The Kelly Criterion : An empricial study of the growth optimal Kelly portfolio, backtested on the Oslo Stock Exchange

Abstract

This study analyzes the performance of the growth optimal Kelly portfolio on the Norwegian stock market from February 2003 through December 2022. To measure the strategy’s alpha, we employ the Capital Asset Pricing Model, Fama French’s three-factor model and Carhart’s four-factor model. The Kelly portfolio generates a higher annual growth rate than the benchmark, and consequently a higher ending wealth level. Our results indicate that the strategy generates an annualized alpha of 16.8%, significant on a 1% level. However, the models show very poor explanatory power, prohibiting us from drawing a meaningful conclusion. Furthermore, when accounting for transaction costs, the portfolio no longer achieves a higher wealth level than the benchmark, and the corresponding alpha is only significant on a 10% level, indicating that the strategy is unable to generate risk-adjusted excess returns in the real world.