Does Kelly Portfolio Outperform the Market?

Position sizing is a critical element in effective portfolio management, playing a pivotal role in determining the overall risk and return characteristics of an investment portfolio. Proper position sizing involves allocating an appropriate proportion of capital to each investment, considering factors such as the investor's risk tolerance, investment goals, and overall market conditions. A well-thought-out position sizing strategy not only helps in optimizing returns but, more importantly, it mitigates the impact of potential losses.

One method for capital allocation and position sizing is employing the Kelly criterion. The Kelly criterion aims to optimize the expected growth rate of capital, maximizing the anticipated value of the logarithm of wealth. This strategy is rooted in John Kelly's paper, "A New Interpretation of Information Rate." According to Kelly, in repeated bets, a bettor should act to maximize the expected growth rate of capital, thus maximizing expected wealth at the end.

Reference [1] applies Thorp’s approach, as outlined in "The Kelly Criterion in Blackjack Sports Betting and the Stock Market," [2]  to construct a portfolio in the Norwegian stock market. The formula computes the optimal investment fraction in a set of assets, considering the expected excess returns of the assets and the inverse of the variance-covariance matrix. The authors pointed out,

In this study, we test whether the growth optimal Kelly portfolio is able to beat the benchmark and generate alpha in the Norwegian stock market from February 2003 through December 2022. We find that the Kelly portfolio yields a compound average growth rate of 14.1%, resulting in a final wealth of 16.39 (indexed at 1). This outperforms the OSEBX, who achieves an ending wealth of 10.84 and an annual growth rate of 12%. The Markowitz portfolio underperforms both Kelly and the benchmark. We also find that Kelly and the benchmark achieve nearly identical Sharpe ratios of 0.58, but that Kelly achieves a higher Sortino ratio of 0.95. The Kelly portfolio generates an annual alpha of 16.8% in the three- and four-factor models of Fama French and Carhart. The alpha is significant on a 1% level. However, the beta of the portfolio is low, and our models struggle to explain the excess returns generated by the Kelly portfolio, resulting in a very low 𝑅𝑅2. This leads us to believe that our factor models are not sufficient in explaining the returns of our portfolio, and that the alpha measures are inflated.

This paper presents several interesting findings,

• First, the correlation of the Kelly portfolio with the market is nearly zero.
• Second, the performance is sensitive to transaction costs. We believe that with lower transaction costs, the Kelly portfolio has the potential to outperform the market and display zero correlation with it.
• Third, the Kelly portfolio surpasses the Markowitz mean-variance portfolio in performance.

We also concur with the author that the utilization of options can further enhance the risk-adjusted return.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Jon Endresen and Erik Grødem, The Kelly criterion, an empricial study of the growth optimal Kelly portfolio, backtested on the Oslo Stock Exchange, 2023, Norwegian School of Economics.

[2] Thorp, E. O., The Kelly Criterion in Blackjack Sports Betting and the Stock Market, in: Zenios, S.A. & Ziemba, W.T., Handbook of Asset and Liability Management, Volume 1, 387–428, 2006

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