Learning-Induced Securities Price Volatility

This paper tests whether the high average returns on the S&P 500 index in recent history can be attributed to mistaken expectations (the ex-ante risk premium -- taken to be constant -- is systematically less than the ex-post measured risk premium), or, alternatively, whether can they be explained as the result of selection bias (the U.S. experience is exceptional). The tests reject these hypotheses over the periods 1/81 to 12/97 (p = 0.02), and 1/41-12/60 (p = 0.03). They do not reject over the periods 1/28-12/40 and 1/61-12/80. The tests are based on a bound that the ex-post Sharpe ratios impose on the volatility of the ratio of the market's prior and posterior beliefs about future outcomes. The bound derives from a property of Bayesian learning first noted in an earlier paper. Qualitatively, for the bound not to be violated, higher absolute mean excess returns may need to be accompanied with higher volatility. This should be interpreted as predicting that large price movements (positive as well as negative) may have to be erratic. We confirm this prediction for the S&P 500 data.