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Two essays on the mutual fund industry and an application of the optimal risk allocation model in the real estate market

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Two essays on the mutual fund industry and an application of the optimal risk allocation model in the real estate market

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Content TWO ESSAYS ON THE MUTUAL FUND INDUSTRY AND AN APPLICATION OF THE OPTIMAL RISK ALLOCATION MODEL IN THE REAL ESTATE MARKET By Zhishan Guo A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (BUSINESS ADMINISTRATION) May 2015 Copyright 2015 Zhishan Guo Dedication I dedicate my dissertation to My beloved grandparents and parents And my loving wife Hang. ii Acknowledgements I am indebted to my dissertation committee chair, Fernando Zapatero, for his constant guid- ance and encouragement. I am especially grateful to Christopher Jones, David Solomon, Peter Radchenko, Wayne Ferson, and Andreas Stathopoulos, for helpful comments and sug- gestions. I thank Junbo Wang, Chao Zhuang, Garrett Swanburg, Sakya Sarkar, and seminar participants at University of Southern California for fruitful discussions. iii Table of Contents Dedication ii Acknowledgements iii List of Tables vi List of Figures vii Abstract viii Chapter 1: Horizon Goals and Risk Taking in Mutual Funds 1 1.1 Introduction 1 1.2 Model 5 1.2.1 Setup 5 1.2.2 Optimal Risk Exposure 8 1.2.3 Risk Exposure and Investment Horizon 9 1.2.4 Risk Exposure Beyond t=0 12 1.3 Data 13 1.3.1 Data Sources 13 1.3.2 Variables 15 1.4 Empirical Analysis 19 1.4.1 Investment Horizon and Fund Risk 19 1.4.2 Investment Horizon and Fund Performance 21 1.4.3 Investment Horizon, Fund Risk, and Closet Indexing 22 1.4.4 Investment Horizon, Fund Risk, and the Claim to Focus on the Long Term 23 1.4.5 Propensity Score Balancing 24 1.5 Conclusion 25 Appendix 1 A 27 Appendix 1 B 30 iv Chapter 2: Seller Choice of Risk and Real Estate Seasonality 43 2.1 Introduction 43 2.2 Model 48 2.2.1 Seller and Realtor Conflicts of Interests 50 2.2.2 Risk Aversion, House Value, and Seasonality 51 2.2.3 Convex Payoff Structure and Realtor Optimal Risk Exposure 53 2.3 Data and Variables 56 2.3.1 Measuring Seasonality 56 2.3.2 Risk Aversion, Home Value, and Control Variables 59 2.4 Regression Analysis 60 2.5 Conclusion 63 Chapter 3: Do Mutual Fund Managers Pick Winners within Product Markets? 80 3.1 Introduction 80 3.2 Literature Review 81 3.3 Data 82 3.4 Empirical Results 84 3.5 Conclusion 88 Reference 100 v List of Tables Table 1.1 Summary Statistics 33 Table 1.2a Investment Horizon and Mutual Fund Risk (2006) 34 Table 1.2b Investment Horizon and Mutual Fund Risk (2006-2010) 35 Table 1.2c Investment Horizon and Mutual Fund Risk (2006-2012) 36 Table 1.3 Investment Horizon and Mutual Fund Performance 37 Table 1.4 Investment Horizon and Mutual Fund Risk for Closet Indexers 38 Table 1.5 The Claim to Focus on the Long Term and Mutual Fund Risk 39 Table 1.6 Long Term Focusing Dummy in Two Subsamples 40 Table 1.7 Maximum Evaluation Horizon in Two Subsamples 41 Table 1.8 Propensity Score Balanced Sample 42 Table 2.1 Summary Statistics 75 Table 2.2 Variable Pairwise Correlation 76 Table 2.3 Real Estate Seasonality and Seller Risk Aversion (1997-2013) 77 Table 2.4 Real Estate Seasonality and Seller Risk Aversion (1997-2007) 78 Table 2.5 Real Estate Seasonality and Seller Risk Aversion (2008-2013) 79 Table 3.1 Summary Statistics 92 Table 3.2 Firm Concentration Decile Fund Portfolios and Carhart 4 Factor Alpha 93 Table 3.3 Regression Analysis: Firm Selectivity and Carhart 4 Factor Alpha 94 Table 3.4 Firm Concentration Decile Fund Portfolios and Industry Average Adjusted Return 95 Table 3.5 Regression Analysis: Firm Selectivity and Industry Average Adjusted Return 96 Table 3.6a Sub-Sample Regression Analysis (1996-2002) 97 Table 3.6b Sub-Sample Regression Analysis (2003-2008) 98 Table 3.7 Long Short Portfolio Based On Selectivity Scores 99 vi List of Figures Figure 1.1 Optimal Risk Exposure and Investment Horizon 31 Figure 1.2 Expected Relative Performance and Investment Horizon 32 Figure 2.1 Linear Payoff: Optimal Risk Exposure and Share of Selling Price 65 Figure 2.2 Linear Payoff: Seller Risk Aversion and Seasonality 66 Figure 2.3 Linear Payoff: House Value and Seasonality 67 Figure 2.4 Convex Payoff: Realtor Payoff and Sold Price 68 Figure 2.5 Convex Payoff: Realtor Utility and Sold Price 69 Figure 2.6 Convex Payoff: Optimal Risk Exposure and House Value 70 Figure 2.7 Convex Payoff: House Value and Seasonality 71 Figure 2.8 U.S. Residential Real Estate Market Seasonality 72 Figure 2.9 Distribution of Months with Largest Seasonality 73 Figure 2.10 Distribution of Maximum Seasonality 74 Figure 3.1 Firm Concentration Decile Fund Portfolios and Carhart 4 Factor Alpha 90 Figure 3.2 Firm Concentration Decile Fund Portfolios and Industry Average Adjusted Return 91 vii Abstract My dissertation contains three chapters. The first chapter is based on my job market paper “Horizon Goals and Risk Taking in Mutual Funds.” This paper studies the relationship between mutual fund manager investment horizons and managerial risk-taking decisions. Using a dynamic model, I show that therelation between the investment horizon and optimal risk taking is negative for managers confident in their investment abilities. Consistent with the model implication and manager over-confidence, I find that in general mutual funds reporting longer maximum evaluation horizons have lower risk, and the low risk levels helped these funds mitigate their losses in the financial crisis; for a sub-sample of funds with low active shares (closet indexers) whose managers are possibly less confident in their skills, the link between the investment horizon and fund risk becomes positive and close to zero. The second chapter, “Seller Choice of Risk and Real Estate Seasonality,” applies the optimal risk allocation model to the residential real estate market. This paper analyzes the optimal listing price for real estate sellers/realtors in a reward-risk tradeoff setting. Consistent with prior literature, the optimal listing price for the realtor is lower than that for the seller. However, realtor career concerns generate a convex payoff structure, which mitigates this conflict of interests. Based on the matching theory, the model in the paper indicates that seller risk aversion should negatively relate to real estate seasonality and the house value should positively relate to real estate seasonality. In the empirical part of the paper, I first document great cross-sectional variations in real estate seasonality at the zip code area level, and then test the model implications. Consistent with the model, the percentages of foreign born population and renter occupied housing units, the median house value, the median owner cost excluding mortgages, and the median number of rooms within a house, are positively related to real estate seasonality, while the percentage of married population is negatively related to real estate seasonality. The third chapter, “Do Mutual Fund Managers Pick Winners within Product Markets?” is joint work with Garrett Swanburg, my colleague at University of Southern California. We viii develop a measure of within-industry selectivity by mutual fund managers based on three different industry definitions: Kacperczyk-Sialm-Zheng, Fama-French, and Hoberg-Phillips. We find that managers that are more selective in their investments generate significantly higher risk-adjusted returns. This result also holds when using an industry-adjusted bench- mark based on these three industry definitions. Finally, we find evidence that mutual fund holdings provide information in predicting which individual stocks will perform will achieve higher returns. This research adds to the mutual fund literature which seeks to evaluate the ability of active fund managers to generate returns. ix 1 Horizon Goals and Risk Taking in Mutual Funds 1.1 Introduction This paper studies the connection between mutual fund manager’s investment hori- zons and fund risk. Traditional wisdom suggests that investors with longer horizons should hold more risky assets. 1 However, recent debates on the financial crisis argue that shortsight- edness makes fund managers prefer risky investment. 2 This paper first examines the effect of varying investment horizons in a model that incorporates relative performance concerns and performance-payoff convexity into the classical Merton (1969, 1971) economy. The model shows that the relation between the investment horizon and optimal risk taking depends on the manager’s skill. If managers believe they can outperform the benchmark and the Sharpe ratio of their fund compares favorably with the (upside) volatility of the benchmark, then optimal risk taking will negatively relate to the investment horizon. Ithentestthemodelimplicationsusingdatacollectedfrommutualfundprospectuses. According to SEC Rule S7-12-04, mutual funds are required to report the evaluation periods 1 The old rule of thumb for retirement savers is that 100−age should be the percentage of the portfolio in equities, and the rest in bonds and cash. 2 A Wall Street Journal Article published on June 6, 2014 argues that “fund managers’ relentless focus on short-term results . . . helped drive many banks to take the kinds of risks . . . that tipped the world into financial crisis.” 1 1 Horizon Goals and Risk Taking in Mutual Funds of their portfolio managers in the Statement of Additional Information. Since fund manager compensation depends on the evaluation of manager performance by the investment advisory company, I use the evaluation period as the proxy for the manager investment horizon. Fund compensation structures are stable over time, so I focus on domestic equity funds in 2006, the first year when information on portfolio manager compensation structures is available for all funds. Data collected from the fund prospectuses show that portfolio managers are evaluated over horizons of varying lengths from one year to ten years. Consistent with the model implication and manager over-confidence, I find that funds with longer maximum evaluation horizons have lower risk levels throughout the period from 2006 to 2012. These fundstradelessaggressivelyonmarketriskpremiumandwell-knownassetpricinganomalies. Not surprisingly, during the 18 month stock market downturn from October 2007 to March 2009, funds with longer maximum evaluation horizons suffer from less severe losses compared to their peers. I then test the link between the maximum evaluation horizon and fund risk for closet indexers (i.e., funds with low active shares, Cremers and Petajisto (2009) and Petajisto (2013)). The low active share levels potentially reflect the managers’ lack of confidence in the investment skills. Consistent with the model prediction, I find that the link between risk and maximum evaluation horizons is positive and close to zero for these funds. One concern of usingthemaximumevaluationhorizonastheproxyforinvestmenthorizonisthatinvestment advisory companies are not required to report the weight on various evaluation periods, and it is possible that funds report long maximum evaluation horizons but the real focus is on the short term. I find that after controlling for the maximum evaluation horizon, funds claiming that they focus on the long term have less risk. And this relationship is especially strong for funds reporting long maximum evaluation horizons. This raises the concern for regulators that more information revelation might be necessary. Theoretical models on dynamic asset allocation have linked investment horizons with optimal risk exposure, but the studies typically assume utility functions over intertemporal consumption or final portfolio value, which is not suitable for the mutual fund industry. 2 1 Horizon Goals and Risk Taking in Mutual Funds For example, Kim and Omberg (1996) and Wachter (2002) study how investment horizons affect optimal asset allocation assuming that the risk premium is mean-reverting. Relative performance concerns and the convex performance-payoff structure distinguish the mutual fund managers from individual investors. Fund manager compensation is usually based on the fund’s performance compared to index benchmarks or peer fund performance. Multiple reasons lead to a convex performance-payoff structure. First of all, a stylized fact about the mutual fund industry is that the flow-performance curve is convex. 3 Fund flow is directly linked to investment company profits and thus to portfolio manager compensation. Secondly, portfolio managers receive bonus rewards only when relative performance passes a certain level. 4 Thirdly, top mutual fund managers have the chance to manage hedge funds side-by- side (Cici, Gibson, and Moussawi (2010), Nohel, Wang, and Zheng (2010), Deuskar, Pollet, Wang, and Zheng (2011)).Therefore, models analyzing the influence of investment horizon on individual investors are not suitable for fund managers. Prior papers on mutual fund risk are plenty, but so far have ignored its relationship with investment horizons. For example, the tournament literature (Brown et al. (1996), Chevalier and Ellison (1997), Sirri and Tufano (1998), Kempf and Ruenzi (2008)) analyzes how mutual funds adjust their risk levels based on prior performance. Basak and Makarov (2013), Cuoco and Kaniel (2011), and Sotes-Paladino (2013) study the strategic interactions among portfolio managers. Basak, Pavlova, and Shapiro (2007), Carpenter (2000), and Chen and Pennacchi (2009) examine fund risk and benchmarks. Two recent papers test whether fund managers with long term clientele adopt investment strategies with greater market ex- posure. The evidence is conflicting. Christoffersen and Simutin (2012) show that funds raise their market risk exposure in response to the increase in retirement money in their total net assets. Chuprinin and Massa (2011) show that variable annuity funds, which should have long investment horizons, have lower return volatilities but higher market beta. 5 The 3 Some researchers believe that the shape of the flow-performance curve is open to debate. See Kim (2013). 4 See section 3 for detailed description of fund manager compensation. 5 Variable annuity funds offer capital protection guarantees that distinguish them from open-end mutual funds. The two types of funds are thus not directly comparable in the study of investment horizons. 3 1 Horizon Goals and Risk Taking in Mutual Funds hypotheses in these papers are formed based on the common practitioner advice for retire- ment savers to reduce equity exposure and shift to bond securities as retirement approaches. However, mutual fund managers make investment decisions in an environment very different from that faced by retirement savers, and thus investment suggestions for retirement savers might not be directly applicable to fund managers. This paper shares some empirical conclusions with Ma, Tang, and Gomez (2013), which analyzes portfolio manager compensation structures in 2009. However, this paper focuses on mutual fund risk. The model developed in this paper provides a theoretical foundation for the relationship between evaluation horizons and fund risk, and shows this connection is complex. Additionally, in this paper, I study fund risk for a much longer time period, including the recent financial crisis when careful risk management is the most valu- able. In the end, I do not find a significant link between factor-adjusted performance and evaluation horizons for domestic equity mutual funds. This paper is also broadly related to the vast literature studying mutual fund agency problems and monitoring. Prior work has shown that investment advisory company clientele, fee structures, broker dealers, fund family organizations, adviser/sub-adviser structures, etc. all have an influence on fund trad- ing decisions and performance. 6 This paper provides another perspective and shows how performance evaluation horizons relate to risk and returns. This paper has practical implications for both regulators and individual investors, as well. The finding that manager evaluation horizons relate to risk taking supports the SEC’s effort to promote information revelation in the delegated investment industry. Information onmanagercompensationstructureshelpsinvestorsmakeinvestmentdecisionsmoresuitable to their own needs and circumstances. Investors not willing to bear risk should pay special attention to funds adopting short evaluation horizons. These funds tend to take more risk and thus incur more severe losses during market downturns. 6 Chen et al. (2013), Christoffersen and Simutin (2012), Christoffersen et al. (2012), Cici et al. (2012), Chuprinin and Massa (2011), Evans and Fahlenbrach (2013), Gaspar et al. (2006), Gil-Bazo and Ruiz- Verdu(2009), Johnson(2004), Kahraman(2011), Kuhnen(2009), LesseigandLong(2002), Massa(2003), Nanda et al. (2009), O’Neal (1999), Sialm and Starks (2012). 4 1 Horizon Goals and Risk Taking in Mutual Funds The rest of the paper is organized as follows. Section 2 develops the model. Section 3 describes data sources and variables. Section 4 empirically examines how evaluation horizons relate to fund risk and returns. Section 5 concludes. 1.2 Model 1.2.1 Setup I consider a continuous-time economy on the finite time span [0,T ] along the line of Merton (1969, 1971) and Black and Scholes (1973). Uncertainty is driven by a standard Brownian motion process W. Financial investment opportunities for the portfolio manager are represented by one risky asset S and one risk-less money market account. The interest rate of the money market account is constant at r. The portfolio manager has the ability to select equities to form the risky assetS that follows the geometric Brownian motion process, dS(t)/S(t) =μ s dt +σ s dW (t), (1.1) where the drift term μ S and the volatility term σ S are constant. The portfolio manager makes the dynamic asset allocation decision ω that denotes the fraction of total wealth P invested in the risky portfolio S and thus represents the “risk exposure”. The total wealth process P evolves according to dP (t)/P (t) = ω(t)(μ S −r) +r ! dt +ω(t)σ S dW (t). (1.2) The portfolio manager’s performance is measured against a benchmark wealth pro- cess B. Following Basak, Pavlova, and Shapiro (2007), Carpenter (2000), and Chen and Pennacchi (2009), I assume the benchmark is exogenously given and follows dB(t)/B(t) =μ B dt +σ B dW (t), (1.3) 5 1 Horizon Goals and Risk Taking in Mutual Funds where μ B and σ B are constant. As revealed in different fund prospectuses, mutual fund managerperformanceisusuallybenchmarkedonvariousindexesaswellaspeerperformance. Although it is possible to mimic the index portfolios, it is not easy to copy the trading strategies of competing funds. Here I assume that the portfolio manager cannot trade in the benchmark. This assumption guarantees the completeness of the market and eliminates arbitrage opportunities. It also facilitates the analysis of fund risk exposure. Following Basak, Pavlova, and Shapiro (2007), Basak and Makarov (2013), Chen and Pennacchi (2009), Cuoco and Kaniel (2011), and Sotes-Paladino (2013), I define relative performance as the ratio of the total wealth process controlled by the portfolio manager and the benchmark wealth process, i.e. G(t) =P (t)/B(t). A simple application of Ito’s lemma shows that dG(t) G(t) = ω(t)(μ S −r−σ S σ B )− (μ B −r−σ 2 B ) ! dt + ω(t)σ S −σ B ! dW (t). (1.4) Portfolio manager compensation is modeled as an increasing convex function of rel- ative performance at time T. One stylized fact about the mutual fund industry is that the flow-performance curve is convex. Fund flow is directly linked to investment company prof- its and thus portfolio manager compensation. Moreover, portfolio managers receive bonus reward only when relative performance passes certain level, so the relationship between port- folio manager compensation and relative performance should be convex. In addition, top mutual fund managers have the chance managing hedge funds side-by-side. Basak, Pavlova, and Shapiro (2007), Basak and Makarov (2013), and Cuoco and Kaniel (2011) model fund flow using piecewise functions; Carpenter (2000) models portfolio manager compensation using the payoff of a call option; Chen and Pennacchi (2009) use a smooth convex function. These papers all have the same spirit and here I adopt the compensation function in Chen and Pennacchi (2009) for its tractability. I denote portfolio manager compensation as π and assume that it is a function of relative performance at time T: 6 1 Horizon Goals and Risk Taking in Mutual Funds π[G(T )] = a +bG(T ) ! c , (1.5) where a, b > 0 and c > 1. This guarantees that the compensation structure is increasing and convex, and portfolio manager compensation is always above zero. As common in the theoretical literature studying portfolio manager risk taking in- centives, I assume that the portfolio manager is guided by constant relative risk aversion (CRRA) preferences on the time T total compensation π(T ), u[π(T )] = π(T ) 1−γ 1−γ . (1.6) Hereγ equalsthecoefficientofrelativeriskaversion. Noticethatthecoefficientofrelativerisk aversion γ is multiplied by the performance-payoff convexity parameter c, and the effective riskaversionismeasuredbytheproductofthetwoparameters. Onenecessaryassumptionto keep the model interesting isc(1−γ)< 1, i.e. the concavity of the utility function dominates the convexity of the performance-payoff curve. 7 Otherwise, the fund manager would behave as a risk lover and take as much risk as possible. Notice that this condition is easily satisfied. For any risk aversion coefficient above 1, 1−γ is below zero, and c(1−γ) < 1 is satisfied. For risk aversion coefficient below 1, the condition is satisfied as long as c is not very large. 8 7 Assumptions similar to this one is common in theoretical models using convex performance-payoff struc- tures. For piecewise payoff functions, if the kink in the payoff curve is too sharp, the region that needs to be concavified in the utility function would be wide and the manager would need to take a lot of risk to maximize his utility. See Basak, Pavlova, and Shapiro (2007), Basak and Makarov (2013), and Cuoco and Kaniel (2011). 8 Koijen (2014) argues that the performance-payoff structure for mutual fund is not obvious and uses a linear performance-payoff function. 7 1 Horizon Goals and Risk Taking in Mutual Funds 1.2.2 Optimal Risk Exposure Given the above economic set up, compensation structure, and preferences, the port- folio manager solves the dynamic maximization problem, Max ω(t) E ( π(T ) 1−γ 1−γ ) , (1.7) subject to equation (2.4) by choosing risk exposure ω(t). The following proposition charac- terizes the explicit solution of this maximization problem. Proposition 1 The optimal fraction of assets invested in the risky portfolio S (“risk expo- sure”) at time t is given by ω(t) = μ s −r σ 2 s +A t + ˜ A t exp[−l(T−t)] (1.8) whereA t = fk G(t)σ S exp[(f−1)kW (t)− 1 2 f 2 k 2 t+(l+ 1 2 k 2 )t], ˜ A t = −kg G(t)σ S 1−fexp[−(1− f)kW (t)− 1 2 f 2 k 2 t+ 1 2 k 2 t] ! ,f = c(1−γ) c(1−γ)−1 ,g = a b ,k =σ B − μ S −r σ S , andl = σ B σ S (μ S −r)−(μ B −r). Proof. See appendix. In the standard Merton (1969, 1971) economy, when the investor maximizes utility from final wealth and/or inter-temporal consumption, the optimal fraction of wealth invested in the risky asset equals μ S −r γσ 2 S . It does not depend on the horizon of investment. Proposition 1 shows that incorporating relative performance and the convex compensation structure in the Merton model makes the solution for the optimal asset allocation more complicated. The optimal fraction of assets invested in the risky portfolio S is now made up of three parts. The first part, μs−r σ 2 s , is the standard mean variance component. The second part consists of an exponential term that depends on time t and the time t Brownian motion process W (t). Notice at t = 0, A 0 = fk G(0)σ S . As time passes and W (t) evolves, both time and the Brownian motion start to affect the optimal risk exposure. The influence of time and the 8 1 Horizon Goals and Risk Taking in Mutual Funds Brownian motion process is adjusted by the product of relative performance G(t) and the volatility term of the risky asset σ S . All else equal, managers who have already achieved good relative performance facing large volatilities in the risky asset would want to stay closer to the standard Merton allocation. Similarly, the third part of the optimal asset allocation depends on time t and the Brownian motion process W (t). Most importantly, the third part contains an exponential term of the investment horizonT, showing how the investment horizon affects the optimal risk exposure. 