Loss Averse Asset Pricing and Portfolio Choice
32 Pages Posted: 7 Jan 2015 Last revised: 10 Mar 2018
Date Written: November 5, 2016
Loss aversion is the tendency of people to strongly prefer avoiding losses to acquiring gains. This paper studies how a loss averse investor with Kőszegi et al. (2006) reference-dependent preferences, selects portfolios and prices assets. 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 - LPM1- 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 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. This risky portfolio held in common by all loss averse investors is defined as the market portfolio. It is shown that a market portfolio will exist in any capital market equilibrium based on a generalized risk measure derived from a single-factor beta pricing model. Not only does two-fund separation hold but, perhaps surprisingly, the market portfolio is the tangency portfolio of the (unique) linear efficient frontier.
Keywords: portfolio theory, downside risk, lower partial moment, CAPM, loss aversion
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