al. (2011). IMPLIED ECONOMIC RISK PREMIUMS 3 many economic factors that various models predict and previous studies may have failed to uncover. On the other hand, average implied economic risk premiums tend to be smaller in economic magnitude than those measured by ex post returns. I test and find that two explanations — flat term structure of equity risk premiums assumed in the computation of ICCs if the actual one is downward sloping as in van Binsbergen et al. (2012), and biases in analysts’ earnings forecasts — can be responsible. As expected return estimates, ICCs are a natural tool for predicting future ex post economic risk premiums (or equivalently future ex post returns of mimicking portfolios of economic factors), and hence can help revisit an important economic issue, that is, whether ex ante economic risk premiums are time-varying (second research question). To examine this issue, existing studies (Ferson & Harvey (1991)) either use traditional return predictors such as the price-dividend ratio of the market in a predictive regression but are subject to severe statistical biases such as strong finite sample biases (Stambaugh (1986)), spurious regression and data mining (Ferson et al. (2003)); or existing studies impose structural assumptions that could be too strong (e.g., Ang & Piazzesi (2003)). Those limitations mean that previous conclusions may not be as convincing and robust as we would like. Instead, ICCs offer a new and fairly robust way, from an estimation perspective, to examine the same issue. Moreover, I account for various statistical biases known so far in the literature, and I adopt a relatively simple structure-free framework of factor mimicking portfolios to construct economic risk premiums, rendering more robust or convincing results. I find that implied ex ante economic risk premiums are less persistent than are many traditional return predictors such as the price-dividend ratio of the market. Studies have assumed that conditional risk premiums are highly persistent, based on the regressions of ex post returns on traditional lagged predictors. Less persistence of implied ex ante economic risk premiums suggests that ex ante risk premiums may be more volatile than we thought, and that we can use implied ex ante economic risk premiums in predictive regressions without as much concern about the statistical issues associated with traditional predictors. I find that implied ex ante risk premiums can predict future ex post risk premiums for most economic factors. In an in-sample (IS) analysis, ICCs significantly predict future ex post risk premiums for the size and value factors, the default spread, unexpected inflation, the growth rate of labor income, and the one-month T-bill real return. For many factor risk premiums, the predictability of ICCs strongly holds in the presence of traditional return predictors such as price-dividend ratio, book-to-market ratio, price-earning ratio and so forth. ICCs can predict not only in longer horizons but also in a horizon as short as one month. Further, slopes of ICCs are often larger than one, consistent with a conflict IMPLIED ECONOMIC RISK PREMIUMS 4 between the flat term structure of equity risk premiums assumed in ICCs and an actual downward sloping one. In the out-of-sample (OOS) test, ICCs can significantly predict future ex post risk premiums of the size factor (market-weight version), default spread, inflation, the dividend-price ratio of the stock market, and the one-month T-bill real return. If ICCs are reasonable estimates for expected returns, evidence reflects that ex ante factor risk premiums vary over time for many economic factors. As well, ICCs are a new and powerful predictor with additional information to better track ex ante economic risk premiums. My findings hence extend the evidence of Li et al. (2011), who show that ICCs predict the market-weight version of ex post risk premium of the market factor, to a list of other traded and nontraded economic factors that act as driving forces in various asset pricing models. 3 However, Li et al. (2011) do not explicitly analyze the market factor as a risk factor in a factor model and hence do not consider the unit-beta version of its risk premium, while I examine both unit-beta and market-weight versions but fail to find ICCs’ predictability for the unit-beta version. Although a beta pricing interpretation can naturally explain findings uncovered by ICCs, several issues may introduce errors in ICCs as expected return estimates, and hence could suggest alternative explanations. First, analysts’ earnings forecasts have known biases due to cognitive or incentive reasons (e.g., see Ramnath et al. (2008) for a review), and may result in biased expected returns estimates. To address this concern, I construct alternative ICCs (call them mechanical-ICCs) that employ unbiased earnings forecasts from a statistical model using only public information to forecast earnings. 4 I use mechanical-ICCs to reexamine all the research questions and obtain similar, though weaker, findings. Second, stock prices from which ICCs are inverted can be contaminated with errors, due to psychological biases of investors, slow information diffusion in capital markets, noise trader, general sentiment, or market microstructure, introducing errors in ICCs. Typical errors can be diversified away since economic risk premiums are macro-level variables and rely on diversified factor mimicking portfolios, unless errors are correlated with factor betas of stocks. However, there are two types of errors in prices that are correlated with factor betas of stocks. Extending Hong & Sraer (2012) to a multi-factor setting, due to short-sell constraints, only optimistic opinions in investors’ aggregate disagreements about the common macro factors in cash flows get impounded into pricing, leading to overpricing of 3 The value factor, one of the economic factors considered in this paper, is also studied by a recent working paper Li et al. (2012). They and I both independently examine and find ICCs predict its ex post risk premium. However, I examine both unit-beta and market-weight versions of value risk premium while they only consider the latter version. 4 Call original ICCs based on analysts’ forecasts analyst-ICCs. IMPLIED ECONOMIC RISK PREMIUMS 5 those common factors. High factor beta stocks can be overpriced since they are more sensitive to overpriced common factors. On the other hand, as is also argued in Shen & Yu (2012), aggregate investor sentiment can cause overpriced high factor beta stocks by a similar mechanism. Aggregate investor sentiment that drives market-wide optimism or pessimism can cause overpricing and underpricing of common macro factors in cash flows. Due to short-sale constraints, we would see overpricing rather than underpricing of common factors and hence overpriced high factor beta stocks, given their large sensitivity to common factors. Since factor mimicking portfolios long high factor beta stocks and short low factor beta stocks, implying overpriced portfolios, both ex post return-based and ICC-based average economic risk premiums could understate true ones, reinforcing the importance of economic factors for driving asset markets. Further, arguably, those two types of errors in prices should impact the version of ex post returns more, further supporting better properties of ICC-based average risk premiums. On the other hand, because errors in stock prices introduce measurement errors in not only ICCs but also ex post risk premiums that ICCs predict, common measurement errors could result in spurious predictability, since the same prices are employed in both sides of the predictive regressions. There is no way to totally rule out this mispricing explanation for predictability, but I conduct several analyses supporting the interpretation that time-varying ex ante economic risk premiums are at least one major reason for the predictive power of ICCs. (1) I test and find similarly strong forecast ability of ICCs when I introduce an extra one-month lag between ICCs and future ex post economic risk premiums to avoid using the same stock prices for both sides of the predictive regressions. This finding demonstrates that short-lived mispricing, such as bid-ask bounce, nonsynchrous error, or short-term underreaction errors, should not account for the predictability of ICCs, since short-lived price errors can only predict ex post risk premiums in the near future, for example, within the next month. (2) For two types of mispricing caused by aggregate investors’ disagreement or sentiment, if aggregate disagreement or sentiment are time-varying, resulting in time-varying pricing errors, we could expect spurious predictability when using ICCs as long as the resulting errors are autocorrelated to a sizeable extent. Since time-varying pricing errors are essentially functions of time-varying aggregate disagreement or sentiment, the autocorrelation of pricing errors (or equivalently spurious predictability) essentially reflects using aggregate disagreement (sentiment) today to predict aggregate disagreement (sentiment) tomorrow. Hence I include aggregate disagreement or sentiment in the predictive regressions to control for spurious predictability. I continue to find predictability of ICCs in the presence of them, indicating that those two types of mispricing would not capture the ICCs’ predictability. IMPLIED ECONOMIC RISK PREMIUMS 6 (3) I run a horse race of predictability between analyst-ICCs and mechanical-ICCs. Since mechanical-ICCs are backed out from stock prices using rational and unbiased model-based earnings forecasts, the predictability of any price errors is likely inherited and represented better by mechanical-ICCs than by analyst-ICCs. Hence, any predictive power of analyst-ICCs in the horse race may be mainly driven by time-varying ex ante economic risk premiums. Further, since the only difference between two ICCs is the choice of earnings forecasts, the horse race can shed light on the relative superiority of the two versions of earnings forecasts for a context of time-series return prediction. I find sustainedly strong forecasting power of analyst-ICCs in the presence of mechanical-ICCs, again supporting time-varying ex ante economic risk premiums as well as establishing that analysts’ earnings forecasts contain useful information—beyond what is in model-based earnings forecasts—that helps better predict economic risk premiums. (4) If ICCs reflect time-varying ex ante economic risk premiums, implied ex ante economic risk premiums should be correlated contemporaneously with theoretical drivers of time-varying risk premiums in recent asset pricing models — the habit (or surplus consumption ratio) in Campbell & Cochrane (1999), the consumption volatility in Bansal & Yaron (2004), and the model uncertainty of economy in Drechsler (2011). I test and find that implied ex ante economic risk premiums correlate significantly contemporaneously with at least one of those drivers. I also test and find robustness to alternative choices for several aspects of the specification of the adopted ICC model, such as alternative speeds of reversion of forecasts of earnings growth and plowback rate towards their steady state counterparts, and alternative ICC models using firm-level earnings-price ratios and earnings forecast-price ratios as ICCs. Finally, it is important to interpret the empirical results in view of the total number of tests conducted. A multiple comparisons analysis strongly supports priced economic factors from an ex ante ICC perspective and weakly supports time-varying ex ante economic factor risk premiums. This paper extends the literature of economic risk premiums, which includes research in both the stock market (e.g., Chen et al. (1986), Ferson & Harvey (1991), Campbell (1996), and McElroy & Burmeister (1988)) and the bond market (e.g., the research started by Ang & Piazzesi (2003) that incorporates economic factors into the term structure models for Treasury yields). One hurdle in this literature is the fragile and insignificant evidence of average economic risk premiums. Two recent studies, both based on ex post returns, try to conquer that hurdle. Shen & Yu (2012) show that average economic risk premiums measured by ex post returns are significant and more consistent with economic theories in a low market sentiment state when markets are likely more efficient. Balduzzi & IMPLIED ECONOMIC RISK PREMIUMS 7 Moneta (2011) exploit high-frequency ex post returns of bond futures and show that average risk premiums associated with macroeconomic announcements are significant. Instead, this paper exploits direct estimates of ex ante expected stock returns and discovers significant average economic risk premiums from an ex ante perspective. Research Design This section describes the construction of firm-level implied costs of capital, the construction of implied or ex post economic risk premiums by using factor-mimicking portfolios to aggregate firm-level ICCs or ex post returns, and the data. The Construction of Firm-level Implied Costs of Capital This subsection describes the construction of firm-level implied costs of capital at the monthly frequency. I adopt the ICC model in Pástor et al. (2008) and Li et al. (2011), since they demonstrate the superiority of this model in a time-series context, which is the context of the second research question in this paper. Given the price and prevailing forecasts of all of the future earnings of a stock, the ICC of this stock is the implied discount rate that is backed out from the following equation: P t = T X k=1 FE t+k (1−b t+k ) (1+q t ) k + FE t+T+1 q t (1+q t ) T , (1.1) whereP t is the stock price at time t,FE t+k is the forecast at time t of one-period cash flow in k years, b t+k is the forecast of plowback rate and 1−b t+k is the forecast of payout ratio, T is number of periods necessary for the economy to reach a terminal steady state (15 years), and q t is the ICC of the stock at time t. 5 Earnings forecasts of the stocks for years t+1,t+2 andt+3 directly come from IBES analysts’ consensus forecasts of earnings (FE t+1 , FE t+2 , and FE t+3 ) and long-term growth rates (Ltg). When there are missing earnings forecasts for any of these three years, I follow the practice in the literature and use the earnings forecasts for the prior period and the forecasts of long-term growth rates to infer them. To get earnings forecasts from year t+4 tot+T +1, I assume that the earnings growth rate reverts from the year t+3 growth rate g t+3 =FE t+3 /FE t+2 −1 to a steady-state rate g by the terminal year t+T +1. Hence the 5 In a latter section, I show that results are robust to the choice of T. IMPLIED ECONOMIC RISK PREMIUMS 8 earnings forecasts from year t+4 to t+T +1 are computed by the equations below: g t+k =g t+k−1 ×exp[log(g/g t+3 )/(T−1)] (1.2) FE t+k =FE t+k−1 ×(1+g t+k ), (1.3) where g is the economy-wide steady-state earnings growth rate, computed as the historical average of the log annual nominal GDP growth rates up to the year of time t. The forecasts of plowback rates for years t+1 and t+2 are assumed to be one minus the actual dividend payout rates of firms, calculated by dividing dividends from the most recent fiscal year by earnings from the same period. When recent dividend payout ratios are not available due to missing/negative dividends or earnings, I follow the practice in the literature and compute a plowback rate of a firm as the median rate across all firms in the corresponding industry-size portfolio to which that firm belongs. Industry-size portfolios are constructed by first sorting the firms into 49 industries based on Fama French classification and then sorting within each industry into three groups by firms’ market capitalizations. To get the forecasts of plowback rates from year t+3 to year t+T, I assume that the plowback rate in year t+2 (b t+2 ) reverts linearly to a steady-state rate b by the terminal year t+T +1. The plowback rates from year t+3 to t+T +1 are computed as b t+k =b t+k−1 − b t+2 −b T−1 ,∀3≤k≤T +1. (1.4) The steady-state plowback rate b is determined by assuming that in the steady state, the growth rate in earnings g is equal to the product of the return on investment ROI and the plowback rate b (i.e., g =ROI∗b). Further, since the competition drives the return on investment to the cost of capital in the steady state, we have ROI =q t and the steady-state plowback rate is b=g/q t . Given analysts’ earnings forecasts and the forecasts of plowback rates, firm-level ICCs q t are backed out in each month from the equation (1.1). To trim outliers, I delete the ICCs above 100% and below zero. In the analysis, I choose to work with implied risk premiums (IRPs) and compute IRPs by subtracting the yield to maturity of one-month T-bill from the ICCs as follows: IRP t =q t −Tbill t . (1.5) Finally, monthly ICCs or IRPs constructed from equations (1.1) and (1.5) are both annualized rates, and are converted into monthly terms by dividing them by 12. IMPLIED ECONOMIC RISK PREMIUMS 9 The Construction of Factor Risk Premiums The construction of economic factor risk premiums requires portfolios that mimic the variation of economic factors, i.e., mimicking portfolios. In doing so, the risk premiums of mimicking portfolios represent the risk premiums of economic factors of interest. The key is to determine the weights of mimicking portfolios. Specifically, I adopt unit-beta mimicking portfolios, 6 the portfolio weights of which (w t =(w 0 t ,w f t ,w mkt t ) 0 ) are determined by the following function of factor betas of base assets (β t =(1,β f t ,β mkt t ) 0 ) w t =β t (β 0 t β t ) −1 , (1.6) where w f t , w mkt t and w 0 t are respectively weights of portfolios mimicking the economic factor (f) of interest and the market factor, and the weight of a portfolio that has no exposure to the economic factor of interest and the market factor. β f t and β mkt t are instruments for the conditional factor loadings of base assets on the economic factor of interest and the market factor, and the dating convention shows that the conditional betas are formed using only the information available up to month t. I follow Ferson & Harvey (1991) to construct the instruments for the conditional factor loadings. At the end of every month t, I run the following time-series regression for each base asset i, with the economic factor of interest and the market factor as regressors, using the past five years (minimum three years) of data up to month t: r i,τ =a i,t +β f i,t f τ +β mkt i,t r mkt,τ + i,τ , ∀τ =t−59,...,t (1.7) where r i,τ is the monthly excess return for asset i, f τ and r mkt,τ are the economic factor of interest and the market factor (market excess return), and i,τ is the regression residual. Controlling for the market factor follows Ferson & Harvey (1991) and is motivated by Merton (1973)’s Intertemporal Capital Asset Pricing Model (ICAPM). The intuition of mimicking portfolio weights in equation (1.6) is that portfolios long high factor beta base assets and short low factor beta base assets to highlight the exposure to the factors of interest. Specifically, resulting portfolios will have unit beta exposure to the factor of interest and zero beta exposures to all other factors which are the market factor in my design. I choose, as base assets for constructing unit-beta mimicking portfolios, 25 value-weighted (VW) Fama-French portfolios, constructed by myself from the NYSE-AMEX-NASDAQ universe of stocks for which ex post returns and ICCs are 6 see Balduzzi & Robotti (2008) for an evaluation of unit-beta mimicking portfolios. IMPLIED ECONOMIC RISK PREMIUMS 10 available. I consider portfolios rather than individual stocks as base assets in order to incur fewer estimation and measurement errors when estimating factor betas of base assets. Finally, I apply the base assets’ ex post returns or ICCs to the weights of factor mimicking portfolios and obtain ex post or implied ex ante economic risk premiums (λ t+1 =(λ 0 t+1 ,λ f t+1 ,λ mkt t+1 ) 0 and λ ICC t =(λ ICC,0 t ,λ ICC,f t+1 ,λ ICC,mkt t+1 ) 0 ) as λ t+1 =w 0 t r t+1 λ ICC t =w 0 t IRP t (1.8) where r t+1 and IRP t are ex post returns in excess of one-month T-bill return and IRPs of base assets in month t+1 and month t. λ f and λ mkt measure the time-varying (ex post or ex ante) risk premiums of economic factor f and the market factor, or equivalently the (ex post or ex ante) risk premiums of unit-beta factor mimicking portfolios that have a unit conditional beta with the factor of interest and zero conditional betas with all other factors. A convenient and exactly equivalent way to implement a unit-beta mimicking portfolio is to run the following Fama-MacBeth cross-sectional regressions every month t using the base assets’ factor beta exposures as regressors: r i,t+1 =λ 0 t+1 +λ f t+1 β f i,t +λ mkt t+1 β mkt i,t +u i,t+1 (1.9) IRP i,t =λ ICC,0 t +λ ICC,f t β f i,t +λ ICC,mkt t β mkt i,t +u ICC i,t . (1.10) I consider both traded and nontraded economic factors in the study. For traded (market, size, and value) factors which are portfolios themselves, I also consider an alternative and convenient way to construct their mimicking portfolios and risk premiums. I use the market composition weights of individual stocks constituting each traded factor as the mimicking portfolio weights, and then apply firm-level ex post returns or ICCs accordingly to obtain alternative risk premiums. I label these alternative risk premiums as the "market-weight" versions and those based on unit-beta mimicking portfolios as the "unit-beta" versions. Data My sample covers a period between January 1981 and December 2010. The cutoff point stems from the fact that analysts’ earnings forecasts are available for relatively few firms before 1981. Monthly consensuses of analysts’ earnings forecasts are from I/B/E/S; annual accounting information of firms is from Compustat; and monthly stock pricing information is from CRSP. I only consider firms with common shares traded on the NYSE, AMEX, or NASDAQ. The one-month T-bill yield is from CRSP. To compute excess IMPLIED ECONOMIC RISK PREMIUMS 11 returns, risk-free returns are one-month T-bill ex post returns obtained from Professor Kenneth French’s website. 7 I obtain nominal GDP growth rates from the Bureau of Economic Analysis, and the data start from 1930. The economy-wide steady-state earnings growth rate as of every year is computed as the historical average of log annual GDP growth rates up to that year. When constructing firm-level ICCs, I use the accounting information from the most recent fiscal year which ends at least three months prior to the month in which the ICC is computed. This way, I can ensure that only public information as of the time is used. I examine a list of 12 economic factors, measured monthly. The list includes both traded and nontraded factors. Traded factors are market, value and size factors (Mkt, Value and Size). These factors can capture most of the variation of stock returns sorted by size and book-to-market equity, and are argued as risk factors (e.g., Fama & French (1993) and Fama & French (1996)). Market factor (Mkt) is the return of the value-weighted portfolio of all stocks on the NYSE, AMEX, and NASDAQ in excess of one-month T-bill return, from CRSP. Value and size factors (Value and Size) are constructed in the standard manner (Fama & French (1993) and Chan et al. (1998)). I construct size portfolios by sorting stocks into deciles at the end of every June by their market capitalizations at the end of June. The value portfolios are likewise constructed by sorting stocks into deciles at the end of June using their book-to-market ratios as of the end of the previous calendar year. NYSE breakpoints are used. I value-weight all sorted portfolios to construct the monthly returns of size or book-to-market equity sorted deciles. Size (value) factor is then computed as the return spread of decile one (decile ten) over decile ten (decile one). The other nine factors are nontraded ones, including financial ratios and pure macro-factors. The first five factors include the trailing dividend-to-price ratio of S&P 500 (D/P), the term spread (TS), the default spread (DEF), the market volatility factor (VXO) and the market liquidity factor (LIQ). These economic factors are motivated by Merton (1973)’s ICAPM, as they represent the first and second moments of changing investment opportunity faced by investors, and thus should help explain asset returns. In addition, VXO may also be motivated by the long-run risk (LRR) model in Bansal & Yaron (2004). The trailing dividend-to-price ratio of S&P 500 (D/P) is the 12-month moving sum of dividends paid on the S&P 500 index divided by the S&P 500 index. Data are from Professor Robert Shiller’s website. The term spread (TS) is the yield spread of a 10-year government bond over a 1-year government bond. Data come from the Federal Reserve Bank of St. Louis. The default spread (DEF) is the yield spread of Moody’s 7 http://mba.tuck.dartmouth.edu/pages/faculty/ken.french IMPLIED ECONOMIC RISK PREMIUMS 12 seasoned Baa corporate bond over a 10-year government bond. The data come from the Federal Reserve Bank of St. Louis. The market volatility factor (VXO) is the monthly Chicago Board Options Exchange volatility index. The data are from Chicago Board Options Exchange VXO daily index. I sample daily VXO data at month end to obtain the monthly measure and data span from January 1986 to December 2010. The market liquidity factor (LIQ) is the monthly market-wide liquidity measure constructed in Pastor & Stambaugh (2003). The data are from Professor Lubos Pastor’s website. The next factor is consumption growth rate (NSCG), the underlying pillar in consumption-based asset pricing models which date from Lucas (1978), Breeden (1979), and Breeden et al. (1989). Recent influential studies include Campbell & Cochrane (1999) and Bansal & Yaron (2004). NSCG is the monthly log growth rate of seasonally-adjusted, real, nondurable consumption plus service. I obtain the data from the Bureau of Economic Analysis. One explanation for the failure of CAPM is that the empirical test did not measure correctly the actual market portfolio which includes not only financial assets but also human capital. Hence it is important to include a human capital variation to help describe market portfolio risk. One way to proxy human capital variation is to use labor income growth rate (LIG), as in Jagannathan & Wang (1996) and Campbell (1996). I hence include LIG as another plausible economic factor. Labor income growth rate (LIG) is the monthly log growth rate of the real received compensation of employees. The real received compensation is converted from nominal one using inflation. The data are from the Bureau of Economic Analysis. The final two factors are inflation (INF) and one-month T-bill real return (REALTB). Term structure literature such as Cox et al. (1985) treats these as building blocks for pricing Treasury securities. Inflation (INF) is the monthly log growth rate of CPI for all urban consumers (all items). The data are from the Federal Reserve Bank of St. Louis. The one-month T-bill real return (REALTB) is converted from a one-month T-bill nominal return using inflation. The one-month T-bill nominal return is from Professor Kenneth French’s website. Unlike the three traded factors, the nontraded factors introduced may contain substantial predictable parts, while actual economic factors should be factor innovations. Hence I obtain nontraded factor innovations as the actual nontraded economic factors by fitting all factors (traded and nontraded ones) together to a first order vector autoregressive (VAR) model, and standardizing resulting shocks of nontraded factors so that they have the same standard deviations as that of the market factor, for convenient IMPLIED ECONOMIC RISK PREMIUMS 13 comparisons among factors. 