1.2.3 Risk Exposure and Investment Horizon Clearly, optimal risk exposure is affected by the investment horizon, but does longer investment horizon makes the manager take more or less risk? The answer is not obvious. The values of the parameters f, g, k, and l affect the relation between the optimal risk exposure ω(t) and the evaluation horizon T. Moreover, whether the optimal risk exposure ω(t) increases or decreases with evaluation horizonT depends on the stochastic processG(t) and the Brownian motion process W (t). Despite the above complexities, at t = 0, G(0) and W (0) are known, and thus it is feasible to algebraically analyze the link between the initial optimal risk exposure ω(0) and the evaluation horizon T. The following corollary summarizes this link. Corollary 1 Given a coefficient of relative risk aversion greater than 1, the initial optimal risk exposure ω(0) decreases (increases) with the evaluation horizon T if kl< (>)0. ω(0) is not dependent on T if kl = 0. Proof. See appendix. Corollary 1 shows that the relation between the initial optimal risk exposure ω(0) and the evaluation horizon T depends on the signs of k and l, which both have special meanings. As defined in proposition 1, l = σ B σ S (μ S −r)− (μ B −r). I divide l by σ B and denote l 0 = μ S −r σ S − μ B −r σ B . Since σ B > 0, l and l 0 have the same sign. l 0 equals the difference 9 1 Horizon Goals and Risk Taking in Mutual Funds between the Sharpe ratio of the risky asset and the Sharpe ratio of the benchmark. The sign of the parameter l 0 raises a long-time research question: whether portfolio managers have the ability to outperform their benchmarks. 9 Berk and Green (2004) believe that portfolio managers have skills but all the economic rent are seized by the mutual funds through expenses and diseconomy of scale. Recent research has used various measures, such as active share, return gap, and industry concentration to distinguish skilled managers (Cremers and Petajisto (2009), Kacperczyk, Sialm, and Zheng (2005, 2008)). It worth noting that the Sharpe ratio of the risky asset S does not need to represent the real investment ability of the portfolio manager. Literature on overconfidence shows how investors’ (mis)belief of their ability affects their performance (Barber and Odean (2001), and Putz and Ruenzi (2008)). Portfolio managers make investment decisions as ifl> 0 as long as they think they have the ability to beat the benchmark. Montier (2009) once asked a sample of over 500 professional managers if they were above average at their jobs. “An impressive 74% responded in the affirmative. Indeed many of them wrote comments such as ’I know everyone thinks they are, but I really am’!”. Apparently, at least 24% of these managers cannot be above average in theory. If the question is whether the managers can beat a passive index, the percentage responding “yes” would probably be even higher. If managers believe that they can beat the benchmark, the optimal risk exposure ω(t) would negatively relate to the evaluation horizon T if k is negative. As defined in proposition 1, k =σ B − μ S −r σ S . It is the volatility of the benchmark minus the Sharpe ratio of the risky security. A negative k means that the portfolio manager Sharpe ratio is larger than the volatility of the benchmark. This is reasonable in normal economic conditions. A skilled portfolio manager has better control over her relative performance if her ability is good enough compared to the volatility of the benchmark. Another way of viewing this 9 Research on portfolio manager performance goes back to Jensen (1969), who shows that good perfor- mance does not persist. Though later studies are more optimistic about mutual fund manager skills (Grinblatt and Titman (1992), Elton, Gruber, Das, and Hlavka (1993), Hendricks, Patel, and Zeckhauser (1993), Brown and Goetzmann (1995), Grinblatt, Titman, and Wermers (1995), and Elton, Gruber, Das, and Black (1996)), Carhart (1997) concludes that common factors in the stock market, expenses, and transaction costs explain most of the persistence in mutual fund returns. 10 1 Horizon Goals and Risk Taking in Mutual Funds condition is to divide the parameterk by the volatility termσ S . Notice now μ S −r σ 2 S represents the standard Merton asset allocation in the risky security, and σ B σ S is the portfolio allocation in the risky security that perfectly hedges the volatility in relative performance (See equation 2.4). Similar to l, the value of the parameter k depends on the investment ability of the manager. If the manager is capable enough so that the standard Merton allocation is higher than the allocation that results in zero volatility in relative performance, then k is negative. In the case of the mutual fund industry, I take a pessimistic view that managers do not have abilities to beat the market and estimatek assuming the Sharpe ratio of the risky asset S and the volatility of the benchmark are close to those of the Fama and French (1996) market portfolio. k is negative in the whole sample period from 1926 to 2012, the relatively calm period after the 1980s 10 , and the period from 2006 to 2012 when the stock market experienced substantial turmoil. According to Corollary 1, if portfolio managers think they have skills to beat the benchmark and the benchmark is not too volatile, compensation systems evaluating per- formance over longer horizons encourage portfolio managers to be more careful at taking risk, confirming the industry wisdom on the financial crisis. It should be noted that this relation may not hold in all money management industries at all times. If the portfolio manager is evaluated based on a very volatile benchmark so she has little control over her relative performance, extending the evaluation horizon would make the portfolio manager more aggressive at taking risk. For example, Pastor and Stambaugh (2012) point out that predictive variance and observed variance are different because parameters are uncertain and have to be estimated. Lack of information can make predictive variance from the manager’s perspective very large although the real variance is low. If the portfolio manager thinks he has no skills and can barely mimic the return of the benchmark, then the evaluation horizon would be irrelevant to risk taking. 10 The Great Moderation literature (Kim and Nelson 1999, McConnell and Perez-Quiros 2000, Blachard and Simon 2001, Stock and Watson 2002, etc.) shows that macroeconomic volatilities reduced sharply in the 1980s. 11 1 Horizon Goals and Risk Taking in Mutual Funds 1.2.4 Risk Exposure Beyond t=0 Up to this point, I have analyzed the relation between initial optimal risk exposure ω(0) and the evaluation horizon T. For t > 0, the relation should be the same since the real evaluation horizon is T−t. If the relation holds for T− 0 with T changing, it should also hold forT−t withT changing. Skeptical readers might point out that in Corollary 1 I normalized the relative performanceG(0) to 1. At timet,G(t) should be different for funds with various evaluation horizons since they have different initial risk exposure. And the value of G(t) affects risk taking at t. Examining the level of optimal risk exposure for t> 0 allowingG(t) to evolve according to Proposition 1 is complicated because ω(t) is a function of the Brownian motion W (t) and the stochastic process G(t). One way to overcome this complexity is to study the expected value of ω(t). I resort to Monte Carlo simulations to examine this expected value numerically. To check if the relation between optimal risk exposure and performance evaluation horizon att = 0 holds fort> 0, I simulateM = 3000 paths of optimal risk exposureω(t) for each evaluation horizon T according to equation 2.8. I choose Δt = 1 and set T = hΔt so h represents the length of the evaluation horizon. At each t, I estimate the expected value of the optimal risk exposure by averaging ω(t) over these 3000 paths. 11 Figure 1a plots the paths of the expected value of ω(t) with T = 12, T = 24, and T = 36 periods for the case that k < 0 and l> 0, i.e. the manager’s Sharpe ratio is higher than that of the benchmark and the standard Merton asset allocation in the risky security is larger than the allocation perfectly hedges the volatilities in relative performance. 12 It can be easily seen from figure 1a that longer investment horizons lead to lower risk exposure. The path for T = 12 lies above the path for T = 24, and the path for T = 36 is at the bottom. This is consistent with Corollary 1 that optimal risk exposure decreases with the investment horizon. All three paths have negative slopes, showing that the optimal risk exposure for the manager decreases 11 Increasing the number of paths M to 5000 or 10000 does not generate material gain in accuracy. 12 I leta =b = 1,c = 2, andγ = 2. The figure does not change qualitatively if I use other parameter values. 12 1 Horizon Goals and Risk Taking in Mutual Funds as the final time periodT approaches and the effective investment horizonT−t shortens. It is important to point out that this is not contradictory to Corollary 1. Since the initial risk exposure differs for various investment horizons, relative performance after t = 0 would be different. And the difference in relative performance will be reflected in risk exposure after t = 0. Figure 1b plots the relative performance for the case that k < 0 and l > 0 for two investment horizons. Since the manager has the ability to outperform the benchmark, the relative performance rises in expectation as time passes. Notice that the curve for T = 12 lies above the curve for T = 36, which is resulted from the higher risk exposure in the case ofT = 12. Intuitively, since the manager has the investment ability to beat the benchmark, he can take less risk and be more patient when the investment horizon is longer. As time passes and his performance exceeds the benchmark, the need to take lower risk to lock in good performance dominates the effect of the decrease in the investment horizon. 1.3 Data I test the predictions of the above model using information on the mutual fund in- dustry. This section describes data sources and how variables are formed. 1.3.1 Data Sources Data used in the paper are collected from two sources: the CRSP Survivorship- Biased Free Mutual Fund Database and the SEC Edgar website. From the CRSP Mutual Fund Database, Icollect information on fund name, management companyname, investment objectivecode, totalassetsundermanagement, dateofinception, expenseratio, andturnover ratio. I focus on US domestic equity funds by selecting funds that have investment objective codes with the first two letters “ED”, standing for “equity domestic”. I exclude funds with total net assets under management below five million US dollars and funds with date of inception in the last year. 13 1 Horizon Goals and Risk Taking in Mutual Funds Information on fund portfolio manager compensation structures is downloaded from the SEC Edgar website. Since March 2005, all mutual funds are required to report the portfolio manager compensation structure in Part B, statement of additional information, of the prospectus. Specifically, each fund needs to state if the portfolio manager’s compensation andfundperformancearedirectlyrelated; iftheyaredirectlyrelated,thefundneedstoreveal the performance evaluation horizon. I downloaded the 2006 prospectus of all US domestic equitymutualfundsbecause2006isthefirstyearwhenallfundsreporttheportfoliomanager compensation structure at least once. For mutual funds that release several prospectuses in 2006, I downloaded the earliest one. I randomly picked mutual funds and checked if the compensation structure changes over time. I found that the compensation structure is very stable. It is to some extent intricate to collect information about fund portfolio manager compensation structures. The first problem is that usually one prospectus contains infor- mation about a series of mutual funds. In this case, I first locate the advisory/sub-advisory company that is responsible for the day-to-day trading decisions for each fund in part A of the prospectus, and then collect information on how the advisory/sub-advisory company compensates its portfolio managers in part B, statement of additional information. The second complexity is the “manager of managers” structure. Some advisory companies hire several sub-advisory companies to make the day-to-day trading decisions for one mutual fund. I exclude funds that are managed by more than one sub-advisory company. The first reason is that different sub-advisory companies have different compensation structures, and since funds do not report the percentage of total net assets managed by each sub-advisory company, it is not possible to identify which compensation structure is the most important or take the weighted average of the evaluation horizons. The second reason is that it is generally easy to change sub-advisers. Usually, the decision to change a sub-adviser within a manager-of-managers structure is made by the mutual fund board of directors. The decision does not need to be approved by fund shareholders as long as the decision is made public 14 1 Horizon Goals and Risk Taking in Mutual Funds sixty days before the sub-adviser is changed. In my sample, 65.21% of all the US domestic equity mutual funds directly link the portfolio manager compensation with fund performance. Among these funds, 93.83% have information about performance evaluation horizons clearly stated. In the end, I manage to collect information on performance evaluation horizons for 61.19% of US domestic equity mutual funds. These funds manage 82.27% of total net assets managed by all US domestic equity mutual funds. 1.3.2 Variables Using information on fund compensation structures, I create the variables measuring the length of the investment horizon. The main proxy for the investment horizon is the maximum evaluation horizon considered when determining portfolio manager compensation. Thisisthemostdirectandintuitivemeasure,andIuseitforthemajorityoftheempiricaltest in the paper. Mutual funds are not required to report how they calculate portfolio manager compensation. It is possible that some mutual funds report a long maximum evaluation horizon just to make their prospectuses look more attractive to potential investors, but actually they only assign a very low weight to long term performance when determining portfolio manager compensation. I supplement maximum evaluation horizon by the second measure: the long term focusing dummy. The long term focusing dummy equals one if the investment advisory company openly claims that it assigns a higher weight or it focuses on long term performance when determining portfolio manager compensation. The long term focusing dummy also equals one if the investment advisory company clearly states that it does not consider the most recent one year performance. For the rest of the mutual funds, the long term focusing dummy equals zero. For example, if an investment advisory company reports that portfolio manager compensation is based on 1, 3, and 5 year performance, focusing on 3 and 5 year performance, then maximum evaluation horizon would be 5 and the long term focusing dummy equals one. The two variables do not change if an investment 15 1 Horizon Goals and Risk Taking in Mutual Funds advisory company reports that portfolio manager compensation is based on 3 and 5 year performance. If an investment advisory company reports that compensation is based on 1 and 3 year performance, then maximum evaluation horizon would be 3 and long term focusing dummy would be 0. To better illustrate how I formed the evaluation horizon measures, it is useful to look at a real world example. Below is the section describing manager compensation from the prospectus of Fidelity Advisor Value Strategies Fund. 13 “The portfolio manager’s bonus is based on several components. The primary com- ponents of the portfolio manager’s bonus are based on the pre-tax investment performance of the portfolio manager’s fund(s) and account(s) measured against a benchmark index and within a defined peer group assigned to each fund or account. The pre-tax investment per- formance of the portfolio manager’s fund(s) and account(s) is weighted according to the portfolio manager’s tenure on those fund(s) and account(s) and the average asset size of those fund(s) and account(s) over the portfolio manager’s tenure. Each component is calcu- lated separately over the portfolio manager’s tenure on those fund(s) and account(s) over a measurement period that initially is contemporaneous with the portfolio manager’s tenure, but that eventually encompasses rolling periods of up to five years for the comparison to a benchmark index, rolling periods of up to three years for the comparison to a Morningstar peer group, and rolling periods of up to five years for the comparison to a Lipper peer group.” For this fund, it is clear that the maximum evaluation horizon is 5 years. Since the fundprospectusdoesnotspecifyifthefundassignsahigherweighttolongtermperformance, the long term focusing dummy equals zero. Mutual fund return and characteristics data are obtained from the CRSP Mutual Fund Database. CRSP lists each share class of a mutual fund as a single fund. I first aggregate the share class level variables into fund level variables. I sum up the total net assets of all share classes of a fund as the total net assets of the fund. Expense ratio and 13 Allmutualfundprospectusescanbedownloadedathttp://www.sec.gov/edgar/searchedgar/prospectus.htm 16 1 Horizon Goals and Risk Taking in Mutual Funds turnover ratio of a fund are the value weighted average of the expense ratios and turnover ratios of all share classes. Date of inception of the fund is the earliest date of inception of all share classes. To calculate total loads, I first sum up maximum front load and maximum rear load of each share class as share class total loads, and then take the weighted average of share class total loads as total loads of the fund. I create the variable fund size by taking the natural log of fund total net assets. Log fund age is the natural log of the number of months since the date of inception. Family size is the natural log of the total net assets under management of the fund family. Log number of funds in family is the natural log of the total number of equity funds in the fund family. I use three variables to measure fund performance. The first measure is the Carhart 4-factor alpha, calculated according to the following model: FundReturn t −rf t =α +β 1 mktrf t +β 2 hml t +β 3 smb t +β 4 mom t +e. Fund return is the monthly fund return. rf is the risk free rate, mktrf, hml, and smb are the Fama-French factors, and mom is the momentum factor. α is the Carhart 4-factor alpha. To account for the variation in factor loadings, I also consider the conditional version of the four factor model (Ferson and Schadt (1996)). I follow Kacperczyk, Sialm, and Zheng (2005) and include interaction terms of the market risk premium and various macro-economic variables: FundReturn t −rf t =α+β 1 mktrf t +β 2 hml t +β 3 smb t +β 4 mom t + 4 X i=1 β 1,i [z i,t−1 (mktrf t )] +e, where z i,t−1 ’s are the demeaned lagged Treasury bill yield, dividend yield of the S&P 500 Index, Treasury yield spread, and corporate bond quality spread. 14 14 Data on these Macro-economic variables are downloaded from Amit Goyal’s website at http://www.hec.unil.ch/agoyal/. See Goyal and Welch (2008) for details. 17 1 Horizon Goals and Risk Taking in Mutual Funds The third performance measure is the return percentile. I first calculate the aggre- gated return of all funds. Then I group the funds by their investment objective codes. The percentile of the aggregated return among funds sharing the same investment objective code is the return percentile measure. To measure fund risk, I use four variables formed using monthly return data for various periods in 2006-2012. Return volatility is the standard deviation of monthly returns. Style mean normalized return volatility is calculated by dividing return volatility by the average return volatility of the funds with the same investment objective code. Carhart model systematic risk is the standard deviation of the Carhart model systematic return, which is calculated by taking the product of the beta coefficients and the corresponding monthly factors. Carhart model idiosyncratic risk is the standard deviation of Carhart model idiosyncratic return, which is the regression error term of the Cahart 4-factor model. Data on active share is downloaded from Petajisto’s website. 15 I take the average of the active shares of each fund in 2005. Following Cremers and Petajisto (2009), I define a fund as a closet indexer if the average active share is below 60%. 16 By definition, about half of the value of an index will have above-average returns and the other half will have below- average returns. Therefore, any fund with an active share below 50% is actually combining an active fund and an index fund. Table 1 reports the summary statistics of the above variables. Fund size, log fund age, expense ratio, turnover ratio, total loads, family size, and the log number of funds in family are measured at the end of 2005. I report return volatility, Style mean normalized return volatility, Carhart model systematic risk, and the Carhart model idiosyncratic risk measured using monthly return data in 2006, while in the empirical analysis I also include regressions of risk measures calculated over longer time periods. Since in the empirical analysis I focus on the comparison of the influence of evaluation horizons in the financial crisis and the whole sample period from 2006 to 2012, I report the unconditional and conditional Carhart 15 http://www.petajisto.net/data.html 16 Using other cutoffs such as 50% and 70% does not change the results materially. 18 1 Horizon Goals and Risk Taking in Mutual Funds four factor alpha and the return percentile calculated using data from 2006 to 2012. The number of observations for the closet indexer dummy is lower than the other variables. This reflects the more restrictive sample selection method used by Cremers and Petajisto (2009). I include sector funds while Cremers and Petajisto (2009) do not. This accounts for more than half of the difference. I also include funds that invest both in domestic and international equities, while Cremers and Petajisto require funds to invest mainly in domestic stocks. The evaluation horizon demonstrates considerable variation across funds. The mean maximum evaluation horizon is around 4.3 years. While some funds only evaluate their portfolio managers based on the most recent one year performance, some other funds consider performance as long as 10 years. The mean value of the long term focusing dummy equals 0.415, indicating that 41.5% of the funds that have portfolio manager compensation directly linked to performance openly claim that they focus on the long term performance or state that they do not consider the most recent one year performance. 1.4 Empirical Analysis 1.4.1 Investment Horizon and Fund Risk Section2showsthattherelationbetweenfundmanagerrisktakingandtheevaluation horizon depends on the manager’s belief on her investment skill. If the manager thinks she can outperform the benchmark, then risk taking would negatively relate to the evaluation horizon. If the manager thinks she can barely match the return of the benchmark, then the evaluation horizon would have no influence on risk taking. I first assume that managers think they have skills. After all, it is hard to believe that practitioners go to work everyday thinking their effort adds no value to their client’s account. I then try to differentiate the mutual funds using active share as a proxy for managers’ belief on their skills. Assuming managers think that they have skills, I form the following hypothesis. Hypothesis 1 Mutual fund risk is negatively related to the maximum evaluation horizon. 