Conditional Risk Premiums and the Value Function of Prospect Theory

Abstract

This paper examines whether stock returns are consistent with the value function of prospect theory. We find that beta given a gain yields positive conditional premiums on returns while beta given a loss yields negative conditional premiums. This reflects the fact that the value function is concave for gains and convex for losses, implying risk-averse behavior for gains and risk-seeking behavior for losses respectively. Furthermore, the absolute value of the premiums is greater for losses, which is in line with the value function being steeper in this state. These new findings provide indication that investors behave according to prospect theory.

Keywords:

• Behavioral finance
• CAPM
• Conditional risk
• Portfolio choice
• Prospect theory

Notes

1 Compared to Fama and MacBeth (1973), we increased the number of formed portfolios, to account for the fact that we separate portfolios in the third step into portfolios that generated a gain or loss respectively. In this way, the estimates are still sufficiently precise.

2 Note that the formed portfolios are used for four years of estimation, that is $4·12=48$ estimates of realized premiums for betas.