Maximizing Relative Wealth Using Leverage: The Role of Risk Aversion

Abstract

Investors can use leverage to increase the returns and profit of an investment. The so-called Kelly criterion is traditionally used to determine the optimal leverage factor for maximizing an investor’s absolute wealth. However, using the Kelly criterion may lead to too risky decisions for rational investors without log utility, rendering it not applicable for risk averse investors. Further, investor success is more often than not evaluated as the relative performance against a benchmark, making the case for maximizing relative wealth rather than absolute wealth. We propose a risk-adjusted Kelly criterion based on quadratic utility for maximizing the investors’ wealth relative to a generic reference. Our model enables us to derive the optimal leverage decision for rational investors seeking to maximize relative wealth given investor risk aversion, thereby allowing risk averse investors to benefit from leverage. Quadratic utility also enables optimizing of leverage independent of the returns-density-function assumption so that the skewness and kurtosis of asset returns do not violate the assumptions of the model. Our findings demonstrate the rationale for risk averse investors to use leverage in maximizing relative wealth. Our study provides useful understanding of relative wealth accumulation using leverage and the role of risk aversion.