19 1 Horizon Goals and Risk Taking in Mutual Funds To test this hypothesis, I regress mutual fund return volatility, style mean normalized return volatility, Carhart model systematic risk, and the Carhart model idiosyncratic risk cross-sectionally on the maximum evaluation horizon, controlling for fund size, log fund age, expense ratio, turnover ratio, total loads, family size, and the log number of funds within the family. Siegel (2008) and Pastor and Stambaugh (2012) point out that return variance measured over various horizons can be very different. Therefore, when I measure fund risk using monthly return data, I require that the fund exists throughout the whole period to guarantee that all fund risk is measured over the same horizon. This leads to a tradeoff between the length of the measurement period and the number of observations. Using risk measures calculated over longer time periods results in more survivorship bias. To address this issue, I perform the same regression analysis on risk measures calculated over different time periods. Table 2a shows the result of the regressions on risk measures calculated using monthly returns in 2006. Notice that the coefficients of the maximum evaluation horizon are all neg- ative and statistically significant. This suggests that mutual fund managers facing longer evaluation horizons take less risk both in absolute terms and in comparison with their peers. The regression on Carhart model systematic risk shows that they trade the market risk premium and well-known asset pricing anomalies less aggressively, while the regression on Carhart model idiosyncratic risk shows that they also take more diversified positions. Table 2b and table 2c show the results of the same regressions for the period from 2006 to 2008 and from 2006 to 2012. Measuring fund risk over a longer time period leads to fewer obser- vations; however, the result is very similar to that in table 2a. The above results support the hypothesis that mutual fund managers with longer investment horizons take less risk. This is consistent with the model implication for the case that managers think they have the ability to outperform the benchmark. 20 1 Horizon Goals and Risk Taking in Mutual Funds 1.4.2 Investment Horizon and Fund Performance The empirical evidence up to this point supports hypothesis 1 that mutual funds evaluating their portfolio managers over longer horizons have lower risk. Responsible risk management is the most valuable in bad market conditions. Therefore, funds with longer evaluation horizons should protect their investors from huge losses in the financial crisis. To check this idea, I separately examine fund performance in two time periods. The first time period is the whole sample period from 2006 to 2012. The second time period is the 18 month period from October 2007 to March 2009 during which the stock market falls substantially. Studying fund performance in these two periods is necessary for the identification of the influence of risk taking. In the financial crisis, better performance can be generated by either better investment skills or more conservative investment at the first place. Here tests using the whole sample period act as the control group. For 2006-2012, I also include the conditional Carhart model risk adjusted returns to account for potential alterations in factor loadings. Table 3 reports the results of the regressions of the Carhart 4 factor alpha and the return percentile on the maximum evaluation horizon, controlling for various fund character- istics. None of the coefficients of the maximum evaluation horizon in the regressions of the Carhart 4 factor alpha are significant, showing that funds with various evaluation horizons do not differ in their investment ability besides trading the market risk premium and well- known stock market anomalies. This is confirmed by the regressions of the return percentile from 2006 to 2012. The coefficients of the maximum evaluation horizon in this regressions is close to zero and statistically insignificant. In contrast, the coefficient of the maximum evaluation horizon is positive and statistically significant in the regression of the return per- centile during the 18 month market downturn. Controlling for other fund characteristics, funds with one year longer maximum evaluation horizons rank about 1.5% higher among their peers. This finding suggests that the difference in risk taking of funds with various evaluation horizons reflects itself in fund performance in bad market conditions. 21 1 Horizon Goals and Risk Taking in Mutual Funds 1.4.3 Investment Horizon, Fund Risk, and Closet Indexing The model predicts that if managers believe that they can outperform their bench- mark, longer investment horizon should lead to lower risk taking. The above empirical evidence supports this idea. Although optimism seems ingrained in the psyphe of the in- vestment professionals, not all managers have skills or believe they have skills. Cremers and Petajisto (2009) discover that some fund managers engage in closet indexing, i.e. having low deviations from the index while claiming to be an active fund. Having low levels of active share can be an evidence of lack of skill or lack of confidence. And according to the model, longer investment horizons should have no or positive influence on the risk taking of these managers. In this subsection, I test the following hypothesis. Hypothesis 2 Risk of closet indexers is not related to or positively related to the maximum evaluation horizon. To test the hypothesis, I add the closet indexer dummy and its interactive term with the maximum evaluation horizon into the regressions in section 4.1. If risk of closet indexers is not related to or positively related to the evaluation horizon, the coefficient of the interactive term should be positive and the sum of the coefficients of the interactive term and the maximum evaluation horizon should be positive or close to zero. Table 4 shows the regressionresults. consistentwiththemodelprediction, theinteractivetermofthemaximum evaluation horizon and the closet indexer dummy has a positive and statistically significant coefficient for all risk measures. The coefficient of the maximum evaluation horizon remains negative and statistically significant. Notice that the sum of the coefficient of the interactive term and the maximum evaluation horizon is positive for all risk measures, consistent with the model prediction that the connection between investment horizon and risk taking is positive for unskilled managers. 22 1 Horizon Goals and Risk Taking in Mutual Funds 1.4.4 Investment Horizon, Fund Risk, and the Claim to Focus on the Long Term The empirical evidence up to this point supports the model implication that fund risk negatively relates to the investment horizon for managers confident in their skills. One problem of using the maximum evaluation horizon as the proxy for the investment horizon is that funds are not required to report the weight on various evaluation periods. It is possible that funds report long maximum evaluation horizons to attract customers but still focus on the short term when compensating their managers. To address this concern, I add the long term focusing dummy to the regressions in section 4.1. Table 5 shows the results of the regressions. For brevity, I do not report the control variables. Itisclearthatthemaximumevaluationhorizonstillhavenegativeandstatistically significant coefficients. For risk measured from 2006 to 2012, the long term focusing dummy also has negative and statistically significant coefficients. It seems that the two variables both contain useful information on the evaluation horizon not captured by the other at least for 2006-2012. If funds report long maximum evaluation horizons to attract customers, whether a fund claims an emphasis on the long term should be especially important for funds with long maximum evaluation horizons. To test this idea, I divide the sample into two sub-samples according to the values of the maximum evaluation horizon. In table 6, I separately examine the connection between long term focusing dummy and mutual fund risk for funds with maximum evaluation horizon below and above the median. Consistent with table 5, the long term focusing dummy is negatively related to return volatility, style mean normalized volatility, and Carhart model systematic risk in both sub-samples. However, the coefficients ofthelongtermfocusingdummyinthetwosub-samplesdifferintheirstatisticalsignificance. For funds with maximum evaluation horizon below or equal to 4 years, it seems that whether the mutual fund reports an emphasis on the long horizon have insignificant influence on fund risk. On the contrary, in the sub-sample of funds with maximum evaluation horizon above 23 1 Horizon Goals and Risk Taking in Mutual Funds 4 years, the coefficients of the long term focusing dummy become statistically significant. This raises the concern for mutual fund clients and regulators that without any information on the weight of evaluation horizons, it is hard to obtain a full picture of the real investment horizon fund managers face. In table 7, I separately examine the connection between maximum evaluation horizon and mutual fund risk for funds with long term focusing dummy equal to 0 and 1. Consistent with Table 2, the maximum evaluation horizon is negatively related to return volatility, style mean normalized volatility, and Carhart model systematic risk in both sub-samples. The coefficients of the maximum evaluation horizon in the two sub-samples differ in their statis- tical significance. For the sub-sample of funds reporting an emphasis on the long horizon, none of the coefficients of the maximum evaluation horizon are statistically significant. For the sub-sample of funds with the long term focusing dummy equal to 0, the coefficients of the maximum evaluation horizon are all negative and statistically significant. Intuitively, if a fund claims an emphasis on the long term in its compensation structure, it has to place a higher weight on manager long term performance, and then the length of the maximum evaluation horizon no longer has great influence on manager risk taking. 1.4.5 Propensity Score Balancing In the previous analysis, I test empirically the predictions of the model. One problem ofthetestisthatevaluationhorizonsareendogenouslydetermined. Itispossiblethatmutual funds with long and short evaluation horizons are different intrinsically, and I am “comparing apples to oranges”. In a perfect laboratory setting, to test the effect of evaluation horizon on fund risk taking, I would need to randomly assign long and short evaluation horizons to fund portfolio managers. To alleviate this concern, I calculate the propensity score of the mutual fund having the maximum evaluation horizon above-median using observable fund characteristics. If evaluation horizons are randomly assigned, the propensity score of funds having above-median maximum evaluation horizons should be close to the proportion of 24 1 Horizon Goals and Risk Taking in Mutual Funds funds having above-median maximum evaluation horizons in the sample. This means that funds with extreme propensity scores are most likely to be different from the rest of the funds. And the endogeneity issue is the most severe for these funds. I trim observations with propensity scores below 0.1 or above 0.9 and redo the key tests in section 4. Table 8 shows the results of the regressions of fund risk on the maximum evaluation horizon. It is clear that the results in the previous section hold after trimming. The coefficients of the maximum evaluation horizon remain negative and statistically significant. 1.5 Conclusion This paper examines the connection between mutual fund manager investment hori- zons and fund risk. I first study this connection using a dynamic asset allocation model derived from the standard Merton (1969, 1971) setting. Incorporating relative performance concerns and the convex compensation structure into the Merton model, the optimal risk ex- posure is no longer fixed. It depends on the investment horizon and the relative performance. Specifically, for managers confident in their invest abilities, longer investment horizons make the manager more conservative at taking risk. If a manager thinks he cannot outperform the benchmark, the relation between investment horizon and risk taking can be zero or positive. I collect information on mutual fund compensation structures from fund prospec- tuses, and use information on the time periods over which investment companies evaluate fund manager performance to form proxies for manager investment horizons. I show that in general mutual funds with longer maximum evaluation horizons have lower risk. Most meaningful to investors, I find that lower risk levels of these funds helped them mitigate losses during the 2008 financial crisis. I then test the model prediction for funds with low levels of active share. I find for the closet indexers, longer evaluation horizon is related to more risk taking. This paper confirms the industry wisdom that shortsightedness of mutual fund managers lead to strong incentives to take risk in most cases, but also shows that the 25 1 Horizon Goals and Risk Taking in Mutual Funds connection between investment horizon and fund manager risk taking is complex and can be different in various circumstances. 26 1 Horizon Goals and Risk Taking in Mutual Funds Appendix 1.A Proof of Proposition 1 I use the martingale/duality approach developed by Cox and Huang (1989) and Karatzas, Lehoczky, and Shreve (1987) to solve for the optimal risk exposure ω(t). Denote μ A =μ S −r−σ S σ B and μ B =r−μ B +σ 2 B . Then the dynamic process that relative performance follows can be written as dG(t) G(t) = ω(t)μ A +μ B ! dt + ω(t)σ S −σ B ! dW (t). (1.9) Consider the dynamic process Z(t) = exp[− μ A σ S W (t)− (μ B + σ B σ S μ A )t− 1 2 ( μ A σ S ) 2 t]. (1.10) whichissimilartothe“statepricedensity”process. Then dZ(t) Z(t) =− μ A σ S dW (t)−(μ B + σ B σ S μ A )dt. Simple application of the Ito’s lemma shows that dG(t)Z(t) G(t)Z(t) = ω(t)σ S −σ B − μ A σ S ! dW (t). (1.11) Therefore E{G(T )Z(T )} = G(0), and G(t)Z(t) is a martingale process. Write the La- grangian L = E{ a +bG(T ) ! c(1−γ) } +λ G(0)−E{G(T )Z(T )} ! . (1.12) The first order condition shows G(T ) = 1 b ( λZ(T ) cγb ) 1 c(1−γ)−1 − a b . (1.13) Since G(t)Z(t) is a martingale process, G(t)Z(t) = E t {G(T )Z(T )} = E t { 1 b ( λ cγb ) 1 cγ−1 Z(T ) cγ cγ−1 − a b Z(T )}. (1.14) 27 1 Horizon Goals and Risk Taking in Mutual Funds Denote e = 1 b ( λ cγb ) 1 c(1−γ)−1 , f = cγ cγ−1 , and g = a b . Then G(t)Z(t) = E t {eZ(T ) f −gZ(T )} =eZ(t) f E t {( Z(T ) Z(t) ) f }−gZ(t)E t { Z(T ) Z(t) } (1.15) Denotek =− μ A σ S andl =μ B + σ B σ S μ A =r−μ B + σ B σ S (μ S −r). ThenZ(t) = exp[kW (t)− (l + 1 2 k 2 )t]. G(t)Z(t) = eZ(t) f E t {exp[fk(W (T )−W (t))−f(l + 1 2 k 2 )(T−t)]} −gZ(t)E t {exp[k(W (T )−W (t))− (l + 1 2 k 2 )(T−t)]} = eZ(t) f exp[ 1 2 f 2 k 2 (T−t)−f(l + 1 2 k 2 )(T−t)] −gZ(t)exp[ 1 2 k 2 (T−t)− (l + 1 2 k 2 )(T−t)] = e∗exp[fkW (t)−f(l + 1 2 k 2 )t + 1 2 f 2 k 2 (T−t)−f(l + 1 2 k 2 )(T−t)] −g∗exp[kW (t)− (l + 1 2 k 2 )t + 1 2 k 2 (T−t)− (l + 1 2 k 2 )(T−t)] = e∗exp[fkW (t) + 1 2 f 2 k 2 (T−t)−f(l + 1 2 k 2 )T ] −g∗exp[kW (t)− 1 2 k 2 t−lT ]. (1.16) Normalize G(0) = 1. Then λ can be solved from 1 = E{G(T )Z(T )}. (1.17) After some algebra, e = 1 +g∗exp(−lT ) exp( 1 2 f 2 k 2 T− 1 2 fk 2 T−flT ) (1.18) 28 1 Horizon Goals and Risk Taking in Mutual Funds Applying Ito’s lemma to equation (A.8) dG(t)Z(t) = (...)dt = + ( fke∗exp[fkW (t) + 1 2 f 2 k 2 (T−t)−f(l + 1 2 k 2 )T ] = −kg∗exp[kW (t)− 1 2 k 2 t−lT ] ) dW (t) (1.19) Comparing diffusion terms with equation (A.3), G(t)Z(t) ω(t)σ S −σ B − μ A σ S ! = fke∗exp[fkW (t) + 1 2 f 2 k 2 (T−t)−f(l + 1 2 k 2 )T ] −kg∗exp[kW (t)− 1 2 k 2 t−lT ]. (1.20) And ω(t) = 1 G(t)σ S ( fke∗exp[(f− 1)kW (t) + 1 2 f 2 k 2 (T−t)−f(l + 1 2 k 2 )T + (l + 1 2 k 2 )t] −kg∗exp[−l(T−t)] ) + μ s −r σ 2 s . (1.21) Plug e into ω(t), ω(t) = μ s −r σ 2 s + 1 G(t)σ S ( fkexp[(f− 1)kW (t)− 1 2 f 2 k 2 t + (l + 1 2 k 2 )t] −kgexp[−l(T−t)] 1−fexp[−(1−f)kW (t)− 1 2 f 2 k 2 t + 1 2 k 2 t] !) (1.22) where f = c(1−γ) c(1−γ)−1 , g = a b , k =σ B − μ S −r σ S , and l = σ B σ S (μ S −r)− (μ B −r). 29 1 Horizon Goals and Risk Taking in Mutual Funds Appendix 1.B Proof of Corollary 1 According to equation (A.14), at t = 0, G(0) = 1 and W (0) = 0 ω(0) = μ s −r σ 2 s + 1 σ S fk−kg(1−f)exp[−lT ] ! . (1.23) Taking the derivative of ω(0) with respect to T generates dω(0) dT = 1−f σ S kglexp[−lT ] ! . (1.24) Since c(1−γ)< 1, 1−f = −1 c(1−γ)−1 > 0. σ S > 0, g = a b > 0, and exp[−lT ]> 0, so the sign of dω(0) dT is determined by the sign of kl. 30 1 Horizon Goals and Risk Taking in Mutual Funds 0 5 1 0 1 5 2 0 2 5 3 0 3 5 0 .8 3 0 .8 4 0 .8 5 0 .8 6 0 .8 7 0 .8 8 0 .8 9 0 .9 0 .9 1 tim e t (M an ager h as in v estm en t ability . k< 0, L> 0) T =1 2 T =2 4 T =3 6 Figure 1.1. This figure plots the expected optimal risk exposure for the manager that has the investment ability with investment horizons 12, 24, and 36 periods. Specifically, the manager’s Sharpe ratio is higher than that of the benchmark, and the standard Merton asset allocation in the risky security for the manager is larger than the allocation perfectly hedges the volatlities in relative performance. 31 1 Horizon Goals and Risk Taking in Mutual Funds 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 1 .0 5 1 .1 1 .1 5 1 .2 1 .2 5 1 .3 1 .3 5 1 .4 1 .4 5 tim e t (M an ager h as in v estm en t ability . k< 0, L> 0) T =1 2 T =3 6 Figure 1.2. This figure plots the expected relative performance for the first 12 time periods of the manager that has the investment ability with investment horizons 12 and 36 periods. Specifically, the manager’s Sharpe ratio is higher than that of the benchmark, and the standard Merton asset allocation in the risky security for the manager is larger than the allocation perfectly hedges the volatlities in relative performance. 32 1 Horizon Goals and Risk Taking in Mutual Funds Table 1.1 Summary Statistics Variable Number of Mean Standard Minimum Maximum Observations Deviation Fund size 1230 6.0286 1.6772 2.3025 11.837 Log fund age 1171 4.7992 0.8610 1.9459 6.8855 Expense ratio 1220 0.0122 0.0043 0 0.0260 Turnover ratio 1216 0.9007 1.2325 0 20.18 Total loads 1230 0.0246 0.0217 0 0.0849 Family size 1230 9.4905 1.9069 3.1223 13.1169 Log number of funds within the family 1230 2.7259 0.9089 0 4.5325 Return volatility 1230 0.0287 0.0131 0.0085 0.1001 Style mean normalized return volatility 1230 0.9876 0.2794 0.3345 2.9888 Carhart model systematic risk 1230 0.0272 0.0124 0.0050 0.0882 Carhart model idiosyncratic risk 1230 0.0143 0.0112 0.0009 0.0769 Carhart four factor alpha 840 -0.0005 0.0020 -0.0130 0.0097 Conditional Carhart four factor alpha 840 0.0001 0.0028 -0.0166 0.0197 Return percentile 840 0.5247 0.2767 0.0035 1 Maximum evaluation period 1180 4.1516 1.8074 1 10 Long term focusing dummy 1230 0.4252 0.4945 0 1 Closet indexer dummy 894 0.1342 0.3410 0 1 This table reports the summary statistics of the mutual fund sample. Fund characteristics are measured at the end of 2005. Fund risk variables are measured using monthly returns in 2006. Fund performance variables are calculated using monthly returnns from 2006 to 2012. Closet indexer dummy is calculated using active share data in 2005. 33 1 Horizon Goals and Risk Taking in Mutual Funds Table 1.2 a Investment Horizon and Mutual Fund Risk (2006) Variables Return volatility Style mean normalized Carhart model Carhart model return volatility systematic risk idiosyncratic risk Maximum evaluation horizon -0.000307*** -0.0118*** -0.000284** -0.000212** (0.000117) (0.00414) (0.000111) (9.77e-05) Fund size -0.000437** -0.0115* -0.000402** -0.000339** (0.000188) (0.00680) (0.000185) (0.000166) Log fund age 0.000761** 0.0232** 0.000682** 0.000634** (0.000299) (0.0109) (0.000292) (0.000250) Expense ratio 0.309*** 12.48*** 0.268*** 0.278*** (0.0704) (2.619) (0.0680) (0.0616) Turnover ratio 0.000375 0.0133 0.000369 0.000157 (0.000309) (0.00999) (0.000282) (0.000258) Total load -0.0460*** -1.665*** -0.0431*** -0.0392*** (0.0120) (0.434) (0.0117) (0.0102) Family size -8.44e-05 -0.00606 -0.000114 -7.06e-05 (0.000262) (0.00961) (0.000256) (0.000230) Log number of funds in family 0.000946** 0.0405** 0.000960** 0.000349 (0.000475) (0.0173) (0.000465) (0.000409) Constant 0.0295*** 0.830*** 0.0282*** 0.0137*** (0.00341) (0.117) (0.00335) (0.00263) Style fixed effect yes yes yes yes Observations 1,113 1,113 1,113 1,113 R-squared 0.693 0.073 0.681 0.687 This table shows the regressions of mutual fund risk on the maximum evaluation horizon, controlling for fund size, log fund age, expense ratio, turnover ratio, total loads, family size, and the log number of funds in family. Varaibles are described in Section 2.2. Robust standard errors are shown in the parenthesis. Risk variables are measured using monthly returns in 2006. Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 34 1 Horizon Goals and Risk Taking in Mutual Funds Table 1.2 b Investment Horizon and Mutual Fund Risk (2006-2010) Variables Return volatility Style mean normalized Carhart model Carhart model return volatility systematic risk idiosyncratic risk Maximum evaluation horizon -0.000422*** -0.00686*** -0.000386*** -0.000214* (0.000134) (0.00231) (0.000132) (0.000110) Fund size 0.000359 0.00674* 0.000410* 8.88e-05 (0.000223) (0.00381) (0.000211) (0.000187) Log fund age -0.000555* -0.00901 -0.000564* -0.000338 (0.000333) (0.00570) (0.000305) (0.000279) Expense ratio 0.377*** 6.657*** 0.304*** 0.313*** (0.0794) (1.382) (0.0784) (0.0696) Turnover ratio 0.000553 0.00943 0.000613* 0.000545 (0.000348) (0.00573) (0.000324) (0.000352) Total load -0.0596*** -1.018*** -0.0534*** -0.0333*** (0.0132) (0.224) (0.0124) (0.0103) Family size -0.000129 -0.00324 -0.000201 -0.000128 (0.000286) (0.00493) (0.000274) (0.000233) Log number of funds in family 0.00205*** 0.0361*** 0.00204*** 0.00107** (0.000547) (0.00944) (0.000527) (0.000443) Constant 0.0835*** 0.886*** 0.0748*** 0.0336*** (0.00247) (0.0364) (0.00210) (0.00228) Style fixed effect yes yes yes yes Observations 949 949 949 949 R-squared 0.631 0.135 0.483 0.493 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 35 1 Horizon Goals and Risk Taking in Mutual Funds Table 1.2 c Investment Horizon and Mutual Fund Risk (2006-2012) Variables Return volatility Style mean normalized Carhart model Carhart model return volatility systematic risk idiosyncratic risk Maximum evaluation horizon -0.000368*** -0.00628*** -0.000309** -0.000197* (0.000129) (0.00234) (0.000126) (0.000106) Fund size 0.000206 0.00436 0.000267 0.000119 (0.000215) (0.00386) (0.000203) (0.000183) Log fund age -0.000394 -0.00651 -0.000385 -0.000467* (0.000327) (0.00589) (0.000300) (0.000280) Expense ratio 0.388*** 7.297*** 0.311*** 0.296*** (0.0797) (1.465) (0.0797) (0.0697) Turnover ratio 0.000410 0.00728 0.000488* 0.000486 (0.000310) (0.00538) (0.000290) (0.000313) Total load -0.0515*** -0.933*** -0.0456*** -0.0315*** (0.0126) (0.225) (0.0118) (0.00993) Family size -0.000370 -0.00804 -0.000459* -0.000150 (0.000276) (0.00499) (0.000267) (0.000238) Log number of funds in family 0.00218*** 0.0409*** 0.00220*** 0.00100** (0.000531) (0.00967) (0.000517) (0.000451) Constant 0.0547*** 0.918*** 0.0496*** 0.00945*** (0.00412) (0.0728) (0.00402) (0.00301) Style fixed effect yes yes yes yes Observations 839 839 839 839 R-squared 0.650 0.143 0.499 0.487 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 36 1 Horizon Goals and Risk Taking in Mutual Funds Table 1.3 Investment Horizon and Mutual Fund Performance 2006-2012 October 2007 - March 2009 Carhart four Return Percentile Conditional Carhart Carhart four Return Percentile Variables factor alpha four factor alpha factor alpha Maximum 3.54e-05 0.00695 4.45e-05 0.000121 0.0147*** evaluation horizon (3.14e-05) (0.00562) (3.77e-05) (8.42e-05) (0.00477) Fund size -8.50e-05* -0.0165** -0.000151*** 0.000170 -0.00552 (4.50e-05) (0.00812) (5.36e-05) (0.000121) (0.00709) Log fund age 0.000139* 0.0349** 0.000202** 0.000502*** 0.0403*** (7.85e-05) (0.0140) (9.21e-05) (0.000188) (0.0121) Expense ratio -0.0111 1.960 0.00590 -0.0114 -8.057*** (0.0174) (3.136) (0.0198) (0.0402) (2.649) Turnover ratio -0.000150** -0.00762 -0.000186** -5.41e-05 -0.00456 (7.10e-05) (0.00860) (8.35e-05) (0.000135) (0.00755) Total load -0.00400 -1.258** -0.00704** -0.00557 0.479 (0.00269) (0.494) (0.00309) (0.00674) (0.443) Family size 0.000180*** 0.0274** 0.000252*** -1.07e-06 0.00455 (6.06e-05) (0.0117) (7.07e-05) (0.000165) (0.0101) Log number of -0.000226* -0.00720 -0.000362*** -0.000264 -0.0562*** funds in family (0.000116) (0.0216) (0.000136) (0.000311) (0.0199) Constant 0.000655 0.200 0.00415*** -0.00771** 0.553*** (0.000572) (0.135) (0.000652) (0.00310) (0.167) Style fixed effect yes no yes yes no Observations 797 797 797 993 993 R-squared 0.401 0.049 0.614 0.450 0.064 This table reports the result of the regressions of Carhart factor adjusted returns and return percentiles on the maximum evaluation period, controlling for expense ratio, turnover ratio, log fund age, fund size, total loads, family size, and the log number of funds within the family. Section 3.2 describes these variables in detail. Robust standard errors are reported in the parentheses. Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 37 1 Horizon Goals and Risk Taking in Mutual Funds Table 1.4 Investment Horizon and Mutual Fund Risk for Closet Indexers Variables Return volatility Style mean normalized Carhart model Carhart model return volatility systematic risk idiosyncratic risk MaxEval*ClosetIndexer 0.000632** 0.0227** 0.000559** 0.000371* (0.000254) (0.00965) (0.000248) (0.000199) Maximum evaluation horizon -0.000450*** -0.0169*** -0.000382*** -0.000288** (0.000147) (0.00543) (0.000142) (0.000133) Closet indexer dummy -0.00634*** -0.246*** -0.00539*** -0.00511*** (0.00127) (0.0487) (0.00125) (0.00104) Fund size -0.000307 -0.00673 -0.000302 -0.000327* (0.000203) (0.00749) (0.000200) (0.000181) Log fund age 0.00118*** 0.0371*** 0.00118*** 0.000710** (0.000346) (0.0127) (0.000339) (0.000293) Expense ratio 0.307*** 12.98*** 0.310*** 0.180** (0.0866) (3.356) (0.0841) (0.0746) Turnover ratio 0.000949** 0.0332** 0.000858** 0.000589* (0.000422) (0.0150) (0.000397) (0.000339) Total load -0.0468*** -1.757*** -0.0493*** -0.0350*** (0.0141) (0.533) (0.0138) (0.0125) Family size -0.000179 -0.00868 -0.000202 -0.000202 (0.000277) (0.0103) (0.000272) (0.000250) Log number of funds in family 0.000945* 0.0401** 0.00104** 0.000620 (0.000515) (0.0189) (0.000506) (0.000457) Constant 0.0334*** 0.675*** 0.0316*** 0.0227*** (0.00312) (0.0969) (0.00304) (0.00276) Style fixed effect yes yes yes yes Observations 809 809 809 809 R-squared 0.502 0.115 0.516 0.452 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 38 1 Horizon Goals and Risk Taking in Mutual Funds Table 1.5 The Claim to Focus on the Long Term and Mutual Fund Risk Variables Return volatility Style mean normalized Carhart model Carhart model return volatility systematic risk idiosyncratic risk Part a Long term focusing dummy 4.28e-05 0.00130 6.27e-05 3.38e-05 (0.000438) (0.0158) (0.000421) (0.000374) Maximum evaluation horizon -0.000308*** -0.0118*** -0.000285*** -0.000212** (0.000116) (0.00410) (0.000110) (9.68e-05) Observations 1113 1113 1113 1113 R-squared 0.693 0.073 0.681 0.687 Part b Long term focusing dummy -0.000624 -0.0110 -0.000574 -8.04e-05 (0.000535) (0.00747) (0.000505) (0.000491) Maximum evaluation horizon -0.000437*** -0.00624*** -0.000419*** -0.000221 (0.000162) (0.00229) (0.000158) (0.000150) Observations 993 993 993 993 R-squared 0.626 0.118 0.451 0.503 Part c Long term focusing dummy -0.000919** -0.0167** -0.000760* -0.000119 (0.000424) (0.00755) (0.000389) (0.000325) Maximum evaluation horizon -0.000356*** -0.00607*** -0.000299** -0.000196* (0.000127) (0.00231) (0.000124) (0.000105) Observations 839 839 839 839 R-squared 0.651 0.147 0.501 0.487 39 1 Horizon Goals and Risk Taking in Mutual Funds Table 1.6 Long Term Focusing Dummy in Two Subsamples Maximum evaluation horizon≤ 4 years Maximum evaluation horizon > 4 years Variables Return Style mean normalized Carhart model Carhart model Return Style mean normalized Carhart model Carhart model volatlity return volatility systematic risk idiosyncratic risk volatlity return volatility systematic risk idiosyncratic risk Long term focusing -0.000250 -0.00467 -0.000296 -0.000338 -0.00117* -0.0218** -0.00115** -0.000287 dummy (0.000629) (0.0115) (0.000593) (0.000507) (0.000595) (0.0108) (0.000559) (0.000481) Fund size 0.000752** 0.0143** 0.000814** 0.000168 0.000162 0.00348 0.000205 2.19e-05 (0.000330) (0.00605) (0.000317) (0.000283) (0.000239) (0.00440) (0.000224) (0.000175) Log fund age -0.000744 -0.0131 -0.000915** -0.000564 1.21e-05 0.000670 -2.26e-05 -0.000340 (0.000471) (0.00859) (0.000433) (0.000415) (0.000408) (0.00754) (0.000390) (0.000325) Expense ratio 0.572*** 10.60*** 0.463*** 0.496*** 0.365*** 7.121*** 0.311*** 0.101 (0.127) (2.346) (0.127) (0.109) (0.102) (1.885) (0.0996) (0.0850) Turnover ratio 0.000784* 0.0134* 0.000718* 0.000713 0.00100* 0.0175* 0.000655 -0.000214 (0.000448) (0.00780) (0.000407) (0.000451) (0.000559) (0.0101) (0.000519) (0.000447) Total load -0.0741*** -1.335*** -0.0638*** -0.0718*** -0.0470*** -0.917*** -0.0430*** -0.00317 (0.0191) (0.356) (0.0186) (0.0162) (0.0152) (0.281) (0.0147) (0.0120) Family size -0.000827** -0.0155** -0.000878** -8.84e-08 -0.000258 -0.00514 -0.000169 -0.000103 (0.000398) (0.00737) (0.000385) (0.000332) (0.000301) (0.00553) (0.000285) (0.000262) Log number of funds 0.00233*** 0.0430*** 0.00242*** 0.00116* 0.00154** 0.0281** 0.00132** 0.000335 within the family (0.000749) (0.0139) (0.000728) (0.000643) (0.000647) (0.0116) (0.000607) (0.000506) Constant 0.0410*** 0.677*** 0.0406*** -0.00583 0.0775*** 0.903*** 0.0679*** 0.0343*** (0.00549) (0.0980) (0.00506) (0.00527) (0.00275) (0.0480) (0.00254) (0.00227) Style fixed effect yes yes yes yes yes yes yes yes Observations 427 427 427 427 424 424 424 424 R-squared 0.592 0.198 0.434 0.474 0.677 0.111 0.535 0.532 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 40 1 Horizon Goals and Risk Taking in Mutual Funds Table 1.7 Maximum Evaluation Horizon in Two Subsamples Long term focusing dummy=0 Long term focusing dummy=1 Variables Return Style mean normalized Carhart model Carhart model Return Style mean normalized Carhart model Carhart model volatility return volatility systematic risk idiosyncratic risk volatility return volatility systematic risk idiosyncratic risk Maximum evaluation -0.000447*** -0.00812*** -0.000356** -0.000308** -0.000392 -0.00697 -0.000494 0.000243 horizon (0.000144) (0.00265) (0.000143) (0.000131) (0.000396) (0.00698) (0.000369) (0.000214) Fund size 0.000732** 0.0138** 0.000723** 0.000443* 8.33e-05 0.00217 0.000145 -0.000294 (0.000314) (0.00575) (0.000304) (0.000263) (0.000264) (0.00486) (0.000251) (0.000202) Log fund age -0.00108** -0.0191** -0.00112** -0.000797* 1.78e-05 -3.43e-05 6.27e-06 -2.22e-05 (0.000496) (0.00906) (0.000467) (0.000416) (0.000374) (0.00688) (0.000367) (0.000337) Expense ratio 0.397*** 7.326*** 0.307** 0.489*** 0.465*** 9.062*** 0.413*** 0.0934 (0.128) (2.363) (0.128) (0.111) (0.0867) (1.624) (0.0851) (0.0792) Turnover ratio 0.000340 0.00584 0.000420 0.000398 0.00124** 0.0218** 0.000953 0.000804 (0.000288) (0.00509) (0.000279) (0.000300) (0.000618) (0.0110) (0.000627) (0.000527) Total load -0.0330** -0.592* -0.0287* -0.0484*** -0.0712*** -1.347*** -0.0658*** -0.000751 (0.0165) (0.307) (0.0161) (0.0141) (0.0167) (0.308) (0.0158) (0.0137) Family size -0.000790 -0.0147 -0.000775 -0.000293 -0.000428 -0.00837 -0.000450* -0.000232 (0.000487) (0.00903) (0.000472) (0.000418) (0.000279) (0.00521) (0.000265) (0.000214) Log number of 0.00330*** 0.0606*** 0.00303*** 0.00162** 0.00102** 0.0191** 0.00126** 0.000114 funds in family (0.000975) (0.0180) (0.000947) (0.000818) (0.000515) (0.00934) (0.000498) (0.000400) Constant 0.0779*** 0.927*** 0.0693*** 0.0256*** 0.0596*** 0.942*** 0.0583*** 0.0173*** (0.00309) (0.0547) (0.00287) (0.00249) (0.00270) (0.0501) (0.00261) (0.00225) Style fixed effect yes yes yes yes yes yes yes yes Observations 463 463 463 463 334 334 334 334 R-squared 0.635 0.180 0.432 0.456 0.685 0.162 0.615 0.607 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 41 1 Horizon Goals and Risk Taking in Mutual Funds Table 1.8 Propensity Score Balanced Sample Variables Return volatility Style mean normalized Carhart model Carhart model return volatility systematic risk idiosyncratic risk Maximum evaluation horizon -0.000307*** -0.0118*** -0.000284** -0.000212** (0.000117) (0.00414) (0.000111) (9.77e-05) Fund size -0.000437** -0.0115* -0.000402** -0.000339** (0.000188) (0.00680) (0.000185) (0.000166) Log fund age 0.000761** 0.0232** 0.000682** 0.000634** (0.000299) (0.0109) (0.000292) (0.000250) Expense ratio 0.309*** 12.48*** 0.268*** 0.278*** (0.0704) (2.619) (0.0680) (0.0616) Turnover ratio 0.000375 0.0133 0.000369 0.000157 (0.000309) (0.00999) (0.000282) (0.000258) Total load -0.0460*** -1.665*** -0.0431*** -0.0392*** (0.0120) (0.434) (0.0117) (0.0102) Family size -8.44e-05 -0.00606 -0.000114 -7.06e-05 (0.000262) (0.00961) (0.000256) (0.000230) Log number of funds in family 0.000946** 0.0405** 0.000960** 0.000349 (0.000475) (0.0173) (0.000465) (0.000409) Constant 0.0295*** 0.830*** 0.0282*** 0.0137*** (0.00341) (0.117) (0.00335) (0.00263) Style fixed effect yes yes yes yes Observations 1,113 1,113 1,113 1,113 R-squared 0.693 0.073 0.681 0.687 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 42 2 Seller Choice of Risk and Real Estate Seasonality 2.1 Introduction Return-risk tradeoff is common in all financial markets. Ever since Markowitz (1951) analyzedtheoptimalportfolioassuminginvestors“considerexpectedreturnadesirablething and variance of return an undesirable thing,” various research has been developed to solve for the “optimal risk exposure”. Real estate sellers face the same problem when choosing the listing prices of their houses. On one hand, they can list their houses low and realize a quick sale. On the other hand, they can list their houses high and be patient, expecting the arrival of generous buyers who really value their houses. By listing the houses high, the sellers take on great risk. Real estate buyers usually prefer new listings to dated listings. If the generous buyers do not appear and the houses are not sold for an extensive period of time, the sellers might have to accept offers lower than what they could have got if they had lower original listing prices, not to mention the time value of money they lost while waiting. In this paper, I model the reward-risk tradeoff and solve for the optimal listing price of a real estate seller in a setting that resembles the optimal allocation problem in the classical Merton (1969, 1971) environment. I empirically test the model implications on the 43 2 Seller Choice of Risk and Real Estate Seasonality cross-sectional variations in real estate price seasonality, as well. The model has several implications for the real estate market. The first implication relates to the conflict of interests between sellers and realtors. Realtors’ payoff in real estate transactions consists of fixed portions of the sold prices, (commission), usually around 2-3%. Since the realtor’s share of the sold price is much less than that of the seller, the realtor has an incentive to convince the seller to take low risk and realize a quick sale. This implication is consistent with traditional wisdom and academic findings. Levitt and Syverson (2008) find that housing units owned by real estate agents stay on the market longer and are sold at higher prices. Hendel et al (2009) find that hiring real estate agents do not necessarily generate higher sale prices. 1 In addition, the model has implications for the cross-sectional variationinrealestateseasonality, whichis, tothebestknowledgeoftheauthor, notrecorded in prior literature. According to the matching theory (Wheaton 1990), the larger the housing turnover, the better the chance of finding a house that matches the buyer’s need. And thus the buyer would be willing to pay a higher price. Reflected in the model, the matching theory implies that in the summer, when more transactions take place, the seller can realize a larger reward in the expected selling price by taking risk and choosing a high listing price. This results in more risk taking and higher listing prices in the summer, creating a short time bubble and thus the price seasonality. 2 Two factors affect the degree of seasonality in the reward-risk tradeoff setting. First of all, less risk-averse sellers have greater incentives to take advantage of the increase in the reward of risk taking. And thus real estate markets in areas where sellers are less risk-averse will have more price seasonality. Secondly, the house value affects the optimal listing price. Sellers of more valuable houses have greater incentives to take advantage of the increase in the reward for risk, as long as the cost of real estate transaction does not increase linearly with the value of the house. Moreover, career concerns 1 Shy (2012) models the listing decision in a different way but has similar implications for the conflict of interest between sellers and realtors. 2 According to the matching theory, house values should be higher in summer even without any risk taking behavior by the sellers. The assumption of higher house values does not affect the model implications so I ignore it. See section 2 for detailed settings and explanations. 44 2 Seller Choice of Risk and Real Estate Seasonality result in a nonlinear payoff structure for the realtor. When the payoff to the realtor consists ofthecommissionandthepossibleexpansionoffuturecustomerbases, realtorssellinghouses whose value falls in a region close to the realtors’ sales record would have stronger incentives to have a high listing price facing an increase in the reward of risk taking. Both effects imply that areas where houses are more valuable will have larger seasonal price fluctuations. In the model I illustrate these comparative statics in detail. In the empirical part of the paper, I first summarize the price seasonality in the U.S. residential real estate market using zip code level data from 1997 to 2013. Utilizing the change in monthly median sold prices of residential housing units within a time interval of a year, I create a measure of seasonality for each month and each zip code area. Consistent with traditional wisdom, the national average of all zip code area median sold prices shows high seasonality in summer and low seasonality in winter. Moreover, the zip code area seasonality measures exhibit substantial cross-sectional variations. Although most of the zip code areas have the highest seasonality in the summer months, a sizable portion of the zip code areas have the highest seasonality in other months. Focusing on the zip code areas that have the most common seasonality patterns, i.e. those with highest seasonality in summer, the seasonality measures range from 1% to more than 20%. I test the model implications by performing cross-sectional regressions of the seasonality measure in summer months on variablesproxyingforriskaversionandthevalueofthehousingunits. Consistentwithmodel predictions, the percentages of foreign born population and renter occupied housing units are positively related to seasonality. The percentage of married population is negatively related to seasonality. And the value of the housing units, the number of rooms, and homeowner cost excluding mortgages are positively related to seasonality. All coefficients are statistically significant. I also test the model for various sub-periods. This paper contributes to the literature by applying the settings of optimal asset allocation to the analysis of real estate market prices. Since Merton (1971), various asset al- locationproblemshavebeenstudiedaroundtheselectionbetweenarisk-lessbondandarisky 45 2 Seller Choice of Risk and Real Estate Seasonality asset whose return follows a Gaussian process. Constantinides (1986), Davis and Norman (1990), and Cadenillas and Pliska (1999) study the impact of transaction costs. Detemple (1986), Dothan and Feldman (1986), Gennotte(1986), and Cvitanic, Lazrak, Martellini, and Zapatero (2002) study the optimal asset allocation with incomplete information. Carpen- ter (2000), Basak, Pavlova, and Shapiro (2007), Panageas and Westerfield (2009), Basak and Makarov (2013), and Buraschi, Kosowski, and Sritrakul (2014) analyze the optimal risk exposure under non-linear payoff structures. The model in this paper is less complicated. During the period that a house is sold, the fluctuation in the real estate market is usually much less than the variation of stock prices. And unlike investors, house buyers do not need to constantly trade their assets. Therefore, I model the choice of listing price as a single- period discrete-time decision. Also for tractability and interpretation, I assume that the selling price follows the normal distribution and that the expected value and the variance of the selling price is linear in the listing price. Despite the simplicity of the model, it correctly reflects the conflict of interests between sellers and realtors and explains the cross-sectional variations in real estate seasonality. This paper also relates to the study on the influence of non-linear payoff structures on agent behaviors. Convex payoff structures are common in various principal-agent rela- tionships. Hedge fund managers receive performance fees when the net asset value (NAV) of the fund exceeds the highest NAV (high-water mark) it has achieved. The high-water mark provision in the managers’ compensation contract resembles a call option issued by the fund investors (Goetzmann, Ingersoll, and Ross 2003). Mutual funds are not allowed to sign asymmetric performance-payoff contract with their investors. Instead, the convexity of their performance-payoff structure results from the convex shape of the performance-cash flow curve. (Brown, Harlow, and Starks (1996), Chevalier and Ellison (1997), Sirri and Tu- fano (1998), Berk and Green (2004)). Prior literature on realtor behaviors has restricted the realtor payoff to a linear function of the selling price. However, this view ignores the agents’ career concerns. According to the National Association of Realtors (NAR), as of 46 2 Seller Choice of Risk and Real Estate Seasonality May 2013, the NAR already has about one million members. In such a competitive market, sales records are crucial to attracting customers. Home owners and potential buyers are more likely to interview and hire realtors that have sold houses at prices comparable to their budgets. And thus selling a house at a high price not only brings sizable commissions, but also expand the future customer base. If the house value is close to the realtor’s sales record, the combination of commissions and career concerns produces a convex payoff structure that results in risk taking incentives much stronger than those generated by a simple linear envi- ronment. The realtor’s incentive to take extra risk mitigates the conflict of interests between the sellers and realtors. The model provides useful guidance for real estate sellers looking for realtors. Sellers can benefit from the convex payoff structure by hiring realtors with sales record comparable to their house value. In addition, this paper contributes to the study of real estate seasonality. Real estate seasonality is well known. In fact, people are almost so used to seasonally adjusted real estate indexes that seasonality itself does not attract much researchers’ interests. However, Granger, the 2003 Nobel Prize winner in economics, has pointed out in his 1978 paper that “ignoring consideration of causation [of seasonality] can lead to imprecise or improper definitionsofseasonalityandconsequentlytomisunderstandingofwhyseriesrequireseasonal adjustment...” 3 Traditional wisdom generally attributes real estate seasonality to weather. Some other explanations include the change in the length of daylight (Kaplanski and Levy 2012) and the educational needs of school-age children (Hardling, Rosental and Simons 2003). This paper provides explanations for the cross-sectional variations in seasonality based on the matching theory that links seasonal fluctuations in quantity with those in price. To the best knowledge of the author, this paper is the first to document and analyze the substantial cross-sectional variations in seasonality of the U.S. real estate market at the zip code level. It establishes connections between real estate seasonality and realtor risk taking, local demographics, and the characteristics of the housing units. 3 See, for example, the website of the National Association of Realtors on the methodology in calculating existing-home sales statistics. http://www.realtor.org/topics/existing-home-sales/methodology. 47 2 Seller Choice of Risk and Real Estate Seasonality Seasonal patterns are not unique in the real estate market. The finance literature has uncovered and analyzed many yearly asset pricing anomalies that cannot be explained by risk-based reasons. In the equity market, small-cap stocks tend to perform better than large-capstocks atthe beginningof theyear (Keim(1983), Roll(1983)). Explanations ofthis phenomenon includes tax-loss selling by retail investors and window dressing by institutional investors (Roll (1983), Ritter (1988) Haugen and Lakonishok (1988), Musto (1997)). Both limit the demand for poor performing stocks at year end, and in the following days of the new year the demand shifts up. In the asset management literature, Zweig (1997) shows that equity funds on average outperform the market on the last trading day of the year, and under-perform on the first trading day of the next year. Carhart, et al. (2002) demonstrate that equity-fund prices are significantly inflated at the end of quarters. The explanation is that fund managers execute purchase orders to the stocks in their portfolios near the close of the market, and thus “mark up” the return of their portfolios. This paper follows the above research and examines how the rational behaviors of the market participants influence the seasonal fluctuations in the real estate market. The rest of the paper is organized as follows. Section 2 develops a model of a real estate seller facing the reward-risk tradeoff and summarizes the implications of his optimal risk taking behavior on real estate listing prices. Section 3 describes data and variables in the empirical analysis. Section 4 tests the hypotheses derived from the model. Section 5 concludes. 2.2 Model In this section, I consider a model of a real estate seller/realtor facing the common reward-risk tradeoff and choosing the listing price to maximize her utility. The listing price affects both the expected selling price and the risk of the real estate transaction. The seller 48 2 Seller Choice of Risk and Real Estate Seasonality and the realtor can list the housing unit high and be patient, in the expectation of finding a generous buyer. However, at the same time, the seller and the agent bear the risk that the housing unit won’t be sold for an extensive period of time. Having the housing unit on the market for too long is bad. Real estate buyers usually prefer new listings to dated listings. After a while on the market, the housing unit would receive much less attention. If the seller and the realtor does not find a buyer in the short term, they might have to accept offers lower than what they could have got if they had a lower listing price. To reflect this idea, I assume the selling priceP of the housing unit follows a normal distributionN[μ,σ]. I assume that the standard deviation of the sale price σ is a function of the distance between the listing priceL and a variable representing the intrinsic value of the housing unitV. The higher the listing price L above the intrinsic value V, the greater risk the seller and the realtor bear. When the listing price L is low enough compared to the intrinsic value V, the housing unit can be sold at no risk. The idea is simple. In normal market conditions, when the listing price is low enough, there is always a buyer ready to make the purchase at the listing price. The reward in taking risk is the increase in the expected selling price. I assume that the expected selling price μ is positively related to the distance between the listing price L and V, as well. For tractability and interpretation, I assume that σ =L−V and μ = ¯ μ +α(L−V ). When L equals V, there is no risk. And V can be understood as the zero risk listing price. Notice how the distribution of the selling price mimics the distribution of the return of a portfolio allocated between a risk-free bond and a risky asset. Here ¯ μ resembles the return of the risk-free bond, α resembles the risk premium of the risky asset, L−V resembles the portfolio allocation to the risky asset (risk exposure), and the risk term of the risky asset equals 1. Modeling the listing decisions of real estate sellers and realtors with the asset alloca- tion setting ignores the complexities of the connections between the listing price and the risk and reward in real estate transactions. In asset allocation problems, the portfolio expected return and variance can be derived directly from those of the individual assets, but there 49 2 Seller Choice of Risk and Real Estate Seasonality is no rule specifying that the expected value and the variance of the selling price are linear functions of the listing price. However, this setting is rich enough to generate intuitive and useful implications for the real estate market. And the implications should remain valid in more complex setting. This setting also ignores some tricks commonly used by realtors. For example, realtors sometimes list the house at a low price in order to boost the traffic and thus realize a high selling price. In this case,L in the model can be understood as the target price under which no offers will be accepted. 