Kelly Portfolio Analysis

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Given a set of assets (characterized by their expected returns, volatilities, and correlations), the Kelly criterion says to choose the asset weights that maximize expected portfolio return.


In the plot, is the continuously compounded portfolio return (a random variable), the axis is the standard deviation of , and the axis is its expectation. Further, the Kelly portfolio is shown in red (and its asset weights are tabulated at the top, starting with the risk-free asset weight, with leverage allowed), the user portfolio is shown in yellow, and the individual assets (including the risk-free asset) are shown as blue dots. The solid blue line is the boundary of all possible portfolios; the upper boundary is the Kelly efficient frontier. (It rolls over because the Kelly efficient frontier, unlike the Markowitz efficient frontier, is multi-period.)

In this Demonstration, a portfolio weight of 1 means 100% (shorting of assets is also allowed), a return of 0.10/yr means 10%/yr, and a volatility of 0.20 means 20%/ (which means that in 1 year the standard deviation of return is 20%/yr and that in 4 years the standard deviation of return is 10%/yr).


Contributed by: Stephen Schulist (March 2011)
Open content licensed under CC BY-NC-SA




D. G. Luenberger, Investment Science, New York: Oxford University Press, 1998 pp. 427–435.

J. L. Kelly, Jr., "A New Interpretation of Information Rate", Bell Sys. Tech. J, 35(4), 1956 pp. 917–926.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.