Efficient Use of Conditioning Information: A Sharpe Ratio Based Test of Return Predictability

Abstract

In this paper we propose a new Sharpe ratio based test of asset return predictability. Intuitively, a variable that predicts returns is of value to an investor if it allows the construction of 'managed' portfolios that expand the unconditional mean-variance efficient frontier, and thus the investor's opportunity set. The maximum Sharpe ratio achievable using the predictive information efficiently therefore provides a convenient measure of the extent to which predictability matters. We build on the conditional asset pricing theory of Hansen and Richard (1987) to explicitly characterize the difference in maximum squared Sharpe ratios with and without conditioning information. We show that this difference is directly related to the R^2 of a predictive regression. Our test statistic is closely related to the Wald test for the regression coefficient. Under the null hypothesis of no predictability, the difference in squared Sharpe ratios is zero. Rejection of the null hypothesis thus implies that the presence of return predictability significantly expands the mean-variance frontier.

Using our test, we find that at short (monthly) horizon, using the consumption-wealth ratio as predictor variable, (Lettau and Ludvigson, 2001), we clearly reject the null hypothesis of no predictability. In contrast, dividend yield has at most marginal effect. However, at longer horizons the effect of dividend yield becomes more pronounced. An important implication of our results is that neither the fixed-weight three-factor Fama-French (1988) model, nor the Carhart (1996) model, can be viable conditional asset pricing models when consumption-wealth ratio is chosen as the conditioning variable. Our analysis is closely related to, and extends the work of Ferson and Siegel (2001), Bekaert and Liu (2001), and Kirby (1998).

Keywords: asset pricing, return predictability, mean-variance analysis, conditioning information

JEL Classification: C12, G11, G12