2.2.1 Seller and Realtor Conflicts of Interests Under the above setting of the expectation and variance of the selling price, the seller and the realtor each solves for the optimal listing price individually. I assume the payoff to the seller and realtor equals Π i =θ i P−C i (2.1) whereirepresentseitherthesellerortherealtor,θ representstheshareofthesellingpricethe seller or the realtor acquires, and C represents the fixed costs of the real estate transaction. For the seller, the cost includes the need to move and clean the house, time to look for a realtor and read all the files, and the transaction fees. For the realtor, the cost includes the minimum amount of effort the realtor needs to exert in order to finish the transaction. Since the interactions between the seller and the realtor is not the focus of the paper, I do not model the realtor’s choice of effort and the negotiation process between the seller and the realtor. I assume seller’s and the realtor’s preferences are both represented by a CRRA utility function: U(Π) = Π 1−γ i 1−γ i (2.2) The seller and the realtor might differ in their level of risk aversion. Under the above setting, the seller and the realtor each chooses the optimal listing price by solving the maximization 50 2 Seller Choice of Risk and Real Estate Seasonality problem below, Max L E{U(P )} I use numerical method to solve for the optimal listing price. One comparative statics especiallyinterestingistheconnectionbetweentheshareofthesellingpriceθ andtheoptimal risk exposure (L−V). Figure 1 plots this connection for three levels of risk aversion. It is intuitive that less risk averse sellers/realtors choose higher levels of risk exposure. Each curve shifts upward, meaning that the larger the share of the selling price, the higher the optimal risk exposure. In the real estate market, realtors usually takes 2-3% of the selling price as their commission and the rest goes to the sellers. This means the optimal listing price for the realtor is much lower than that of the seller. The realtors have the incentive to persuade the seller to accept low offers and finish the transactions quickly. This phenomenon is well documented in the real estate market. 4 The second observation from Figure 2 is that the slope of the curve is deeper for low shares of the selling price than for high shares. This means that the change in the share of the selling price matters more when the share is small compared to the cost term C. Skeptical readers might point out when drawing the curves I keep the cost term constant, and the fixed cost of real estate transactions are probably different for sellers and realtors. However, as long as C realtor C seller > θ realtor θ seller , the negative relation between the share of the selling price and the optimal risk exposure will hold. 2.2.2 Risk Aversion, House Value, and Seasonality The above subsection illustrates how the reward-risk tradeoff setting in the real estate market leads to the implication on the well documented conflicts of interests between sellers and realtors. The same setting has many other implications. This subsection examines the connection between risk aversion, house value, and seasonality. It is worth noting that this paper is not about the cause of seasonality. Instead, I build the model based on the 4 See Levitt and Syverson (2008) and Hendel et al (2009). 51 2 Seller Choice of Risk and Real Estate Seasonality well-established matching theory and studies what the matching theory predicts about the cross-sectional variation in real estate seasonality under a reward-risk environment. According to the matching theory, all houses are unique and different potential buyers have distinct valuations on them. Each house can be sold at a high price if the house well matches the buyer’s need. In summer when more transactions take place in the housing market, it is more likely that the house can be matched to a buyer that really values it. Reflected in the model, when housing turnover increases, for any given level of risk expo- sure/listing price, the seller/realtor has a better chance of finding a generous buyer, so α in the model increases. According to the matching theory, the zero risk price V should also positively relate to housing turnover. Since its value does not affect the model implication on seasonality, I keep it fixed. Notice thatα resembles the risk premium of the risky asset in the asset allocation problem. When the risk premium increases, optimal risk exposure rises accordingly. In the real estate market, when the reward for risk increases in the summer, sellers/realtors takes more risk by choosing higher listing prices. The risk taking behavior creates a short time bubble and adds on to the seasonal patterns in the real estate market. I first examine how risk aversion affects seasonality, i.e. the second partial derivative, ∂ 2 L ∂γ∂α . Intuitively, the increase in α represents a rise in the reward for risk. The incentive to take advantage of this reward increase should be stronger for less risk-averse seller. In Figure 2, I plot the optimal listing price with respect to risk aversion for the two levels of α. It is clear that the high α curve lies above the low α curve, showing that the optimal risk level increases with the reward for risk. Both curves slope downward, indicating that the optimal risk exposure negatively relates to risk aversion. The third curve represents the seasonality. To be consistent with the seasonality measure introduced in the empirical analysis later in the paper, I calculate the seasonality as the difference between the summer and winter optimal listing price over the winter optimal listing price, i.e. Lsummer−L winter L winter . The negative slope of the seasonality curve implies that areas where the sellers are more risk averse should have less real estate seasonality. 52 2 Seller Choice of Risk and Real Estate Seasonality The second factor that might affect seasonality is the value of the house,V. In Figure 3, I plot the optimal risk exposure with respect to the zero risk listing price V for two levels of α. It is clear that the optimal risk exposure increases with the house value. Moreover, the difference between the winter and summer optimal listing prices also positively relates to the house value. The third curve represents seasonality. The figure indicates that areas where houses are more valuable should have more seasonality. 2.2.3 Convex Payoff Structure and Realtor Optimal Risk Exposure In the above analysis, I assume that the payoff to the sellers and the realtors are linear functions of the selling price. Although this assumption might be correct for the seller, various reasons can make the payoff to the realtor non-linear. Unlike the seller, who seldom participates in the real estate market, realtors help buyers and sellers make real estate transactions all the time. The selling price of previous transactions can influence the realtor’s chance of being hired, as well as the potential selling price in the future. In this subsection, I consider the influence of realtor sales record on her payoff function. According to the National Association of Realtors (NAR), as of May 2013, the NAR already has about one million members. In such a competitive market, sales records are crucial to attracting customers. Home owners and potential buyers are more likely to interview and hire realtors that have sold houses at prices higher than their budgets. And thus selling a house at a high price not only brings sizable commissions, but also expand the future customer base. If the house value is close to the realtor’s sales record, the combination of commissions and career concerns produces a convex payoff structure that results in risk taking incentives very different from those generated by a simple linear environment. To build the convex payoff structure for the realtor, I let the realtor payoff contain two parts. The first part is the standard fixed portion of the sale price (commission), θP. The second part is the additional payoff from the expansion of customer bases resulted from 53 2 Seller Choice of Risk and Real Estate Seasonality selling the housing unit above the highest sale price the real estate agent has achieved. I assume that this part of the payoff equals λ(P−SR) + , which resembles the payoff from a call option with a strike price SR. SR denotes the sales record and the real estate agent realizes this payoff only if the sale priceP is aboveSR. The agent’s total payoff thus equals: Π =θP +λ(P−SR) + −C (2.3) Figure 4 depicts the agent’s payoff function. Different from the traditional linear payoff curves, the agent’s payoff curve in the model kinks upward at the sales recordSR. Marginal payoff from selling the house at higher prices is larger in the region to the right of the sales record SR than that to the left of SR. Plug in the payoff equation to the utility function. The utility function can be rewrit- ten as: U(P ) =          (θP−C) 1−γ 1−γ P <SR ((θ+λ)P−λSR−C) 1−γ 1−γ P≥SR (2.4) Figure 5 depicts this utility function. It is noticeable that, since the the real estate agent’s payoff function is nonlinear, the utility function is not globally concave. The dash line that is tangent to the utility curve represents the concavification of the utility curve. Certain strategies that randomize sale prices within the two tangent points yield higher expected returns. When the house value is around the sales record, the realtor can take advantage of this non-concavity by adopt a more risky strategy. Prior studies on non-linear payoff functions in the continuous time environment solve the concavified object function for the optimal strategy. The model in this paper is one- period and the maximization problem is non-constrained, so I directly use the numerical method to solve for the optimal listing price L. In Figure 6, I depict the optimal risk level for both the seller and the realtor. The realtor’s payoff function follows equation (3) and I normalize the realtor’s sales record SR to 1. As expected, when the house value is far 54 2 Seller Choice of Risk and Real Estate Seasonality away from the sales record, the influence of the payoff convexity is ignorable. The realtor’s optimal listing price is below the optimal listing price of the seller, reflecting the conflict of interests between the seller and the realtor. This is not surprising. According to the model setup, increasing the standard deviation of the sale price by 10% only raises the expected sale price by α%. However, as the house value gets closer to the sales record, the optimal risk level for the realtor rises sharply. This is because adopting a riskier strategy not only raises the expected value, but also takes advantage of the convexity of the payoff curve. Intuitively, when the realtor knows that there’s little hope that the house can be sold above the sales record, the agent has little incentive to list high. In contrast, when the realtor thinks there is possibility that the housing unit can be sold above the sale record, the realtor has the incentive to “gamble”. It is worth notice that, unlike the case in the hedge fund and mutual fund industry, the gambling behavior of the realtor benefits the seller. The Realtor’s career concern make her optimal listing price closer to that of the seller. In plain words, realtors put a high premium on houses that have the potential to be sold above their sales record. This is especially important for sellers looking for realtors to represent them in the real estate transaction. Although realtors with high sales record might have good knowledge and experience, they might not be the perfect ones to hire under all circumstances. A realtor whose sales record is comparable to the house value can better represents the seller’s interests. The above subsection predicts that seasonality positively relates to house value. It is interesting to check how the convex payoff structure of the realtors affects this relation. In Figure 7, I plot the optimal risk levels for the realtor given the convex payoff structure and the corresponding seasonality. The most observable feature of the seasonality curve is the bump when the house value gets closer to the sales record. Intuitively, when the reward for risk increases in summer, the region where the realtor chooses to “gamble” expanded, creating the bump in the difference between summer and winter optimal risk levels. More valuable houses are more likely to fall into this “bump” region. 55 2 Seller Choice of Risk and Real Estate Seasonality 2.3 Data and Variables The empirical part of the paper focuses on the test of the model implications on the cross-sectional differences in real estate seasonality. I acquire data from various sources. Zip code area monthly median sold prices of residential housing units and the monthly number of transactions from July 1997 to October 2013 are downloaded from Zillow.com. Early months contain many missing values. To ensure data quality and completeness, if a month has the number of transactions missing or below 10, I assign a missing value to the median sold price. And if in a year, the number of missing median sold prices exceeds 2, I exclude the year from the sample. Zip code area demographic data are downloaded from U.S. Census Bureau through American FactFinder. I focus on the 2000 census and the 2010 census and collected information on population, age, race and ethnicity, number of households and housing units, vacancy, rent and leasing information, education, employment, wealth, etc. Geographic and climatic data are obtained from 1981-2010 U.S. Climate Normals downloaded from National Climate Data Center website. The National Climate Data Center does not have information for each zip code area, instead, the U.S. National Oceanic and Atmospheric Administration has weather stations that record temperature and weather information across the country. I link the zip code areas with these weather stations by locating the closest weather station for each zip code area using the haversine formula. The haversine formula calculates the surface distance between two points on a sphere given the latitudes, longitudes, and radius. I exclude zip code areas that do not have a weather station within 30 miles, however, most of the zip code areas have at least one weather station within a much shorter distance. 2.3.1 Measuring Seasonality To test the model implications, I need to have a measure for seasonality. For each month and each zip code area, I create the seasonality measure by dividing the median 56 2 Seller Choice of Risk and Real Estate Seasonality sold price by the average of the median sold price half a year before and half a year after, i.e. Seasonality montht = Price montht / 1 2 (Price month t−6 +Price month t+6 ). Assuming the real estate price is the product of one core component and one seasonal component, and the core component varies at a constant half-year rateR, then the seasonal measure can be simplified, i.e. Seasonality = Core montht ∗Seasonal montht 1 2 (Core montht ((1−R)∗Seasonal month t−6 + (1 +R)∗Seasonal month t+6 )) = Seasonal montht / 1 2 (Seasonal month t−6 +Seasonal month t+6 ). Since montht−6 and montht+6 are the same month in consecutive years, and the seasonal pattern is cyclical, Seasonal month t−6 and Seasonal month t+6 should roughly be the same, and Seasonality =Seasonal montht /Seasonal month t−6 . Intuitively, the seasonal measure excludes the influence of regular rises in the real estate market and focuses on the fluctuations as a result of seasonality. For ease of reference, I use seasonality and seasonality measure interchangeably in the rest of the paper. Figure 8 depicts the equal weighted average of the seasonality measures of all zip code areas over time. The shaded areas correspond to the summer months, June, July and August. Consistent with traditional wisdom, summer months have higher seasonality than winter months, and the spring and fall months have seasonality in between. It might be surprising that almost in all years the highest seasonality appear in September, but considering the time it takes for real estate transactions to go through, all the deals that close in September were probably negotiated in the previous one or two months. The scale of seasonality is significant. On average, the summer median sold prices are four to twelve percent higher than the winter prices. The same seasonality pattern repeats every year until 2010, when the October seasonality measure is much higher than the September one. This probably reflects the recovery of the 2008 real estate market crisis. The same seasonality 57 2 Seller Choice of Risk and Real Estate Seasonality pattern reappears after 2011. Hiding behind Figure 8 and the well-known fact that the real estate market is hot in summer lies substantial cross-sectional variations at the zip code area level. I calculate the seasonality measures for each month and each zip code area, and take the average of the seasonality measures of the same months across years. Figure 9 depicts the distribution of months that have the highest average seasonality. Noticeably, it is the most common that summer months have the largest seasonality. More than a quarter of the zip code areas have the highest seasonality in August. In addition, more than 15% of the zip code areas have the largest seasonality in July and September. Although the highest seasonality most common appear in the summer months, there are zip code areas that have the highest seasonality in all other months. The seasonality measure not only varies along the time dimension, but also differs greatly on its scale. Figure 10 depicts the distribution of maximum seasonality. To create Figure 10, I first calculate the average seasonality measure of the same month across years for each zip code area, and then record the months that have the highest seasonality and the value of the seasonality measure. Zip code areas that have larger maximum seasonality show greater seasonal fluctuations in their real estate market. Most of the zip code areas show seasonal fluctuations below 10%. Some zip code areas have seasonal fluctuations as high as 20%, while some zip code areas have almost no seasonal fluctuations. In the following regression analysis, I focus on the zip code areas that have the maxi- mum seasonality in summer. I do not consider why certain areas do not have the maximum seasonality in summer because the model does not have any implication on this issue. Zip code areas that have the maximum seasonality in other seasons might be fundamentally distinct from those that have the maximum seasonality in summer. And the mechanism through which one variable affects seasonality can be very different for these two groups of areas. For example, some zip code areas in Hawaii have the maximum seasonality in win- ter. And the number of tourists in winter is probably the most important factor affecting 58 2 Seller Choice of Risk and Real Estate Seasonality seasonality for these areas. To correctly explain seasonality in Hawaii, I have to control for winter tourism. However, for areas that have the maximum seasonality in spring, some other variables might be the most important factors. By analyzing only zip code areas that have the maximum seasonality in summer, I focus on the areas that have the most common and representative seasonal patterns. 2.3.2 Risk Aversion, Home Value, and Control Variables The model implies that zip code areas where the sellers are more risk-averse should havelowerseasonality. Iuseseveralvariablestoproxyfortherisk-aversionofthesellers. The first variable is the percentage of foreign born population. Migrating from a foreign country represents a large change in one’s life and is risky. It is understandable that people that choosetomigrateshouldbeless-riskaversethanthosestayattheirhomecountry. Therefore, sellers at zip code areas where there’s a large percentage of foreign born population should on average be less risk-averse. The second variable is the percentage of renter occupied housing units. A large percentage of renter occupied housing units means that a large portion of the homeowners are investors. Generally, investors should be less risk-averse than average home owners. The third variable is the percentage of married population. Spivey (2010) and Schmidt (2008) show that people that are more risk-averse tend to marry at an earlier age. Light and Ahn (2010) show that people that are more risk-averse tend to avoid getting divorced. Therefore, sellers at zip code areas where there is a large percentage of married population should on average be more risk-averse. The model also implies that the intrinsic value of the housing unit positively relate to the real estate agent’s risk taking behavior. I use several variables to proxy for the value of the housing unit. The first one is the value of the housing unit reported in the 2000 and 2010 census. Value is the respondent’s estimate of how much the property would sell for if it were for sale, which might not be precise. I use two other variables to help proxy for 59 2 Seller Choice of Risk and Real Estate Seasonality the intrinsic value of the housing unit. Median homeowner cost measures how much the homeowner needs to spend on maintaining the housing unit. All else equal, the more the homeowner spends on the pool, lawn, or garden, the more valuable the housing unit should be. The other variable is the number of rooms. Larger houses should be more valuable. The most important control variable is the winter temperature. I obtain the average November, December, and January temperature over the 30 years from 1981 to 2010 from the National Climate Data Center. I do not include the June, July, and August average tem- perature because the summer temperature has much less cross-sectional variation. 5 Another important control variable is the latitude of the zip code area. The latitude of the zip code area relates to the yearly change in the number of daylight hours, which affects people’s mood, health, and probably home purchasing decisions (Kaplanski and Levy (2012)). The third control variable is the ratio of the average number of summer transactions over the total number of housing units. This variable measures the liquidity of the local real estate market. Bubbles in asset prices are less likely to exist in a more liquid market. Other control variables measure the ethnic, socioeconomic, and educational characteristics of the popula- tion within a zip code area. Table 1 shows the summary statistics of all variables. Table 2 displays the pairwise correlations of the variables proxying for seller risk aversion and the value of the housing unit. 2.4 Regression Analysis The model in Section 2 predicts that real estate seasonality should negatively relates to seller risk aversion, and positively relates to the house value. In this section, I formally test the following two hypotheses. Hypothesis 3 Zip code areas where the percentages of renter occupied housing units and 5 Adding in the average summer temperature does not increase the adjusted R-square of the regressions and the coefficient of the average summer temperature has very small t statistics. 