Market Sentiment and the Sharpe Ratio: A Prospect Theory Approach

Abstract

Market sentiment drives fluctuations in financial markets, but it is measured with empirical proxies lacking strong theoretical foundations. In a generalization of the Consumption CAPM where the representative agent has a prospect theory probability weighting function, we derive a formula for market sentiment that is approximately a decreasing linear function of the conditional market Sharpe ratio, a sufficient statistic for market performance. Our derived sentiment index is negatively correlated with the realized Sharpe ratio, and positively correlated with empirical sentiment indexes. The components of the conditional Sharpe ratio are sufficient to isolate the systematic components of empirical sentiment indexes.

Keywords: Prospect Theory; EU-Hurwicz Preferences; Sharpe Ratio; Equity Premium; Sentiment Indexes

JEL Classification: G40, G41