Kelly Portfolio Analysis

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).



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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.
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