Risk and Utility in Portfolio Optimization

TL;DR

This paper proposes a modified portfolio optimization method that separately considers risk as the probability of not meeting investment goals and utility as expected utility, especially for long-term investments.

Contribution

It introduces a new framework that distinguishes risk from utility in portfolio optimization, addressing limitations of traditional mean-variance approaches.

Findings

Analytic results for Gaussian distributions.

Empirical analysis using stock-price data.

Optimized portfolio based on the new risk-utility criteria.

Abstract

Modern portfolio theory(MPT) addresses the problem of determining the optimum allocation of investment resources among a set of candidate assets. In the original mean-variance approach of Markowitz, volatility is taken as a proxy for risk, conflating uncertainty with risk. There have been many subsequent attempts to alleviate that weakness which, typically, combine utility and risk. We present here a modification of MPT based on the inclusion of separate risk and utility criteria. We define risk as the probability of failure to meet a pre-established investment goal. We define utility as the expectation of a utility function with positive and decreasing marginal value as a function of yield. The emphasis throughout is on long investment horizons for which risk-free assets do not exist. Analytic results are presented for a Gaussian probability distribution. Risk-utility relations are explored via empirical stock-price data, and an illustrative portfolio is optimized using the empirical data.