Mutual Fund Performance with Learning Across Funds

This paper is based on the premise that knowledge about the alphas of one set of funds will influence an investor's beliefs about other funds. This will be true insofar as an investor's expectation about the performance of a fund is partly a belief about the abilities of mutual fund managers as a group and, more generally, a belief about the degree to which financial markets are efficient. We develop a simple framework for incorporating this prior dependence' and find that it can have a substantial impact on the cross-section of posterior beliefs about fund performance as well as asset allocation. Under independence, the maximum posterior mean alpha increases without bound as the number of funds increases and 'extremely large' estimates are randomly observed. This is true even when fund managers have no skill. In contrast, with prior dependence, investors aggregate information across funds to form a general belief about the potential for abnormal performance. Each fund's alpha estimate is shrunk toward the aggregate estimate, mitigating extreme views. An additional implication is that restricting the estimation to surviving funds, a common practice in this literature, imparts an upward bias to the average fund alpha.

Pricing model performance and the two-pass cross-sectional regression methodology

Since Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973), the two-pass cross-sectional regression (CSR) methodology has become the most popular approach for estimating and testing asset pricing models. Statistical inference with this method is typically conducted under the assumption that the models are correctly specified, that is, expected returns are exactly linear in asset betas. This assumption can be a problem in practice since all models are, at best, approximations of reality and are likely to be subject to a certain degree of misspecification. We propose a general methodology for computing misspecification-robust asymptotic standard errors of the risk premia estimates. We also derive the asymptotic distribution of the sample CSR R2 and develop a test of whether two competing linear beta pricing models have the same population R2. This test provides a formal alternative to the common heuristic of simply comparing the R2 estimates in evaluating relative model performance. Finally, we provide an empirical application, which demonstrates the importance of our new results when applied to a variety of asset pricing models.Econometric models ; Asset pricing

Model comparison with Sharpe ratios

We show how to conduct asymptotically valid tests of model comparison when the extent of model mispricing is gauged by the squared Sharpe ratio improvement measure. This is equivalent to ranking models on their maximum Sharpe ratios, effectively extending the Gibbons, Ross, and Shanken (1989) test to accommodate the comparison of nonnested models. Mimicking portfolios can be substituted for any nontraded model factors, and estimation error in the portfolio weights is taken into account in the statistical inference. A variant of the Fama and French (2018) 6-factor model, with a monthly updated version of the usual value spread, emerges as the dominant model

What is the expected return on a stock?

We derive a formula for the expected return on a stock in terms of the risk-neutral variance of the market and the stock's excess risk-neutral variance relative to that of the average stock. These quantities can be computed from index and stock option prices; the formula has no free parameters. The theory performs well empirically both in and out of sample. Our results suggest that there is considerably more variation in expected returns, over time and across stocks, than has previously been acknowledged

Pricing Model Performance and the Two-Pass Cross-Sectional Regression Methodology

Since Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973), the two-pass cross-sectional regression (CSR) methodology has become the most popular approach for estimating and testing asset pricing models. Statistical inference with this method is typically conducted under the assumption that the models are correctly specified, i.e., expected returns are exactly linear in asset betas. This can be a problem in practice since all models are, at best, approximations of reality and are likely to be subject to a certain degree of misspecification. We propose a general methodology for computing misspecification-robust asymptotic standard errors of the risk premia estimates. We also derive the asymptotic distribution of the sample CSR R2 and develop a test of whether two competing beta pricing models have the same population R2. This provides a formal alternative to the common heuristic of simply comparing the R2 estimates in evaluating relative model performance. Finally, we provide an empirical application which demonstrates the importance of our new results when applied to a variety of asset pricing models.

Understanding Portfolio Efficiency with Conditioning Information *

Abstract I develop two new types of portfolio efficiency when returns are predictable. The first type maximizes the unconditional Sharpe ratio of excess returns and differs from unconditional efficiency unless the safe asset return is constant over time. The second type maximizes conditional mean-variance preferences and differs from unconditional efficiency unless, additionally, the maximum conditional Sharpe ratio is constant. Using stock data, I quantify and test their performance differences with respect to unconditionally and fixed-weight efficient returns. I also show the relevance of the two new portfolio strategies to test conditional asset pricing models