60 2 Seller Choice of Risk and Real Estate Seasonality foreign born population are higher and where the percentage of married population is lower should have more real estate price seasonality. Hypothesis 4 Zip code areas where the median house value, the median owner cost exclud- ing mortgages, and the median number of rooms in the housing unit are higher should have more real estate price seasonality. To test the two hypotheses above, I perform the following cross-sectional regression: Seasonality k,i,j =α +β 1 RiskAversion k +β 2 HouseValue k +ρControl k + i Seasonality k,i,j refers to the average July, August, and September seasonality measure from year i to year j for the zip code area k. According to section 3.1, the measure of monthly seasonality depends on the assumption that the growth rate in the non-seasonal part of the real estate price is constant. When this assumption is violated, the monthly seasonality measures would mistakenly contain fluctuations in the non-seasonal part of the real estate price. Taking the average of the seasonality measures of the summer months over several years mitigates this concern. RiskAversion k is a vector of three variables proxying for the seller risk aversion for zip code area k. The three variables are the percentage of foreign population, the percentage of renter occupied housing units, and the percentage of married population. HouseValue k is a vector of three variables proxying for the value of the housing units for zip code area k. The three variables are median house value, homeowner cost, and the number of rooms. β 1 , β 2 , and ρ are vectors of coefficients correspondingly. According to the hypotheses, the percentage of foreign population, the percentage of renter occupied housing units, the median house value, the homeowner cost, and the number of rooms should positively relate to seasonality, while the percentage of married population should negatively relate to seasonality. I first calculate the dependent variable using the whole sample period from 1997 to 2013, and the independent variables are obtained from the 2000 census. Table 3 displays 61 2 Seller Choice of Risk and Real Estate Seasonality the regression result. The first three columns shows the result of the regression without state fixed effects. Consistent with the hypotheses, zip code areas where the sellers are less risk-averse and the housing units are more valuable have higher real estate seasonality. The percentages of foreign born population and renter occupied housing units, median house value, home owner cost, and the number of rooms all have positive coefficients. And the coefficient of the percentage of married population is negative. The coefficients of these six variablesareallstatisticallysignificant. Consistentwithtraditionalwisdom, thecoefficientof winter temperature is negative and statistically significant, showing that severity in winter is a major factor affecting real estate price seasonality. The variable latitude serves as a proxy for the difference in summer and winter length of daylight. Surprisingly, latitude is negatively related to seasonality. This means that controlling for other variables, zip code areas in the north, where the difference in winter and summer lengths of daylight is greater, have less housing market seasonality. The coefficient of the liquidity measure is negative and statistically significant. In a more liquid market, any predictable price fluctuations are less likely to exist. The fourth to the sixth column of table 3 displays the result of the same regression including state fixed effects. After demeaning the independent variables by state averages, the signs of the coefficients of the variables proxying for seller risk aversion and housing unit value stay unchanged. Only the percentages of foreign born and married population become statistically insignificant. This means that the model implication hold not only across the country, but also within each state. 1997to2013isalongtimeperiodandmostoftheindependentvariableswouldchange in these many years. I perform the same regression analysis but calculate the dependent variables using data of two sub-samples. The first sub-sample contains housing price data from 1997 to 2007 (before the burst of the housing bubble), while the second sub-sample contains housing price data from 2008 to 2013. For the second sub-sample, I form the independent variables using the 2010 census. Table 4 displays the result of the regression analysis on the first sub-sample. The signs and statistical significance of the coefficients of 62 2 Seller Choice of Risk and Real Estate Seasonality the variables proxying for seller risk aversion and housing unit value are all very similar to those in the analysis on the full sample. Table 5 displays the result of the regression analysis on the second sub-sample. The real estate market is very volatile from 2008 to 2013. The assumption of constant growth rate in the non-seasonal component of the real estate price is likely violated for many zip code areas. Even after taking the average over these six years, the seasonality measure can be imprecise. In addition, in some of these years, real estate agents not necessarily have more business in summer than in winter, so the model implication might not apply. Indeed, the number of observations dropped by more than a half from over 3520 to 1723, showing that, in the years during and right after the burst of the housing bubble, a lot fewer zip code areas have the maximum seasonality in summer. In spite of the volatile real estate market conditions, the regression analysis on the second sub-sample still support the hypotheses. Only the sign of the coefficient of the percentage of renter occupied housing unit reverses but the coefficient is not statistically significant. As in the analysis on the full-sample, after adding in state fixed effects, the coefficient of the percentage of foreign born population loses its statistical significance. 2.5 Conclusion Return-risk tradeoff is very common in all financial markets. Real estate sellers, when choosing the listing price, face a similar problem. I solve for the optimal listing price of the seller/realtor in a setting resembling the optimal asset allocation problem well studied in the finance literature. The implications of the model is twofold. First of all, it addresses the conflict of interests between the seller and the realtor. Consistent with traditional wisdom andacademicfindings, themodelindicatesthattheoptimallistingpriceforthesellerislower than that for the realtor. However, this problem is mitigated by the seller’s career concerns when the house value is close to the seller’s sales record. This is especially meaningful 63 2 Seller Choice of Risk and Real Estate Seasonality for sellers searching for realtors to represent them in real estate transactions. Although realtors with high sales record might have good knowledge and experience that is desirable to the seller, realtors with sales record comparable to the house value might have their incentives better aligned with the interests of the seller. Secondly, the model in the paper provides an explanation to the cross-sectional differences in real estate seasonality. In a reward-risk tradeoff setting, it is natural that seller’s risk aversion and house value both affect the alteration in optimal listing prices in response to the changes in reward for risk. The setting of the model is simple. However, all the model implications are intuitive and straightforward, and they should hold in more complex environment. The empirical analysis uncovers the great cross-sectional variances in real estate seasonality at the zip code area level and confirms the model implications. For potential buyers and sellers in the real estate market, it is wise to pay attention to the local housing seasonal fluctuations hiding behind the metropolitan level real estate indexes. 64 2 Seller Choice of Risk and Real Estate Seasonality 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 Share of selling price Optimal risk exposure low risk aversion ( γ = 2) medium risk aversion ( γ = 3) high risk aversion ( γ = 5) Figure 2.1. Linear Payoff: Optimal Risk Exposure and Share of Selling Price 65 2 Seller Choice of Risk and Real Estate Seasonality 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Risk aversion Optimal risk exposure Winter list price (low α ) Summer list price (high α ) Seasonality Figure 2.2. Linear Payoff: Seller Risk Aversion and Seasonality 66 2 Seller Choice of Risk and Real Estate Seasonality 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 House value, V Optimal risk exposure, (L-V) Winter list price Summer list price Seasonality Figure 2.3. Linear Payoff: House Value and Seasonality 67 2 Seller Choice of Risk and Real Estate Seasonality 0 0 .2 0 .4 0 .6 0 .8 S R 1 .2 1 .4 1 .6 0 0 .0 1 0 .0 2 0 .0 3 0 .0 4 0 .0 5 0 .0 6 0 .0 7 S old price Figure 2.4. Convex Payoff: Realtor Payoff and Sold Price 68 2 Seller Choice of Risk and Real Estate Seasonality 0 .9 0 .9 5 S R 1 .0 5 1 .1 S old price Figure 2.5. Convex Payoff: Realtor Utility and Sold Price 69 2 Seller Choice of Risk and Real Estate Seasonality 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 House value, V Optimal risk exposure, (L-V) Seller Realtor Figure 2.6. Convex Payoff: Optimal Risk Exposure and House Value 70 2 Seller Choice of Risk and Real Estate Seasonality 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 House value, V Optimal risk exposure, (L-V) winter list price summer list price seasonality Figure 2.7. Convex Payoff: House Value and Seasonality 71 2 Seller Choice of Risk and Real Estate Seasonality Figure 2.8. US Residential Real Estate Seasonality 72 2 Seller Choice of Risk and Real Estate Seasonality Figure 2.9. Distribution with Months of Largest Seasonality 73 2 Seller Choice of Risk and Real Estate Seasonality Figure 2.10. Distribution of Maximum Seasonality 74 2 Seller Choice of Risk and Real Estate Seasonality Table 2.1 Summary Statistics Number of Mean Standard 25% 50% 75% observations Deviation Seasonality 3521 0.0554713 0.0380864 0.0284999 0.0466034 0.0717938 Foreign born(%) 3520 11.08213 10.81775 3.8 7.1 14.6 Renter occupied(%) 3521 31.4136 15.22734 20.1 29.5 40.7 Married (%) 3520 55.59767 9.564222 49.9 56.5 62.5 Median value 3521 161409.3 97908.83 98600 136200 188900 Owner cost 3521 365.2272 219.1603 275 325 404 Number of rooms 3521 5.588299 0.9040845 5.1 5.5 6.1 Winter temperature 3521 39.9856 12.17968 30.5 38 48.5 Latitude 3521 0.6616424 0.0868724 0.5963054 0.6793193 0.7264987 Liquidity 3521 1.05883 0.2671324 0.35526 0.46319 0.60297 Total population 3521 29067.61 14352.04 18695 26818 36732 Median age 3521 36.43908 5.122389 33.5 36.2 38.8 Black (%) 3521 10.09208 15.61086 1.4 4.1 11.2 Asian (%) 3521 4.221244 6.548564 1 2.1 4.6 Hispanic (%) 3521 10.08861 14.23594 1.9 4.3 11.2 Total households 3521 10953.89 5098.851 7251 10328 13971 Total housing units 3521 11677.05 5377.265 7787 10957 14895 Vacancy rate (%) 3521 6.329679 6.031705 3.2 4.8 7.3 College degree of higher (%) 3520 28.97403 15.4417 17 25.5 38.2 In labor force (%) 3520 65.95679 7.430379 62.1 66.55 70.7 Unemployment rate (%) 3520 3.21392 1.661439 2.1 2.8 3.9 Commute time to work 3520 25.58159 5.495882 21.6 25.1 29.15 Household income 3521 50949.87 17636.55 38044 47210 60404 Mortgage 3521 1245.732 421.2248 942 1161 1444 Median rent 3521 698.9813 204.4153 554 659 802 This table displays the number of observations, mean, standard deviation, median, and the first and third quartiles of the variables measuring seller risk aversion and housing unit value as well as the control variables. 75 2 Seller Choice of Risk and Real Estate Seasonality Table 2.2 Variable Pairwise Correlation Foreign Renter Married (%) Median Owner Number born(%) occupied(%) value cost of rooms Foreign born(%) 1 Renter occupied(%) 0.4219 1 Married (%) -0.2363 -0.8289 1 Median value 0.3014 -0.0169 0.1525 1 Owner cost 0.1049 -0.0722 0.1065 0.4653 1 Number of rooms -0.3989 -0.7724 0.7023 0.1571 0.2218 1 This table displays the pairwise correlations of the variables proxying for seller risk aversion and the value of the housing units. 76 2 Seller Choice of Risk and Real Estate Seasonality Table 2.3 Real Estate Seasonality and Seller Risk Aversion (1997-2013) Coefficient Standard T Statistics Coefficient Standard T Statistics Error Error Foreign born(%) 0.0004284 0.0001402 3.06 0.000089 0.0001614 0.55 Renter occupied(%) 0.0004716 0.0001037 4.55 0.0005434 0.0001108 4.9 Married (%) -0.0004785 0.0001561 -3.07 -0.0002178 0.0001705 -1.28 Median value 9.06E-08 1.97E-08 4.59 1.43E-07 2.36E-08 6.07 Owner cost 0.0000174 3.52E-06 4.94 0.0000168 3.72E-06 4.53 Number of rooms 0.0120085 0.0018935 6.34 0.0133883 0.0021379 6.26 Winter temperature -0.0006776 0.0001101 -6.16 0.0001089 0.0003007 0.36 Latitude -0.0737343 0.0145636 -5.06 -0.0410755 0.0489909 -0.84 Liquidity -0.1474302 0.038195 -3.86 -0.1210345 0.0381082 -3.18 Total population 2.70E-08 2.33E-07 0.12 -1.43E-08 2.35E-07 -0.06 Median age -0.0001605 0.0002648 -0.61 -0.0002298 0.0002752 -0.83 Black (%) -0.0000804 0.0000582 -1.38 -0.0001014 0.0000632 -1.6 Asian (%) -0.0002806 0.0001415 -1.98 -0.0001182 0.000163 -0.73 Hispanic (%) -0.0004619 0.0001021 -4.52 -0.0002002 0.0001146 -1.75 Total households -7.59E-06 2.28E-06 -3.33 -6.86E-06 2.28E-06 -3.01 Total housing units 6.51E-06 1.96E-06 3.33 5.90E-06 1.96E-06 3.01 Vacancy rate (%) -0.0004042 0.0002326 -1.74 -0.000364 0.000232 -1.57 College degree of higher (%) 0.0003781 0.0000842 4.49 0.0004733 0.0000906 5.22 In labor force (%) -0.0008932 0.0001536 -5.82 -0.000772 0.0001588 -4.86 Unemployment rate (%) 0.0006747 0.0005488 1.23 0.0010156 0.000569 1.78 Commute time to work -0.0003932 0.0001498 -2.62 -0.0003638 0.0001739 -2.09 Household income 2.38E-08 1.55E-07 0.15 -1.34E-07 1.68E-07 -0.8 Mortgage -0.0000209 6.11E-06 -3.41 -0.0000343 7.36E-06 -4.66 Median rent -0.0000267 5.68E-06 -4.71 -0.0000217 5.94E-06 -3.65 Urban housing units (%) -0.0260467 0.0043699 -5.96 -0.0272864 0.0045475 -6 Constant 0.1955102 0.0263834 7.41 0.1794576 0.0590882 3.04 Fixed effect No Yes Adjusted R-Square 0.1697 0.2115 Number of observations 3520 3520 77 2 Seller Choice of Risk and Real Estate Seasonality Table 2.4 Real Estate Seasonality and Seller Risk Aversion (1997-2007) Coefficient Standard T Statistics Coefficient Standard T Statistics Error Error Foreign born(%) 0.0004116 0.0001337 3.08 0.0001199 0.0001536 0.78 Renter occupied(%) 0.000499 0.0001008 4.95 0.0005564 0.0001068 5.21 Married (%) -0.0003582 0.0001534 -2.33 -0.000073 0.0001675 -0.44 Median value 6.06E-08 1.98E-08 3.06 1.21E-07 2.39E-08 5.07 Owner cost 0.0000108 3.26E-06 3.32 0.0000105 3.41E-06 3.07 Number of rooms 0.0099381 0.0018585 5.35 0.0101471 0.0020808 4.88 Winter temperature -0.0005112 0.0001092 -4.68 0.0001133 0.0003049 0.37 Latitude -0.0533146 0.0145024 -3.68 0.018637 0.0493566 0.38 Liquidity -0.0543787 0.0194945 -2.79 -0.0496475 0.0194271 -2.56 Total population 2.55E-07 2.11E-07 1.21 1.49E-07 2.12E-07 0.71 Median age -0.0000839 0.0002519 -0.33 -0.0002476 0.0002627 -0.94 Black (%) -0.0000753 0.000057 -1.32 -0.0000671 0.0000619 -1.09 Asian (%) -0.000272 0.0001376 -1.98 -0.0001252 0.0001574 -0.79 Hispanic (%) -0.0005787 0.0000973 -5.95 -0.0003499 0.0001091 -3.21 Total households -7.61E-06 2.15E-06 -3.54 -6.13E-06 2.12E-06 -2.89 Total housing units 5.89E-06 1.87E-06 3.15 4.71E-06 1.85E-06 2.55 Vacancy rate (%) -0.0005122 0.000234 -2.19 -0.0004263 0.0002305 -1.85 College degree of higher (%) 0.0003513 0.0000835 4.21 0.0004795 0.0000889 5.39 In labor force (%) -0.0009785 0.0001491 -6.56 -0.0008987 0.0001545 -5.82 Unemployment rate (%) 0.0009531 0.0005343 1.78 0.0011128 0.0005468 2.04 Commute time to work -0.0004549 0.0001482 -3.07 -0.0002784 0.000171 -1.63 Household income 1.76E-08 1.56E-07 0.11 -8.27E-08 1.68E-07 -0.49 Mortgage -8.91E-06 6.11E-06 -1.46 -0.0000252 7.33E-06 -3.44 Median rent -0.0000278 5.77E-06 -4.82 -0.0000257 5.98E-06 -4.3 Urban housing units (%) -0.0322813 0.0043981 -7.34 -0.0318727 0.0045433 -7.02 Constant 0.1834541 0.0257587 7.12 0.0863965 0.0553736 1.56 Fixed effect No Yes Adjusted R-Square 0.1749 0.2246 Number of observations 3254 3254 78 2 Seller Choice of Risk and Real Estate Seasonality Table 2.5 Real Estate Seasonality and Seller Risk Aversion (2008-2013) Coefficient Standard T Statistics Coefficient Standard T Statistics Error Error Foreign born(%) 0.0005347 0.0002417 2.21 -0.0002892 0.0002915 -0.99 Renter occupied(%) -0.0002517 0.0002101 -1.2 0.0000642 0.000243 0.26 Married (%) -0.0008241 0.0002354 -3.5 -0.0006275 0.0002581 -2.43 Median value 5.55E-08 2.57E-08 2.16 1.01E-07 2.82E-08 3.56 Owner cost 0.0000399 0.0000127 3.14 0.0000301 0.0000181 1.67 Number of rooms 0.0039018 0.0030685 1.27 0.0050992 0.0034356 1.48 Winter temperature -0.0007061 0.0002056 -3.43 0.0002511 0.0005646 0.44 Latitude -0.0999283 0.0256939 -3.89 0.1083133 0.1000508 1.08 Liquidity -3.9492 0.879027 -4.49 -3.774926 1.063541 -3.55 Total population -2.09E-07 4.04E-07 -0.52 1.32E-07 4.19E-07 0.32 Median age -0.0001613 0.000432 -0.37 0.0000861 0.0004768 0.18 Black (%) 0.0001871 0.000112 1.67 0.0000811 0.0001221 0.66 Asian (%) -0.0003358 0.000222 -1.51 0.0002798 0.0002715 1.03 Hispanic (%) -0.0001615 0.000166 -0.97 0.0001732 0.0001912 0.91 Total households -3.35E-06 3.42E-06 -0.98 -6.18E-06 3.50E-06 -1.76 Total housing units 2.27E-06 2.75E-06 0.83 3.91E-06 2.78E-06 1.4 Vacancy rate (%) -0.0005018 0.0004874 -1.03 -0.0011059 0.0005099 -2.17 College degree of higher (%) 0.000428 0.0001557 2.75 0.0003072 0.0001798 1.71 In labor force (%) -0.0005135 0.0002518 -2.04 -0.0004785 0.0002673 -1.79 Unemployment rate (%) 0.0028526 0.0009077 3.14 0.0034265 0.0010547 3.25 Commute time to work -0.0006594 0.0002964 -2.22 -0.0006461 0.0003609 -1.79 Household income 2.14E-07 1.90E-07 1.13 -9.96E-09 2.06E-07 -0.05 Mortgage -0.000025 8.41E-06 -2.97 -0.0000227 9.98E-06 -2.28 Median rent -0.0000106 7.70E-06 -1.38 -2.38E-06 8.48E-06 -0.28 Urban housing units (%) -0.0250573 0.012156 -2.06 -0.0280923 0.0129041 -2.18 Constant 0.2861147 0.0447941 6.39 0.1227689 0.0929273 1.32 Fixed effect No Yes Adjusted R-Square 0.1158 0.1462 Number of observations 1723 1723 79 3 Do Mutual Fund Managers Pick Winners within Product Markets? 3.1 Introduction Inthispaper, wetestwhethermutualfundmanagershaveenoughskilltopickwinners within peer groups. The vast literature on mutual fund performance typically finds that managers of active equity funds do not outperform passive funds on average, after accounting for fees. However, there is a wide distribution of performance which may be explained by varying levels of managerial skill. If a fund manager has superior stock picking ability, we should expect it to be more selective in its holdings. Therefore, we hypothesize that mutual funds exhibiting more highly selectiveportfolioswillsubsequentlyearnhigherreturns. Asecondhypothesis,followingfrom the first, is that stocks picked by such selective funds will perform with high returns. In order to test these hypotheses, we first construct a measure of within-industry firm selectivity for fund managers. We use three separate industry definitions in the analysis, two of which are based on Standard Industry Classification (SIC) coding and the third based on text analysis of product descriptions. By using this measure of selectivity, we begin by testing fund performance with risk-adjusted returns as the outcome variable. As a second approach, 80 3 Do Mutual Fund Managers Pick Winners within Product Markets? we use industry-adjusted returns as the performance outcome as well. In both cases, we find evidence that the more active, selective managers do exhibit higher adjusted returns. The effectisobservableineachhalfofoursub-samplefrom1996-2008, thoughitisstrongestinthe 1996-2002 period. Following this, we move on to examining the returns of individual stocks based on the selectivity of funds which invest in them. By sorting all stocks into quintiles of this publicly available information, we find that the difference between the extreme portfolios is significantly positive in the months following fund holdings disclosures. Thus, the evidence in this paper supports the view that fund managers have ability in picking high-performing stocks within industries. 3.2 Literature Review Research on portfolio manager performance goes back to Jensen (1969), who shows that good performance does not persist. Later studies take a more positive view on mutual fund manager skills (Grinblatt and Titman (1992), Elton, Gruber, Das, and Hlavka (1993), Hendricks, Patel, and Zeckhauser (1993), Brown and Goetzmann (1995), Grinblatt, Titman, and Wermers (1995), and Elton, Gruber, Das, and Black (1996)), showing mutual fund performance is predictable over longer horizons from five to ten years. However, Carhart (1997)findsthatcommonfactorsinthestockmarket, expenses, andtransactioncostsexplain most of this persistence in mutual fund returns. Although it is commonly believed that on average mutual funds do not outperform benchmarks after fees, newer studies discover substantial differences in mutual fund skills. Berk and Green (2004) use a theoretical model to show how all the economic rent created by skilled managers are seized by the investment companies through expenses and diseconomy of scale. From the empirical side, Kacperczyk, Sialm, and Zheng (2008) show that there is a wide variation in the amount of mutual fund returns unexplained by their quarterly holdings. They conclude that the amount of unexplained performance serves as a proxy for skill and 81 3 Do Mutual Fund Managers Pick Winners within Product Markets? uncover a positive link between unexplained performance and future fund returns. Similarly, Cremers and Petajisto (2009) find U.S. domestic equity mutual funds differ considerably in the degree their holdings diverging from the benchmark. They argue that the fact that some fund managers take large bets against their benchmarks reveals their superior skill or information, and find the degree of divergence from benchmarks positively predicts future performance. Wermers, Yao, and Zhao (2012) study the revelation of manager skills and the utilization of fund portfolio holdings to forecast future stock returns. They find that although historic positive alpha of fund managers does not predict future positive alpha, an aggregate of fund holdings according to their managers’ past performance generates a portfolio of superior returns. In a paper similar to ours, Kacperczyk, Sialm, and Zheng (2005) discover a positively link between the industry concentration of mutual fund holdings and fund performance. Their explanation is that if mutual fund managers have skills or information advantage, it is more likely that their skill or information advantage concentrate on a few industries. And thus skilled managers will tend to focus their holdings on these industries. Our paper differs from theirs. Instead of focusing on manager skills on industry selection, we focus on manager skills selecting specific firms within industries. Unskilled fund managers will more likely distribute their holdings across the firms within certain industries, while managers with information advantage will probably utilize their superior information to select only a few stocks. 3.3 Data Data used in the paper are collected from four sources: the CRSP Survivorship- Biased Free Mutual Fund database, the Thomson Reuters Mutual Fund Holdings database, the CRSP US Stock Database, and the Text-Based Network Industry Classification data on Hoberg-Phillips Data Library. The sample period is from 1996 to 2008. From the CRSP 82 3 Do Mutual Fund Managers Pick Winners within Product Markets? Mutual Fund Database, we collect information on investment objective code, total assets under management, date of inception, fund return, expense ratio, and turnover ratio. I focus on US domestic equity funds by selecting funds that have investment objective codes with the first two letters “ED”, standing for “equity domestic”. Index funds are excluded by their names. I exclude funds with total net assets under management below five million US dollars and funds with date of inception within a year. From Thomson Reuters Mutual Fund Holdings database, we collect information on fund equity holdings. We exclude funds holding fewerthan10stocks. Inthecasethatthereportingdateandthevintagedatearedifferent, we include observations with the earliest vintage date. From the CRSP US Stock Database, we collect information on stock returns, stock prices, and number of shares outstanding. From the Hoberg-Phillips Data Library, we download text-based industry classifications for each firm in our sample. This approach to identifying competitors developed by Gerard Hoberg and Gordon Phillips uses the text of product descriptions from SEC 10K filings to compare firms. We use the Fixed Industry Classification (FIC) set of 300 industries. The dataset was developed and introduced by Hoberg and Phillips (2010a, 2010b). The advantage of the HP data is that firms are linked to competitors based on product descriptions rather than industry classifications, which are somewhat subjective and are often too rigid to capture a firm’s actual product offerings. Our measure of within-industry selectivity (Firm Slectivity) is constructed using three distinct industry classification systems: Kacperczyk-Sialm-Zheng, Fama-French, and Hoberg-Phillips. The KSZ method contains 10 industries and the Fama-French method con- tains 49, each of which relies on Standard Industry Classification (SIC) codes. Using each of these industry definitions, we construct FirmSelectivity = 1− 1 m P m i=1 (n i /N i ) , where ni is the number of firms the fund holds in industry i, Ni is the total number of firms in industry i, and m is the number of industries the fund invest in. In other words, itrepresents the average number of firms per industry that the fund manager does not invest in. Thus, the variable ranges from 0 to 1 with higher values representing more selective managers. 