Risk Preference and Indirect Utility in Portfolio-Choice Problems

Abstract

We consider a portfolio-choice problem with one risky and one safe asset, where the utility function exhibits decreasing absolute risk aversion (DARA). We show that the indirect utility function of the portfolio-choice problem need not exhibit DARA. However, if the (optimal) marginal propensity to invest is positive for both assets, which is true when the utility function exhibits non-decreasing relative risk aversion, then the DARA property is carried over from the direct to the indirect utility function.