8 Their risk premiums reflect what one will be compensated for taking the factor risk if the factor shock is as volatile as the market factor. The base assets of the unit-beta factor mimicking portfolios are 25 VW Fama-French portfolios, constructed by myself from the NYSE-AMEX-NASDAQ universe of stocks for which ex post returns and ICCs are available. For the three traded factors, alternative "market-weight" mimicking portfolios, that do not involve beta estimation, are determined by the market composition weights of individual stocks constituting each of three factors. To examine the relative informativeness of ICCs for future ex post economic risk premiums, I include return predictors that have been proposed in the literature as controls in the predictability analyses as follows: The first three predictors, term spread (TS), default spread (DEF), and trailing dividend-to-price ratio of the S&P 500 (D/P), are described earlier. There are an additional four predictors. Trailing earning-to-price ratio of the S&P 500 (E/P) is the 12-month moving sum of earnings on the S&P 500 index divided by the S&P 500 index. Monthly data are from Professor Robert Shiller’s website. The book-to-market ratio (b/m) is the ratio of book value to market value for the Dow Jones Industrial Average. For the months from March to December, this is computed by dividing the book value at the end of the previous year by the price at the end of the current month. For the months of January and February, this is computed by dividing the book value at the end of two years ago by the price at the end of the current month. Monthly data come from Professor Amit Goyal’s website. Long-term rate of return (LTR) is the return on long-term government bonds. Monthly data are from Professor Amit Goyal’s website. Stock variance (SVAR) is the sum of the squared daily returns on the S&P 500 index within a month. Monthly data are from Professor Amit Goyal’s website. Although many other predictors have been examined in the literature, I do not include them given the results in Welch & Goyal (2008) and Li et al. (2011), who fail to find their significant in-sample or out-of-sample predictability. Table 1.1 shows summary statistics of implied ex ante economic risk premiums and traditional return predictors. Columns AC(1) and AC(12) report the autocorrelations at the lags of 1 and 12. ICC-based economic risk premiums tend to be less persistent than traditional predictors, and this is particularly the case when compared with price-denominated predictors such as D/P, E/P, and b/m. Studies have assumed that 8 One exception is that liquidity factor shock LIQ directly comes from Professor Lubos Pastor’s website. The other exception is volatility factor VXO, which spans from 1986 to 2010, and whose shock is obtained by fitting the factor to a first order autoregressive (AR) model. Further, when fitting factors to VAR(1) I use a longer sample from July 1963 to December 2010, while I focus on a shorter time period from January 1981 to December 2010 when I construct and evaluate factor risk premiums. When I construct rolling conditional factor betas of base assets, I use the sample starting from January 1976 so that estimated conditional betas can start from January 1981. IMPLIED ECONOMIC RISK PREMIUMS 14 conditional risk premiums are highly persistent, based on the regression using traditional predictors. The lower persistence of ICCs reflects that ex ante risk premiums may be more volatile than we thought, and that I can be less concerned, in predictability tests, about the statistical issues—e.g., strong finite sample biases (Stambaugh (1986)), spurious regression, and data mining (Ferson et al. (2003))—that have seriously annoyed traditional predictors. Main Results Average Economic Risk Premiums This section studies average economic risk premiums. Conceptually, as ex ante measures, ICCs can mitigate excessive noise and finite sample biases induced by unexpected returns in ex post returns, and ICCs can fit theoretical predictions about ex ante factor risk premiums more closely, thus ICCs should have more power to uncover priced economic factors than ex post returns. Evidence supports this prediction. Table 1.2 reports average economic risk premiums measured with ex post returns (columns one and four) and ICCs (columns three and six). T-ratios corrected for heteroskedasticity and serial correlation using the Generalized Method of Moment (GMM) standard errors with the Newey-West corrections are reported. Panel A shows risk premiums of traded factors, for which both unit-beta and market-weight versions are reported. Ex post returns show that some or all of three traded factors are not significantly priced, depending on the version of mimicking portfolios used. For example, none of the three risk premiums achieves statistical significance in the unit-beta version. On the other hand, irrespective of the version of mimicking portfolios, the ICCs suggest lower levels of average risk premiums but always achieve strong statistical significance. For example, the market-weight version of the market risk premium is lower (5.52% per year) with the ICCs, and higher (6.36% per year) with the ex post returns, consistent with the finding in Claus & Thomas (2001). Size premium turns out to be considerably stronger with the ICCs. It is not statistically significant (a t-ratio of 0.94 or 0.7) with ex post returns, while its implied premium is both economically and statistically significant (a t-ratio of 4.5 or 4.7). The market-weight (unit-beta) version of the value risk premium indicates a statistically (in)significant value effect in ex post returns, while the ICCs always achieve high estimation precision with much stronger significance. Finally, the value premium measured with the ICCs (around 1.08% or 1.68% per year) is also lower than that with ex post returns (2.52% or 6.96% per year). 9 9 Market-weight version of results are consistent with previous studies (e.g., Hou et al. (2010) and Wu & Zhang (2011)) that examine asset pricing anomalies using ICCs. IMPLIED ECONOMIC RISK PREMIUMS 15 Panel B is for nontraded factors. In terms of magnitude, factor risk premiums measured with the ICCs tend to be smaller than those measured with ex post returns, and sometimes smaller by an order of magnitude. For example, absolute risk premiums range from around 2.4% per year to 14.4% per year when measured with the ex post returns, but range from around 0.12% per year to 3.6% per year when measured with the ICCs. Statistically, except for TS and RealRF, risk premiums of non-traded factors are insignificant when measured with ex post returns. But almost all of the implied factor risk premiums are significant statistically. For example, using ICCs, the market volatility (VXO) is significantly negatively priced, confirming previous studies such as Ang et al. (2006). Using ex post returns, the VXO risk premium is insignificant even though its sign is consistently negative. 10 For most economic factors, ICCs support significantly nonzero factor risk premiums which ex post returns fail to uncover. The reason is that ex post return based risk premiums are too volatile, since ex post returns contain excessively noisy unexpected returns which ex ante ICCs can avoid. Table 1.3 shows this, as it reports much higher standard deviations of ex post economic risk premiums than those of implied ones. For example, the inflation risk premium has a standard deviation of 105.76% per year with ex post returns, compared to 6.52% per year with ICCs. Excessive volatilities of ex post returns lead to large standard errors and poor estimation precisions, and hence the ICCs provide more power to uncover priced economic factors than ex post returns. Overall, the evidence implies that from an ex ante perspective many economic factors are actually priced, and the evidence resurrects the important role of many economic factors that various models predict and previous studies such as Shanken & Weinstein (2006) may have failed to uncover. Another interesting pattern from the analysis so far is that many economic factors are compensated at a lower level of average risk premiums from an ex ante ICC perspective than from an ex post perspective. I test and find that two explanations — flat term structure of equity risk premiums assumed in the computation of ICCs, and biases in analysts’ earnings forecasts — can be responsible. Term structure of equity risk premiums The first explanation is based on the term structure of equity risk premiums. Let me 10 Ang et al. (2006) find significant risk premium of VXO using ex post returns. They use more powerful base assets, VXO beta-sorted portfolios, to construct the mimicking portfolio of VXO. Instead, this study uses common base assets (25 Fama-French portfolios) that are not specifically designed to explore the VXO risk premium, and thus should have lower power than Ang et al. (2006) when both use ex post returns to measure VXO risk premium. This can explain the insignificant VXO risk premium I find with ex post returns. IMPLIED ECONOMIC RISK PREMIUMS 16 first introduce several notations. I express the stock price at time t as P t =E t D t+1 +P t+1 1+μ t =E t D t+1 1+μ t +E t D t+2 +P t+2 (1+μ t+1 )(1+μ t ) (1.11) = ∞ X k=0 E t D t+k+1 Q k s=0 (1+μ t+s ) =E t D t+1 1+μ t + ∞ X k=1 E t D t+k+1 Q k s=0 (1+μ t+s ) (1.12) = ∞ X k=0 E t [D t+k+1 ] (1+y t,k ) k+1 =E t D t+1 1+y t,0 + ∞ X k=1 E t [D t+k+1 ] (1+y t,k ) k+1 (1.13) where P t is price at time t, D t+1 is dividend paid during period t+1, μ t is the expected (net) return from period t to t+1 known at the beginning of the period, and the first and second equations derive by following or iterating the definition of the stock price. The third equation rewrites the price equation using y t,k which represents the one-period equity yield (or equity risk premiums if subtracting one-period yield of a risk-free asset) of the dividend strip with maturity k, and y t,k is known at the beginning of the period t+1. Equity yields are an analogue of bond yields in the fixed income market. The difference is that equity yields contain an additional component compensating investors for bearing the dividend strip risk. The ICCs assume a flat term structure of equity risk premiums/yields (i.e., y t,k 1 =y t,k 2 ∀k 1 ,k 2 ) and hence are approximately a weighted average of equity risk premiums/yields across short and long maturities. On the other hand, by comparing equations (1.12) and (1.13), expected returns (μ t ) embedded in one-period ex post returns may actually roughly equal the equity risk premium/yield at short maturity, i.e., μ t ≈y t,0 . If the actual term structure of equity risk premiums/yields is downward sloping as documented by van Binsbergen et al. (2012), the ICCs will be lower (higher) than equity risk premiums/yields at shorter (longer) maturities. Hence, the ICCs are higher than μ t and can achieve lower magnitudes of factor risk premiums than ex post returns. To test this explanation, I examine one resulting prediction based on an empirical measure of stocks’ durations. The prediction is, if the downward-sloping term structure is similar across all of the stocks, the differences between ex post and ICC-based risk premiums should be smaller for stocks with shorter durations, since shorter durations mean that those stocks’ dividends concentrate more on shorter maturities, and their ICCs will be calculated by assigning more weights to equity risk premiums/yields at shorter maturities in the averaging. IMPLIED ECONOMIC RISK PREMIUMS 17 Empirically, I measure the duration of a stock (Dur) at time t as follows: Dur t =− ∂lnP t ∂ln(1+q t ) = 1 P t [ T X k=1 k FE t+k (1−b t+k ) (1+q t ) k + ∞ X k=T+1 k FE t+T+1 (1+q t ) k ] = 1 P t [ T X k=1 k FE t+k (1−b t+k ) (1+q t ) k +FE t+T+1 q t (T +1)+1 q 2 t (1+q t ) T ], (1.14) where the first equality follows the definition of duration in fixed income literature, q t is the ICC at time t, and the second equality derives from applying directly the equation of the ICC definition. Every month I sort stocks into quintiles based on Dur t and form both equal-weight and value-weight portfolios. I report, in Table 1.4, resulting differences between the two versions of risk premiums of all quintiles as well as the spread between the extreme quintiles. The risk premium differences monotonically increase with quintile durations and the spread between extreme quintiles is statistically and economically significant, supporting the prediction. Biases In Analysts’ Earnings Forecasts Finally, it seems natural to consider biases in analysts’ earnings forecasts as one potential explanation. To test this explanation, I correct the biases using alternative unbiased model-based earnings forecasts and use the alternative forecasts to construct alternative mechanical-ICCs so as to reexamine average economic risk premiums (see the latter section of mechanical-ICCs for details). Columns two and five in Table 1.2 report the results. For 11 out of 15 cases, mechanical-ICCs report higher levels of factor risk premiums than analyst-ICCs. However, in 6 out of those 11 cases, mechanical-ICC based risk premiums are still substantially lower than ex post versions. Hence, biases in analysts’ earnings forecasts can help, but can not fully explain the lower levels of analyst-ICC based factor risk premiums. Predicting Ex Post Economic Risk Premiums As expected return estimates, ICCs are a natural tool to predict future ex post factor risk premiums and help revisit whether ex ante economic risk premiums are time-varying. Li et al. (2011) have shown that, using the market-weight version of the factor mimicking portfolio, the implied risk premium of the market factor can predict its future ex post risk premium. I extend their framework and study the predictability for risk premiums of other traded and nontraded economic factors that act as driving forces in various asset pricing models. Moreover, for traded factors, I examine their risk premiums based on not only the IMPLIED ECONOMIC RISK PREMIUMS 18 market-weight version of mimicking portfolios as in Li et al. (2011), but also the unit-beta version. I test the predictability of ICCs both in sample and out of sample. IS Analysis I first conduct the in-sample analysis. I use the multi-period forecasting regression in studies such as Fama & French (1989) and Li et al. (2011): K X k=1 r t+k K =a+b 0 X t + t+K , (1.15) where r t+k is the ex post factor risk premium at time t+k, X t is a vector of predictive variables, b is a vector of slope coefficients, t+K is the residual, and K is the prediction horizon. I report the asymptotically consistent t-statistics for the regression coefficients. Since multi-period forecasting regressions use overlapping observations, residuals are serially correlated. Hence I use the standard errors computed using GMM with the Newey-West correction for serial correlation and conditional heteroskedasticity (Hansen (1982) and Newey & West (1987)) and then compute the t-statistics. Further, return predictability literature has uncovered various finite-sample biases on the estimates and standard errors of the slope coefficients in the predictive regressions (Stambaugh (1986), Richardson & Stock (1989), and Richardson & Smith (1991)). To deal with all these biases simultaneously, I rely on bootstrapping simulation to make inferences by simulating the finite-sample distributions of the t-statistics of the regression slopes under the null hypothesis of no predictability. The bootstrapping procedures follow Li et al. (2011) and are detailed in the appendix. I conduct predictive regressions for six different horizons (1, 12, 24, 36, 48, and 60 months). However, since same data are used for all predictive horizons, the statistics of the regressions are correlated across horizons and hence we cannot infer overall predictability from any single regression (see, e.g., Boudoukh et al. (2008)). Instead, a test of joint predictability across all horizons is necessary. To handle this issue, I compute the sum of the squared slope coefficients across all horizons as the statistic to test the null hypothesis that the slopes at different horizons are jointly zero. I again rely on bootstrapping simulation to assess the significance of that statistic by simulating its finite sample distribution under the null of no predictability. Table 1.5 focuses on the three traded factors and reports the results of using implied factor risk premiums to predict future ex post risk premiums. Two panels correspond to the results from two versions of the factor mimicking portfolios. There are two column blocks in this table. The left block reports the case in which ICCs are included as the only IMPLIED ECONOMIC RISK PREMIUMS 19 regressor, while the right block reports the case in which other controlling predictors (DP, EP, bm, TS, DEF, ltr, and svar) are included as regressors as well. Column b is the slope coefficient for the ICCs. Column p−value reports the bootstrapped one-side (positive-side) p-values for the asymptotical t-statistics (column t(b)) of slope coefficients. I report positive-side p-values, since the slope coefficients should be positive in the predictive regressions given that the ICCs represent expected returns. Panel A in the table first verifies that, using the market-weight version of the factor mimicking portfolio, the implied market risk premium significantly predicts its future ex post one (with a p-value of 0.047 in the joint predictability test when there are no other controlling predictors), consistent with the finding in Li et al. (2011). Further, panel A shows that the ICCs also exhibit significant predictability for the size and value factors. For these two factors, the joint predictability test highly significantly rejects the null hypothesis of no predictability at the 1% level, when there are no other controlling predictors. The predictability of the ICCs continues to hold in the presence of controlling predictors, with the statistical significance reduced slightly. On the other hand, using the unit-beta version of the factor mimicking portfolios, panel B reveals weaker evidence for the predictability of the ICCs. The ICCs no longer predict the ex post market factor risk premium but continue to predict the ex post size and value premiums. More errors and noise introduced in beta estimations may result in weaker evidence. However, sustainedly strong predictability for ex post size and value premiums in both market-weight and unit-beta versions may assure us more that ex ante size and value premiums are time-variant. Further, in both panels, the predictability of ICCs is much more pronounced for the size and value factors than for the market factor. For example, using the market-weight version, p-values of the joint predictability test for the size and value factors are much smaller, by an order of magnitude, than for the market factor. This is consistent with the following explanation. Analysts, specializing in one or a few industries, are more informative about the relative performance of firms within an industry, such as the relative performance of firms with opposing sizes or book-to-market equity, than about the overall performance level of an industry. Hence, an aggregation of ICCs would lead to the observation that ICCs can predict spread based factors (the size and value factors) better than the level based factor (the market factor). Table 1.6 reports the predictability of ICCs for future ex post risk premiums of non-traded factors. When used alone as the predictor, ICCs can significantly predict risk premiums of DEF, INF, and RealRF. The joint predictability test highly significantly rejects the null hypothesis of no predictability at the 1% level for them. After I include controlling predictors (DP, TS, DEF, ltr, and svar), the predictability of ICCs still holds IMPLIED ECONOMIC RISK PREMIUMS 20 for DEF. More controls also cause ICCs to show marginally significant power to predict the risk premium of LIG (a p-value of around 0.066 for the joint predictability test). Across horizons, the predictability of ICCs not only is particularly significant in long horizons but it can also appear in a horizon as short as one month for factors such as the value factor, DEF, INF, and RealRF. This is interesting since typical findings in the predictability literature are about long horizons. On the other hand, it is perhaps not surprising since ICC-based predictors are less persistent, as shown in Table 1.1 and hence they have more power to track economic risk premiums in the higher frequency. Overall, IS analysis suggests that implied ex ante factor risk premiums can significantly predict future ex post risk premiums for many economic factors. If ICCs are estimates of ex ante expected returns, we should expect their slope coefficients in predictive regressions to be one, at least when no other predictors are included. However, those coefficients almost always appear to be above one when ICCs show the predictive power. There are two explanations, one more specific and one more general. First, as discussed earlier, the flat term structure of equity risk premiums/yields assumed in the computation of the ICCs suggests that ICCs may be regarded as a weighted average of equity risk premiums/yields across short and long maturities, and that ICCs should be lower than actual one-period expected returns of stocks embedded in ex post returns, if the actual term structure is downward-sloping. Hence, a slope above one can arise when using ICCs to predict future ex post risk premiums. Moreover, such deviations of ICCs from actual expected returns should make it harder to find the predictability of ICCs for ex post economic risk premiums. Therefore, the uncovered strong predictability of ICCs may be considered as conservative evidence of time-varying ex ante economic risk premiums, as reflected by the ICCs. Second, there can be a more general explanation, based on the log-linearization framework of Campbell & Shiller (1988) who express log stock price p t =log(P t ) as p t = k 1−ρ +(1−ρ) ∞ X j=0 ρ j E t (d t+1+j )− ∞ X j=0 ρ j E t (r t+1+j ) = k 1−ρ +(1−ρ) ∞ X j=0 ρ j E t (d t+1+j )− ∞ X j=0 ρ j E t (μ t+j ). r t+1 is the log ex post one-period stock return, μ t+j =E t+j (r t+1+j ) is the expected log one-period stock return conditional on information one-period aback, d t =log(D t ) is the log dividend at time t, ρ=1/(1+exp(d−p)), k =−log(ρ)−(1−ρ)log(1/ρ−1) andd−p is the average log dividend-price ratio. To compute the ICCs in this framework, we assume IMPLIED ECONOMIC RISK PREMIUMS 21 icc t =E t (μ t+j ) and have p t = k 1−ρ +(1−ρ) ∞ X j=0 ρ j E t (d t+1+j )−icc t ∞ X j=0 ρ j . Clearly the ICC inverted from the previous equation is a weighted average of E t (μ t+j ), i.e., icc t = 1 P ∞ j=0 ρ j ∞ X j=0 ρ j E t (μ t+j ). It seems reasonable to assume that μ t is a stationary process with an unconditional mean of μ. Then we can compute the covariance between E t [μ t+j ] and μ t as Cov(E t [μ t+j ],μ t )=E[(E t [μ t+j ]−μ)(μ t −μ)]=E[(μ t+j −μ)(μ t −μ)] =Cov(μ t+j ,μ t )=Cov(l 0,j +l 1,j μ t + t+j ,μ t )=l 1,j Var(μ t ) where μ t+j =l 0,j +l 1,j μ t + t+j is a projection of μ t+j on μ t so that Cov(μ t , t+j )=0 and |l 1,j |<1 given the stationarity of μ t . Then the covariance between icc t and μ t is Cov(icc t ,μ t )= 1 P ∞ j=0 ρ j ∞ X j=0 ρ j l 1,j Var(μ t )≤ 1 P ∞ j=0 ρ j ∞ X j=0 ρ j |l 1,j |Var(μ t )<Var(μ t ), meaning that a regression of icc t on μ t , icc t =l 0 +l 1 μ t +e t , has a slope 0<l 1 =Cov(icc t ,μ t )/Var(μ t )<1. Hence we could expect a slope above one when using icc t alone to predict ex post returns which embed expected returns μ t . OOS Analysis