Expected Surplus Growth Compared with Mean–Variance Optimization

Abstract

In this article, the authors revisit a neglected paper written by Rubinstein in which he advocated a generalized logarithmic utility function. The profession has rather ignored his model in favor of the mean–variance approach, for reasons that are well known. The authors note that generalized logarithmic utility allows us to identify absolute risk aversion more directly and intuitively than the approaches adopted in mean–variance portfolio construction. They demonstrate that, for top-level asset allocation in which the conditions required by mean–variance are satisfied and mean–variance gives a good approximation to expected utility, generalized logarithmic utility gives essentially the same answer. In situations not suited to mean–variance, such as the inclusion of derivatives in portfolios or, more generally, when higher moments in return and utility probability distributions are unavoidable, Rubinstein’s model appears superior and seems particularly well suited to multi-asset investment. The authors’ simplified Bayesian model shows out-of-sample advantages for broad US asset allocation for the 2000 through mid-2020 period.

TOPICS: Quantitative methods, statistical methods, portfolio theory, portfolio construction

Key Findings

• ▪ Maximizing the expected Rubinstein utility increases expected surplus growth for conservative investors and for those who do not rebalance frequently. Markowitz’s risk aversion parameter is replaced without requiring subjective judgement of aversion to return variance.

• ▪ Bayesian prediction can incorporate both scenario priors and observed return data in a simple grid form. This increases model flexibility and decreases sensitivity to errors in estimates of return probability distribution parameters.

• ▪ We demonstrate out-of-sample advantages for Rubinstein utility with simplified Bayesian prediction in broad US stock, bond, and cash allocation for the most recent decades. This is based on a prior inferred from earlier history, including the 1929 crash.