Prospect Theory and the Risk-Return Tradeoff

Abstract

This paper studies the cross-sectional risk-return tradeoff in the stock market. One of the most fundamental principles in finance is that risk averse investors demand compensation for bearing risk. However, instead of a positive risk-return relation, recent empirical studies document a low-risk anomaly, i.e., low-risk firms tend to earn higher average returns. To understand this puzzle, we apply prospect theory (PT) and mental accounting (MA) in this study. Prospect theory posits that when facing prior loss relative to a reference point, individuals tend to be risk-seeking, rather than risk-averse. This implies that, among stocks where average investors face prior losses, there should be a negative risk-return relation. By contrast, among the stocks where most investors face capital gains, the traditional positive risk-return relation should emerge since average investors of these stocks are risk averse. Therefore, suppose stocks are different subject to PT/MA effects, the two opposite but monotonous relations between risk and return would be obscured if pooling all together. This in turn suggests that PT/MA could potentially account for the low-risk anoamly. To test our proposition, we first utilize the capital-gains-overhang (CGO) in Grinblatt and Han (2005) to capture individual stocks' exposure to PT/MA effects. Conditional on different levels of CGO, we next examine the risk-return relations using several intuitive measures of risk. We construct six risk proxies using Compustat, CRSP and I/B/E/S datasets: CAPM beta, stock return volatility, firm age, cash flow volatility, analysis forecast dispersion, and idiosyncratic stock volatility. Our preliminary results show strong support to PT/MA effects. The classical positive risk-return tradeoff holds but only among firms with prior capital gains. By contrast, among firms with prior capital losses instead, higher risk implies lower returns. Our explanation of the negative risk-return relation under PT/MA framework is important. From the practitioner's perspective, our results suggest that not all risk will be compensated. Indeed, only among the firms with positive capital gain, there is a positive risk-return relation. Our results also provide a refinement on the low-risk anomaly by showing that the low-risk anomaly only exists among the firms with prior capital losses. Thus, a strategy based on a simple refinement on the existing low-risk anomaly can be yield a larger alpha.