Model uncertainty, performance persistence and flows

Investors’ concerns about model uncertainty result in an additional risk premium in security prices (Hansen et al. 1999, 2002; Anderson et al. 2003; Hansen and Sargent 2006). In asset allocation, ignoring model uncertainty leads to perceived utility loss as high as 4.8% per year (Avramov 2002). Fama and French (1997) point out that model uncertainty is one of the problems in calculating industry costs of equity and show that the CAPM of Sharpe (1964) and the three-factor model of Fama and French (1993) can produce industry costs of equity estimates that differ by 2% or more. Pastor and Stambaugh (1999) find that model uncertainty also contributes to the difficulty in estimating individual firms’ costs of equity.

A number of papers apply Bayesian econometric techniques to study topics such as performance evaluation, portfolio choice and performance persistence in the mutual fund industry (e.g., Baks et al. 2001; Pastor and Stambaugh 2002a, b; Avramov and Wermers 2006; Busse and Irvine 2006; Jones and Shanken 2005; Friesen 2004; Huij and Verbeek 2007). These papers focus on parameter uncertainty, while my paper focuses on model uncertainty.

Berk and Green (2004) demonstrate that skilled managers may not have consistently good performance and fund returns need not be predictable if the supply of capital by investors is competitive and managers experience decreasing returns to scale.

Investment Company Fact Book 2007, Table 1 (http://​www.​ici.​org/​pdf/​07fb_​datasec_​1.​pdf).

In my sample that spans the period 1980–2003, I find that the average expense ratio of actively managed equity funds is 1.42% per year, while the average expense ratio of equity index funds is 0.64% per year. Actively managed bond and balanced funds also have higher average expense ratios than their passively managed counterparts.

The existence of skilled fund managers is consistent with semi-strong form efficiency if such managers possess private information.

Frohlich (1991) evaluates the performance of stock, bond and balanced funds using a measure based on the arbitrage pricing theory of Ross (1976). In contrast, my study investigates performance persistence and flow-performance sensitivity in a large sample of stock, bond and balanced funds.

These results are based on BMA alphas estimated with a skeptical prior belief in managerial skill and a 36-month estimation window. Using an alternative prior belief or a longer estimation window does not change my conclusions qualitatively.

Gruber (1996) also reports outflows from poorly performing funds. To sort funds into deciles, he uses a model that attributes fund return to the equity market, the bond market, a size factor and a growth factor.

Using exact monthly fund flow data of UK mutual funds between 1992 and 2000, Keswani and Stolin (2008) document the smart money effect in the UK, which is attributed to the buying decisions of both retail and institutional fund investors. The authors also document the smart money effect in the US using monthly mutual fund data available from 1991. Their results suggest that data frequency and sample period selection can affect tests of the smart money effect.

Christopherson et al. (1998) propose using net of benchmark returns as a solution to the problem of persistent estimation error in alphas.

Pastor and Stambaugh (2002a) use seemingly unrelated passive assets to evaluate equity mutual fund performance. Kosowski et al. (2007) find that the methodology of Pastor and Stambaugh (2002a) also helps to predict hedge fund returns.

Jones and Shanken (2005) and Friesen (2004) relax the prior independence assumption by specifying a hierarchical prior for fund alphas. A complete relaxation of the prior independence assumption requires the specification of hierarchical priors for both the fund alpha and regression coefficients. Such priors result in analytically intractable posterior distributions and require the use of Markov Chain Monte Carlo simulation techniques (see e.g., Koop 2003).

In Sect. 8.6, I explore the impact of using the more extreme prior belief of no skill.

Nanda et al. (2004) show that the flow-performance relation can vary across share classes with different load structures. In Sect. 8.9, I discuss this issue and show that inferences about the flow-performance relation are robust to the consolidation of share classes.

In the CRSP Database, not all funds switched to monthly reporting of total net assets starting from 1991. In my own sample, two funds only reported quarterly total net assets in 1991—Seligman Frontier Fund and Lazards Funds: Equity Portfolio.

I also use a longer estimation window of 60 months for funds with available data. Estimation is implemented on a rolling basis. Further details are in Sects. 5.1 and 6.

I use two estimation windows: 36 and 60 months.

“Appendix A” lists the variables in each model.

When I repeat the analysis of Table 1 using model probabilities estimated with a less skeptical prior belief or a 60-month estimation window, I obtain similar results. Identities of the top three models are the same in all robustness checks.

For example, if model j is the CAPM, then \( x_{i,j,t} \) is the market portfolio return in January 1983, and \( \overline{{b_{i,j} }} \) is the posterior mean of fund i’s market beta estimated from the previous 36 months.

Throughout the paper, I use Newey and West (1987) heteroskedasticity-and-autocorrelation consistent (HAC) standard errors to compute p values. The lag length is set to 6 months for computing the HAC covariance matrix. I also experiment with lag lengths of 3, 9, and 12 months and obtain qualitatively similar inferences. Hamilton (1994, pp. 282–283) describes the computation of the HAC covariance matrix and standard errors.

