Mean-Variance Portfolio Selection with Reference Dependent Preferences

Abstract

We study S-shaped utility maximization for the standard portfolio selection problem with one risky and one risk-free asset. We derive a mean-variance criterium of choice, which preserves reference dependence and the reflection effect. Subsequently we study diversification possibilities and obtain the demand for the risky asset. We close the paper with an alternative interpretation of the criterium in terms of target-based decision making.

Asset Return and Wealth Dynamics with Reference Dependent Preferences and Heterogeneous Beliefs

“…We used the notion of an S-shaped utility presented in Gerasymchuk (2007) to construct the demand for the risky asset. In order to sustain realistic underlying risk aversion properties of the demand function, we modified the demand corresponding to the normal utility by replacing the risk aversion coefficient by the one of the arctangent utility.…”

“…The demand for the risky asset π i,t = argmax π i,t {U (W i,t+1 )} has been derived in a closed form for a special case of a general S-shaped utility, namely, for the normal utility function in Gerasymchuk (2007). The demand is given by…”

“…The return Rt is usually not included in the information set It, especially whenever the Walrasian scenario is used for the market clearing price derivation, in order to retain explicit form of the final system.3 Section 3 inGerasymchuk (2007).…”