Recent studies emphasize out-of-sample (OOS) predictability when evaluating return predictability. Following Campbell & Thompson (2008), Welch & Goyal (2008), Rapach et al. (2010), and Li et al. (2011), who focus on the risk premium of the market factor, I assess whether, out of sample, ICCs predict future ex post risk premiums for a list of economic factors. OOS Analysis: Forecast Construction The framework for analyzing risk premium predictability is the following predictive regression model: r fac t+1 =a fac +b fac 0 x fac t + fac t+1 , (1.16) where r fac t+1 is the monthly ex post economic risk premium for factor fac, x fac t is the vector of monthly predictors for r fac t+1 , and fac t+1 is the error term. I compute OOS forecasts in a IMPLIED ECONOMIC RISK PREMIUMS 22 recursive way as in Welch & Goyal (2008). The whole sample with a length of T is divided into two periods, an estimation period which covers the first k periods and an OOS forecast period that covers the residual periods. That is, the OOS forecast starts from r fac k+1 until r fac T . To form a forecast of r fac t+1 with t≥k, I first use ordinary least square to estimate the equation (1.16) using periods from time 1 to time t and get the parameter estimatesb a fac t and b b fac t . Then I applyb a fac t and b b fac t to the vector of predictors at time t and obtain the OOS forecast of r fac t+1 as b r fac t+1 =b a fac t + b b fac 0 t x fac t . (1.17) In the end, I obtain a time series of OOS forecasts of economic risk premiums ({b r fac t } T t=k+1 ) based on the predictors{x fac t } T−1 t=k . I consider two models with two different choices of predictors: one using implied ex ante economic risk premiums as a single predictor, and the other one with no predictor, corresponding to b fac =0 in equation (1.16). To evaluate OOS predictability, I need to designate a benchmark forecasting model and construct the OOS forecasts r fac t of that model. In this section, I consider as the benchmark forecasting model the model with no predictor, as in Campbell & Thompson (2008) and Welch & Goyal (2008), which means a historical average of r fac t is used to produce OOS forecasts. OOS Analysis: Forecast Evaluation I follow the literature and use out-of-sample R 2 (R 2 oos ) to compare different predictive models. It is defined as R 2 oos =1− P T t=k+1 (r fac t −b r fac t ) 2 P T t=k+1 (r fac t −r fac t ) 2 . The R 2 oos statistic measures the reduction in the mean squared prediction error (MSFE) for the forecast from the alternative predictive model (b r fac t ) relative to the forecast from the benchmark or null predictive model (r fac t ). To statistically test whether the alternative model has a lower MSFE than the benchmark model, or equivalently the null of R 2 oos ≤0 against the alternative of R 2 oos >0, I implement the Clark & West (2007) MSFE-adjusted statistic. This is the adjusted version of the statistic in Diebold & Mariano (1995) and West (1996) that tests equal MSFE between competing forecasts. I adopt the Clark & West (2007) statistic because I am comparing nested models in the analysis, and the statistic in Diebold & Mariano (1995) and West (1996) has a non-standard normal distribution when comparing nested forecasts (Clark & McCracken (2001), McCracken (2007)). To obtain the Clark & West (2007) IMPLIED ECONOMIC RISK PREMIUMS 23 MSFE-adjusted statistic, I first compute CWstat t+1 =(r fac t+1 −r fac t+1 ) 2 −[(r fac t+1 −b r fac t+1 ) 2 −(r fac t+1 −b r fac t+1 ) 2 ], and then regress CWstat t+1 on a constant. Finally, I obtain the p-value of R 2 oos from the one-sided (positive-side) test of the t-statistic of the estimated constant. OOS Analysis: Forecasting Results Following Li et al. (2011), the estimation period ends at December, 1997. I.e., the estimation period is from January 1981 to December 1997, and the forecast period is from January 1998 to December 2010. This choice is motivated by the finding in Welch & Goyal (2008) that many traditional return predictors perform poorly after the late 1990s. Further, implied economic risk premiums can contain short-run cyclical noise, caused by short-run cyclical noise in corporate earnings, as is argued in Li et al. (2011), Campbell & Shiller (1988), and Campbell & Shiller (1998). Since my OOS test is conducted in the one-month horizon, the impact of the noise for the predictability of ICCs is severe. Similar to Li et al. (2011), Campbell & Shiller (1988), and Campbell & Shiller (1998), I use five-year moving averages of implied economic risk premiums as my actual out-of-sample forecasting variables. Table 1.7 reports the out-of-sample forecasting results. There are four column-blocks, each reporting R 2 oos first and then the p-value of the test comparing the two forecasting models. Different rows represent different economic factors. The first column-block tests the alternative model using implied ex ante economic risk premiums as a sole predictor against the null model, using historical averages as OOS forecasts. ICCs can significantly predict ex post risk premiums for many factors, such as D/P at the 10% level and the size factor (market-weight version), DEF, INF, and RealRF at the 5% level. For the market-weight version of the risk premium of the market factor, the predictability is significant only at the 10% level, weakly consistent with the finding in Li et al. (2011). Overall, the OOS analysis suggests that ICCs can significantly predict future ex post risk premiums for many economic factors. Takeaway If ICCs are reasonable estimates for expected returns, their strong predictability in both IS and OOS analyses reflects that ex ante economic risk premiums vary over time for many economic factors and that ICCs serve as a new and powerful predictor that has additional information to better track ex ante economic risk premiums. IMPLIED ECONOMIC RISK PREMIUMS 24 Several Issues Although a beta pricing interpretation can naturally explain findings uncovered by the ICCs, several issues may introduce errors into the ICCs as expected return estimates, or into the factor mimicking portfolio weights, and hence could suggest alternative explanations. First, analysts’ earnings forecasts have known biases, and may not represent actual cash flow forecasts that get incorporated in equilibrium stock pricing. Second, stock prices from which the ICCs are inverted can be contaminated with errors. Third, factor beta estimations can introduce errors or noise into weights of factor mimicking portfolios. This section addresses these issues. Finally, since the specification in the adopted ICC model makes assumptions in many aspects such as the speed of reversion of forecasts for earnings growth and plowback rate, this section also examines the sensitivity of the main findings to those aspects. Biases in Analysts’ Earnings Forecasts Previous studies (e.g., see Ramnath et al. (2008) for a review) find that analysts’ forecasts can be biased for cognitive or incentive reasons. Hence, using analysts’ forecasts may result in biased expected return estimates and may affect the inferences. To address this concern, I employ alternative earnings forecasts from a statistical model using only public information, and plug them into the same ICC machinery (equation (1.1)). The resulting ICCs are called mechanical-ICCs. In this subsection, I use mechanical-ICCs to measure ex ante economic risk premiums and repeat the main analyses. Earnings Forecasts Using a Pooled Cross-sectional Model and Mechanical-ICCs I adopt the pooled cross-sectional model in Hou et al. (2010) to forecast earnings of individual firms. Hou et al. (2010) show that their model-based earnings forecasts are better than analysts’ forecasts in terms of coverage, forecast bias, and earnings response coefficient. Also, ICCs derived from their model-based earnings forecasts exhibit greater reliability than those derived from analysts’ earnings forecasts, in terms of the cross-sectional correlation with subsequent returns, after controlling for the proxies for cash flow news and discount rate news. Similar earning forecast models are employed in studies such as Fama & French (2006) and Wu & Zhang (2011). Specifically, for every month between 1970 and 2010, I estimate the following pooled cross-sectional regression using the previous ten years of annual accounting data with an IMPLIED ECONOMIC RISK PREMIUMS 25 ending date at least three months prior to that month: E j,t+τ =β 0 +β 1 EV j,t +β 2 TA j,t +β 3 DIV j,t +β 4 DD j,t +β 5 E j,t +β 6 NEGE j,t +β 7 ACC j,t + j,t+τ , (1.18) where E j,t+τ (τ =1,2,3) denotes the earnings before extraordinary items of firm j in year t+τ, and all explanatory variables are measured at the end of year t. EV j,t is the enterprise value of the firm (defined as the total asset plus the market value of equity minus the book value of equity), TA j,t is the total asset, DIV j,t is the dividend payment, DD j,t is a dummy variable that equals 0 (1) for firms that (do not) pay dividends, NEGE j,t is a dummy variable that equals 1 for firms with negative earnings (0 otherwise), and ACC j,t is total accruals. Total accruals are computed as the change in current assets (Compustat item ACT) plus the change in debt in current liabilities (Compustat item DLC) minus the change in cash and short-term investments (Compustat item CHE) and minus the change in current liabilities (Compustat item LCT). To mitigate the effects of extreme observations, I winsorize each variable annually at the 0.5 and 99.5 percentiles. The requirement of a lag of three months on the data ending date for the previous ten years of accounting data ensures that only public information available as of every month is used to forecast the future earnings. The average monthly coefficients from estimating equation (1.18) for τ =1,2,3 in my sample are reported in Table 1.8. They are similar to the results in Hou et al. (2010). Every month I compute the model-based earnings forecasts for subsequent three future years by applying historically estimated coefficients from equation (1.18) to the most recent set of publicly available, non-winsorized, firm characteristics. For this step, again, to ensure only public information available as of every month is used, I use the data with the fiscal year ending within the previous one whole year and that is at least three months prior to the month of forecasts. After constructing the model-based earning forecasts for the subsequent three future years (FE t+1 , FE t+3 , and FE t+3 ), I calculate the long-term growth rates for individual firms as Ltg =(FE t+3 /FE t+2 +FE t+2 /FE t+1 )/2−1. Finally, following the same procedures as constructing analyst-ICCs, I obtain mechanical-ICCs of individual firms. Results Columns two and five in Table 1.2 report the results using mechanical-ICCs to measure average economic risk premiums. Similar to the case using analyst-ICCs, average economic risk premiums measured with mechanical-ICCs tend to be more statistically significant than those measured with ex post returns. This finding is consistent with the conclusions IMPLIED ECONOMIC RISK PREMIUMS 26 in the main analyses that using ex ante measures has more power to uncover priced economic factors than using ex post returns, and that, from an ex ante perspective, many economic factors are actually priced and hence should play more important roles in explaining the stock market than what we knew before. Tables 1.9 and 1.10 report the IS predictive analysis of mechanical-ICCs. Mechanical-ICCs exhibit significant predictability for the ex post risk premiums of DEF and RealRF when there are no other controlling predictors (see left blocks of the tables). The predictability of mechanical-ICCs not only is significant in long horizons but can also appear in a horizon as short as one month. However, as reflected in the right blocks of the tables, the predictability of mechanical-ICCs for those two factors is subsumed when I add controlling predictors. The second column-block in Table 1.7 reports the OOS predictive analysis of mechanical-ICCs. It tests the alternative model using mechanical-ICCs as a sole predictor against the null model using historical averages as OOS forecasts. I find that mechanical-ICCs can significantly predict ex post risk premiums of some factors such as the market factor (market-weight version), DEF, INF, and RealRF at the 5% level. If mechanical-ICCs are alternative reasonable estimates for expected returns, the predictability evidence also suggests that ex ante economic risk premiums vary over time for some factors; although the evidence is less pronounced than in the main analyses using analyst-ICCs. Overall, the results of mechanical-ICCs reach weaker statistical significance than those of analyst-ICCs. This is expected since the construction of mechanical-ICCs involves far more estimations from the step of forecasting earnings and hence injects more noise into mechanical-ICCs. In addition, financial analysts may also embed additional information in their earnings forecasts, above and beyond model-based earnings forecasts, that helps better capture ex ante economic risk premiums and leads to better empirical performance. However, general conclusions based on mechanical-ICCs are the same as those in the main analyses. Errors In Prices Stock prices can be contaminated with errors, introducing errors in ICCs as expected return estimates. Hence errors in prices may suggest alternative interpretations for uncovered empirical results. Those errors could arise for various reasons, such as psychological biases of investors when assessing fundamentals or trading assets (Daniel et al. (1998), Barberis et al. (1998), Shefrin & Statman (1985), and Frazzini (2006)), slow information transmission in capital markets (Hong & Stein (1999)), noise trader (De Long et al. (1990)), general sentiment (Baker & Wurgler (2006)), or market microstructure (e.g., IMPLIED ECONOMIC RISK PREMIUMS 27 bid-ask bounce and nonsynchronous trading). However, typical errors could be diversified away and not affect my empirical results, since economic risk premiums are macro-level variables and rely on diversified factor mimicking portfolios, unless errors are correlated with factor betas of stocks. There are two potential types of errors in prices that are correlated with factor betas of stocks. In a single-factor setting, Hong & Sraer (2012) argue that, due to the short-sell constraints, only optimistic opinions in investors’ aggregate disagreements about the common macro factors in cash flows get impounded into pricing, leading to overpricing of those common factors. High market beta stocks can be overpriced since they are more sensitive to the overpriced common factors. Extending the same argument to a multi-factor setting, high factor beta stocks also can be overpriced. 11 On the other hand, as is argued in Shen & Yu (2012), aggregate investor sentiment could cause overpriced high factor beta stocks by a similar mechanism. Aggregate investor sentiment that drives market-wide optimism or pessimism can cause overpricing and underpricing of common macro factors in cash flow. Due to the short-sale constraints, we would see overpricing rather than underpricing of common factors and hence overpriced high factor beta stocks, given their large sensitivity to common factors. Next I discuss the implications of errors in prices for my empirical results, and particularly focus on those two types of errors. Average Economic Risk Premiums Two types of errors lead to overpriced high factor beta stocks and hence overpriced factor mimicking portfolios, since mimicking portfolios are long high factor beta stocks and short low factor beta stocks. Overpriced mimicking portfolios will certainly lead to understated average risk premiums measured with ex post returns. However, for those measured with ICCs, such an understatement may not always arise. If pricing errors come only from irrational forecasts of stock cash flows due to aggregate investors’ disagreement or sentiment, and discount rates used in the equilibrium are still rational, then correct rational discount rates can still be recovered as ICCs from the present-value model, as long as we feed that model with those irrational cash flow forecasts and resulting irrational prices in equilibrium. In this case, ICC-based average economic risk premiums are correct. On the other hand, if pricing errors come partially or fully from irrational discount rates investors use to price stocks due to investors’ disagreement or sentiment (e.g., "glamour" stocks favored by investors may get discounted at a less rate than a rational one), then 11 Hong & Sraer (2012) explain a flatter security market line in the data than what CAPM predicts. For rational explanations, Black (1972) develops a CAPM with a borrowing constraint and Frazzini & Pedersen (2013) extend his insight and develop a model where the interaction between agents with a borrowing constraint or a margin constraint generates a flatter security market line in which high market beta stocks have lower expected returns than what CAPM predicts. IMPLIED ECONOMIC RISK PREMIUMS 28 ICCs will be different from rational discount rates, and overpriced mimicking portfolios should lead to understated ICC-based average risk premiums. Further, if those two types of mispricing affect average factor risk premiums measured by both ex post and ICC measures, ex post versions should incur bigger impacts for the following reason: Ex post returns (R t+1 ) are not only a sum of expected returns (E equilibrium t [R t+1 ]) and unexpected returns ( equilibrium t+1 ) in the (rational or irrational) equilibrium, but they are also a sum of rationally expected returns (E rationalExp t [R t+1 ]) and rationally unexpected returns ( rationalExp t+1 ) given information at time t, i.e., R t+1 =E equilibrium t [R t+1 ]+ equilibrium t+1 =E rationalExp t [R t+1 ]+ rationalExp t+1 . If the equilibrium is rational, E rationalExp t [R t+1 ]=E equilibrium t [R t+1 ]; if the equilibrium is irrational, the equilibrium unexpected returns can still be predicted based on rational expectation using information at time t (i.e., E rationalExp t [ equilibrium t+1 ]6=0). As a result, we have the relation E rationalExp t [R t+1 ]=E equilibrium t [R t+1 ]+E rationalExp t [ equilibrium t+1 ]. Overpriced factor mimicking portfolios mean (1) their equilibrium expected returns (E equilibrium t [R t+1 ]) could be lower than ones in a rational equilibrium and (2) rational expectations of their equilibrium unexpected returns are negative (E rationalExp t [ equilibrium t+1 ]<0). Since ICCs will be affected by only issue (1) while ex post returns are affected by both issues (1) and (2), ICC-based average factor risk premiums should be affected less by pricing errors. 12 Overall, errors caused by aggregate investors’ disagreement or sentiment imply that ex post return-based and ICC-based average economic risk premiums uncovered in the paper could both understate true ones, reinforcing the importance of economic factors for driving asset markets. Further, the ex post return-based version should understate true average risk premiums more, supporting the better properties of the ICC-based version. Predictability of ICCs for Ex Post Economic Risk Premiums Since errors in stock prices will introduce measurement errors not only in ICCs but also in ex post risk premiums that ICCs predict, common measurement errors could result in spurious predictability, since the same stock prices are employed in both sides of the predictive regressions, implying an alternative mispricing-based explanation for ICCs’ 12 AnotherinformalargumentthatdrawsthesameconclusionistodefineICC t =e t /p t andR t+1 =p t+1 /p t for simplicity where e t and p t are earnings forecast and price of stock. Let Δ t be the pricing error and p ∗ t be the correct price so that p t = p ∗ t + Δ t . Assuming that e t is a rational forecast, uncorrelated with Δ t , and that p t+1 =p ∗ t+1 which means the stock price gets corrected at time t + 1, impacts of the pricing error at time t on ex post return and ICC are ∂Rt+1 ∂Δt = −p ∗ t+1 (p ∗ t +Δt) 2 and ∂ICCt ∂Δt = −et (p ∗ t +Δt) 2 . Since it is reasonable to think e t < p∗ t+1 on average, the pricing error may impact more the ex post version of average factor risk premiums. IMPLIED ECONOMIC RISK PREMIUMS 29 predictability. To discuss this explanation, the persistence of mispricing is important. See the following predictive regression, R t+τ 1 ,t+τ 2 = P t+τ 2 P t+τ 1 =a+b∗ICC(P t ,.)+e t+τ 2 , where ICC(P t ,.) means that ICC at timet is a function of stock priceP t and other variables, and P t contains a mispricing component t . The spurious predictability induced by the mispricing component t hence depends on the autocorrelation of between t and t+τ 2 , as well as betweent andt+τ 1 . If errors in prices are transient and revert to mean zero quickly, then they can show predictability for ex post risk premiums only in the very near future. If errors are persistent, spurious predictability for the more distant future is possible. Some mispricing, such as that due to market microstructure, is transient and will get corrected within a day or a week. For other types of mispricing such as those due to irrationality of investors, it is impossible to evaluate their time-series properties without first laying out correct prices from a rational equilibrium. However, we may choose to infer potential autocorrelation of mispricing based on previous papers documenting the time series predictability that has been argued with mispricing interpretations. 13 At the market or portfolio level, Poterba & Summers (1988), Fama & French (1988), Lo & MacKinlay (1988), Cutler et al. (1991) and Moskowitz et al. (2012) find negative autocorrelation in the long horizons of 3−5 years, or positive autocorrelation at the short period of less than one year for asset returns. Assets include US and global equities, housing, collectibles, and futures on various asset classes. Those findings suggest at least two types of mispricing components in stock prices which either take a long swing to dissipate or get corrected pretty soon. Quantitatively, at an annual frequency, Warusawitharan and Whited (2012) use a structural model and estimate a serial correlation of 0.4−0.7 for the stock misevaluation component, meaning that it takes about 3 quarters to 2 years for mispricing to dissipate by half. 14 For the two types of mispricing that are particularly of concern for this study and are induced by aggregate investors’ disagreement or sentiment, if aggregate disagreement or sentiment are time-varying, driving time-varying pricing errors, we could expect spurious predictability when using ICCs as long as the resulting pricing errors are autocorrelated to a sizeable degree. Since aggregate disagreement or sentiment are the drivers, the autocorrelations of resulting errors could be approximately measured by those of drivers, 13 There is also a large literature of cross-sectional return predictability that is arguably a reflection of mispricing. However, those studies such as momentum (Jegadeesh & Titman (1993)), long-term reversal (Bondt & Thaler (1985), Bondt & Thaler (1987)), or post-event return drifts (e.g., Bernard & Thomas (1989)), if interpreted as mispricing, do not help my issue much since those studies focus on how one set of firms outperform their peers on average over the next period, rather than on how the outperformance of one set of firms relative to their peers varies over the next few periods in the time series. 14 Let ρ be the autocorrelation of mispricing and it takes n years for mispricing to dissipate by half, i.e., ρ n = 1/2. Then ρ = 0.4− 0.7 means n = 0.75− 2 years. IMPLIED ECONOMIC RISK PREMIUMS 30 which are 0.96−0.98 at a monthly frequency or imply that 17−34 months are necessary for mispricing to dissipate by half. 15 In my view, there is no way to totally rule out the mispricing explanation for the predictability of ICCs, but I conduct several analyses supporting the interpretation that time-varying ex ante economic risk premiums are at least one major reason for the predictive power of ICCs. Firstly, I introduce a one-month lag between ICC predictors and future ex post economic risk premiums, and conduct predictive tests again. Such a one-month lag avoids the case of the same price being used in both sides of predictive regressions. The one month lag length is enough to avoid spurious predictability due to short-lived mispricing such as bid-ask bounce, nonsynchrous errors, or short-term underreaction errors. For brevity, I report the results without tabulating them. 16 I find no qualitative change and very small quantitative changes in the results for both IS and OOS predictability of ICCs. This finding demonstrates that short-lived mispricing cannot account for the predictability of ICCs. However, two types of mispricing, induced by aggregate investors’ disagreement or sentiment, could still cause spurious predictability since, as reported, they are more persistent with an autocorrelation of 0.96−0.98 at a monthly frequency. Since those time-varying pricing errors are essentially functions of time-varying aggregate disagreement or sentiment, the autocorrelation of pricing errors (or equivalently spurious predictability) essentially reflects using aggregate disagreement (sentiment) today to predict aggregate disagreement (sentiment) tomorrow. Hence in the second analysis, I include aggregate disagreement or sentiment as regressors in the predictive regressions to control for spurious predictability. I continue to find predictability of ICCs in the presence of them. 17 Thus, those two types of mispricing would not capture the predictability of ICCs. Thirdly, I test and show the sustainedly strong predictive power of analyst-ICCs, when they are running a predictability horse race with mechanical-ICCs. Since mechanical-ICCs are backed out from stock prices using rational and unbiased model-based earnings forecasts, the predictability of any price errors is likely inherited and represented better by mechanical-ICCs than by analyst-ICCs. Hence, any predictive power of analyst-ICCs in the horse race may be mainly driven by time-varying ex ante economic risk premiums. Further, since the only difference between the two ICCs is the choice of earnings forecasts, the superiority of one version of ICCs in the horse race must stem from the superiority of the 15 The measure of monthly aggregate investors’ disagreement follows Hong & Sraer (2012) and the measure of market sentiment follows Baker & Wurgler (2006). 