Besides model averaging risk-adjusted returns, I also measure future fund returns in two different ways. For each decile and the 10–1 portfolio, I calculate the average excess return (in excess of the risk-free rate) and a risk-adjusted return (alpha) defined with respect to a specific return generating model. For equity funds, the risk-adjusted return is Carhart’s (1997) four-factor alpha. For bonds funds, the risk-adjusted return is the alpha defined with respect to the model in Blake et al. (1993). For balanced funds, the risk-adjusted return must account for the fact that such funds can invest in both equities and bonds. Therefore, I employ the model in Elton et al. (1996a) and Gruber (1996) because it accounts for risks in these two asset classes (see “Appendix A”). Using these alternative measures of future fund returns, I find evidence of return predictability for balanced, equity and bond funds. These results are available from the author upon request. In Sect. 8.3, I examine the robustness of my results using net of benchmark returns to measure post-ranking performance.

Results of the intermediate portfolios are available from the author upon request.

Findings based on dollar cash flow are available from the author upon request.

As mentioned in Sect. 4, I assign equity funds to one of six investment objectives: small company growth, other aggressive growth, growth, income, growth, growth and income and maximum capital gain. Bond funds fall into one of three investment objectives: government bonds, mortgage-backed securities, and corporate bonds. Balanced funds represent a single investment objective.

I compute standard deviation only if a fund has a complete record of 12 monthly returns in a year.

Since I create the fractional and quintile performance ranks separately for each investment objective, it is never the case that I compare funds from different objective groups in constructing these ranks.

All alpha measures are estimated using data from the previous 36 months and come from the output of the Bayesian estimation (see Sect. 3.2). I estimate Sharpe ratio using monthly returns from the previous 12 months.

I obtain similar findings when I (1) estimate a bivariate VAR with three lags, and (2) use funds with continuous returns and flows for at least 12 months.

I continue to find evidence of persistence when funds are ranked using BMA alphas estimated with a less skeptical prior belief and a 36-month estimation window. I do not find evidence of persistence using the longer 60-month estimation window, regardless of the prior belief in skill. I do not compute Spearman correlation for Panel D because there are only two portfolios; the Best–Worst spread conveys the same information as the Spearman correlation in this case.

As an additional robustness check, I replace the CRSP index with the S&P 500 index to compute post-ranking alphas for equity and balanced funds. Making this change does not affect my findings. To ensure that results for balanced funds are robust to the benchmark’s allocation between stocks and bonds, I repeat my analyses using two alternative benchmarks. The first allocates equal weight (50%) to both the CRSP and Lehman indexes, the second allocates 70% weight to the CRSP index and 30% weight to the Lehman index. I obtain similar results using these alternative benchmarks.

The ten industry-sorted stock portfolios are from Ken French’s website. I thank him for generously providing the data. The ten industries are: (1) consumer nondurables, (2) consumer durables, (3) manufacturing, (4) energy, (5) business equipment, (6) telephone and television transmission, (7) wholesale, retail and some services, (8) healthcare, medical equipment and drugs, (9) utilities, and (10) other. The first three bond portfolios are portfolios of long-term, intermediate-term and short-term government bonds. The fourth portfolio is a portfolio of low-grade corporate bond. The long- and intermediate-term government bond portfolios are from Ibbotson Associates. The short-term government bond portfolio is the Merrill Lynch 1-to-3 year Treasury index (from Datastream). The low-grade corporate bond portfolio is the Merrill Lynch High Yield index (from Datastream).

Term premium for long-term Treasury securities is 10-year Treasury bond yield minus 3-month Treasury bill yield, term premium for 1-year Treasury securities is 1-year Treasury bill yield minus 3-month Treasury bill yield, default premium for corporate bonds is BAA corporate bond yield minus AAA corporate bond yield, default premium for commercial paper is 3-month commercial paper yield minus 3-month T-bill yield, 12-month production growth is calculated using the total Industrial Production index (G.17 supplement). All yields and the total Industrial Production index are obtained from the Federal Reserve Board. The CPI series is from the Bureau of Labor Statistics.

Throughout Sect. 8, whenever I estimate flow-performance regressions, I also examine the flows to deciles sorted by past BMA alphas. The decile-based analyses produce results similar to those of the flow-performance regressions. In addition, all flow-performance regression results are robust to the use of HIGHPERF, MIDPERF and LOWPERF as performance measures.

The assumption here is that flows occur at the end of the quarter (or year).

The alternative approach of estimating missing total net assets increases the sample slightly from 26,342 to 26,352 fund-years.

In Bayesian econometrics, precision is the inverse of variance. A prior standard deviation of 0.00001 translates into a precision of 1/(0.00001)² = 1e10.

Results based on BMA alphas estimated with a 60-month estimation window are qualitatively similar.

Nanda et al. (2004) study funds that offer three classes: A, B and C. Class A charges a front-end load, while Class B and C do not. However, classes B and C charge a contingent deferred sales load (CDSL) when investors sell out of the fund. Class B’s CDSL typically starts at 5% in the first year and declines over time. Class C’s CDSL is at 1% in the first year and is usually waived thereafter. Class B shares are typically converted into Class A shares after 6–8 years, but not Class C shares. All three classes have to pay an annual 12b-1 fee, with class A incurring a lower 12b-1 fee than classes B and C.

See Carlin and Louis (2000) for a detailed discussion of the empirical Bayes approach.

In Sect. 4, I provide details of the mutual fund investment objectives. The reader should note that I use all funds having at least 60 months of data only for specifying the values of the prior hyperparameters. For the empirical analyses, I retain funds with at least 37 months of data (see Sect. 4).

See Zellner (1971) and Poirier (1995) for further details.

Poirier (1995, p. 543).