83 3 Do Mutual Fund Managers Pick Winners within Product Markets? We also include a measure of investment concentration that has previously been found to be related to fund performance. Following Kacperczyk, Sialm, and Zheng (2005), we include the Industry Concentration Index, the sum of squared differences between the fund’s weight in each industry and the market weight in each industry. Again, we use the three industry measures to construct this index in our testing. In Table I, we present summary statistics of the variables used in the paper. It contains the selectivity measures, the industry concentration measures, standard mutual fund covariates, and adjusted fund returns. 3.4 Empirical Results In this section, we take several approaches to test the main hypothesis – that more highly selective funds will exhibit superior performance. We begin by dividing funds into deciles based on our firm selectivity measure. In this approach, decile 1 contains those funds that are the most selective and decile 10 contains those that are most diversified in their product market peer groups of investment. In order to properly account for risk in evaluating and comparing fund returns, we implement the Carhart (1997) four-factor model to derive the alpha of returns. Table II presents resulting alphas and standard errors for each decile in months 1, 2, and 3 following the corresponding report date that produced the selectivity measure. The measure is calculated using three separate industry classification methods: the Fama-French 49 industries, the Kacperczyk-Sialm-Zheng 10 industries, and the Hober-Phillips 300 fixed industry classification. One pattern evident in the table is that more selective funds have higher abnormal returns than those of more diversified funds in the first month after reporting holdings. Figure I plots the performance of funds in this month across all deciles. For each of the three industry definitions, there is a clear downward trend showing lower performance as the funds become more diversified in product markets. Indeed, all three methods of calculating 84 3 Do Mutual Fund Managers Pick Winners within Product Markets? selectivity show a significantly positive alpha for the difference between deciles 1 and 10. Typically, this outcome is driven by alphas being highly negative for the diversified deciles and close to zero for the selective ones. This indicates that selective funds are earning returns just nearly enough to compensate for trading costs, whereas diversified funds perform much more poorly. Interestingly, the pattern actually reverses in the third month following the reporting of holdings. This reversion of returns is statistically significant for the Fama-French and Hoberg-Phillips definitions of industries. One potential concern with the previous univariate findings is that the selectivity measure could be highly correlated with other fund-level characteristics. This could alter the interpretation of the previous findings. In order to account for such characteristics, we next run multivariate regressions of fund returns. Additionally, to ensure that our measure of selectivity is not picking up industry-level concentration by fund managers, as was exam- ined by Kacperczyk et al. (2005), we include industry concentration measures for all three classification systems. In addition to controlling for industry-level concentration, inclusion of this measure allows for comparison of significance between the two methods of evaluating specialization of the manager. The KSZ approach identifies managers that focus on specific industries whereas our selectivity measure identifies those who specialize in specific firms within industries. All regression models include year and style fixed effects. Standard errors are robust and clustered by fund. In Table III, we regress Carhart four-factor alpha from the first month after reporting on fund selectivity, industry concentration, and fund characteristics. The regression models in the first three columns using Fama-French firm selectivity show a slightly positive but statistically insignificant effect on risk-adjusted performance. All three variants of industry concentration are also positive but insignificant in these models. The next three columns, using KSZ-defined industries in the selectivity measure, also show positive but insignificant effects on performance. 85 3 Do Mutual Fund Managers Pick Winners within Product Markets? In contrast, the Hoberg-Phillips definitions of firm selectivity yield highly significant coefficients. With a coefficient of more than 72 basis points, this implies a one standard deviation increase in selectivity corresponds to a XX monthly basis point increase in alpha. ThisequatestoXXannualincreaseinrisk-adjustedreturn. Clearly, thefactthattheHoberg- Phillips product markets are much more finely derived allows the measure to outperform Fama-French and KSZ industry definitions. The results of the tests give evidence that more selective managers are able to achieve higher returns than managers who mostly diversify within product markets, after adjusting for risks and fund characteristics. We next turn to a critical test in determining whether mutual fund managers are able to select winners wthin product market groups. Using the three measures of industry groups, we construct a benchmark portfolio for each fund based on its stated holdings. We use the average return for all stocks within each held stock’s peer group as its benchmark return. Weighting these by the corresponding weights in the fund’s holdings yields a portfolio bench- mark. In our tests, we use the excess returns of the return of stocks held by the fund minus this benchmark return as the dependent variable to measure the performance in picking the best opportunities within industries. Using the HP product market classification allows for a very unique and novel assessment of stock-picking ability within groups of competitors. Figure II again shows a clear negative relationship between performance and diver- sification within product markets. Table IV shows that in the first month after reporting, there tends to be a positive difference between the most selective and least selective funds based on this benchmark performance measure. While the difference is not statistically significant using Fama-French industry definitions, it is highly significant both statistically and economically using KSZ and HP definitions. In fact, with HP industry classifications, there is nearly a 1% difference in excess returns between the two extreme deciles. Again, as was evident in preceding tests of performance, the effect appears to vanish and even reverse in subsequent months. However, none of the negative differences have significance in these tests. To account for fund characteristics, we present multivariate regressions with the in- 86 3 Do Mutual Fund Managers Pick Winners within Product Markets? dustry benchmark as the dependent variable in Table V. The results show that there is a strong, positive relationship between selectivity and performance when using Fama-French and Hoberg-Phillips industry classifications. Again, the significance of these two industry definitions is likely attributable to their finer segmentation of product markets. In contrast, the industry concentration measure used by KSZ has little predictive power in these tests. This indicates that selection within product markets is a better indicator of ability than concentration among industries. The sample in the previous tests used a panel of data from 1996-2008. In order to better understand the magnitude of this effect over time, we next divide this sample into two periods and run the same model. This will reveal whether the results are driven by a particular sub-period in the previous sample. In Table VI, Panel A shows tests using data from 1996-2002 with the four-factor, risk-adjusted fund returns in the first month after reporting as the dependent variable. Of the three selection variables – Fama-French, KSZ, and Hoberg-Phillips – all are positive, with the Hoberg-Phillips measure producing a highly statistically significant coefficient estimate. In Panel B, the latter period, 2003-2008, is used as a sub-sample. Again, all coefficients of the selectivity variable are positive, with the Hoberg-Phillips measure being the most statistically significant. However, the effect appears much smaller in magnitude within this sub-sample period than in the first. Finally, we check the returns of individual stocks that are held by mutual funds. Our previous results have shown that the funds exhibiting more firm selectivity generate higher portfolio returns. This implies that stocks held by these selective funds should outperform stocks held by less selective, more diversified funds. This serves as a vital check of the validity of the prior results, but also provides an extra piece of significant information. Since mutual fund holdings are required to be made publicly available on a quarterly basis, an investor can glean information from the types of funds holding a particular stock being considered. Since mutual funds report their holdings every three months (and the month of reporting varies from fund to fund), we devise a system of sorting stocks into portfolios 87 3 Do Mutual Fund Managers Pick Winners within Product Markets? each month based on the 1st, 2nd, and 3rd, month of holdings information. For example, on January 1, a portfolio is created based on funds that reported holdings on December 31. A second portfolio is created based on funds reporting on November 30 and a third from those reporting on October 31. This method of separating by report date allows us to extract out the value of the information over time since older reports may have become stale and outdated after more than a month. For each month, we sort stocks into quintiles based on the selectivity of the funds holding that stock within its industry group. That is, the average percentage of stocks in the industry that the fund did not invest in. Quintile 1 contains stocks that are held with the most selectivity and quintile 5 contains those with the least. In Table VII, we present the results of the stock sorting procedure. Though it is not monotonic, there does seems to be a trend in each of the three monthly groups where the less selective portfolios have a lower return. Although there is not a significantly high return in quintile 1, it is much better-performing than the least selective. This is clear from the significantly high alpha calculated as the difference between quintiles 1 and 5 in each monthly group. The largest such difference is seen in Month 1 – where the most recent holdings data is used for portfolio construction. However, Month 2 and Month 3 also show statistically significant and positive alphas in the difference between these portfolios, meaning there appears to be persistence in the value of the information. Ultimately, these results give more evidence that selective managers are picking winners in product market groups since the more selectively held stocks outperform those held by more diversified funds. 3.5 Conclusion The question of whether mutual fund managers add value over passive investment strategies is highly relevant and has been the focus of debate in academic and media dis- cussions. In this paper, we take a novel approach to address this question by examining the investments of fund managers at the product market level. The contributions are a 88 3 Do Mutual Fund Managers Pick Winners within Product Markets? new measure of within-industry firm selectivity as well as a product market benchmark for assessing the performance of funds. Our main finding is that more active fund managers do achieve higher risk- and industry-adjusted returns. This result holds for the three industry definitions, but is most significant using the Hoberg-Phillips text-based fixed industry classification. Additionally, we find that mutual fund holding disclosures can provide valuable information in predicting which stocks will perform best in the subsequent months. In sum, the results of the paper show that active fund managers do add value to their investors by picking inners within the product markets in which they specialize. 89 3 Do Mutual Fund Managers Pick Winners within Product Markets? Figure 3.1. This figure plots the Carhart 4 factor alphas for fund decile portfolios for the 1st month after the report date. At each report date, we divide the funds into deciles according to the Firm Selectivity, which is defined as FS = 1− 1 m P m i=1 n i /N i , where n i is the number of firms the fund holds in industry i, N i is the total number of firms in industry i, and m is the number of industries the fund invests in. Industries are defined using the Fama-French, Kacperczyk-Sialm-Zheng (KSZ), and Hoberg-Phillips measures respectively. 90 3 Do Mutual Fund Managers Pick Winners within Product Markets? Figure 3.2. This figure plots the industry average adjusted return for fund decile portfolios for the 1st month after the report date. The industry average adjusted return measures the fund’s ability to select stocks within industries, and is defined as IndARet t = P n i=1 w i,t (R i,t −IndAverage i,t ), where n is the number of stocks the fund holds, w i is the weight of stock i in the fund, R i is the stock return, IndAverage i is the equally weighted average return of all stocks in stock i’s industry. At each report date, we divide the funds into decilesaccordingtotheFirmSelectivity, whichisdefinedasFS = 1− 1 m P m i=1 n i /N i , wheren i is the number of firms the fund holds in industry i,N i is the total number of firms in industry i, and m is the number of industries the fund invests in. Industries are defined using the Fama-French, Kacperczyk-Sialm-Zheng (KSZ), and Hoberg-Phillips measures respectively. 91 3 Do Mutual Fund Managers Pick Winners within Product Markets? Table 3.1 Summary Statistics Variable Number of Observation Mean Standard Deviation Min Max Fama French Firm Selectivity 31670 0.959 0.053 0 0.998 KSZ Firm Selectivity 31670 0.983 0.025 0.364 0.999 Hoberg Phillips Firm Selectivity 31670 0.914 0.062 0 0.995 Fama French Industry Concentration Index 31670 0.106 0.13 0.001 1.031 KSZ Industry Concentration Index 31670 0.111 0.118 0.001 0.979 Hoberg Phillips Industry Concentration Index 31670 0.104 0.137 0.001 1 Log Fund Size 31670 5.768 1.815 1.609 12.173 Log Fund Age 31670 4.929 0.853 1.079 6.923 Fund Expense Ratio 31670 0.013 0.004 0 0.069 Fund Turnover Ratio 31670 0.858 0.85 0 25.786 Log Fund Family Size 31670 7.378 2.245 1.609 12.862 Carhart Alpha 31670 -0.001 0.017 -0.182 0.263 Fama French Indudstry Average Adjusted Return 31670 -0.003 0.031 -0.526 0.366 KSZ Industry Average Adjusted Return 31670 -0.003 0.031 -0.519 0.375 Hoberg Phillips Industry Average Adjusted Return 31670 -0.003 0.03 -0.4 0.308 92 3 Do Mutual Fund Managers Pick Winners within Product Markets? Table 3.2 Univariate Analysis: Firm Concentration Decile Fund Portfolios and Carhart 4 Factor Alpha Fama-French Industries KSZ Industries Hoberg-Phillips Industries 1st month 2nd month 3rd month 1st month 2nd month 3rd month 1st month 2nd month 3rd month Decile 1 0.023 -0.184* -0.177* -0.018 -0.128 -0.19** -0.024* -0.161** -0.193*** (Most concentrated) -0.106 -0.0922 -0.0896 -0.1 -0.0815 -0.0921 -0.0846 -0.061 -0.0686 Decile 2 -0.092 -0.106 -0.085 -0.136 -0.155* -0.099 -0.081 -0.141 -0.13 -0.095 -0.0777 -0.0916 -0.093 -0.0819 -0.0916 -0.0974 -0.0852 -0.0791 Decile 3 -0.201* -0.055 -0.078 -0.207** -0.114 -0.06 -0.164 -0.119 -0.11 -0.11 -0.0993 -0.11 -0.101 -0.0765 -0.0761 -0.108 -0.0813 -0.0889 Decile 4 -0.209* -0.058 -0.014 -0.164 -0.036 -0.034 -0.189* -0.098 -0.106 -0.121 -0.0948 -0.112 -0.103 -0.0782 -0.0991 -0.0976 -0.0728 -0.0821 Decile 5 -0.209* -0.063 0.0099 -0.205** -0.066 -0.056 -0.207** -0.073 -0.021 -0.107 -0.1 -0.0968 -0.0968 -0.0886 -0.102 -0.101 -0.0907 -0.099 Decile 6 -0.32** -0.115 -0.027 -0.254** -0.082 -0.031 -0.181 -0.051 -0.006 -0.13 -0.0911 -0.112 -0.106 -0.0846 -0.092 -0.122 -0.0859 -0.124 Decile 7 -0.28** -0.129 -0.071 -0.25** -0.031 -0.018 -0.293** -0.052 -0.002 -0.106 -0.0885 -0.102 -0.113 -0.0871 -0.112 -0.122 -0.108 -0.118 Decile 8 -0.27** -0.041 -0.077 -0.252* -0.067 -0.006 -0.228** 0.041 -0.015 -0.117 -0.0917 -0.113 -0.125 -0.0997 -0.122 -0.108 -0.1 -0.125 Decile 9 -0.225** 0.0461 -0.052 -0.209** -0.026 -0.006 -0.313*** -0.036 -0.053 -0.0963 -0.0778 -0.0949 -0.129 -0.101 -0.122 -0.112 -0.0922 -0.108 Decile 10 -0.203** -0.041 -0.001 -0.292 -0.039 -0.073 -0.308 -0.055 0.0647 (Most diversified) -0.0922 -0.0636 -0.0797 -0.108 -0.0793 -0.0964 -0.124 -0.0959 -0.105 Decile 1 - Decile 10 0.226** -0.143 -0.176* 0.274** -0.089 -0.117 0.283** -0.106 -0.258*** -0.0967 -0.09 -0.0901 -0.107 -0.0748 -0.106 -0.11 -0.0822 -0.0897 Spearman Rank Correlation -0.09734 0.06078 0.05983 -0.11501 0.06102 0.07548 -0.11938 0.06646 0.0961 P-Value 0.0614 0.2435 0.251 0.027 0.2417 0.1473 0.0216 0.2022 0.0648 *** 1% significance, ** 5% significance, * 10% significance 93 3 Do Mutual Fund Managers Pick Winners within Product Markets? Table 3.3 Regression Analysis: Firm Selectivity and Carhart 4 Factor Alpha Dependent variable: Carhart 4 factor alpha Fama-French FS 0.00135 -0.00155 KSZ FS 0.00481 -0.00378 Hoberg-Phillips FS 0.00762*** 0.00778*** 0.00722*** -0.0019 -0.00191 -0.00187 Fama-French ICI 0.00166 0.00122 -0.00162 -0.00162 KSZ ICI 0.00131 0.00109 -0.00184 -0.00182 Hoberg-Phillips ICI 0.00192 -0.00165 Log fund total net asset 0.000484*** 0.000490*** 0.000505*** 0.000506*** 0.000505*** -0.00012 -0.000121 -0.00012 -0.000119 -0.00012 Log fund age -0.000191 -0.000192 -0.000231 -0.000228 -0.000242 -0.000223 -0.000226 -0.000222 -0.000223 -0.000219 Expense ratio -0.0622*** -0.0622*** -0.0620*** -0.0620*** -0.0622*** -0.0198 -0.0197 -0.0199 -0.0198 -0.02 Turnover ratio 0.000253 0.000244 0.000232 0.000227 0.00024 -0.000172 -0.000171 -0.000172 -0.00017 -0.000172 Log family size -0.000174** -0.000179** -0.000183** -0.000187** -0.000174** -8.76E-05 -8.77E-05 -8.74E-05 -8.76E-05 -8.70E-05 Constant 0.000276 0.000317 0.000912 0.00092 0.000841 -0.00113 -0.00115 -0.00113 -0.00114 -0.00113 Year fixed effects yes yes yes yes yes Style fixed effects yes yes yes yes yes Clustered by fund by fund by fund by fund by fund Observations 31,351 31,351 31,351 31,351 31,351 R-squared 0.032 0.032 0.033 0.033 0.033 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 94 3 Do Mutual Fund Managers Pick Winners within Product Markets? Table 3.4 Univariate Analysis: Firm Concentration Decile Fund Portfolios and Industry Average Adjusted Return Fama-French Industries KSZ Industries Hoberg-Phillips Industries 1st month 2nd month 3rd month 1st month 2nd month 3rd month 1st month 2nd month 3rd month Decile 1 0.0931 -0.681 0.104 0.182 -0.22 0.194 0.343 -0.483 0.301 (Most concentrated) -0.847 -0.874 -0.617 -0.736 -0.726 -0.587 -0.748 -0.822 -0.672 Decile 2 -0.111 -0.432 0.314 -0.008 -0.369 0.0671 -0.063 -0.532 0.0821 -0.709 -0.745 -0.491 -0.742 -0.687 -0.51 -0.721 -0.75 -0.56 Decile 3 -0.536 -0.549 0.422 -0.129 -0.388 0.4 -0.098 -0.533 0.0648 -0.679 -0.614 -0.476 -0.669 -0.708 -0.508 -0.704 -0.688 -0.562 Decile 4 -0.427 -0.521 0.535 -0.413 -0.253 0.259 -0.197 -0.59 0.0407 -0.644 -0.591 -0.443 -0.677 -0.69 -0.484 -0.693 -0.656 -0.504 Decile 5 -0.612 -0.453 0.522 -0.333 -0.448 0.429 -0.33 -0.399 0.229 -0.622 -0.561 -0.462 -0.681 -0.665 -0.498 -0.64 -0.62 -0.504 Decile 6 -0.6 -0.457 0.491 -0.56 -0.195 0.529 -0.418 -0.48 0.204 -0.633 -0.564 -0.415 -0.655 -0.617 -0.487 -0.597 -0.555 -0.403 Decile 7 -0.723 -0.484 0.462 -0.641 -0.294 0.553 -0.69 -0.408 0.503 -0.589 -0.544 -0.433 -0.645 -0.566 -0.442 -0.579 -0.538 -0.401 Decile 8 -0.525 -0.445 0.448 -0.586 -0.336 0.698 -0.591 -0.364 0.419 -0.583 -0.533 -0.39 -0.603 -0.516 -0.444 -0.55 -0.529 -0.428 Decile 9 -0.588 -0.265 0.237 -0.75 -0.247 0.819* -0.554 -0.395 0.335 -0.561 -0.601 -0.418 -0.586 -0.493 -0.416 -0.546 -0.493 -0.406 Decile 10 -0.502 -0.312 0.159 -0.681 -0.148 0.597 -0.591 -0.37 0.458 (Most diversified) -0.583 -0.587 -0.43 -0.547 -0.484 -0.399 -0.533 -0.445 -0.388 Decile 1 - Decile 10 0.595 -0.369 -0.0556 0.863*** -0.0717 -0.404 0.934** -0.112 -0.158 -0.373 -0.338 -0.329 -0.307 -0.334 -0.337 -0.426 -0.47 -0.522 Spearman Rank Correlation -0.05677 -0.01322 0.00932 -0.07775 -0.02824 0.068 -0.08633 -0.04696 0.04275 P-Value 0.2827 0.8026 0.8601 0.1409 0.5933 0.198 0.102 0.3744 0.4187 *** 1% significance, ** 5% significance, * 10% significance 95 3 Do Mutual Fund Managers Pick Winners within Product Markets? Table 3.5 Regression Analysis: Firm Selectivity and Industry Average Adjusted Return Dependent variable: industry average adjusted return Fama-French Industries KSZ Industries Hoberg-Phillips Industries Firm Selectivity 0.0206*** 0.00541 0.0198*** -0.00774 -0.00914 -0.00657 Industry concentration index 0.00512 0.00775 0.00671 -0.00493 -0.00497 -0.00477 Log fund total net asset 0.000448 0.000601** 0.000589** -0.000275 -0.000276 -0.000254 Log fund age 0.00130*** 0.00142*** 0.00106** -0.000468 -0.000471 -0.00044 Expense ratio -0.0488 -0.0189 -0.0372 -0.0426 -0.0251 -0.025 Turnover ratio -0.00174*** -0.00160*** -0.00150*** -0.000438 -0.000425 -0.000422 Log family size -0.00103*** -0.00115*** -0.00102*** -0.0002 -0.000202 -0.000189 Constant 4.09E-06 -0.00115 -0.00142 -0.00241 -0.00237 -0.00231 Year fixed effects yes yes yes Style fixed effects yes yes yes Clustered by fund by fund by fund Observations 30,101 30,101 30,101 R-squared 0.146 0.151 0.168 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 96 3 Do Mutual Fund Managers Pick Winners within Product Markets? Table 3.6 a Sub-Sample Regression Analysis (1996-2002): Carhart 4 Factor Alpha And Firm Selectivity Dependent Variable: Carhart 4 Factor Alpha Fama-French Industries KSZ Industries Hoberg-Phillips Industries Firm Selectivity 0.00609 0.0132* 0.0247*** -0.00716 -0.00753 -0.00558 Industry Concentration Index 4.19E-05 -0.000315 0.00358 -0.00687 -0.00581 -0.00786 Log Fund Total Net Asset 0.000937*** 0.000601** 0.000589** -0.000182 -0.000276 -0.000254 Log Fund Age -0.000366 0.00142*** 0.00106** -0.000297 -0.000471 -0.00044 Expense Ratio -0.0809 -0.0189 -0.0372 -0.0654 -0.0251 -0.025 Turnover Ratio 0.000503* -0.00160*** -0.00150*** -0.000263 -0.000425 -0.000422 Log Family Size -0.000400*** -0.00115*** -0.00102*** -0.000142 -0.000202 -0.000189 Constant 0.00044 0.000479 0.00182 -0.0022 -0.0022 -0.00215 Year Fixed Effects Yes Yes Yes Style Fixed Effects Yes Yes Yes Clustered By Fund By Fund By Fund Observations 14,424 14,424 14,424 R-squared 0.04 0.04 0.042 Robust Standard Errors In Parentheses *** P<0.01, ** P<0.05, * P<0.1 97 3 Do Mutual Fund Managers Pick Winners within Product Markets? Table 3.6 b Sub-Sample Regression Analysis (2002-2008): Carhart 4 Factor Alpha And Firm Selectivity Dependent variable: Carhart 4 factor alpha Fama-French Industries KSZ Industries Hoberg-Phillips Industries Firm Selectivity 0.000995 0.00276 0.00329** -0.00148 -0.00296 -0.00162 Industry Concentration Index 0.00198* 0.00196* 0.00161 -0.00107 -0.00119 -0.00107 Log fund total net asset 1.65E-05 1.97E-05 2.92E-05 -0.000138 -0.000139 -0.000137 Log fund age -0.000105 -0.000102 -0.000142 -0.00026 -0.000261 -0.000259 Expense ratio -0.0587*** -0.0588*** -0.0584*** -0.0222 -0.0222 -0.0223 Turnover ratio -0.000345 -0.000368 -0.000361 -0.000285 -0.000282 -0.000286 Log family size 6.59E-05 6.17E-05 5.90E-05 -8.99E-05 -9.04E-05 -8.94E-05 Constant -0.00248* -0.00246* -0.00204 -0.00136 -0.00137 -0.00137 Year fixed effects yes yes yes Style fixed effects yes yes yes Clustered by fund by fund by fund Observations 16,927 16,927 16,927 R-squared 0.022 0.022 0.022 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 98 3 Do Mutual Fund Managers Pick Winners within Product Markets? Table 3.7 Long Short Portfolio Based On Selectivity Scores Month 1 Month 2 Month 3 Alpha SE P-Value Alpha SE P-Value Alpha SE P-Value Quintile1 0.27% 0.29% 0.3538 -0.28% 0.18% 0.1308 -0.07% 0.18% 0.7121 Quintile2 -1.03% 0.39% 0.0111 -0.06% 0.29% 0.8414 -0.38% 0.20% 0.0648 Quintile3 -0.53% 0.31% 0.0955 -0.51% 0.22% 0.0208 -0.28% 0.23% 0.2147 Quintile4 -0.97% 0.47% 0.0462 -0.80% 0.29% 0.0076 -0.90% 0.27% 0.0012 Quintile5 -0.77% 0.25% 0.0028 -0.77% 0.21% 0.0004 -0.77% 0.22% 0.0005 Quintile1-5 1.04% 0.41% 0.0141 0.49% 0.26% 0.0581 0.70% 0.26% 0.0081 99 References Barber, B. M., T. Odean, 2001, Boys Will Be Boys: Gender, Overconfidence, and Common Stock Investment, Quarterly Journal of Economics, 116(1): 261-292. Basak,S.,andD.Makarov,2013,StrategicAssetAllocationinMoneyManagement,Working Paper, London Business School. Basak, S., A. Pavlova, and A.Shapiro, 2007, Optimal Asset Allocation and Risk Shifting in Money Management, Review of Financial Studies, 20, 1583-1621 Basak, S., A. 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Abstract (if available)

