Kelly Growth and Tangency Portfolios: When Their Weights Coincide

Summary

The document raises how to combine Kelly growth optimization with a desired level of portfolio variance for diversification. Its answer reports a matrix-algebra result: under the stated setup, the portfolio that maximizes the Sharpe ratio has the same composition as the one that maximizes growth. This links the Kelly portfolio to the tangency portfolio, but it does not explain how to impose a separate variance target or derive an allocation under that constraint.

The author then points to a tension with empirical papers, which they say find Kelly portfolios more concentrated and higher in mean and variance than tangency portfolios. The excerpt offers no paper details, assumptions, data, or resolution of that discrepancy. It is therefore useful as a prompt to examine the conditions behind the theoretical equivalence and how practical portfolio constraints or estimation choices may affect observed weights, rather than as a complete optimization procedure.

Key ideas

• The answer claims that unconstrained Kelly and maximum-Sharpe portfolios have the same composition under a matrix-algebra result.
• The original question asks how to combine growth optimization with a target portfolio variance.
• The document reports empirical findings of greater concentration, mean, and variance for Kelly portfolios but does not document them.
• The excerpt does not provide a method for imposing a variance target or reconcile theory with the reported evidence.

Tags

# Kelly criterion for portfolio optimisation with variance optimisation


# Kelly criterion for portfolio optimisation with variance optimisation












I was wondering how Kelly criterion can be used for portfolio optimisation in the case one would like to optimise the portfolio for minimum variance. I understand how the Kelly criterion can be used to decide the allocation for a certain stock, but what if I also would like to make sure I am diversified (= I want to set a certain portfolio variance). In other word is there a way to combine Kelly with mean-variance, or something like that?

## Answer by KIM Kyuhyong (score -1)

https://quant.stackexchange.com/a/76498

After careful study I found that Kelly portfolio composition and the tangent portfolio composition are proved to be the same using matrix algebra. Namely the portfolio composition that maximize the Sharpe ratio is the same as the one that maximize growth rate. But empirical papers show that they are different. Kelly portfolio is condensed and has higher mean and variance than tangent portfolio. I deeply wonder why this happens!!! This is the critical point that is simply ignored and misunderstood in the literature.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.