Gambling as Investment: a Generalized Criterion for Optimal Allocation of Wealth Among Risky Assets

Abstract

The Kelly criterion is the optimal investment strategy under log-utility for allocation of wealth among a range of alternative risky assets when at least one presents a positive expected return. In this paper, we present an all-encompassing framework for estimating Kelly strategies in different types of speculative financial market and under different economic conditions, including bookmaker, pari-mutuel, and exchange markets. In particular, we derive general conditions, which apply in most market settings, for being able to estimate Kelly strategies. Our findings are important for the economic interpretation of betting markets and, in particular, assessing market efficiency.