Asset Allocation Advice: Reconciling Expected Utility with Shortfall Risk
40 Pages Posted: 30 Jun 2004
Date Written: December 2003
Researchers studying the asset allocation problem for long-term investors have employed different investor criterion functions. Some analyses have been based on maximization of expected utility. The most commonly used utilities are quadratic utility, which yields the ubiquitous mean-variance utility function underlying modern portfolio theory, and constant relative risk aversion (CRRA) power utility. Both utilities require an assumed value or measurement of a utility risk aversion parameter appropriate to a particular investor. But there are no scientifically validated procedures for accurately assessing an individual's risk aversion parameter, and some have suggested that all such procedures are doomed to failure.
Other analyses have been based on minimizing the probability of falling short of a particular investor's long-term goals or investable benchmark he/she would like to beat. The target shortfall probability approach may be easier to motivate and explain to investors, and obviates the need to assess a risk aversion parameter. But early criticisms from expected utility advocates cast doubt on the prescriptive usefulness of other criteria that depend on shortfall probabilities.
I argue that conventional CRRA utility and shortfall probability analyses can be reconciled by simply eliminating the conventional assumption that the utility's risk aversion parameter is not ALSO determined by maximization of expected utility. The simplest asset allocation problem is used to illustrate this result. The results are quite sensible, and lead to a re-examination of expected utility advocates' arguments for the conventional use of expected utility and against the minimization of target shortfall probability. Neither the former nor the latter are as important as expected utility advocates believe.
Keywords: Portfolio choice, shortfall risk, large deviations
JEL Classification: G11, D81, C44
Suggested Citation: Suggested Citation