Choosing Kelly-Optimal Portfolios from the Efficient Frontier

Summary

The document asks how to choose among portfolios on a modern portfolio theory efficient frontier when the objective is long-run growth. It points readers to research on Kelly-optimal portfolios, including work on applying the Kelly criterion to stock portfolios. The central connection is that portfolio selection can be framed around maximizing expected growth rather than choosing a portfolio solely by its risk-return position on the frontier.

The response provides references rather than a derivation or worked calculation, so readers will need to consult the cited papers for a rigorous method. It also cautions that results depend on the assumptions used to model returns. In particular, treating stock returns as jointly normally distributed is described as a strong assumption for real-world use. The document does not compare portfolio outcomes or establish that a Kelly-based choice will be superior in practice; it identifies a research direction and flags model risk.

Key ideas

• Kelly betting can frame portfolio choice as maximizing expected growth.
• Research papers are suggested for connecting the Kelly criterion to portfolio construction.
• A joint normal model for stock returns is a strong assumption in practical applications.
• The response supplies references and a caveat, but no derivation or empirical comparison.

Tags

# Combining modern portfolio theory and Kelly betting?


# Combining modern portfolio theory and Kelly betting?












I'm using modern portfolio theory to compute the frontier of efficient portfolios. I'd like to pick the best one in the spirit of Kelly betting, ie. maximising expected growth.

I'm looking for a reference that describes rigorously how I'd go about doing this.

## Answer by Quantopik (score 4)

https://quant.stackexchange.com/a/18285

Maybe you will find the following papers pretty interesting:

> Laureti, P., Medo, M., and Zhang, Y.-C. (2010). Analysis of Kelly-optimal portfolios. Quantitative Finance, 10(7): 689–697.

and

> Nekrasov, Vasily, Kelly Criterion for Multivariate Portfolios: A Model-Free Approach (September 30, 2014).

The last one is available at SSRN.

Particularly, the last one shows how to apply the Kelly Criterion to stock portfolios.

Of course, in my humble opinion, you have to keep attention to what you are going to apply the model for and to the underlying hypothesis; such hypothesis, as, for instance, the joint normally distributed stock returns assumption, are pretty strong for an application of such strategy to the realty.

Hope this helps.

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