Kelly Investing with Iteratively Updated Estimates of the Probability of Success

Abstract

The Kelly criterion is an investment strategy that determines the appropriate fraction of fortune to invest in positive expectation opportunities in order to maximize growth. This thesis investigates the performance of Kelly-related strategies in binary outcome opportunities when the probability of success is unknown and is estimated by a binomial proportion. The performance of strategies based on fixed and updated estimates of the probability of success is investigated through simulated coin tossing and binary stock market option scenarios. It is found that a strategy based on updated estimates perform better, especially when the initial error in estimation is large, but the updated estimates result in a high variance of wealth. Simulations show that a Kelly strategy based on updated estimates can sometimes be improved upon by choosing an appropriate fractional Kelly strategy, or by estimating the probability of success using an appropriate quantile of the Bayesian posterior distribution.