Why Full Kelly and Tangency Portfolios Share the Same Weights

Summary

The document explains why an unconstrained full Kelly portfolio can have the same relative asset weights as a mean-variance tangency portfolio. Its central claim is that maximizing long-run growth leads to maximizing the portfolio’s Sharpe ratio, so the portfolios point in the same direction even when their overall leverage differs.

The question includes an empirical example using monthly returns for a sample of S&P 500 stocks over ten years. The calculated Kelly allocation was highly leveraged; after proportional de-leveraging, its weights matched the mean-variance solution. The accepted answer states that the equivalence is general and refers readers to an external proof, but the proof itself is not reproduced. The result therefore assumes the relevant unconstrained portfolio setup and does not address how constraints, estimation error, or practical trading costs could affect the comparison.

Key ideas

• Under the stated assumptions, full Kelly and mean-variance tangency portfolios have the same relative weights.
• Kelly optimization seeks the allocation with the highest expected growth rate.
• Maximizing growth is linked in the answer to maximizing the Sharpe ratio.
• Differences in leverage can change portfolio scale without changing its relative asset weights.
• The document asserts the equivalence but does not provide the referenced proof.

Tags

# Full Kelly portfolios having same weights as tangency portfolios


# Full Kelly portfolios having same weights as tangency portfolios












I'm currently comparing empirically the differences between Markowitz and Kelly portfolios. I calculated the Kelly weights for monthly return observations over 10 years for a sample of 50 stocks from the S&P 500. Without constraints, I received a highly levered Kelly portfolio of weights summing up to 23 with mean of 85% and std. deviation of 91%. I then de-levered the portfolio proportionally and received the same tangency portfolio with the exact same weights as in the Mean-Variance-Optimization case. I was surprised by this result and wanted to ask you if someone knows why this could be the case or made similar observations.

I’m very grateful for any kind of advice on this subject.

## Answer by JPN (score 2, accepted)

https://quant.stackexchange.com/a/19587

They are the same.

The maximum growth rate is achieved when the Sharpe ratio is maximized.

For the proof, see here.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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