Robert F. Stambaugh

Expected stock returns and volatility

This paper examines the relation between stock returns and stock market volatility. We find evidence that the expected market risk premium (the expected return on a stock portfolio minus the Treasury bill yield) is positively related to the predictable volatility of stock returns. There is also evidence that unexpected stock market returns are negatively related to the unexpected change in the volatility of stock returns. This negative relation provides indirect evidence of a positive relation between expected risk premiums and volatility.

Predicting returns in the stock and bond markets

Abstract Several predetermined variables that reflect levels of bond and stock prices appear to predict returns on common stocks of firms of various sizes, long-term bonds of various default risks, and default-free bonds of various maturities. The returns on small-firm stocks and low-grade bonds are more highly correlated in January than in the rest of the year with previous levels of asset prices, especially prices of small-firm stocks. Seasonality is found in several conditional risk measures, but such seasonality is unlikely to explain, and in some cases is opposite to, the seasonal found in mean returns.

BIASES IN COMPUTED RETURNS An Application to the Size Effect

Abstract Previous estimates of a ‘size effect’ based on daily returns data are biased. The use of quoted closing prices in computing returns on individual stocks imparts an upward bias. Returns computed for buy-and-hold portfolios largely avoid the bias induced by closing prices. Based on such buy-and-hold returns, the full-year size effect is half as large as previously reported, and all of the full-year effect is, on average, due to the month of January.

Investing in equity mutual funds

We construct optimal portfolios of equity funds by combining historical returns on funds and passive indexes with prior views about asset pricing and skill. By including both benchmark and nonbenchmark indexes, we distinguish pricing-model inaccuracy from managerial skill. Even modest confidence in a pricing model helps construct portfolios with high Sharpe ratios. Investing in active mutual funds can be optimal even for investors who believe active managers cannot outperform passive indexes. Optimal portfolios exclude hot-hand funds even for investors who believe momentum is priced. Our large universe of funds offers no close substitutes for the Fama-French and momentum benchmarks.

On the exclusion of assets from tests of the two-parameter model: A sensitivity analysis

Abstract This study investigates the sensitivity of tests of the CAPM to different sets of asset returns. Tests are conducted with market portfolios that include returns for bonds, real estate, and consumer durables in addition to common stocks. Even when stocks represent only 10% of the portfolios value, inferences about the CAPM are virtually identical to those obtained with a stocks-only portfolio. In contrast, inferences are sensitive to the set of assets used in the tests.

Mutual fund performance and seemingly unrelated assets

Estimates of standard performance measures can be improved by using returns on assets not used to de?ne those measures. Alpha, the intercept in a regression of a funds return on passive benchmark returns, can be estimated more precisely by using information in returns on non-benchmark passive assets, whether or not one believes those assets are priced by the benchmarks. A funds Sharpe ratio can be estimated more precisely by using returns on other assets as well as the fund. New estimates of these performance measures for a large universe of equity mutual funds exhibit substantial dierences from the usual estimates.

The information in forward rates : Implications for models of the term structure

Abstract Term-structure models from Cox, Ingersoll, and Ross (1985) imply that conditional expected discrete-period returns on discount instruments are linear functions of forward rates. Tests reject a single-latent-variable model of expected returns on U.S. Treasury bills, but two or three latent variables appear to describe expected returns on bills of all maturities. Expected returns estimated using two-latent-variables exhibit variation with business cycles similar to what Fama (1986) observes for forward rates. Inverted term structures precede recessions and upward-sloping structures precede recoveries.

Asset returns and intertemporal preferences

A representative-agent model with time-varying moments of consumption growth is used to analyze implications about means and volatilities of asset returns as well as the predictability of asset returns for various investment horizons. A comparative-statics analysis using non-expected-utility preferences indicates that, although risk aversion is important in determining the means of both equity returns and interest rates, implications about the volatility and the predictability of equity returns are affected primarily by intertemporal substitution. Lower elasticities of intertemporal substitution are associated with greater variance in the temporary component of equity prices.

On correlations and inferences about mean-variance efficiency

A framework is presented for investigating the mean-variance efficiency of an unobservable portfolio based on its correlation with a proxy portfolio. A sensitivity analysis derives the highest correlation between the proxy and a portfolio that reverses the inference of a test of SHarpe-Lintner tangency. For example, the maximum correlation between the value-weighted NYSE-AMEX portfolio and a portfolio inferred tangent ranges from 0.76 to 0.48. We also test whether the correlation between the proxy and the tangent portfolio exceeds a given level. This hypothesis is often rejected for the NYSE-AMEX proxy at a correlation of 0.7.

On the Size of the Active Management Industry

We argue that active management’s popularity is not puzzling despite the industry’s poor track record. Our explanation features decreasing returns to scale: As the industry’s size increases, every manager’s ability to outperform passive benchmarks declines. The poor track record occurred before the growth of indexing modestly reduced the share of active management to its current size. At this size, better performance is expected by investors who believe in decreasing returns to scale. Such beliefs persist because persistence in industry size causes learning about returns to scale to be slow. The industry should shrink only moderately if its underperformance continues.