Entropic risk measures and their comparative statics in portfolio selection: Coherence vs. convexity

摘要

Highlights?We compare coherent and convex entropic risk measures in portfolio selection.?For both risk measures, risk-taking may be increasing with increasing risk aversion.?Under the coherent version, risk-taking increases when a background risk arises.?Under the convex version, background risk has no effect on risk-taking.AbstractWe conduct a decision-theoretic analysis of optimal portfolio choices and, in particular, their comparative statics under two types of entropic risk measures, the coherent entropic risk measure (CERM) and the convex entropic risk measure (ERM). Starting with the portfolio selection between a risky and a risk free asset (framework of Arrow (1965) and Pratt (1964)), we find a restrictive all-or-nothing investment decision under the CERM, while the ERM yields diversification. We then address a portfolio problem with two risky assets, and