16 Tables are available upon request. 17 For brevity, I again report results without tabulating them. Tables are available upon request. IMPLIED ECONOMIC RISK PREMIUMS 31 earnings forecasts chosen by that version of the ICCs. Hence the horse race can shed light on the relative superiority of two versions of earnings forecasts in a context of time-series return prediction. Tables 1.11 and 1.12 report the IS horse race. For all factors, the predictability of analyst-ICCs totally dominates and subsumes that of mechanical-ICCs. Mechanical-ICCs totally lose predictability, while the predictability of analyst-ICCs remains very significant for the size and value factors (market-weight version), DEF, INF, and RealRF (with p-values of 0.018, 0.005, 0.003, 0.015, and 0.006 in the joint predictability test) but becomes insignificant for the market factor (with a relatively low p-value of 0.134 in the joint predictability test) at the 10% level. In addition, in the presence of mechanical-ICCs, analyst-ICCs become significant for LIG (with a p-value of 0.003 in the joint predictability test). Further, the predictability of analyst-ICCs for different horizons holds as before. Analyst-ICCs perform significantly well for longer horizons for all three traded factors (particularly so for the market-weight version), and for a short, one-month horizon for the value factor (both market-weight and unit-beta versions). On the other hand, significant predictability of analyst-ICCs is also found across all the horizons for nontraded factors except LIG, for which analyst-ICCs mainly track the factor risk premium over short horizons ranging from one month to two years. The last two column-blocks in Table 1.7 report the OOS horse race. In the third (fourth) column-block, the alternative predictive model uses analyst-ICCs (mechanical-ICCs) as a sole predictor, while the null model uses factor mechanical-ICCs (analyst-ICCs) as a sole predictor. The results reveal that while analyst-ICCs beat mechanical-ICCs for some factors (the size factor, consumption growth, and the dividend-price ratio of the S&P 500 index), they lose for the default spread. Overall, the horse race (especially the IS part) suggests the sustainedly strong forecasting power of analyst-ICCs in the presence of mechanical ICCs, supporting the explanation of time-varying ex ante economic risk premiums for the strong predictability of analyst-ICCs in the main analyses. The evidence also implies that analysts’ earnings forecasts contain useful information—beyond what is in model-based earnings forecasts—that helps better predict economic risk premiums. Fourthly, if ICCs reflect time-varying ex ante economic risk premiums, the implied economic risk premiums should be correlated contemporaneously with theoretical drivers of time-varying risk premiums in recent asset pricing models — the habit (or surplus consumption ratio) in Campbell & Cochrane (1999), the consumption volatility in Bansal & Yaron (2004), and the model uncertainty of economy in Drechsler (2011). I test such correlations. I construct a surplus consumption ratio using quarterly nondurable and service IMPLIED ECONOMIC RISK PREMIUMS 32 consumption growth and the parameters in Campbell & Cochrane (1999). I fit an AR(1)-GARCH(1,1) model to quarterly nondurable and service consumption growth to construct consumption volatility, as in Bansal et al. (2005). Finally, I take the cross-sectional dispersion of the quarterly forecasts of the next quarter Real GDP, from the Philadelphia Fed’s Survey of Professional Forecasters (SPF), as the proxy for model uncertainty of economy, similar to Drechsler (2011). I regress contemporaneously implied economic risk premiums on one or all of those drivers and compute t-statistics of regression coefficients using GMM standard errors with the Newey-West correction. I report the results in Tables 1.13 and 1.14. I focus on the three traded factors and the nontraded factors (DEF, INF, LIG, and RealRF), of which ex post risk premiums can be predicted by the ICCs as shown in the main analyses. I find that implied economic risk premiums correlate significantly contemporaneously with at least one of those drivers. For example, the implied risk premium for the default spread is significantly negatively correlated with consumption volatility or the model uncertainty of economy. The results are similar when all of the drivers are included together as regressors. Overall, all the findings are consistent with time-varying ex ante economic risk premiums as at least one major reason for the forecasting ability of ICCs. Errors in Estimates of Factor Betas Since factor betas of base assets, which determine factor mimicking portfolio weights, are not directly observable but require estimation, associated sampling errors could affect measured factor risk premiums. Such errors should impact both ex post and implied factor risk premiums to a similar extent, since to construct them, the same betas are used and the only difference between the two versions of factor risk premiums is whether ex post returns or ICCs of base assets are employed. Therefore, (1) although errors in betas will cause attenuation biases in average factor risk premiums as well as understated t-stats, such impacts apply similarly to both versions of ex post returns and ICCs, and we would still conclude that ICCs have more power to uncover priced economic factors; (2) errors in betas imply that both ex post and implied factor risk premiums are measured with less precision, and hence there are more difficulties finding predictability for ex post factor risk premiums using implied ones. Therefore, the strong predictability of ICCs reported in the paper may serve as conservative evidence of time-varying ex ante economic risk premiums reflected by ICCs. IMPLIED ECONOMIC RISK PREMIUMS 33 Robustness: Terminal Period, E/P, or Forecasted E/P I examine the sensitivity of the main findings to several aspects of the specification of the ICC model adopted. First, I change the number of periods to reach the terminal period (T) in the ICC model. The choice of T assumes the speed for reversion of forecasts of earnings growth and plowback rate towards their steady state counterparts. I change T from T =15 to T =10 and T =20 years and construct new ICCs. Then I repeat the main analyses for those new ICCs. For brevity, I do not tabulate results. 18 I find similar results for the average implied ex ante factor risk premiums as well as the (IS or OOS) predictability of ICCs. Second, at a monthly frequency I construct firm-level earnings-price ratios and earnings forecast-price ratios where the earnings forecast is the analysts’ earnings forecast for the subsequent first year. I use these two ratios as alternative ICCs and repeat the main analyses, since these two ratios may be motivated as ICCs by a present-value model assuming no cash flow growth. However, in a more general present-value model with time-varying expectations of cash flow growth, these two ratios will mix information about both cash flow expectations and discount rates. Hence, they may have less power to uncover ex ante factor risk premiums than the ICCs used in the main analyses. Again, for brevity, I do not tabulate my results. 19 I find that the two price ratios deliver results similar to the main analyses with few exceptions. For example, one exception is that average implied risk premiums for the market volatility and market liquidity factors (VXO and LIQ) are no longer statistically significant when measured by those two price ratios, likely reflecting their diminished power to represent ex ante risk premiums, as argued. Multiple Comparisons This section interprets the empirical results in view of the total number of tests conducted. Such an examination, using multiple comparisons, is important. For the two main research questions or equivalently the three main analyses of this study, my approach is to evaluate the fractions of the tests that reject the null hypothesis (i.e., zero ICC-based average economic risk premiums or no IS or OOS predictability of ICCs) when conducting each analysis. In each of the three main analyses, I treat each test outcome y i , a dummy variable indicating the significant estimate at the 5% level, as one observation. Then the probability of being significant in each test is 5%. Let the total number of tests be N and the correlation between the tests be ρ. The total number of significant estimates P y i follows a 18 Tables are available upon request. 19 Tables are available upon request. IMPLIED ECONOMIC RISK PREMIUMS 34 binomial distribution with a mean of 0.05N and a variance of N(0.05)(0.95)[1+(N−1)ρ]. A t-stat for P y i is then ( P y i −0.05N)/{N(0.05)(0.95)[1+(N−1)ρ]} 0.5 . Test correlation ρ can greatly affect this statistic and lead to a smaller t-stat if it is larger. For this discussion, I try two choices ρ=0.02 and ρ=0.9, since it is not clear how correlated the tests on different economic factors are. On one hand, those factors are motivated by different asset pricing models or empirical facts and hence their tests may not be significantly correlated. On the other hand, different theories may simply capture the same nature from different perspectives and thus can cause highly correlated tests. For the analysis of ICC-based average economic risk premiums, there are 60 tests and 41 significant estimates under the 5% significance level, leading to a binomial t-stat of 15.25 if ρ=0.02 or 3.06 if ρ=0.9. Hence a multiple comparisons perspective suggests significantly priced economic factors from an ex ante ICC perspective, irrespective of the test correlation ρ. Things are more blurred for the IS and OOS predictability analyses. For the IS predictive analysis, there are 1092 tests and 366 significant estimates under the 5% significance level, leading to a binomial t-stat of 9.05 if ρ=0.02 or 1.38 if ρ=0.9. For the OOS predictive analysis, there are 72 tests and 25 significant estimates under the 5% significance level, leading to a binomial t-stat of 7.44 ifρ=0.02 or 1.44 ifρ=0.9. Hence, a multiple comparisons perspective suggests significant IS and OOS predictability of ICCs and a significant variation of ex ante economic risk premiums if the test correlation is low, but the opposite if the correlation is very high. Overall, the multiple comparisons evidence weakly supports time-varying ex ante economic risk premiums. Conclusions and Implications The literature on economic risk premiums has largely been based on ex post returns. My empirical approach is different. I construct and assess implied ex ante risk premiums for a list of economic factors, which are driving forces in various asset pricing models, using direct expected returns estimates—i.e., the implied costs of capital (ICCs). Average risk premiums for most economic factors measured by ICCs are significantly nonzero while those measured by ex post returns are not, since ex post returns are too volatile. The evidence implies that ICCs have more power to uncover priced economic factors than ex post returns, and that many economic factors are actually priced from an ex ante perspective. This resurrects the important role of many economic factors that various models predict and previous studies may have failed to uncover. Second, implied ex ante economic risk premiums significantly predict future ex post ones for most economic factors (e.g., the value and size factors, default spread, inflation, the growth rate of labor income, IMPLIED ECONOMIC RISK PREMIUMS 35 and one-month T-bill real return), both in sample and out of sample, and both with and without the presence of many traditional return predictors. If ICCs are reasonable estimates for expected returns, this finding implies that ex ante factor risk premiums vary over time for many economic factors, and that ICCs are a new and powerful predictor that has additional information to better track ex ante economic risk premiums. Further analyses suggest that biases in analysts’ earnings forecasts or errors in stock prices do not fully explain the evidence uncovered by ICCs, supporting the rational interpretation as at least one major reason for the findings. Finally, taking into account the number of total tests conducted, a multiple comparisons analysis strongly supports priced economic factors from an ex ante ICC perspective and weakly supports time-varying ex ante economic factor risk premiums. The findings in this study have implications. Practitioners can exploit ICCs, to better time or hedge underlying economic forces in asset markets. Policymakers can exploit ICCs to better monitor the economic risks that agents most want to avoid, and they can intervene in time when faced with possible severe disasters. Finally, the patterns of implied ex ante economic risk premiums may represent new empirical regularities, and it will be valuable for academics to consider them when designing asset pricing models or conducting empirical asset pricing tests. For example, average implied economic risk premiums can serve as alternative magnitudes for theoretical researchers to calibrate their asset pricing models, and may lead to a new set of model parameters that can be more consistent with microeconomic evidence. On the other hand, empirical researchers may consider using ex ante expected returns estimates such as ICCs when examining economic factors of their interests, in order to more powerfully uncover results that may be more intuitively consistent with their economic theories. Also, the strong time-series predictability of ICCs raises the possibility that researchers may employ implied ex ante economic risk premiums as powerful conditioning variables when conducting conditional empirical tests. Appendix: The Bootstrapping Procedure This section describes the bootstrapping procedure for the regressions that use both mechanical-ICC based and analyst-ICC based factor risk premiums to predict future ex post ones. The same bootstrapping method applies to other predictive regressions. This procedure follows Li et al. (2011). I pool ex post factor risk premium r t , mechanical-ICC based factor risk premium IRP mechanical t , and analyst-ICC based factor risk premium IRP analyst t in the vector L t =(r t ,IRP mechanical t ,IRP analyst t ) 0 . I then fit a first order vector autoregressive model IMPLIED ECONOMIC RISK PREMIUMS 36 (VAR(1)) to L t as L t+1 =A 0 +A 1 L t +η t+1 , (1.19) where A 0 is a vector, A 1 is a matrix of VAR coefficients, and η t+1 is a vector of VAR residuals. I impose the null hypothesis of no predictability on r t in the VAR by setting the slope coefficients in the equation of r t+1 to zero, and by setting the intercept in the equation of r t to be its unconditional mean. This fitted VAR which exhibits no factor risk premium predictability plays the role of the data generating process for the variable vector (r t ,IRP mechanical t ,IRP analyst t ) 0 in the simulation. Every time I use the fitted VAR to simulate an artificial sample with the same size as that of the actual sample, I first draw the initial observation of L t from a multivariate normal distribution with mean and variance-covariance matrix equal to their historical estimates. Then I feed the VAR with the shocks that are obtained by sampling, without replacement, the estimated actual VAR residuals η t+1 and generate the subsequent observations. I simulate the artificial sample 1,000 times and construct the regression statistics in each sample so as to obtain their empirical finite sample distributions. IMPLIED ECONOMIC RISK PREMIUMS 37 Table 1.1 Summary Statistics of Implied Economic Risk Premiums and Other Predictors Panel A is for implied economic risk premiums, while panel B is for other return predictors. For traded factors, two versions of their implied risk premiums, based on different mimicking portfolios, are reported. The unit-beta version relies on unit-beta factor mimicking portfolios while the market-weight version uses alternative mimicking portfolios which are determined by market composition weights of individual stocks constituting each traded factor. AC(1) andAC(12) are autocorrelations at lags of 1 and 12. Sample spans from 1981:01 to 2010:12. Panel A: ICCs Mean StdDev Max Min AC(1) AC(12) Market-weight version Mkt 0.005 0.002 0.011 0.001 0.94 0.54 Size 0.002 0.002 0.007 -0.005 0.95 0.69 Value 0.001 0.002 0.012 -0.001 0.93 0.29 Unit-beta version Mkt -0.001 0.003 0.006 -0.012 0.90 0.25 Size 0.001 0.001 0.004 -0.003 0.95 0.65 Value 0.001 0.001 0.006 -0.001 0.94 0.61 TS -0.020 0.160 0.382 -0.627 0.94 0.61 DEF -0.065 0.103 0.137 -0.530 0.93 0.45 INF 0.042 0.123 0.543 -0.148 0.94 0.57 NSCG 0.003 0.150 0.229 -0.710 0.95 0.52 LIG -0.037 0.115 0.198 -0.417 0.91 0.47 DP 0.013 0.120 0.587 -0.420 0.92 0.13 RealRF -0.052 0.110 0.167 -0.505 0.93 0.56 VXO -0.031 0.056 0.188 -0.208 0.84 0.10 LIQ 0.04 0.09 0.28 -0.21 0.93 0.29 Panel B: Other predictors Mean StdDev Max Min AC(1) AC(12) DP 0.027 0.012 0.064 0.011 0.99 0.83 EP 0.057 0.025 0.133 0.008 0.98 0.65 bm 0.399 0.238 1.207 0.121 0.99 0.80 TS 0.030 0.014 0.059 -0.022 0.95 0.38 DEF 0.011 0.005 0.034 0.005 0.96 0.45 ltr 0.009 0.032 0.144 -0.112 0.01 -0.04 svar 0.003 0.005 0.056 2.E-04 0.54 0.05 IMPLIED ECONOMIC RISK PREMIUMS 38 Table 1.2 Average Economic Risk Premiums This table reports average factor risk premiums, measured by ex post returns, ICCs, and alternativemechanical-ICCsthatusemodel-basedearningsforecasts. Averageriskpremiums of traded factors are reported in panel A for two versions: unit-beta and market-weight. The unit-beta version relies on unit-beta factor mimicking portfolios while the market-weight version uses alternative mimicking portfolios which are determined by market composition weights of individual stocks constituting each traded factor. For average risk premiums of non-tradedfactors, resultsreportedareforshocksofnon-tradedfactorsthatarestandardized to have the same standard deviations as that of the market factor. All the estimates are in annual percentage terms. GMM with the Newey-West correction is used to compute t-statistics. Newey-West lags are 1 when I measure with ex post returns and 12 when I measure with ICCs. Sample spans from 1981:01 to 2010:12 except for VXO which starts from 1989. Ex post return Mechanical ICC ICC Ex post return Mechanical ICC ICC Panel A: traded factors Unit-beta version Market-weight version Mkt -1.56 -3.00 -1.08 6.36 2.64 5.52 T -0.42 -4.96 -2.08 2.08 7.12 15.01 Size 1.92 1.20 0.96 2.28 3.60 1.92 T 0.94 3.46 4.46 0.70 5.40 4.74 Value 2.52 3.60 1.08 6.96 4.44 1.68 T 1.16 8.5 3.8 2.30 8.20 5.41 Panel B: nontraded factors TS 12.12 -2.40 -1.08 T 2.21 -0.95 -0.72 DEF -4.80 -7.20 -3.60 T -0.86 -2.26 -3.85 INF 9.36 2.76 2.28 T 1.64 1.37 2.01 NSCG 3.84 3.48 0.12 T 0.65 2.00 0.10 LIG -4.80 -1.20 -2.40 T -0.64 -1.04 -2.00 DP -2.40 -1.2 0.72 T -0.56 -0.74 0.67 RealRF -14.4 -4.80 -2.40 T -2.23 -1.83 -2.80 VXO -6.00 -0.48 -1.20 T -0.96 -0.41 -3.55 LIQ 4.80 1.20 2.40 T 0.79 0.75 2.60 IMPLIED ECONOMIC RISK PREMIUMS 39 Table 1.3 Standard Deviations of Economic Risk Premiums This table reports the standard deviations of monthly ex post or implied ex ante factor risk premiums, for both traded and nontraded factors. For traded factors, two versions of their risk premiums, based on different mimicking portfolios, are reported. The unit-beta version relies on unit-beta factor mimicking portfolios while the market-weight version uses alternative mimicking portfolios which are determined by market composition weights of individual stocks constituting each traded factor. For non-traded factors, results are for the case where shocks of non-traded factors are standardized to have the same standard deviations as that of the market factor. All numbers are in annual percentage terms. The sample spans from 1981:01 to 2010:12 except for VXO which starts from 1989. Ex post return Mechanical ICC ICC Ex post return Mechanical ICC ICC TS 103.87 15.62 8.52 Market-weight version Mkt 55.13 2.23 2.13 DEF 104.83 17.05 5.46 Size 56.20 3.84 2.26 INF 105.76 11.67 6.52 Value 53.50 3.11 1.94 NSCG 107.90 10.19 7.97 Unit-beta version Mkt 72.72 4.16 3.21 LIG 133.26 10.21 6.16 Size 38.81 2.05 1.29 DP 94.34 9.48 6.40 Value 39.34 2.35 1.61 RealRF 112.77 13.82 5.83 VXO 100.76 5.31 2.97 LIQ 121.13 9.50 4.58 IMPLIED ECONOMIC RISK PREMIUMS 40 Table 1.4 Ex-post vs Ex-ante Risk Premium Differences For Duration Portfolios Isortstocksintoquintilesbasedonstockdurationslog(Dur)andcomputeportfolios’average risk premium differences between the ex post version (xret t ) and the implied ex ante version (irp t ). I report results for both equal- and value-weighted quintiles, which are columns labeled with (ew) and (vw). Nobs xret t −irp t (ew) xret t −irp t (vw) low est 419 -0.0022 -0.0025 t-stat -0.72 -1.03 2 est 419 0.0025 0.0010 t-stat 0.86 0.44 3 est 419 0.0028 0.0003 t-stat 0.99 0.12 4 est 419 0.0035 0.0015 t-stat 1.21 0.60 high est 419 0.0035 0.0022 t-stat 1.08 0.77 high-low est 419 0.0057 0.0048 t-stat 3.10 2.23 IMPLIED ECONOMIC RISK PREMIUMS 41 Table 1.5 In-sample Risk Premium Predictability Of ICCs (Traded Factor Case) For the three traded factors, this table reports results of using implied factor risk premiums to predict future ex post ones. Two versions of risk premiums of traded factors, based on different mimicking portfolios, are reported. The unit-beta version (Panel B) relies on unit- beta factor mimicking portfolios while the market-weight version (Panel A) uses alternative mimicking portfolios which are determined by market composition weights of individual stocks constituting each traded factor. There are two column blocks in this table. The left block (without control) reports the case where implied factor risk premiums are included as the only predictors while in the right block (with control) other predictors (DP, EP, bm, TS, DEF, ltr, and svar) are included as well. I only report the slope coefficients for implied factor risk premiums, which are in columnb. Columnp−value reports the bootstrapped one-side (positive-side)p-valuesfortheasymptoticalt-statistics(columnt(b))oftheslopecoefficients. t(b) represents the asymptotic t-statistics computed using the GMM standard errors with the Newey-West correction. Row ( P b 2 ) computes the sum of squared slope coefficients at different horizons to test the null hypothesis that the slopes at different horizons are jointly zero. I use bootstrapping to compute the p-value of P b 2 . The sample spans from 1981:01 to 2010:12. Panel A: Market-weight version Mkt without control with control Horizon b t(b) p-value Adj-R-sqr b t(b) p-value Adj-R-sqr 1 2.08 1.02 0.218 0.004 5.20 1.65 0.089 0.036 12 2.19 2.27 0.137 0.064 0.98 0.49 0.425 0.118 24 2.17 3.07 0.107 0.141 1.79 1.77 0.182 0.316 36 2.29 4.27 0.055 0.223 2.38 3.39 0.042 0.573 48 2.01 5.97 0.019 0.271 2.24 5.66 0.006 0.650 60 1.62 5.39 0.046 0.251 1.85 5.74 0.005 0.644 P b 2 25.75 0.047 45.36 0.084 Size without control with control Horizon b t(b) p-value Adj-R-sqr b t(b) p-value Adj-R-sqr 1 1.40 0.69 0.355 4.03E-04 2.74 1.12 0.252 0.070 12 2.12 1.62 0.218 0.055 4.04 4.50 0.008 0.474 24 2.97 3.39 0.077 0.176 3.84 6.05 0.002 0.557 36 3.48 4.21 0.063 0.309 3.35 5.63 0.004 0.584 48 3.57 5.06 0.045 0.406 2.87 5.28 0.01 0.654 60 3.50 5.55 0.041 0.480 1.87 3.74 0.078 0.719 P b 2 52.42 0.005 61.55 0.009 Value without control with control Horizon b t(b) p-value Adj-R-sqr b t(b) p-value Adj-R-sqr 1 3.77 2.55 0.013 1.62E-02 4.58 2.35 0.017 0.015 12 3.74 3.44 0.029 0.157 3.65 2.83 0.055 0.370 24 3.72 3.95 0.043 0.275 2.99 3.65 0.041 0.607 36 3.32 6.06 0.006 0.386 2.38 4.71 0.023 0.667 48 2.78 6.16 0.01 0.449 2.27 4.21 0.042 0.597 60 2.03 5.63 0.02 0.363 1.51 3.08 0.097 0.526 P b 2 64.97 0.004 56.40 0.012 IMPLIED ECONOMIC RISK PREMIUMS 42 Table 1.5 – Continued Panel B: Unit-beta version Mkt without control with control Horizon b t(b) p-value Adj-R-sqr b t(b) p-value Adj-R-sqr 1 -0.22 -0.35 0.641 -0.003 0.15 0.23 0.497 -0.001 12 -0.33 -0.73 0.711 0.000 -0.32 -0.87 0.780 0.158 24 -0.05 -0.14 0.561 -0.003 -0.18 -0.53 0.711 0.234 36 0.16 0.70 0.405 -0.001 0.16 0.59 0.446 0.374 48 0.10 0.57 0.424 -0.002 0.23 1.03 0.376 0.535 60 -0.01 -0.07 0.560 -0.003 0.11 0.36 0.542 0.514 P b 2 0.19 0.993 0.25 0.993 Size without control with control Horizon b t(b) p-value Adj-R-sqr b t(b) p-value Adj-R-sqr 1 1.55 0.79 0.357 0.000 5.51 2.14 0.047 0.027 12 1.23 1.03 0.389 0.024 3.48 3.41 0.035 0.265 24 1.78 2.67 0.184 0.118 3.40 6.43 0.002 0.393 36 2.14 3.60 0.129 0.261 3.14 7.37 0.002 0.524 48 2.20 4.97 0.070 0.390 2.61 8.28 0.001 0.592 60 2.13 5.98 0.050 0.501 1.90 6.09 0.019 0.665 P b 2 21.06 0.187 74.28 0.027 Value without control with control Horizon b t(b) p-value Adj-R-sqr b t(b) p-value Adj-R-sqr 1 3.09 3.48 0.000 0.013 3.85 1.93 0.090 0.006 12 3.65 5.97 0.000 0.233 4.43 4.19 0.016 0.258 24 3.13 5.89 0.007 0.345 3.70 4.85 0.036 0.436 36 2.57 9.10 0.002 0.428 2.33 5.46 0.036 0.556 48 2.12 11.44 0.000 0.461 1.84 5.87 0.027 0.597 60 1.90 10.55 0.001 0.457 1.80 5.98 0.029 0.603 P b 2 47.40 0.048 60.16 0.043 IMPLIED ECONOMIC RISK PREMIUMS 43 Table 1.6 In-sample Risk