The Cross-section of Managerial Ability and Risk Preferences

I use structural portfolio management models to study the joint cross-sectional distribution of managerial ability and risk preferences using manager-level data. The economic restrictions following from theory imply that (i) fund alphas reflect the manager’s ability and risk preferences and that (ii) information in second moments of fund returns can be used to estimate both attributes. The estimation relies on a novel framework to empirically analyze dynamic portfolio-choice models. The findings are twofold. First, the restrictions implied by recently-proposed models of managerial preferences are strongly rejected in the data. Second, introducing relative-size concerns into the manager’s objective delivers plausible estimates and is formally favored over the standard models and reduced-form performance regressions. Based on this model, I document large and skewed heterogeneity in risk preferences, but less dispersion in ability. Risk aversion and managerial ability are highly positively correlated. Finally, ignoring heterogeneity can lead to large welfare losses for an individual investor who allocates capital to actively-managed mutual funds. First version: October 2007. Department of Finance, Stern School of Business, New York University, 44 W. 4th Street, New York, NY 10012; [email protected]; Tel: (212) 998-0924; http://www.stern.nyu.edu/~rkoijen. Koijen is also associated with Netspar. I thank Yacine Aı̈tSahalia, Lieven Baele, Bo Becker, Jonathan Berk, Lans Bovenberg, Michael Brandt, Jennifer Carpenter, Xavier Gabaix, Eric Ghysels, Alexei Goriaev, Marty Gruber, Tim Johnson, Eugene Kandel, Ron Kaniel, Peter Kondor, Anthony Lynch, Theo Nijman, Josh Pollet, Matt Richardson, Viorel Roscovan, Rob Stambaugh, Jules Van Binsbergen, Otto Van Hemert, Stijn Van Nieuwerburgh, Jay Wang, Bas Werker, Rob Whitelaw, and seminar participants at NYU Stern, Stanford GSB, UCLA Anderson School of Management, University of Illinois at Urbana-Champaign, University of Amsterdam, University of Lausanne, and Tilburg University for useful discussions and suggestions. I am also grateful to Martijn Cremers and Antti Petajisto for making their benchmark data available for this paper. I thank NCF/SARA for the use of their supercomputer. An investor’s decision to allocate capital to actively-managed funds relies on the premise that mutual fund managers are endowed with skills that enable them to outperform a passive investment strategy. This premise has spurred a large literature aimed at measuring managerial ability and at characterizing the cross-sectional distribution of managerial talent. The recent view contends that there is a small fraction of managers who are able to significantly recuperate fees and expenses. However, ever since Jensen (1968), the typical approach is to rely on performance regressions to measure skill. In such performance regressions, mutual fund returns in excess of the short rate are regressed on a constant and a set of excess benchmarks returns. The intercept of the performance regression, the manager’s alpha, is then taken as a measure of ability. This reduced-form approach ignores that fund returns are the outcome of a portfolio management problem. In structural portfolio management models, the manager’s ability shapes her investment opportunity set, while the manager’s preferences determine which portfolio is chosen along this investment opportunity set. The fact that a manager chooses along the investment opportunity set that depends on her ability points to two important dimensions of heterogeneity: managerial ability and risk preferences. It turns out that the standard alpha reflects both managerial ability, as defined by the price of risk on the active portfolio, and risk preferences. I show that the restrictions implied by structural portfolio management models can be used to disentangle both attributes. As such, this paper is the first to impose the economic restrictions following from theory to recover the joint cross-sectional distribution of managerial ability and risk preferences. The controversy surrounding the existence of managerial ability is largely the result of inefficient inference. It is well known that averaging (risk-adjusted) returns over short time spans leads to noisy estimates (Merton (1980)). Hence, the estimated cross-sectional distribution of managerial ability reflects not only true heterogeneity, but also, and perhaps predominantly, estimation error. The restrictions implied by structural portfolio management models lead to much sharper estimates of managerial ability and risk aversion because they exploit information in the volatility of fund returns and in the covariance of fund returns with benchmark returns. By combining these estimates, I recover the crosssectional distribution of the standard performance measure, alpha. Figure 1 displays the Jensen (1968), Gruber (1996), and Carhart (1997). Kosowski, Timmermann, Wermers, and White (2006), Cremers and Petajisto (2007), Kacperczyk, Sialm, and Zheng (2005), Elton, Gruber, and Blake (2007). Alternatively, risk adjustments are performed by comparing fund returns to portfolios with matched characteristics (Daniel, Grinblatt, Titman, and Wermers (1997)). Also in this case, risk-adjusted returns are averaged to gauge the manager’s skill. DeTemple, Garcia, and Rindisbacher (2003) and Munk and Sorensen (2004) show that the manager’s investment opportunity set can be summarized by the instantaneous short rate and prices of risk in a continuous-time economy. Nielsen and Vassalou (2004) show that if an investor has to select one fund, then she will prefer the one that has the highest price of risk. This makes the price of risk on the active portfolio a natural measure of ability motivated by portfolio-choice theory. Pastor and Stambaugh (2002b), Lynch andWachter (2007a), and Lynch andWachter (2007b) propose to use longer samples of benchmark returns to sharpen the estimates. Managerial ability is still estimated by averaging risk-adjusted returns over short periods.