Kőszegi-Rabin Preferences, Downside Risk and Loss Averse Portfolio Choice

Abstract

This paper derives the implications for portfolio choice of a loss averse investor with Kőszegi and Rabin (2006) reference-dependent preferences. Returns falling below the investor's target return - his return floor - are regarded as losses. It is shown that the first-order lower partial moment is the natural measure of the risk of loss for such an investor. Two such loss averse investors with different target returns can hold exactly the same efficient portfolio, but the risk of that portfolio will be different for each investor. Loss averse investors face, not one, but an uncountable number of efficient frontiers, all of which are convex but only one of which is linear. The portfolios that reside on these frontiers collectively form the portfolio efficient set. All portfolios in the efficient set are informationally equivalent in the sense that loss averse investors holding different efficient portfolio will nevertheless agree on the relative riskiness of individual securities. One implication is that, if a risk-free security exists, every portfolio in the efficient set contains a combination of the risk-free security and the same risky portfolio.

Keywords: behavioral finance, CAPM, Kőszegi-Rabin preferences, loss aversion, downside risk, lower partial moment, portfolio choice