Abstract My dissertation contains three chapters. The first chapter is based on my job market paper “Horizon Goals and Risk Taking in Mutual Funds.” This paper studies the relationship between mutual fund manager investment horizons and managerial risk-taking decisions. Using a dynamic model, I show that the relation between the investment horizon and optimal risk taking is negative for managers confident in their investment abilities. Consistent with the model implication and manager over-confidence, I find that in general mutual funds reporting longer maximum evaluation horizons have lower risk, and the low risk levels helped these funds mitigate their losses in the financial crisis

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Asset Metadata

Creator Guo, Zhishan (author)

Core Title Two essays on the mutual fund industry and an application of the optimal risk allocation model in the real estate market

School Marshall School of Business

Degree Doctor of Philosophy

Degree Program Business Administration

Publication Date 02/19/2015

Defense Date 02/10/2015

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

Tag mutual fund,OAI-PMH Harvest,optimal risk allocation,Real estate

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Zapatero, Fernando (committee chair), Jones, Christopher S. (committee member), Radchenko, Peter (committee member), Solomon, David (committee member)

Creator Email zhish.guo@gmail.com,zhishang@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-535918

Unique identifier UC11297802

Identifier etd-GuoZhishan-3201.pdf (filename),usctheses-c3-535918 (legacy record id)

Legacy Identifier etd-GuoZhishan-3201.pdf

Dmrecord 535918

Document Type Dissertation

Format application/pdf (imt)

Rights Guo, Zhishan

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

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA