Expected Utility Asset Allocation

Most asset allocation analyses use the mean–variance approach for analyzing the trade-off between risk and expected return. Analysts use quadratic programming to find optimal asset mixes and the characteristics of the capital asset pricing model to determine reasonable optimization inputs. This article presents an alternative approach in which the goal of asset allocation is to maximize expected utility, where the utility function may be more complex than that associated with mean–variance analysis. Inputs for the analysis are based on the assumption of asset prices that would prevail if there were a single representative investor who desired to maximize expected utility.Most asset allocation analyses use the mean–variance approach for analyzing the trade-off between risk and expected return. The investor is assumed to care only about the expected return and standard deviation of return of his or her portfolio. This approach makes it possible to use quadratic programming to find optimal asset mixes. An analogous assumption is made when determining inputs for the optimization phase. A key step is a reverse optimization, in which asset prices are assumed to be those that would prevail if there were a single investor who cared only about portfolio mean and variance and thus the conditions of the capital asset pricing model (CAPM) were met. In some cases, such assumptions are modified to take into account an investor’s views about deviations of asset prices from those consistent with mean–variance equilibrium.This article presents an alternative approach. In the optimization phase, the goal is to select an asset allocation that maximizes expected utility when the utility function may be more complex than that associated with mean–variance analysis. In the reverse optimization phase, inputs for the asset allocation analysis are found that are consistent with the assumption that asset prices are those that would prevail if there were a single representative investor who desired to maximize expected utility and, again, the utility function might be more complex than that associated with mean–variance analysis and the CAPM.The article provides algorithms for efficiently performing the computations for both the optimization and reverse optimization analyses. It also shows that the approach can be considered a generalization of the usual mean–variance analysis because the results obtained when quadratic utility functions are used will be the same as those produced by using standard mean–variance analyses.Although only experience with practical applications can determine the extent to which this more general approach could actually improve investment decisions, it offers the prospect for dealing with a number of aspects of asset allocation and doing so in a single integrated manner. It may well provide better asset allocations than mean–variance analysis in at least some circumstances.