Premium Predictability Of ICCs (Nontraded Factor Case) For the nontraded factors, this table reports the results of using implied ex ante factor risk premiumstopredictfutureexpostfactorriskpremiums. Therearetwocolumnblocksinthis table. The left block (without control) reports the case where implied factor risk premiums are included as the only predictors while in the right block (with control) other predictors (DP, TS, DEF, ltr, and svar) are included as well. I only report the slope coefficients for the implied factor risk premiums, which are in column b. Column p−value reports the bootstrapped one-side (positive-side) p-values for the asymptotical t-statistics (column t(b)) of the slope coefficients. t(b) is the asymptotic t-statistics computed using the GMM standard errors with the Newey-West correction. Row ( P b 2 ) computes the sum of squared slope coefficients at different horizons to test the null hypothesis that the slopes at different horizons are jointly zero. I use bootstrapping to compute the p-value of P b 2 . The sample spans from 1981:01 to 2010:12 except for VXO which starts in 1989. TS without control with control Horizon b t(b) p-value Adj-R-sqr b t(b) p-value Adj-R-sqr 1 -0.04 -0.05 0.558 -0.003 1.34 1.07 0.164 0.001 12 0.08 0.15 0.514 -0.002 0.97 1.43 0.215 0.101 24 0.37 1.20 0.319 0.020 1.34 3.04 0.072 0.207 36 0.14 0.58 0.452 0.003 0.80 2.94 0.087 0.234 48 -0.02 -0.09 0.576 -0.003 0.39 1.79 0.227 0.217 60 -0.12 -0.88 0.706 0.006 0.06 0.38 0.487 0.202 P b 2 0.18 0.929 5.31 0.168 DEF without control with control Horizon b t(b) p-value Adj-R-sqr b t(b) p-value Adj-R-sqr 1 2.58 2.25 0.02 0.015 0.49 0.35 0.426 0.062 12 3.32 4.47 0.011 0.180 2.43 2.77 0.065 0.430 24 3.65 4.95 0.016 0.347 3.01 3.87 0.026 0.543 36 2.95 5.61 0.01 0.442 2.13 4.18 0.023 0.638 48 2.28 5.50 0.016 0.496 1.44 3.50 0.05 0.680 60 1.62 5.57 0.022 0.429 0.73 2.45 0.138 0.670 P b 2 47.55 0 22.35 0.023 INF without control with control Horizon b t(b) p-value Adj-R-sqr b t(b) p-value Adj-R-sqr 1 1.93 2.17 0.031 0.011 1.55 1.31 0.127 0.041 12 1.57 3.61 0.022 0.102 0.54 0.97 0.303 0.249 24 1.25 3.21 0.059 0.118 0.04 0.08 0.549 0.293 36 1.20 5.69 0.01 0.185 0.23 0.71 0.418 0.366 48 1.23 10.09 0.001 0.292 0.38 1.79 0.229 0.484 60 1.25 8.97 0.001 0.382 0.28 1.56 0.28 0.616 P b 2 12.26 0.036 2.99 0.488 IMPLIED ECONOMIC RISK PREMIUMS 44 Table 1.6 – Continued NSCG without control with control Horizon b t(b) p-value Adj-R-sqr b t(b) p-value Adj-R-sqr 1 -0.56 -0.45 0.708 -0.001 -1.12 -0.94 0.884 0.011 12 -0.59 -0.89 0.771 0.019 -1.01 -1.82 0.927 0.081 24 -0.85 -2.78 0.946 0.099 -1.20 -3.13 0.973 0.203 36 -0.35 -1.44 0.82 0.024 -0.65 -1.94 0.876 0.219 48 0.03 0.13 0.588 -0.003 -0.35 -1.18 0.771 0.290 60 0.22 1.42 0.377 0.016 -0.39 -2.18 0.886 0.476 P b 2 1.56 0.645 4.40 0.302 LIG without control with control Horizon b t(b) p-value Adj-R-sqr b t(b) p-value Adj-R-sqr 1 2.69 2.64 0.016 0.013 3.22 2.50 0.014 0.008 12 1.57 2.79 0.055 0.068 1.72 2.66 0.052 0.110 24 0.77 1.74 0.194 0.031 0.63 1.61 0.196 0.071 36 0.15 0.42 0.438 -0.001 -0.15 -0.42 0.598 0.062 48 0.21 1.00 0.342 0.004 -0.09 -0.41 0.596 0.080 60 0.32 2.05 0.203 0.023 -0.07 -0.34 0.598 0.194 P b 2 10.47 0.14 13.75 0.066 DP without control with control Horizon b t(b) p-value Adj-R-sqr b t(b) p-value Adj-R-sqr 1 -2.53 -1.68 0.957 0.026 -1.94 -1.42 0.92 0.047 12 -2.05 -2.05 0.92 0.161 -1.77 -2.33 0.942 0.251 24 -0.21 -0.28 0.609 -6.E-06 -0.11 -0.18 0.588 0.195 36 -0.03 -0.05 0.572 -0.003 -0.12 -0.27 0.594 0.185 48 0.19 0.54 0.466 0.004 0.03 0.07 0.542 0.181 60 0.40 1.50 0.311 0.043 0.23 0.75 0.415 0.204 P b 2 10.81 0.031 6.99 0.097 RealRF without control with control Horizon b t(b) p-value Adj-R-sqr b t(b) p-value Adj-R-sqr 1 2.93 2.51 0.014 0.020 2.46 1.82 0.055 0.057 12 2.51 3.06 0.044 0.134 0.83 0.99 0.301 0.353 24 2.36 3.43 0.049 0.193 0.28 0.42 0.467 0.438 36 2.22 5.77 0.017 0.288 0.47 1.17 0.327 0.561 48 2.15 7.83 0.003 0.392 0.70 2.76 0.11 0.672 60 2.14 8.02 0.004 0.472 0.77 2.81 0.111 0.756 P b 2 34.60 0.001 8.14 0.219 VXO without control with control Horizon b t(b) p-value Adj-R-sqr b t(b) p-value Adj-R-sqr 1 -0.48 -0.15 0.554 -0.004 0.35 0.10 0.516 0.028 12 -0.05 -0.03 0.535 -0.004 0.44 0.24 0.453 0.176 24 -0.90 -0.82 0.703 0.012 -0.08 -0.07 0.524 0.206 36 -1.13 -1.57 0.817 0.033 -0.34 -0.43 0.613 0.301 48 -1.50 -2.28 0.882 0.088 -0.18 -0.27 0.594 0.446 60 -1.77 -2.93 0.922 0.159 -0.03 -0.07 0.542 0.605 P b 2 7.71 0.498 0.47 0.994 IMPLIED ECONOMIC RISK PREMIUMS 45 Table 1.6 – Continued LIQ without control with control Horizon b t(b) p-value Adj-R-sqr b t(b) p-value Adj-R-sqr 1 0.80 0.48 0.35 -0.002 2.11 1.27 0.16 0.021 12 -0.35 -0.40 0.65 -0.001 0.37 0.44 0.47 0.163 24 -0.89 -1.38 0.81 0.020 -0.39 -0.51 0.70 0.167 36 -0.18 -0.28 0.65 -0.002 0.37 0.53 0.51 0.249 48 0.28 0.55 0.50 0.001 0.78 1.42 0.35 0.292 60 0.38 0.79 0.46 0.007 0.73 1.52 0.36 0.351 P b 2 1.80 0.80 6.03 0.45 IMPLIED ECONOMIC RISK PREMIUMS 46 Table 1.7 Out-of-sample Risk Premium Predictability Of ICCs This table reports out-of-sample results of using ICCs or mechanical-ICCs to predict future ex post economic risk premiums. The predictors that are actually used in the test are the resulting ones after I perform 60-month moving averages on the ICC or mechanical-ICC based ex ante factor risk premiums. The forecast evaluation period is 1998:01-2010:12. In the first (second) column block, the alternative predictive model uses the ICCs (mechanical- ICCs) as the sole predictor while the null model uses historical averages of ex post economic risk premiums as the OOS predictions. In the third (fourth) column block, the alternative predictive model uses the ICCs (mechanical-ICCs) as the sole predictor while the null model uses mechanical-ICCs (ICCs). For traded factors, two versions of their risk premiums, based on different mimicking portfolios, are examined. The unit-beta version relies on unit-beta factor mimicking portfolios while the market-weight version uses alternative mimicking port- folios which are determined by market composition weights of individual stocks constituting each traded factor. ICC vs hist-ave Mech-ICC vs hist-ave Analyst vs Mech Mech vs Analyst R 2 oos p-value R 2 oos p-value R 2 oos p-value R 2 oos p-value Panel A: Traded Factors Market-weight version: Mkt 0.012 0.083 0.015 0.036 -0.003 0.405 0.003 0.245 Size 0.036 0.011 -6.00E-05 0.332 0.036 0.004 -0.037 0.969 Value 0.003 0.234 -0.002 0.480 0.005 0.165 -0.005 0.527 Unit-beta version: Mkt -0.001 0.941 -0.002 0.562 0.001 0.334 -0.001 0.512 Size -0.002 0.448 -0.004 0.748 0.001 0.290 -0.001 0.421 Value 0.007 0.218 0.000 0.351 0.007 0.184 -0.007 0.592 Panel B: Nontraded Factors TS -0.010 0.875 0.002 0.295 -0.013 0.751 0.012 0.127 DEF 0.033 0.010 0.022 0.023 -0.055 0.659 0.053 0.000 INF 0.026 0.037 0.015 0.044 0.012 0.194 -0.012 0.654 NSCG 0.001 0.131 -0.002 0.795 0.003 0.031 -0.003 0.955 LIG -0.009 0.448 -0.011 0.773 0.002 0.252 -0.002 0.373 DP 0.008 0.074 -0.009 0.864 0.017 0.007 -0.017 0.974 RealRF 0.044 0.018 0.031 0.008 0.013 0.196 -0.013 0.598 VXO -0.003 0.213 -0.009 0.714 0.006 0.158 -0.006 0.308 LIQ -0.001 0.607 -0.007 0.803 0.006 0.159 -0.006 0.714 IMPLIED ECONOMIC RISK PREMIUMS 47 Table 1.8 Regressions for the Model-based Earnings Forecasts This table reports the time-series averages of monthly regression coefficients from earnings forecasts using pooled cross-sectional regressions. For every month between 1970 and 2010, I estimate the pooled cross-sectional regression equation (1.18) using the previous ten years of accounting data which end at least three months prior to that month. EV j,t is the enterprise value of the firm (defined as total assets plus the market value of equity minus the book value of equity), TA j,t is the total assets, DIV j,t is the dividend payment, DD j,t is a dummy variable that equals 0 for dividend payers and 1 for non-payers, E j,t is the earnings before extraordinary items of firm j in year t+τ, NEGE j,t is a dummy variable that equals 1 for firms with negative earnings (0 otherwise), andACC j,t is total accruals. Total accruals are computed as the change in current assets (Compustat item ACT) plus the change in debt in current liabilities (Compustat item DLC) minus the change in cash and short term investments (Compustat item CHE) and minus the change in current liabilities (Compustat item LCT). To mitigate the effects of extreme observations, I winsorize each variable annually at the 0.5 and 99.5 percentiles. R-sq is the time-series average R-square from the monthly regressions. OLS t-statistics are reported in parenthesis. Years Ahead Intercepts EV TA DIV DD E NEGE ACC R-sq 1 4.430 0.013 -0.007 0.257 -5.035 0.670 -1.525 -0.065 0.840 (25.9) (37.43) ( -20.27) ( 27.44) ( -25.86) (113.83) (-8.06) ( -41.64) 2 6.571 0.018 -0.008 0.363 -7.095 0.558 -0.749 -0.063 0.784 ( 22.43) ( 35.83) (-14.58) ( 25.84) ( -21.76) (71.72) (-3.63) (-20.58) 3 8.116 0.022 -0.009 0.366 -7.950 0.532 -0.369 -0.087 0.756 (23.75) ( 40.25) (-14.28) (22.25) (-26.88) (56.98) (-1.72) (-20.55) IMPLIED ECONOMIC RISK PREMIUMS 48 Table 1.9 In-sample Predictability of Mechanical-ICCs (Traded Factor Case) For the three traded factors, this table reports the results of using the mechanical-ICC based ex ante factor risk premiums to predict future ex post ones. For the traded factors, two versions of their risk premiums, based on different mimicking portfolios, are reported. The unit-beta version (Panel B) relies on unit-beta factor mimicking portfolios while the market- weight version (Panel A) uses alternative mimicking portfolios which are determined by market composition weights of individual stocks constituting each traded factor. There are two column blocks in this table. The left block (without control) reports the case where the mechanical-ICCs are included as the only predictors while in the right block (with control) other predictors (DP, EP, bm, TS, DEF, ltr, and svar) are included as well. I only report the slope coefficients for mechanical-ICCs, which are in columnb. Columnp−value reports the bootstrapped one-side (positive-side) p-values for the asymptotical t-statistics (column t(b)) of the slope coefficients. t(b) is the asymptotic t-statistics computed using the GMM standard errors with the Newey-West correction. Row ( P b 2 ) computes the sum of squared slope coefficients at different horizons to test the null hypothesis that the slopes at different horizons are jointly zero. I also use bootstrapping to compute the p-value of P b 2 . The sample spans from 1981:01 to 2010:12. Panel A: Market-weight version Mkt without control with control Horizon b t(b) p-value Adj-R-sqr b t(b) p-value Adj-R-sqr 1 1.54 0.92 0.287 0.001 6.17 1.55 0.1 0.035 12 1.32 1.49 0.272 0.025 -2.55 -1.19 0.802 0.129 24 0.66 1.05 0.422 0.012 -4.49 -3.85 0.991 0.403 36 0.97 2.00 0.314 0.047 -1.98 -2.36 0.943 0.541 48 1.00 2.60 0.253 0.078 -0.92 -1.52 0.848 0.569 60 0.99 2.93 0.226 0.109 0.57 1.27 0.221 0.560 P b 2 7.45 0.394 69.74 0.067 Size without control with control Horizon b t(b) p-value Adj-R-sqr b t(b) p-value Adj-R-sqr 1 -0.20 -0.22 0.644 -0.003 -1.36 -1.97 0.983 0.071 12 -0.79 -1.02 0.798 0.013 -1.63 -3.31 0.992 0.423 24 -1.91 -3.39 0.953 0.093 -1.59 -3.46 0.968 0.466 36 -2.03 -4.55 0.973 0.130 -1.26 -3.11 0.939 0.494 48 -1.92 -4.67 0.968 0.145 -0.96 -2.60 0.902 0.576 60 -1.49 -3.57 0.927 0.106 -0.39 -1.30 0.791 0.676 P b 2 14.31 0.032 9.70 0.089 Value without control with control Horizon b t(b) p-value Adj-R-sqr b t(b) p-value Adj-R-sqr 1 1.32 1.35 0.157 0.003 1.64 1.12 0.232 0.004 12 0.78 1.20 0.295 0.015 -0.62 -0.91 0.79 0.295 24 0.63 1.21 0.373 0.017 -0.45 -1.13 0.801 0.516 36 0.71 1.77 0.308 0.042 -0.10 -0.32 0.668 0.562 48 0.60 2.09 0.284 0.051 -0.01 -0.02 0.625 0.440 60 0.33 1.29 0.41 0.022 -0.47 -1.59 0.844 0.450 P b 2 3.71 0.419 3.51 0.648 IMPLIED ECONOMIC RISK PREMIUMS 49 Table 1.9 – Continued Panel B: Unit-beta version Mkt without control with control Horizon b t(b) p-value Adj-R-sqr b t(b) p-value Adj-R-sqr 1 -0.50 -0.50 0.667 -0.002 -0.96 -0.98 0.823 0.001 12 0.82 1.58 0.174 0.026 0.44 1.43 0.180 0.163 24 0.87 1.89 0.176 0.058 0.71 2.04 0.119 0.271 36 0.50 1.36 0.270 0.027 0.66 2.48 0.092 0.423 48 0.27 1.10 0.315 0.009 0.41 2.74 0.084 0.557 60 0.41 2.11 0.177 0.031 0.56 3.51 0.032 0.576 P b 2 2.16 0.436 2.54 0.337 Size without control with control Horizon b t(b) p-value Adj-R-sqr b t(b) p-value Adj-R-sqr 1 -0.01 -0.02 0.604 -0.003 -0.09 -0.13 0.674 0.010 12 -0.83 -1.59 0.878 0.020 -0.66 -1.41 0.885 0.170 24 -0.96 -2.77 0.920 0.052 -0.56 -1.41 0.844 0.194 36 -0.75 -2.53 0.875 0.048 -0.31 -1.01 0.765 0.260 48 -0.60 -2.13 0.817 0.042 -0.27 -1.00 0.751 0.356 60 -0.27 -1.23 0.734 0.010 0.04 0.21 0.600 0.514 P b 2 2.61 0.564 0.92 0.874 Value without control with control Horizon b t(b) p-value Adj-R-sqr b t(b) p-value Adj-R-sqr 1 0.58 0.49 0.346 -0.002 0.54 0.41 0.434 -0.008 12 1.46 2.65 0.064 0.077 1.06 1.39 0.290 0.084 24 1.50 3.34 0.071 0.146 0.84 1.76 0.269 0.204 36 1.54 4.63 0.056 0.259 0.66 2.16 0.241 0.405 48 1.34 6.64 0.025 0.311 0.69 3.16 0.168 0.464 60 1.10 5.85 0.045 0.263 0.62 2.65 0.242 0.443 P b 2 10.11 0.159 3.41 0.677 IMPLIED ECONOMIC RISK PREMIUMS 50 Table 1.10 In-sample Predictability of Mechanical-ICCs (Nontraded Factor Case) For the nontraded factors, this table reports the results of using the mechanical-ICC based ex ante factor risk premiums to predict future ex post ones. There are two column blocks in this table. The left block (without control) reports the case where the mechanical-ICCs are included as the only predictors while in the right block (with control) other predictors (DP, TS, DEF, ltr, and svar) are included as well. I only report the slope coefficients for the mechanical-ICCs, which are in column b. Column p−value reports the bootstrapped one-side (positive-side) p-values for the asymptotical t-statistics (column t(b)) of the slope coefficients. t(b)istheasymptotict-statisticscomputedusingtheGMMstandarderrorswith the Newey-West correction. Row ( P b 2 ) computes the sum of squared slope coefficients at different horizons to test the null hypothesis that the slopes at different horizons are jointly zero. I use bootstrapping to compute the p-value of P b 2 . The sample spans from 1981:01 to 2010:12 except for VXO, which starts in 1989. TS without control with control Horizon b t(b) p-value Adj-R-sqr Horizon b t(b) p-value Adj-R-sqr 1 0.29 0.80 0.243 -0.001 1 0.51 1.38 0.131 0.001 12 -0.12 -0.67 0.667 0.001 12 0.02 0.11 0.538 0.066 24 -0.30 -2.54 0.889 0.048 24 -0.30 -2.12 0.876 0.131 36 -0.43 -4.30 0.961 0.172 36 -0.47 -4.37 0.964 0.337 48 -0.42 -7.09 0.991 0.257 48 -0.48 -7.37 0.994 0.468 60 -0.31 -7.04 0.982 0.212 60 -0.38 -7.21 0.994 0.462 P b 2 0.64 0.4 P b 2 0.95 0.333 DEF without control with control Horizon b t(b) p-value Adj-R-sqr Horizon b t(b) p-value Adj-R-sqr 1 0.89 2.00 0.042 0.018 1 -0.19 -0.35 0.678 0.062 12 0.73 1.79 0.197 0.082 12 -0.43 -1.07 0.781 0.395 24 0.70 1.87 0.287 0.112 24 -0.55 -1.59 0.806 0.449 36 0.59 2.28 0.287 0.155 36 -0.43 -2.02 0.828 0.552 48 0.52 3.38 0.212 0.233 48 -0.19 -1.43 0.737 0.591 60 0.44 3.69 0.212 0.281 60 -0.16 -1.66 0.778 0.642 P b 2 2.63 0.053 P b 2 0.77 0.471 INF without control with control Horizon b t(b) p-value Adj-R-sqr Horizon b t(b) p-value Adj-R-sqr 1 0.56 0.95 0.187 0.001 1 0.11 0.18 0.4 0.036 12 0.27 0.67 0.328 0.006 12 -0.54 -1.65 0.814 0.266 24 0.32 1.09 0.314 0.017 24 -0.72 -4.22 0.977 0.350 36 0.47 2.53 0.156 0.065 36 -0.38 -2.04 0.812 0.387 48 0.69 5.73 0.027 0.208 48 -0.01 -0.09 0.518 0.471 60 0.74 5.51 0.042 0.298 60 0.00 -0.03 0.503 0.607 P b 2 1.73 0.231 P b 2 0.97 0.462 IMPLIED ECONOMIC RISK PREMIUMS 51 Table 1.10 – Continued NSCG without control with control Horizon b t(b) p-value Adj-R-sqr Horizon b t(b) p-value Adj-R-sqr 1 -0.04 -0.06 0.584 -0.003 1 0.04 0.06 0.565 0.007 12 -0.62 -2.02 0.927 0.036 12 -0.74 -2.25 0.946 0.081 24 -1.00 -5.32 0.997 0.212 24 -0.89 -3.88 0.979 0.208 36 -0.76 -6.08 0.996 0.188 36 -0.54 -3.40 0.968 0.242 48 -0.54 -4.70 0.979 0.127 48 -0.32 -2.29 0.901 0.306 60 -0.49 -3.73 0.948 0.131 60 -0.34 -3.33 0.97 0.494 P b 2 2.49 0.173 P b 2 1.85 0.285 LIG without control with control Horizon b t(b) p-value Adj-R-sqr Horizon b t(b) p-value Adj-R-sqr 1 -0.18 -0.23 0.578 -0.003 1 0.02 0.03 0.466 -0.010 12 -0.49 -0.95 0.725 0.014 12 -0.39 -0.76 0.667 0.051 24 -0.54 -1.46 0.75 0.031 24 -0.56 -1.65 0.799 0.087 36 -0.38 -1.51 0.744 0.028 36 -0.45 -1.95 0.83 0.099 48 -0.16 -0.83 0.64 0.006 48 -0.23 -1.36 0.734 0.096 60 -0.10 -0.64 0.612 0.002 60 -0.23 -1.50 0.749 0.218 P b 2 0.75 0.732 P b 2 0.77 0.728 DP without control with control Horizon b t(b) p-value Adj-R-sqr Horizon b t(b) p-value Adj-R-sqr 1 1.15 1.26 0.12 0.010 1 0.87 0.95 0.162 0.035 12 0.56 0.85 0.317 0.024 12 -0.24 -0.49 0.602 0.141 24 0.23 0.45 0.442 0.005 24 -0.19 -0.48 0.562 0.197 36 -0.26 -0.71 0.65 0.016 36 -0.44 -1.60 0.739 0.207 48 -0.50 -1.62 0.757 0.096 48 -0.62 -2.60 0.864 0.250 60 -0.62 -2.53 0.833 0.218 60 -0.72 -3.48 0.922 0.326 P b 2 2.39 0.25 P b 2 1.94 0.42 RealRF without control with control Horizon b t(b) p-value Adj-R-sqr Horizon b t(b) p-value Adj-R-sqr 1 0.91 1.62 0.091 0.009 1 0.39 0.66 0.247 0.049 12 0.60 1.46 0.193 0.039 12 -0.41 -1.25 0.77 0.357 24 0.58 1.77 0.221 0.055 24 -0.76 -4.39 0.973 0.495 36 0.72 3.36 0.105 0.143 36 -0.31 -1.83 0.76 0.570 48 0.93 5.82 0.028 0.344 48 0.19 1.26 0.285 0.657 60 0.92 6.07 0.028 0.413 60 0.26 2.09 0.185 0.742 P b 2 3.76 0.049 P b 2 1.10 0.351 VXO without control with control Horizon b t(b) p-value Adj-R-sqr Horizon b t(b) p-value Adj-R-sqr 1 -0.30 -0.23 0.631 -0.004 1 -0.51 -0.41 0.741 0.028 12 -0.79 -0.97 0.758 0.015 12 -1.36 -2.07 0.921 0.216 24 -1.75 -3.02 0.928 0.141 24 -1.80 -4.08 0.981 0.342 36 -1.61 -3.31 0.939 0.115 36 -1.13 -2.73 0.907 0.350 48 -0.91 -2.04 0.85 0.041 48 -0.42 -1.08 0.734 0.453 60 -0.20 -0.47 0.686 -0.002 60 0.25 0.80 0.462 0.608 P b 2 7.23 0.261 P b 2 6.88 0.376 IMPLIED ECONOMIC RISK PREMIUMS 52 Table 1.10 – Continued LIQ without control with control Horizon b t(b) p-value Adj-R-sqr Horizon b t(b) p-value Adj-R-sqr 1 0.06 0.10 0.467 -0.003 1 0.54 0.76 0.213 0.017 12 -0.69 -1.70 0.878 0.017 12 -0.45 -0.88 0.659 0.169 24 -1.17 -3.07 0.936 0.076 24 -1.60 -3.99 0.965 0.296 36 -0.81 -1.84 0.801 0.033 36 -1.16 -2.91 0.895 0.311 48 -0.07 -0.15 0.564 -0.003 48 -0.52 -1.20 0.693 0.275 60 0.48 1.12 0.358 0.015 60 0.11 0.31 0.391 0.316 P b 2 2.74 0.221 P b 2 4.70 0.069 IMPLIED ECONOMIC RISK PREMIUMS 53 Table 1.11 The Horse Race Between Two Versions of ICCs (Traded Factor Case) For the three traded factors, this table reports the results of the multivariate predictive regression using both the mechanical-ICC and the analyst-ICC based ex ante factor risk premiums to predict future ex post ones. For traded factors, two versions of their risk premiums, based on different mimicking portfolios, are reported. The unit-beta version (Panel B) relies on unit-beta factor mimicking portfolios while the market-weight version (PanelA)usesalternativemimickingportfolios, whicharedeterminedbymarketcomposition weights of individual stocks constituting each traded factor. I report the slope coefficients in columns b. Column p−value reports the bootstrapped one-side (positive-side) p-values for the asymptotical t-statistics (columnt(b)) of the slope coefficients. t(b) is the asymptotic t-statistics computed using the GMM standard errors with the Newey-West correction. Row ( P b 2 ) computes the sum of squared slope coefficients at different horizons to test the null hypothesis that the slopes at different horizons are jointly zero. I use bootstrapping to compute the p-value of P b 2 . The sample spans from 1981:01 to 2010:12. Panel A: Market-weight version Mechanical-ICC Analyst-ICC Mkt Horizon b t(b) p-value b t(b) p-value Adj-R-sqr 1 -0.12 -0.06 0.57 2.18 0.81 0.263 0.001 12 -0.67 -0.41 0.646 2.75 1.48 0.214 0.064 24 -1.87 -2.14 0.87 3.66 3.75 0.058 0.194 36 -1.04 -1.37 0.756 3.12 3.82 0.067 0.249 48 -0.61 -1.04 0.698 2.49 4.26 0.071 0.284 60 -0.11 -0.27 0.591 1.71 3.94 0.098 0.249 P b 2 5.44 0.829 44.59 0.134 Size Horizon b t(b) p-value b t(b) p-value Adj-R-sqr 1 0.001 0.001 0.558 1.40 0.67 0.34 -0.002 12 -0.45 -0.63 0.685 1.97 1.49 0.249 0.057 24 -1.26 -2.36 0.896 2.56 2.80 0.131 0.212 36 -1.23 -2.96 0.903 3.08 3.48 0.086 0.352 48 -1.09 -3.01 0.868 3.22 4.30 0.047 0.448 60 -0.60 -1.64 0.761 3.30 4.95 0.047 0.495 P b 2 4.83 0.223 43.11 0.018 Value Horizon b t(b) p-value b t(b) p-value Adj-R-sqr 1 0.60 0.55 0.356 3.45 2.03 0.032 0.015 12 -0.01 -0.01 0.552 3.74 3.04 0.044 0.154 24 -0.26 -0.56 0.656 3.87 3.69 0.044 0.276 36 -0.12 -0.36 0.624 3.40 5.38 0.021 0.385 48 -0.11 -0.49 0.646 2.85 5.55 0.025 0.449 60 -0.21 -0.97 0.712 2.17 5.23 0.04 0.369 P b 2 0.50 0.937 65.31 0.005 IMPLIED ECONOMIC RISK PREMIUMS 54 Table 1.11 – Continued Panel B: Unit-beta version Mechanical-ICC Analyst-ICC Mkt Horizon b t(b) p-value b t(b) p-value Adj-R-sqr 1 -0.49 -0.46 0.666 -0.03 -0.04 0.519 -0.005 12 0.98 1.92 0.141 -0.71 -1.50 0.820 0.035 24 0.97 2.07 0.140 -0.41 -1.13 0.750 0.063 36 0.51 1.37 0.265 -0.03 -0.12 0.555 0.024 48 0.27 1.07 0.322 0.01 0.03 0.520 0.006 60 0.45 2.19 0.163 -0.17 -0.81 0.693 0.032 P b 2 2.67 0.358 0.69 0.931 Size Horizon b t(b) p-value b t(b) p-value Adj-R-sqr 1 0.15 0.19 0.467 1.59 0.79 0.354 -0.003 12 -0.74 -1.39 0.839 1.13 0.94 0.435 0.039 24 -0.87 -2.51 0.903 1.70 2.49 0.209 0.160 36 -0.63 -2.30 0.854 2.08 3.36 0.162 0.294 48 -0.47 -1.90 0.782 2.16 4.68 0.090 0.417 60 -0.13 -0.75 0.630 2.12 5.79 0.056 0.502 P b 2 1.96 0.649 20.17 0.203 Value Horizon b t(b) p-value b t(b) p-value Adj-R-sqr 1 -0.45 -0.33 0.647 3.39 2.47 0.020 0.011 12 0.45 0.77 0.364 3.37 4.70 0.005 0.237 24 0.58 1.31 0.316 2.77 4.78 0.030 0.361 36 0.75 2.29 0.218 2.09 6.67 0.014 0.473 48 0.69 3.59 0.125 1.67 7.44 0.008 0.521 60 0.49 2.87 0.216 1.57 7.55 0.016 0.494 P b 2 2.01 0.675 40.12 0.102 IMPLIED ECONOMIC RISK PREMIUMS 55 Table 1.12 The Horse Race Between Two Versions of ICCs (Nontraded Factor Case) For the nontraded factors, this table reports the results of the multivariate predictive regres- sion using both the mechanical-ICC and the analyst-ICC based ex ante factor risk premiums to predict future ex post ones. I report the slope coefficients in columnsb. Columnp−value reports the bootstrapped one-side (positive-side) p-values for the asymptotical t-statistics (columnt(b)) of the slope coefficients. t(b) is the asymptotic t-statistics computed using the GMM standard errors with the Newey-West correction. The row ( P b 2 ) computes the sum of squared slope coefficients at different horizons to test the null hypothesis that the slopes at different horizons are jointly zero. I use bootstrapping to compute the p-value of P b 2 . The sample spans from 1981:01 to 2010:12 except for VXO which starts in 1989. Mechanical-ICC Analyst-ICC TS Horizon b t(b) p-value b t(b) p-value Adj-R-sqr 1 0.36 0.91 0.218 -0.33 -0.36 0.667 -0.003 12 -0.17 -0.74 0.704 0.21 0.33 0.446 0.001 24 -0.47 -3.54 0.952 0.73 2.77 0.097 0.119 36 -0.56 -5.47 0.988 0.57 4.67 0.029 0.247 48 -0.50 -9.25 0.998 0.37 3.92 0.079 0.304 60 -0.34 -8.67 0.994 0.14 1.84 0.288 0.220 P b 2 1.06 0.304 1.17 0.569 DEF Horizon b t(b) p-value b t(b) p-value Adj-R-sqr 1 0.62 1.10 0.166 1.28 0.82 0.269 0.018 12 0.10 0.24 0.477 3.12 3.59 0.031 0.178 24 -0.03 -0.10 0.588 3.71 4.67 0.018 0.345 36 0.004 0.02 0.564 2.94 4.94 0.017 0.440 48 0.12 0.94 0.441 2.08 3.93 0.048 0.502 60 0.19 1.77 0.357 1.29 3.31 0.085 0.463 P b 2 0.45 0.551 39.82 0.002 INF Horizon b t(b) p-value b t(b) p-value Adj-R-sqr 1 -0.49 -0.54 0.703 2.57 1.66 0.079 0.010 12 -0.84 -1.80 0.878 2.60 3.45 0.023 0.141 24 -0.58 -1.80 0.828 1.95 3.39 0.048 0.146 36 -0.38 -1.33 0.747 1.66 3.93 0.031 0.199 48 0.05 0.23 0.468 1.16 3.72 0.037 0.291 60 0.09 0.41 0.43 1.13 3.71 0.045 0.381 P b 2 1.44 0.384 22.51 0.019 IMPLIED ECONOMIC RISK PREMIUMS 56 Table 1.12 – Continued Mechanical-ICC Analyst-ICC NSCG Horizon b t(b) p-value b t(b) p-value Adj-R-sqr 1 0.18 0.26 0.416 -0.66 -0.50 0.738 -0.004 12 -0.51 -1.44 0.835 -0.32 -0.42 0.68 0.038 24 -0.86 -3.94 0.973 -0.40 -1.31 0.809 0.227 36 -0.78 -4.67 0.979 0.06 0.22 0.544 0.186 48 -0.69 -4.73 0.974 0.39 1.78 0.285 0.163 60 -0.73 -6.11 0.993 0.60 4.71 0.048 0.247 P b 2 2.65 0.162 1.21 0.759 LIG Horizon b t(b) p-value b t(b) p-value Adj-R-sqr 1 -1.93 -1.86 0.957 4.66 3.08 0.005 0.023 12 -1.77 -2.62 0.949 3.23 3.41 0.021 0.200 24 -1.40 -2.99 0.946 1.98 3.20 0.042 0.172 36 -0.73 -2.23 0.863 0.79 1.61 0.226 0.065 48 -0.40 -1.30 0.736 0.56 1.46 0.248 0.035 60 -0.39 -1.84 0.796 0.67 2.70 0.093 0.070 P b 2 9.69 0.033 37.42 0.008 DP Horizon b t(b) p-value b t(b) p-value Adj-R-sqr 1 0.70 0.85 0.2 -2.21 -1.50 0.944 0.027 12 0.14 0.23 0.416 -1.98 -2.04 0.917 0.161 24 0.21 0.34 0.408 -0.11 -0.13 0.591 0.003 36 -0.30 -0.66 0.58 -0.16 -0.26 0.634 0.016 48 -0.50 -1.37 0.669 -0.04 -0.08 0.618 0.093 60 -0.59 -2.05 0.745 0.13 0.35 0.561 0.220 P b 2 1.24 0.452 8.87 0.058 RealRF Horizon b t(b) p-value b t(b) p-value Adj-R-sqr 1 0.01 0.01 0.487 2.92 1.61 0.089 0.017 12 -0.38 -0.88 0.724 3.13 3.18 0.024 0.140 24 -0.40 -1.12 0.745 3.00 3.83 0.021 0.204 36 -0.09 -0.28 0.562 2.36 3.91 0.021 0.287 48 0.41 1.64 0.216 1.47 3.19 0.056 0.417 60 0.38 2.09 0.196 1.49 3.94 0.026 0.497 P b 2 0.62 0.65 37.29 0.003 VXO Horizon b t(b) p-value b t(b) p-value Adj-R-sqr 1 -0.28 -0.22 0.646 -0.45 -0.14 0.579 -0.007 12 -0.79 -0.96 0.763 0.12 0.08 0.523 0.011 24 -1.69 -3.02 0.922 -0.45 -0.46 0.627 0.141 36 -1.49 -3.13 0.915 -0.73 -1.06 0.726 0.126 48 -0.60 -1.46 0.755 -1.31 -1.94 0.835 0.102 60 0.35 1.05 0.44 -1.90 -3.00 0.913 0.162 P b 2 6.27 0.35 6.29 0.61 IMPLIED ECONOMIC RISK PREMIUMS 57 Table 1.12 – Continued LIQ Horizon b t(b) p-value b t(b) p-value Adj-R-sqr 1 -0.03 -0.05 0.525 0.81 0.49 0.399 -0.005 12 -0.67 -1.61 0.853 -0.13 -0.14 0.626 0.014 24 -1.10 -3.04 0.916 -0.64 -1.07 0.789 0.085 36 -0.81 -2.01 0.793 0.01 0.01 0.6 0.030 48 -0.15 -0.33 0.565 0.32 0.69 0.492 -0.001 60 0.42 1.06 0.362 0.27 0.61 0.524 0.017 P b 2 2.51 0.264 1.25 0.903 IMPLIED ECONOMIC RISK PREMIUMS 58 Table 1.13 Correlations With Theoretical Drivers (Traded Factor Case) I regress implied ex ante economic risk premiums on the contemporaneous theoretical driver- s for time-varying risk premiums. The drivers considered as regressors include S t (surplus consumption ratio from Campbell and Cochrane (1999)), σ 2 c (conditional variance of con- sumption growth as in Bansal and Yaron (2004)), andQ t (model uncertainty of the economy as in Drechsler (2011)). Quarterly frequency is used. Slope coefficients and their t-statistics are reported. T-statistics are computed using GMM standard errors with a Newey-West lag of 4. The sample spans from the first quarter of 1981 to the fourth quarter of 2010. For traded factors, two versions of their risk premiums, based on different mimicking portfolios, are reported. The unit-beta version (Panel B) relies on unit-beta factor mimicking portfo- lios while the market-weight version (Panel A) uses alternative mimicking portfolios, which are determined by market composition weights of individual stocks constituting each traded factor. Panel A: Market-weight version S t σ 2 c Q t AdjRsqr Mkt Est 0.002 -0.007 T 0.276 Est 78.576 0.174 T 3.256 Est 0.003 0.091 T 2.240 Est 0.001 66.795 0.001 0.182 T 0.196 2.858 1.069 Size Est 0.009 0.009 T 0.776 Est -85.042 0.105 T -1.940 Est -0.004 0.131 T -2.081 Est 0.012 -47.184 -0.004 0.190 T 1.269 -1.511 -2.113 Value Est -0.001 -0.009 T -0.235 Est 130.953 0.386 T 2.643 Est 0.003 0.117 T 1.708 Est -0.001 120.651 0.001 0.384 T -0.173 2.555 1.089 IMPLIED ECONOMIC RISK PREMIUMS 59 Table 1.13 – Continued Panel B: Unit-beta version S t σ 2 c Q t AdjRsqr Mkt Est 0.000 -0.009 T -0.052 Est -72.141 0.033 T -0.790 Est -0.005 0.119 T -1.974 Est 0.006 -19.582 -0.005 0.109 T 0.779 -0.279 -2.267 Size Est 0.004 0.004 T 0.632 Est -44.856 0.095 T -2.034 Est -0.002 0.110 T -2.046 Est 0.006 -26.137 -0.002 0.160 T 1.000 -1.621 -2.001 Value Est 0.000 -0.009 T 0.034 Est 124.041 0.508 T 3.453 Est 0.004 0.231 T 2.485 Est -0.001 107.109 0.002 0.542 T -0.219 3.284 1.975 IMPLIED ECONOMIC RISK PREMIUMS 60 Table 1.14 Correlations With Theoretical Drivers (Nontraded Factor Case) I regress implied ex ante economic risk premiums on the contemporaneous theoretical driver- s for time-varying risk premiums. The drivers considered as regressors include S t (surplus consumption ratio from Campbell and Cochrane (1999)), σ 2 c (conditional variance of con- sumption growth as in Bansal and Yaron (2004)), andQ t (model uncertainty of the economy as in Drechsler (2011)). Quarterly frequency is used. Slope coefficients and their t-statistics are reported. T-statistics are computed using GMM standard errors with a Newey-West lag of 4. The sample spans from the first quarter of 1981 to the fourth quarter of 2010. S t σ 2 c Q t AdjRsqr TS Est -0.273 -0.007 T -0.444 Est -6651.310 0.093 T -1.523 Est -0.412 0.198 T -2.313 Est 0.111 -3170.860 -0.358 0.203 T 0.200 -1.051 -2.219 DEF Est 0.496 0.016 T 1.100 Est -7568.130 0.371 T -3.642 Est -0.176 0.099 T -2.177 Est 0.493 -6812.540 -0.068 0.389 T 1.228 -3.213 -1.312 INF Est -0.090 -0.009 T -0.293 Est 6523.270 0.155 T 1.511 Est 0.397 0.313 T 3.301 Est -0.479 2953.757 0.360 0.347 T -1.399 0.853 3.353 NSCG Est -0.601 0.004 T -1.512 Est -9040.750 0.182 T -1.648 Est -0.387 0.175 T -1.942 Est -0.388 -6700.390 -0.250 0.246 T -0.897 -1.409 -1.487 IMPLIED ECONOMIC RISK PREMIUMS 61 Table 1.14 – Continued LIG Est 1.259 0.098 T 4.232 Est -4493.630 0.077 T -1.354 Est -0.179 0.063 T -1.463 Est 1.448 -2420.050 -0.186 0.221 T 4.854 -0.880 -2.553 DP Est -0.015 -0.009 T -0.046 Est 785.025 -0.007 T 0.246 Est 0.108 0.016 T 0.676 Est -0.163 -413.640 0.121 -0.001 T -0.391 -0.154 0.764 RealRF Est 0.288 -0.003 T 0.917 Est -6690.130 0.220 T -2.163 Est -0.349 0.319 T -3.924 Est 0.601 -3647.170 -0.303 0.405 T 1.846 -1.491 -4.171 VXO Est -0.144 -0.006 T -0.683 Est -2633.060 0.082 T -4.874 Est -0.138 0.093 T -3.274 Est -0.007 -2170.390 -0.116 0.132 T -0.040 -3.687 -2.669 LIQ Est -0.692 0.052 T -2.180 Est 401.624 -0.008 T 0.202 Est -0.028 -0.006 T -0.360 Est -0.673 380.666 -0.011 0.035 T -2.009 0.197 -0.131 FUNDAMENTAL VALUES, PRICE DEVIATIONS, AND FUND MANAGERS 62 Chapter 2 Fundamental Values, Price Deviations, and the Skills of Mutual Fund Managers Introduction According to the 2011 Investment Company Fact Book, U.S. domestic equity mutual fund managers collectively managed over 5 trillion dollars at the end of 2010. A significant portion of this amount is actively managed. Even a conservative 1% additional expense for active management implies that investors pay nearly 50 billion dollars more to managed funds than to index funds. Naturally, investors would like to know whether and how active mutual fund managers add values to justify their higher expenses relative to passively managed index funds. Despite the extensive literature devoted to this topic, those questions remain unsettled in a satisfactory way. Starting with Jensen (1968), studies based on fund returns find that managers do not add value before cost and underperform the market after cost. On the other hand, studies using fund holdings (e.g., Grinblatt & Titman (1989), Grinblatt & Titman (1993), Ferson & Khang (2002), and Daniel et al. (1997) (DGTW)) find that on average mutual fund managers have investment abilities before cost, while Ferson & Mo (2012) propose new holding-based performance measures and do not find investment FUNDAMENTAL VALUES, PRICE DEVIATIONS, AND FUND MANAGERS 63 abilities. Further, to understand fund managers’ performance, a classical perspective decomposes managers’ abilities into market timing ability and selectivity, i.e., the abilities to time market-wide factors and to pick mispriced stocks. 1 However, the evidence for either of these types of ability is mixed at best. Why can’t previous studies detect significant and reliable investment performance, at least for average mutual fund managers? One possible reason is that classical performance decomposition may have low power, since managers may use finer skills to help them time market-wide factors or to pick stocks, and only a finer decomposition can help detect those skills. For example, fund managers may only be good at predicting future fundamental values of stocks when selecting stocks, but that skill may be hard to detect with the selectivity measure computed under classical performance decomposition. This is because residual parts of future stock prices relative to future fundamental values can be very noisy, leading to poorly estimated selectivity, since selectivity reflects a sum of managers’ skills to predict both future fundamental values as well as the residual parts. In such a case, a finer performance decomposition may help pinpoint finer types of skills (e.g., the skill to predict fundamental values), and can more easily reveal managers’ abilities. Further, a finer decomposition can help describe managers’ investment styles better, and may provide guidance to identify skilled individual managers. In this study I propose such a new decomposition on top of classical measure of selectivity, and examine whether and how fund managers select stocks by looking into their selectivity components. This new decomposition divides fund managers’ selectivity into two components. The first involves predicting future movements of stocks’ fundamental values, measured using tangible information such as accounting information and analysts’ forecasts. The second is attributed to foreseeing future deviations of stock prices from their fundamental values. On one hand, managers may predict tomorrow’s accounting information and analysts’ earnings forecasts so as to predict tomorrow’s stock fundamental values. For example, suppose a candy firm develops a new chocolate. Markets expect $1 more in earnings per share (EPS) tomorrow while a fund manager may understand better tomorrow’s market demand for that chocolate and predict a $1.5 increase in EPS tomorrow. That is, this fund manager has better information for tomorrow’s fundamental value of this candy firm. On the other hand, managers may also predict stocks’ future price deviations from their fundamental values as explained by concurrent tangible information. The price of a stock can deviate from its fundamental value due to noise, feedback trading (trade based on past price changes), irrational expectations (irrational waves of optimism and pessimism), limits of arbitrage, or some other inefficiency. For example, in bubble periods, fund managers may 1 A few exceptions are Ferson & Mo (2012), Da et al. (2011), and Busse & Tong (2012). FUNDAMENTAL VALUES, PRICE DEVIATIONS, AND FUND MANAGERS 64 choose to ride bubbles and long overvalued stocks in anticipation of continuing overvaluation due to limits of arbitrage and continuing overoptimism of investors. "Value investing" is another example where value investors predict that the undervaluation will shrink in the future. I operationalize fundamental values of stocks with the residual income model (sometimes referred to as the Edwards-Bell-Ohlson (EBO) valuation equation) which expresses fundamental stock values as a sum of book equity values and fundamental values of all future residual incomes. Price deviations are then defined as the differences between stock prices and fundamental values. Stock returns hence reflect a sum of two components, the variation of fundamental values and varying price deviations of stocks over time. Accordingly, fund managers’ selectivity is divided into their ability to predict those two return components. I apply the new decomposition to US active equity mutual funds to describe fund managers’ investment styles in a new way, reflecting their focuses on return components when investing. The logic used to determine the new styles is that a larger selectivity component in the new decomposition may reflect fund managers’ preference for digging for information about the stock return component associated with that selectivity part. Hence, a fund manager, with a large performance component associated with stock fundamentals (price deviations) but with a small component associated with the rest of stock returns, is classified as a fundamental (mispricing) type manager. There are several findings based on these new styles. Average fund managers are mispricing types who focus on price deviation information to guide their investments. Across different subgroups with different claimed traditional styles (growth, growth & income, and income), the preference for price deviation information continues to hold for managers except growth & income fund managers, who show no significant preference for fundamental or price deviation information when investing. It is possible that the new style is related to fund managers’ overall skills and hence may predict future fund performance. It could be the case that managers who like collecting fundamental information have a better chance to generate a superior performance, while it also could be the case that managers who keep close eyes on price movements that cannot be explained by fundamentals have skills. I test and find that neither of the two performance components from the new decomposition nor the total performance measure can predict future fund performance. This is likely due to excessive noise in the measures constructed. Hence, the new styles seem not to be related to future fund performance. However, it could be the case that fund managers classified by the new styles do not FUNDAMENTAL VALUES, PRICE DEVIATIONS, AND FUND MANAGERS 65 exhibit their expertise all the time, but only show skills over periods around specific events that are predominantly affecting fundamentals, or the extent of price deviations. Hence, concentrating on those specific events may be more effective in uncovering fundamental or mispricing managers’ skills. Specifically, earnings announcements, analyst recommendation announcements, and stocks’ ex-dividend days are likely three events respectively about fundamentals (the first event) and price deviations (the latter two events) for the following reason. Earnings information is central for investors to assess fundamentals; recommendations are issued based on a comparison of ongoing stock prices and fair prices (or fundamental values) in analysts’ minds, likely reflecting the information of price deviations; dividends effective on ex-dividend days reduce stock prices and may lower arbitrage costs (Pontiff (2006)), therefore potentially shrinking the degree of mispricing. Given these three events and based on the new styles proposed, I test and find evidence consistent with the following predictions: fundamental type fund managers perform better during earnings announcements while mispricing style managers do better during the other two types of events. Moreover, those managers’ out-performance during the events comes only from stocks they actively sell rather than those actively bought. Further, around analyst recommendation announcements, all of the fund managers exhibit significant performance from stocks they actively sell and that performance is stronger (weaker) for mispricing (fundamental) managers. Overall, all the evidence supports the new styles potentially capturing fund managers’ preference for fundamental or mispricing information when investing. Why can the new styles predict fund managers’ performance around events? Since the new styles of fund managers are essentially a weighted sum of the new styles applied to stocks, one possible answer to the question is that the new styles, when applied to stocks, reflect a stock characteristic that predicts stock returns unrelated to what are controlled when evaluating fund performance (i.e., size, book-to-market equity, and momentum), and that is exploited by managers when investing. I test and find that the new styles applied to stocks indeed predict future stock returns around events. Further, that stock return predictability actually comes from the predictive power of fundamental value-price ratios proposed in Frankel & Lee (1998). Hence, the evidence suggests that the out-performance of fundamental or mispricing style managers around events is at least partially driven by the managers’ exploitation of the stock return predictability that is attributed to the stocks’ fundamental value-price ratios, and that is unexplained by size, book-to-market equity, and momentum for which typical fund performance evaluation controls. FUNDAMENTAL VALUES, PRICE DEVIATIONS, AND FUND MANAGERS 66 A Model for Stock Return Decomposition Studies such as Frankel & Lee (1998) and Lee et al. (1999) show that a stock price P t+1 can deviate from its fundamental value V t+1 by an t+1 in the short run, although in the long run arbitrage forces cause the price to converge to the fundamental value: P t+1 =V t+1 + t+1 . (2.1) I use the residual income model (sometimes referred to as Edwards-Bell-Ohlson (EBO) valuation equation) to represent the fundamental value V t+1 . The model states that with clean surplus accounting, fundamental value can be written as reported book value, plus an infinite sum of discounted residual incomes: 2 V t+1 =B t+1 + ∞ X i=1 E t+1 [NI t+i+1 −(r e ·B t+i )] (1+r e ) i =B t+1 + ∞ X i=1 E t+1 [(ROE t+i+1 −r e )·B t+i ] (1+r e ) i (2.2) where B t+1 is the book value at time t, E t+1 [.] is the expectation based on the information available at time t+1, NI t+i+1 is the net income for period t+i+1, r e is the cost of equity capital, andROE t+i+1 is the after-tax return on the book equity for period t+i+1. This model is identical to the dividend discount model in theory, but provides a more convenient framework linking the accounting numbers and the firm value. Equation (2.2) splits the firm value into two components: a measure of the capital invested (book equity) and a measure of the value of future growth or the present value of all future residual incomes. Residual income (or abnormal earnings), is defined as earnings minus a charge for the use of capital (as measured by the previous period book value multiplied by the cost of capital). The equation highlights that the stock value should include not only the historical value of capital invested but also the value of future wealth-creating activities. Combining 2 The clean surplus accounting relation requires that all gains and losses affecting book value are included in earnings; that is, the change in book value is equal to earnings minus dividends. FUNDAMENTAL VALUES, PRICE DEVIATIONS, AND FUND MANAGERS 67 equations (2.1) and (2.2), we have a model to decompose the total stock return: R t+1 = P t+1 P t ·N t+1 = V t+1 P t ·N t+1 + t+1 P t ·N t+1 = V t+1 P t+1 ·R t+1 +(1− V t+1 P t+1 )·R t+1 (2.3) =R Funda t+1 +R PrcDev t+1 (2.4) where N t+1 is the factor to control for the share adjustment due to dividends and share splits or repurchases between periods t and t+1. R Funda t+1 and R PrcDev t+1 are respectively defined as the fundamental value return and the price deviation return. Equation (2.4) tells us that the return from holding a stock can come from the variation of either the fundamental value or the short-run deviation of the stock’s price from its fundamental value. Hence, if fund managers have investment skills, they must possess the superior return information about one or both of these two channels. Model Implementation I operationalize the components in equation (2.2) using analysts’ earnings forecasts largely following Frankel & Lee (1998) and Lee et al. (1999) and I implement the model at a quarterly frequency. Specifically, I compute the fundamental value for each firm every quarter as: V t+1 =B t+1 +GV t+1 GV t+1 = (FROE t+2 −r e ) (1+r e ) B t+1 + (FROE t+3 −r e ) (1+r e ) 2 B t+2 +TV (2.5) where B t+1 is the book value from the most recent publicly available quarterly financial statement as of time t+1 divided by the number of shares outstanding at time t+1 from CRSP.r e is the cost of equity capital for which I use the risk-free rate plus a constant stock risk premium, due to significant imprecisions of estimates of risk premiums using models such as CAPM or the Fama French three-factor model (Fama & French (1997)). FROE t+i is forecasted ROE for period t+i. For the first three years, I forecast earnings FEPS t+i explicitly using I/B/E/S mean forecasted EPS for year t+i and compute forecasted ROE as FEPS t+i /B t+i−1 . Hence I essentially assume that I/B/E/S analyst’s earnings forecasts represent the expectations of the market. Beyond the third year, FROE is forecasted by FUNDAMENTAL VALUES, PRICE DEVIATIONS, AND FUND MANAGERS 68 linearly fading the period t+3 ROE to the median industry ROE by year t+T. I use a fade rate in an attempt to capture the long-term erosion of abnormal ROE over time. B t+i =B t+i−1 +FEPS t+i −FDPS t+i where FDPS t+i is the forecasted dividend per share for year t+i, estimated using the current dividend payout ratio (k) from most recent publicly available annual financial statements. Specifically, FDPS t+i =FEPS t+i ·k. TV is the terminal value which is the value for all residual incomes beyond period T. It is estimated to be the value of a perpetuity with the payment per period equal to the residual income in period T. I choose T =3 and can express TV as: TV = (FROE t+T+1 −r e ) r e (1+r e ) 2 B t+2 . (2.6) In theory, T should be set large enough for firms to reach their competitive equilibrium. However, our ability to forecast future ROEs diminishes quickly over time, and forecasting errors are compounded in longer expansions. To obtain target industry ROEs, I group all stocks into 49 industry classifications (Fama & French (1997)). The industry target ROE is the median of past ROEs from all profitable firms in the same industry. At least 5 years, and up to 10 years, of past data are used to compute this median. It is important that the quarterly or annual financial statements used to construct return components are publicly available by the time the associated quarterly stock return is realized. I address this concern by using a lag of at least three months between the time of quarterly and annual financial statements and the time when the associated quarterly stock return is realized, when I implement the return decomposition. Data I study the sample period between 1984 and 2010 and merge the Center for Research in Security Prices Mutual Fund database with the Thompson mutual fund holdings database using MFLINK. I obtain fund characteristics (fund name, investment styles, turnover, size (TNA), expense ratio, and first offer date) and reported fund returns from the CRSP mutual fund database. The Thompson mutual fund holdings database provides long positions in domestic common stock holdings of mutual funds and investment styles of funds. I focus on US domestic active equity mutual funds, excluding fixed income, international, money market, sector and index funds. 3 I subject the funds to a number of 3 I identify US domestic equity funds with Lipper codes (’EIEI’, ’G’, ’I’, ’GI’, ’LCCE’, ’LCGE’, ’LCVE’, ’MCCE’, ’MCGE’, ’MCVE’, ’MLCE’, ’MLGE’, ’MLVE’, ’SCCE’, ’SCGE’, ’SCVE’), Strategic Insight codes (’AGG’, ’GMC’, ’GRI’, ’GRO’, ’ING’, ’SCG’) or Wienburger codes (’G’, ’G-I’, ’GCI’, ’LTG’, ’MCG’, ’SCG’, FUNDAMENTAL VALUES, PRICE DEVIATIONS, AND FUND MANAGERS 69 screens to mitigate omission bias (Elton et al. (2001)), incubation and back-fill bias (Evans (2010)). I exclude observations prior to the reported year of fund organization, and exclude funds that do not report a year of organization or which have initial total net assets (TNA) below $15 million in their otherwise eligible first year to enter our data set. I combine multiple share classes for a fund, value-weighting with the TNA of each share class. I categorize resulting mutual funds into four groups ("growth", "growth & income", "income", and "other"). 4 I conduct analyses on the mutual fund portfolios since many individual funds have limited time series data, and I form equally-weighted fund portfolios. Monthly stock pricing data come from CRSP and both quarterly and annual accounting data come from Compustat. The monthly risk-free rate is the one-month T-bill rate, and is downloaded from Professor Kenneth French’s website. DGTW benchmarks are downloaded from Russ Wermers’ web site. 5 Monthly analysts’ consensus earnings forecasts are from I/B/E/S. Decomposing Fund Performance: New Styles Equation (2.4) points out two channels through which fund managers can collect the information to generate performance. Accordingly, I decompose the managers’ performance into elements from those two channels. The measure of the fund managers’ performance follows the selectivity measure (CS) in Daniel et al. (1997). Although fund managers’ performance can involve more than selectivity, I focus on selectivity since it is a good starting point for illustrating the new finer performance decomposition conducted on top of the classical timing versus selectivity perspective. I decompose the selectivity into two components, relating to fund managers’ abilities to predict the fundamental part and the ’IEQ’, ’I’, ’I-G’) and exclude funds with Thomson-Reuters styles (1, 5, 6, 7) or with CRSP policy (’C & I’, ’Bal’, ’Bonds’, ’Pfd’, ’B & P’, ’GS’, ’MM’, ’TFM’). I identify index funds both by Lipper objective codes (SP, SPSP) and by searching the funds’ names with key word "index". 4 I identify "growth" funds with Lipper codes (’G’), Strategic Insight codes (’AGG’, ’GRO’) or Wienburger codes (’G’, ’MCG’, ’LTG’); I identify "growth & income" funds with Lipper codes (’GI’), Strategic Insight codes (’GRI’) or Wienburger codes (’G-I’, ’GCI’); I identify "income" funds with Lipper codes (’EIEI’, ’I’), Strategic Insight codes (’ING’) or Wienburger codes (’IEQ’, ’I’, ’I-G’); any residual funds are assigned to the group of "other". 5 The DGTW benchmarks are available via http:// www.smith.umd.edu /faculty /rwermers /ftpsite /Dgtw /coverpage.htm. FUNDAMENTAL VALUES, PRICE DEVIATIONS, AND FUND MANAGERS 70 price deviation part of stock returns, in the following way: CS =E((Aweight t ) 0 [R t+1 −R Bench t+1 ]) =E((w t −E[w t ]) 0 [R t+1 −R Bench t+1 ])=E((w t −w b t ) 0 [R t+1 −R Bench t+1 ]) =E((w t −w b t ) 0 [R Funda t+1 −R Funda,Bench t+1 ])+E((w t −w b t ) 0 [R PrcDev t+1 −R PrcDev,Bench t+1 ]) =CS Funda +CS PrcDev (2.7) where w t is the portfolio’s holding weight at the end of quarter t, E[w t ]=w b t is the passive holding weight fund managers would choose if they do not have superior information for investments, and Aweight t =w t −E[w t ]=w t −w b t which defines the active weight managers choose when deviating from the passive holding weight. I try three types of passive holding weights: the holding weights from the previous report date, the holding weights from the previous report date which have been updated in a buy and hold manner, and contemporaneous weights of the market portfolio. 6 R Bench t+1 is the vector of gross returns of the DGTW characteristic benchmarks. R Funda t+1 , and R PrcDev t+1 are the vectors of the fundamental parts and the price deviation parts of the total gross stock returns. R Funda,Bench t+1 , and R PrcDev,Bench t+1 are the vectors of the fundamental parts and the price deviation parts of gross returns of the DGTW benchmarks, constructed by value-weighting return components of stocks that constitute each DGTW benchmark. CS, CS Funda and CS PrcDev define total selectivity and its two components from the new decomposition. The new decomposition offers a new way to describe fund styles, reflecting fund managers’ focuses on return components when investing. The logic used to determine the new styles is that a larger selectivity component from the new decomposition may reflect fund managers’ increased favoritism for digging up information about the stock return component associated with that selectivity part. For example, a fund manager, with a larger fundamental component (CS Funda ) but with a smaller mispricing component (CS PrcDev ), belongs to a type who likes more (less) collecting fundamental (price deviation) information to guide her investments. Table 2.1 reports performance components of average mutual funds as well as fund subgroups. The last column suggests that average mutual funds do not have selectivity as a whole or across different subgroups. Regarding the new styles, average fund managers (row of "All") focus on price deviation information rather than fundamentals to guide their investments. If I examine the different subgroups, the preference for price deviation information continues to hold for average 6 I only report results using the holding weights from the previous report date as the passive holding weights. Similar results are obtained for the other two types. FUNDAMENTAL VALUES, PRICE DEVIATIONS, AND FUND MANAGERS 71 managers, except growth & income fund managers who show no significant preference for fundamental or price deviation information when investing. The Analysis of Individual Funds It is possible that the new style is related to fund managers’ overall skills and hence may predict future fund performance. It could be the case that managers who like collecting fundamental information have a better chance to generate superior performance, while it also could be the case that mispricing type managers who keep close eyes on price movements that cannot be explained by fundamentals have skills. To explore this issue, at each quarter end, I sort funds into deciles based on funds’ average performance components achieved in the past eight quarters to identify fundamental type or price-deviation type managers, and compute post-sorting overall performance of equal-weight fund deciles. Table 2.2 reports the results. Irrespective of sorting variables, the performance of all fund deciles is insignificant statistically, and so are the spreads between extreme deciles. Hence neither the two performance components from the new decomposition nor the total performance measure can predict future fund performance. This is likely due to excessive noise in the measures constructed. Overall, the new styles seem to be unrelated to future fund performance. Event Studies It could be the case that fund managers classified by the new styles do not exhibit their expertise all the time, but only show skills over periods around specific events that are predominantly affecting either fundamentals or the extent of price deviations. Hence concentrating on those specific events may help uncover fundamental or mispricing managers’ skills. Specifically, earnings announcements, analyst recommendation announcements, and stocks’ ex-dividend days are likely three events respectively about fundamentals (the first event) and price deviations (the latter two events) for the following reason. Earnings information is central for investors to assess fundamentals; recommendations are issued based on a comparison of ongoing stock prices and fair prices (or fundamental values) in analysts’ minds, likely reflecting the information of price deviations; dividends effective on ex-dividend days reduce stock prices and may lower arbitrage costs (e.g., Pontiff (2006)), therefore potentially shrinking the degree of mispricing. 7 Given these three events and based on the new styles proposed, we can make 7 For arbitrage short positions, one type of arbitrage holding cost comes from the opportunity cost asso- ciated with using at least part of the short sale proceeds as collateral for borrowing the securities to short. FUNDAMENTAL VALUES, PRICE DEVIATIONS, AND FUND MANAGERS 72 the following predictions: fundamental type fund managers perform better during earnings announcements while mispricing style managers do better during the other two types of events. I test the event period out-performance of fund managers in the new styles by examining the event performance of stocks managers actively hold in excess of the passive holdings (i.e., active weights Aweight t ). Stock event performance is measured for a period (-1,+1) around events. I explore the event performance respectively for stocks that funds hold in less than the passive holding weights (Aweight t <0 or "active sell") and those in more than the passive holding weights (Aweight t >0 or "active buy"). If fundamental type fund managers perform better during earnings announcements, then the stocks they actively buy (sell) should perform better (worse) during that type of event. Similarly, stocks that mispricing type fund managers actively buy (sell) should perform better (worse) during analyst recommendation announcements or stock ex-dividend days. Specifically, to identify fundamental type or price-deviation type managers, at every quarter end, I sort funds into deciles by performance components (CS Funda and CS PrcDev ), averaged over the past eight quarters. Then I compute fund performance during periods (-1,+1) around each type of event for post-sorting equal-weight fund deciles, using stocks that they actively hold and that experience the event (Table 2.3). I report the event performance of stocks that funds actively sell in column blocks "ActiveSell" and those that funds actively buy in column blocks "ActivelyBuy". I report two types of post-sorting performances measured respectively by market-adjusted stock returns around the event ("maret") calculated as raw stock returns minus the market return, and by DGTW-benchmark adjusted stock returns around the event ("baret") calculated as raw stock returns minus DGTW benchmark returns based on size, book-to-market equity and momentum. Panel A reports earnings announcements. Sorting on CS Funda suggests that more fundamental oriented managers in the new styles actively sell stocks that have significantly worse performance during the event (a t-stat of−2.65 and a magnitude of−11 basis points per three-days in a quarter for the characteristic-adjusted performance spread between stocks actively sold by the more fundamental oriented managers and by those who are less so), but do not exhibit the ability to actively buy stocks that have better event Further, the deviation from desired investment strategies due to having to meet collateral requirements can be another type of arbitrage holding cost. Dividend payments can lower stock prices and hence the impacts of collateral requirements, thus reducing both types of holding costs. On the other hand, for arbitrage long positions, major arbitrage holding cost is the loss from bearing the uncompensated idiosyncratic risk asso- ciated with those positions, since arbitrageurs tend to be undiversified. That cost would be proportional to prices or market capitalizations of long positions. Hence, dividend payments that lower stock prices can lower that major arbitrage cost for long undervalued stocks. FUNDAMENTAL VALUES, PRICE DEVIATIONS, AND FUND MANAGERS 73 performance, reflecting the fundamental managers’ superior knowledge of subsequent fundamental events (i.e., earnings announcements). Sorting on CS PrcDev or on total selectivity CS to identify more mispricing-oriented managers or more generally skillful managers does not show any significant relationship with the event performance of stocks actively bought or sold. For analyst recommendation announcements in panel B, sorting on CS PrcDev shows that more mispricing oriented managers actively sell stocks that have significantly worse performance during the event (a t-stat of−2.68 and a magnitude of−12 basis points per three-days in a quarter for the characteristic-adjusted performance spread between stocks actively sold by the more mispricing oriented managers and by those who are less so), but again do not exhibit the ability to actively buy stocks that have better event performances. This reflects mispricing managers’ superior knowledge of subsequent events likely driven mainly by mispricing information. On the other hand, more fundamental-oriented managers identified by sorting on CS Funda actively sell stocks that perform less poorly in the subsequent event, consistent with their lack of expertise to predict events driven mainly by mispricing information, given their focuses on fundamental information. There is another interesting pattern in panel B. Fund managers, irrespective of their new styles or rankings based on total selectivity CS, all actively both sell and buy stocks that perform poorly subsequently in the recommendation events. Although the wide-spread negative event performance of actively-sold stocks in panel B suggests that fund managers can predict analysts’ new recommendations that result in poor stock event reactions, the failure of fund managers to avoid buying stocks that go down during the events is a little puzzling. Further, the negative underperformance is much more significant both economically and statistically for stocks that managers actively sell than for those actively bought. Hence, the gains from stocks actively sold can more than cover the losses from those bought. Overall, more explorations are necessary to understand the stocks that managers actively buy before analyst recommendation announcements. Finally, for stocks’ ex-dividend days in panel C, sorting on performance components (CS Funda and CS PrcDev ) or on total selectivity CS are not related to event performance of stocks fund managers actively buy or sell. Overall, all the evidence from the event study is consistent with the new styles potentially capturing fund managers’ preference for fundamental or mispricing information when investing and with the prediction that fundamental (mispricing) style managers excel during events related mainly to fundamentals (mispricing). Moreover, the out-performance of those managers comes only from stocks they actively sell rather than those actively bought. Further, around analyst recommendation announcements, all of the fund managers exhibit significant performance FUNDAMENTAL VALUES, PRICE DEVIATIONS, AND FUND MANAGERS 74 from stocks they actively sell, and that performance is stronger (weaker) for mispricing (fundamental) managers. Further Explorations Why can the new styles predict managers’ performance around those two events? Since the new styles of fund managers are essentially a weighted sum of the new styles applied to stocks, one possible answer to the question is that the new styles, when applied to stocks, reflect a stock characteristic which predicts stock returns unrelated to what is controlled when evaluating fund performance (i.e., size, book-to-market equity, and momentum), and which is exploited by managers when investing. To test this possibility, I compute performance components (CS Funda and CS PrcDev ) for stocks by treating them as if they are individual mutual funds and therefore obtain the new styles applied to stocks. Every quarter, I sort stocks on stock-level components (CS Funda and CS PrcDev ) into equal-weight deciles and again compare characteristic-adjusted returns of stock deciles around subsequent events. High CS Funda (CS PrcDev ) predicts high (low) stocks’ returns around earnings announcements, while high CS Funda (CS PrcDev ) predicts low (high) stocks’ returns around analyst recommendation announcements. Hence, the out-performance of fundamental or mispricing style managers around those two events are at least partially driven by their exploitation of the stock return predictability attributed to firm-level CS Funda and CS PrcDev , and unexplained by size, book-to-market equity, and momentum. There is a hint about what really drives the stock return predictability of CS Funda and CS PrcDev . Firm-level CS Funda and CS PrcDev are essentially average return components, R funda t+1 and R PrcDev t+1 , adjusted for size, book-to-market equity, and momentum. In equation (2.3), we can see that R funda t+1 = V t+1 P t+1 ·R t+1 and R PrcDev t+1 =(1− V t+1 P t+1 )·R t+1 , implying that the predictability of R funda t+1 and R PrcDev t+1 (or CS Funda and CS PrcDev ) for future stock returns must come from that of V t+1 P t+1 and/or R t+1 (i.e., stocks’ fundamental value-price ratios and/or returns). 8 I test that implication by running two Fama-MacBeth cross-sectional regressions of future stock event returns on preceding stock characteristics. In the first test, I use characteristic-adjusted R t+1 (i.e., CS) and CS Funda (CS PrcDev ) as regressors. CS Funda (CS PrcDev ) continue to show predictability for future adjusted stock returns around earnings announcements, but they lose significant predictive power for analyst recommendation announcements. On the other hand, the significant predictability for adjusted stock event returns always holds for characteristic-adjusted returns R t+1 (i.e., 8 The stock return predictability of fundamental value-price ratios Vt+1 Pt+1 has been uncovered in Frankel & Lee (1998). FUNDAMENTAL VALUES, PRICE DEVIATIONS, AND FUND MANAGERS 75 CS), signalling a residual momentum effect that is uncleaned by the DGTW adjustment. In the second regression, I use characteristic-adjusted R t+1 (i.e., CS) and characteristic-adjusted V t+1 P t+1 as regressors. Characteristic-adjusted V t+1 P t+1 show the same slope signs and predictive power as CS Funda (CS PrcDev ) in both types of events. Overall, the analyses reflect that the predictability of firm-level CS Funda or CS PrcDev for stock event returns comes from the predictive power of fundamental value-price ratios proposed in Frankel & Lee (1998), particularly for the events of earnings announcements. Conclusion Classical perspective decomposes portfolio performance into security selectivity and market timing ability. I propose a new perspective to further decompose the performance of mutual fund managers into their abilities to predict future movements of stocks’ fundamental values and future variation of the deviations of stock prices from fundamental values. I implement the new decomposition based on portfolio holdings of mutual funds. Applying the new decomposition as a new way to describe fund managers’ investment styles, I find that average fund managers, as a whole or across groups with different claimed investment orientations except the group of growth & income funds, are price deviation types who focus more on price deviations of stocks and less on fundamental information to guide their investments, while growth & income fund managers do not exhibit a significant preference for fundamental or price deviation information when investing. Finally, analyses from the event study show some significant evidence that the new styles can predict fund managers’ performance around announcements of new earnings or analysts’ new recommendations, supporting that the new styles potentially capture fund managers’ preference for fundamental or mispricing information when investing. Further analyses suggest that the event performance predictability of the new styles is at least partially driven by managers’ exploitation of the stock return predictability attributed to stocks’ fundamental value-price ratios proposed in Frankel & Lee (1998), and unexplained by size, book-to-market equity, and momentum. FUNDAMENTAL VALUES, PRICE DEVIATIONS, AND FUND MANAGERS 76 Table 2.1 Performance Decomposition Of Average Mutual Funds Table reports the selectivity (DGTWcs) and its components related to stocks’ fundamentals and price deviations (DGTWcs Funda and DGTWcs PrcDev ) for average mutual fund man- agers. All performance measures reported are quarterly. Holding weights from the previous report date are the passive holding weights used to compute active weights of funds. Sample spans 1984:Q1-2010:Q4. Nobs DGTWcs Funda DGTWcs PrcDev DGTWcs All 106 -0.0039 0.0040 0.0000 t-stat -6.36 3.99 0.08 Growth 74 -0.0049 0.0050 0.0001 t-stat -2.62 2.06 0.12 Growth & Income 84 0.0000 0.0005 0.0005 t-stat -0.02 0.25 0.36 Income 106 -0.0014 0.0013 -0.0002 t-stat -2.46 2.06 -0.85 Other 106 -0.0045 0.0047 0.0002 t-stat -6.68 4.29 0.36 FUNDAMENTAL VALUES, PRICE DEVIATIONS, AND FUND MANAGERS 77 Table 2.2 Fund Performance Predictability Of New Styles At every quarter end, I sort funds into deciles by average performance components (DGTWcs Funda andDGTWcs PrcDev ) in the new decomposition or by average total performance (DGTWcs), computed using the past eight quarters. Then I report post- sorting fund performance (DGTWcs) of equal-weight fund deciles. All performance measures reported are quarterly. Holding weights from the previous report date are the passive holding weights used to compute active weights of funds. Sample spans 1984:Q1-2010:Q4. Nobs Sort DGTWcs Funda Sort DGTWcs PrcDev Sort DGTWcs decile 1 (lowest) est 98 0.0001 -0.0004 -0.0003 t-stat 0.11 -0.74 -0.37 decile 2 est 98 0.0001 -0.0002 0.0001 t-stat 0.15 -0.47 0.22 decile 3 est 98 0.0002 -0.0002 -0.0004 t-stat 0.25 -0.65 -1.06 decile 4 est 98 0.0001 -0.0003 -0.0001 t-stat 0.09 -0.70 -0.15 decile 5 est 98 -0.0003 -0.0004 -0.0003 t-stat -0.83 -1.07 -0.64 decile 6 est 98 -0.0002 0.0000 -0.0002 t-stat -0.48 -0.05 -0.53 decile 7 est 98 0.0000 0.0001 -0.0001 t-stat 0.04 0.15 -0.15 decile 8 est 98 -0.0002 0.0001 0.0001 t-stat -0.69 0.17 0.11 decile 9 est 98 -0.0005 -0.0002 0.0003 t-stat -1.35 -0.24 0.38 decile 10 (highest) est 98 -0.0004 0.0004 -0.0002 t-stat -0.86 0.33 -0.25 decile 10- decile1 est 98 -0.0005 0.0007 0.0001 t-stat -0.52 0.92 0.20 FUNDAMENTAL VALUES, PRICE DEVIATIONS, AND FUND MANAGERS 78 Table 2.3 Predictability Of New Styles For Before-cost Fund Performance Around Events Threetypesofeventsareexamined: earningsannouncements, analysts’recommendationannouncements, andex-dividenddates. At every quarter end, I sort funds into deciles by average performance components (DGTWcs Funda andDGTWcs PrcDev ) or by average total performance (DGTWcs), computed using the past eight quarters. Then I report before-cost fund performance during the announcement period (-1,+1) around each type of event for post-sorting equal-weight fund deciles. Before-cost fund performance is shown by reporting the holding performance respectively for stocks that funds hold in less than passive holding weights (column blocks ActiveSell) and those in more than passive holding weights (column blocks ActiveBuy). maret is fund performance measured by market-adjusted stock returns, calculated as raw stock returns minus the market return around the events; baret is fund performance measured by DGTW benchmark adjusted stock returns, calculated as raw stock returns minus DGTW benchmark returns (based on size, book-to-market equity and momentum) around the events. All numbers reported are 3-day announcement period performances earned quarterly. Holding weights from the previous report date are the passive holding weights used to compute active weights of funds. The sample spans 1984-2010. FUNDAMENTAL VALUES, PRICE DEVIATIONS, AND FUND MANAGERS 79 Table 2.3 – Continued Panel A: Earnings announcement events Sort DGTWcs Funda Sort DGTWcs PrcDev Sort DGTWcs ActiveSell ActiveBuy ActiveSell ActiveBuy ActiveSell ActiveBuy Nobs maret baret maret baret maret baret maret baret maret baret maret baret decile 1 (lowest) est 98 0.0028 0.0007 0.0028 0.0005 0.0018 -0.0003 0.0018 -0.0002 0.0020 0.0002 0.0021 0.0000 t-stat 3.94 1.45 5.27 1.25 3.15 -0.72 4.07 -0.56 3.51 0.41 4.88 -0.16 decile 2 est 98 0.0027 0.0007 0.0028 0.0006 0.0020 -0.0001 0.0020 -0.0002 0.0023 0.0003 0.0022 0.0001 t-stat 4.17 1.62 6.38 1.91 4.11 -0.20 5.65 -0.74 4.32 0.72 6.23 0.53 decile 3 est 98 0.0022 0.0004 0.0026 0.0006 0.0020 0.0002 0.0018 -0.0002 0.0023 0.0003 0.0021 0.0001 t-stat 3.81 0.93 6.97 2.07 3.91 0.67 5.70 -0.58 4.66 0.95 6.41 0.25 decile 4 est 98 0.0024 0.0006 0.0024 0.0004 0.0022 0.0003 0.0022 0.0001 0.0024 0.0006 0.0022 0.0002 t-stat 4.49 1.83 6.95 1.31 4.46 1.13 6.83 0.49 4.89 1.97 6.90 1.12 decile 5 est 98 0.0023 0.0004 0.0018 -0.0001 0.0024 0.0005 0.0018 0.0000 0.0026 0.0007 0.0021 0.0001 t-stat 4.32 1.26 5.53 -0.26 4.67 1.65 5.79 0.04 5.07 2.07 5.99 0.36 decile 6 est 98 0.0022 0.0004 0.0020 0.0001 0.0024 0.0004 0.0023 0.0004 0.0023 0.0003 0.0023 0.0002 t-stat 4.40 1.37 6.54 0.65 4.49 1.32 6.79 1.97 4.38 0.97 6.85 1.03 decile 7 est 98 0.0022 0.0003 0.0020 0.0001 0.0027 0.0008 0.0024 0.0005 0.0023 0.0004 0.0022 0.0002 t-stat 4.44 1.08 6.07 0.25 4.82 2.24 6.98 2.08 4.16 1.12 6.57 0.74 decile 8 est 98 0.0022 0.0003 0.0018 -0.0001 0.0024 0.0004 0.0027 0.0007 0.0025 0.0006 0.0026 0.0005 t-stat 4.16 1.02 5.19 -0.20 3.95 1.18 6.38 2.28 4.72 1.96 7.28 2.15 decile 9 est 98 0.0020 0.0001 0.0018 -0.0002 0.0024 0.0005 0.0026 0.0003 0.0020 0.0001 0.0023 0.0004 t-stat 3.74 0.31 5.46 -0.69 3.64 1.05 6.25 1.03 3.47 0.31 6.14 1.42 decile 10 (highest) est 98 0.0018 -0.0004 0.0022 0.0001 0.0026 0.0006 0.0027 0.0005 0.0020 0.0001 0.0021 0.0001 t-stat 3.27 -1.22 5.08 0.33 3.48 1.31 5.05 1.22 2.85 0.15 4.55 0.21 decile 10- decile1 est 98 -0.0010 -0.0011 -0.0006 -0.0004 0.0008 0.0009 0.0009 0.0006 0.0000 -0.0001 0.0001 0.0001 t-stat -1.84 -2.65 -1.17 -0.98 1.30 1.84 1.69 1.51 0.02 -0.20 0.17 0.33 FUNDAMENTAL VALUES, PRICE DEVIATIONS, AND FUND MANAGERS 80 Table 2.3 – Continued Panel B: Analyst recommendation announcement events Sort DGTWcs Funda Sort DGTWcs PrcDev Sort DGTWcs ActiveSell ActiveBuy ActiveSell ActiveBuy ActiveSell ActiveBuy Nobs maret baret maret baret maret baret maret baret maret baret maret baret decile 1 (lowest) est 69 -0.0034 -0.0020 -0.0016 -0.0005 -0.0008 -0.0006 -0.0006 -0.0004 -0.0019 -0.0012 -0.0012 -0.0005 t-stat -3.98 -4.57 -2.25 -1.84 -1.22 -1.43 -1.14 -1.81 -2.78 -3.07 -2.09 -2.29 decile 2 est 69 -0.0027 -0.0016 -0.0013 -0.0006 -0.0009 -0.0003 -0.0010 -0.0006 -0.0015 -0.0008 -0.0010 -0.0005 t-stat -3.84 -4.72 -2.21 -2.42 -1.47 -1.12 -1.99 -3.71 -2.48 -2.83 -1.92 -2.83 decile 3 est 69 -0.0019 -0.0010 -0.0010 -0.0004 -0.0007 -0.0002 -0.0007 -0.0002 -0.0013 -0.0006 -0.0010 -0.0006 t-stat -3.04 -3.48 -1.99 -1.98 -1.31 -0.88 -1.49 -1.06 -2.22 -2.33 -2.15 -3.27 decile 4 est 69 -0.0013 -0.0005 -0.0009 -0.0003 -0.0011 -0.0005 -0.0007 -0.0003 -0.0010 -0.0003 -0.0007 -0.0002 t-stat -2.21 -1.96 -1.78 -1.82 -1.91 -2.03 -1.36 -1.74 -1.84 -1.16 -1.73 -1.25 decile 5 est 69 -0.0014 -0.0007 -0.0009 -0.0002 -0.0011 -0.0004 -0.0007 -0.0001 -0.0009 -0.0002 -0.0006 0.0000 t-stat -2.63 -2.83 -1.82 -1.33 -2.07 -1.60 -1.45 -0.74 -1.65 -0.91 -1.33 -0.25 decile 6 est 69 -0.0011 -0.0004 -0.0006 -0.0001 -0.0011 -0.0003 -0.0007 0.0000 -0.0013 -0.0006 -0.0009 -0.0004 t-stat -1.94 -1.46 -1.45 -0.82 -2.01 -1.27 -1.50 -0.28 -2.14 -2.14 -1.95 -2.25 decile 7 est 69 -0.0009 -0.0002 -0.0006 -0.0001 -0.0015 -0.0006 -0.0009 -0.0003 -0.0015 -0.0007 -0.0007 -0.0002 t-stat -1.60 -0.79 -1.32 -0.75 -2.56 -2.38 -1.88 -1.79 -2.54 -2.76 -1.41 -1.18 decile 8 est 69 -0.0009 -0.0003 -0.0006 -0.0002 -0.0020 -0.0012 -0.0010 -0.0003 -0.0013 -0.0005 -0.0007 -0.0001 t-stat -1.49 -1.13 -1.31 -0.93 -3.01 -3.76 -1.73 -1.59 -2.06 -1.67 -1.24 -0.79 decile 9 est 69 -0.0008 -0.0004 -0.0006 -0.0002 -0.0027 -0.0015 -0.0013 -0.0005 -0.0020 -0.0010 -0.0009 -0.0003 t-stat -1.47 -1.36 -1.37 -1.49 -3.76 -4.93 -2.33 -2.09 -3.09 -3.79 -1.80 -1.48 decile 10 (highest) est 69 -0.0007 -0.0004 -0.0007 -0.0006 -0.0032 -0.0018 -0.0014 -0.0005 -0.0025 -0.0014 -0.0012 -0.0004 t-stat -1.12 -1.29 -1.32 -2.71 -3.83 -4.52 -2.06 -1.67 -3.27 -4.40 -1.83 -1.43 decile 10- decile1 est 69 0.0026 0.0015 0.0008 -0.0001 -0.0023 -0.0012 -0.0008 -0.0001 -0.0006 -0.0003 0.0000 0.0001 t-stat 4.47 3.47 1.61 -0.18 -3.71 -2.68 -1.55 0.22 -1.14 -0.66 0.03 0.41 FUNDAMENTAL VALUES, PRICE DEVIATIONS, AND FUND MANAGERS 81 Table 2.3 – Continued Panel C: Dividend Ex-days Sort DGTWcs Funda Sort DGTWcs PrcDev Sort DGTWcs ActiveSell ActiveBuy ActiveSell ActiveBuy ActiveSell ActiveBuy Nobs maret baret maret baret maret baret maret baret maret baret maret baret decile 1 (lowest) est 98 0.0020 0.0003 0.0018 -0.0002 0.0023 0.0002 0.0020 0.0001 0.0020 0.0001 0.0018 -0.0001 t-stat 5.45 0.93 4.78 -0.64 7.02 0.87 6.60 0.26 6.64 0.41 6.36 -0.29 decile 2 est 98 0.0020 0.0005 0.0019 0.0002 0.0022 0.0004 0.0019 0.0003 0.0023 0.0005 0.0018 0.0001 t-stat 6.30 1.72 5.75 0.66 7.26 2.31 6.61 1.74 7.95 2.34 6.20 0.57 decile 3 est 98 0.0019 0.0004 0.0015 -0.0001 0.0024 0.0005 0.0017 0.0002 0.0022 0.0006 0.0017 0.0002 t-stat 7.02 1.89 5.66 -0.58 7.28 2.49 6.06 1.18 7.53 3.03 6.60 0.91 decile 4 est 98 0.0020 0.0005 0.0015 0.0000 0.0020 0.0004 0.0013 -0.0003 0.0020 0.0005 0.0016 -0.0001 t-stat 7.55 2.36 5.78 0.08 6.63 1.85 5.20 -1.56 5.82 2.42 5.93 -0.53 decile 5 est 98 0.0017 0.0003 0.0012 -0.0002 0.0018 0.0003 0.0014 -0.0001 0.0020 0.0004 0.0015 -0.0001 t-stat 6.25 1.33 5.63 -1.20 6.43 1.77 5.38 -1.04 6.78 2.36 5.35 -0.56 decile 6 est 98 0.0017 0.0002 0.0014 -0.0001 0.0018 0.0004 0.0015 0.0000 0.0020 0.0006 0.0015 0.0000 t-stat 5.21 1.05 5.39 -0.77 5.73 1.90 5.61 0.21 6.65 2.66 5.87 0.16 decile 7 est 98 0.0020 0.0005 0.0014 0.0000 0.0020 0.0006 0.0014 -0.0002 0.0018 0.0003 0.0015 -0.0002 t-stat 6.34 2.32 5.62 0.07 7.35 2.97 5.18 -1.36 6.61 1.24 6.00 -1.07 decile 8 est 98 0.0020 0.0003 0.0018 0.0001 0.0018 0.0003 0.0016 0.0000 0.0020 0.0004 0.0016 0.0000 t-stat 6.46 1.82 6.64 0.88 6.76 1.39 6.18 -0.07 6.95 2.19 5.40 0.02 decile 9 est 98 0.0022 0.0004 0.0017 0.0000 0.0019 0.0003 0.0018 -0.0001 0.0018 0.0001 0.0017 -0.0001 t-stat 6.73 2.12 5.24 0.22 5.64 1.15 5.77 -0.28 6.22 0.58 6.45 -0.41 decile 10 (highest) est 98 0.0025 0.0002 0.0020 0.0001 0.0018 0.0001 0.0018 0.0000 0.0018 0.0000 0.0017 0.0000 t-stat 7.87 0.94 6.74 0.56 4.74 0.48 4.52 -0.14 4.97 -0.02 4.66 0.07 decile 10- decile1 est 98 0.0005 0.0000 0.0002 0.0003 -0.0006 -0.0001 -0.0003 -0.0001 -0.0002 -0.0001 -0.0001 0.0001 t-stat 1.62 -0.14 0.43 0.91 -1.49 -0.26 -0.70 -0.27 -0.63 -0.34 -0.29 0.24 ESSAYS IN EMPIRICAL ASSET PRICING 82 References Ang, A., Hodrick, R., Xing, Y., & Zhang, X. 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Abstract (if available)

