Robert F. Stambaugh, Does the Stock Market Rationally Reflect Fundamental Values?: Discussion, The Journal of Finance, Vol. 41, No. 3, Papers and Proceedings of the Forty-Fourth Annual Meeting of the America Finance Association, New York, New York, December 28-30, 1985 (Jul., 1986), pp. 601-602

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.

A four-factor model with two "mispricing" factors, in addition to market and size factors, accommodates a large set of anomalies better than notable four- and five-factor alternative models. Moreover, our size factor reveals a small-firm premium nearly twice usual estimates. The mispricing factors aggregate information across 11 prominent anomalies by averaging rankings within two clusters exhibiting the greatest return co-movement. Investor sentiment predicts the mispricing factors, especially their short legs, consistent with a mispricing interpretation and the asymmetry in ease of buying versus shorting. A three-factor model with a single mispricing factor also performs well, especially in Bayesian model comparisons.

[We find that conditional means and variances of consumption growth vary through time, and this variation appears to be associated with the business cycle. A pricing model with fluctuating means and variances of consumption growth provides implications about conditional moments of returns for both short and long investment horizons, and these implications are explored empirically. The U-shaped pattern of first-order autocorrelations of returns, as well as business cycle patterns in the price of risk, appears to be consistent with the model, but our exploration suggests that other implications about conditional return moments are at odds with the data.]

We find that conditional means and variances of consumption growth vary through time, and this variation appears to be associated with the business cycle. A pricing model with fluctuating means and variances of consumption growth provides implications about conditional moments of returns for both short and long investment horizons, and these implications are explored empirically. The U-shaped pattern of first-order autocorrelations of returns, as well as business cycle patterns in the price of risk, appears to be consistent with the model, but our exploration suggests that other implications about conditional return moments are at odds with the data.

This article presents a mean-variance framework for likelihood-ratio tests of asset pricing models. A pricing model is tested by examining the position of one or more reference portfolios in sample mean-standard-deviation space. Included are tests of both single-beta and multiple-beta relations, with or without a riskless asset, using either a general or a specific alternative hypothesis. Tests with a factor that is not a portfolio return are also included. The mean-variance framework is illustrated by testing the zero-beta CAPM, a two-beta pricing model, and the consumption-beta model.

[This article presents a mean-variance framework for likelihood-ratio tests of asset pricing models. A pricing model is tested by examining the position of one or more reference portfolios in sample mean-standard-deviation space. Included are tests of both single-beta and multiple-beta relations, with or without a riskless asset, using either a general or a specific alternative hypothesis. Tests with a factor that is not a portfolio return are also included. The mean-variance framework is illustrated by testing the zero-beta CAPM, a two-beta pricing model, and the consumption-beta model.]

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.