Abstract The literature on economic risk premiums has largely been based on ex post returns. In Chapter 1, I construct and assess implied ex ante economic risk premiums for a list of economic factors, which are driving forces in various asset pricing models, using direct expected returns estimates--i.e., the implied costs of capital (ICCs). For most economic factors, ICCs support significant nonzero average economic risk premiums which ex post returns fail to uncover since ex post returns are too volatile, implying that many economic factors are actually priced from an ex ante perspective. Second, implied ex ante factor risk premiums are a new and powerful predictor for future ex post returns of factor mimicking portfolios for most economic factors (e.g., value and size factors, default spread, inflation, the growth rate of labor income, and one-month T-bill real return), both in sample and out of sample. Analyses suggest that time-varying ex ante economic risk premiums are at least one major reason for the predictability of ICCs. ❧ In Chapter 2, I show that a stock return can be expressed as a sum of two components, which are a change in the stock's fundamental value measured using tangible information such as accounting information and analysts' forecasts, and a change in the deviation of the stock's price from its fundamental value. I decompose the selectivity of mutual fund managers into their abilities to predict those two return components, and use the new decomposition to describe fund managers' investment styles in a new way, reflecting their focuses on return components when investing. Average fund managers focus on price deviation information rather than fundamentals to guide their investments. Further, there is some significant evidence that these new styles can predict fund managers' performance around announcements of new earnings or new analysts' recommendations, and such performance predictability is at least partially driven by managers' exploitation of the stock return predictability attributed to stocks' fundamental value-price ratios proposed in Frankel & Lee (1998).

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Creator Mo, Haitao (author)

Core Title Essays in empirical asset pricing

School Marshall School of Business

Degree Doctor of Philosophy

Degree Program Business Administration

Publication Date 07/24/2013

Defense Date 06/12/2013

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

Tag economic risk premiums,implied costs of capital,mimicking portfolios,mutual funds,OAI-PMH Harvest

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Ferson, Wayne (committee chair), Jones, Christopher S. (committee member), Ozbas, Oguzhan (committee member), Radchenko, Peter (committee member), Solomon, David (committee member)

Creator Email haitao.mo.2012@marshall.usc.edu,mht116@hotmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-298685

Unique identifier UC11294949

Identifier etd-MoHaitao-1836.pdf (filename),usctheses-c3-298685 (legacy record id)

Legacy Identifier etd-MoHaitao-1836.pdf

Dmrecord 298685

Document Type Dissertation

Format application/pdf (imt)

Rights Mo, Haitao

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

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