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Comparing the Results of the Kelly Criterion and Risk Aversion: Quick Look Practical Alternatives to Portfolio Optimization

Abstract

Both the Kelly Criterion, developed by John Kelly while at Bell Labs, and Risk Aversion, first applied in the oil industry by John Cozzolino, are methods that attempt to mitigate the risk of Gambler's Ruin via suggested working interest levels for investments. How do they compare? What information is necessary to do both calculations?

Gambler's Ruin is a plausible circumstance where an investor makes good choices but due to a series of unfortunate outcomes the overall series of investments loses money.

John Cozzolino recommended applying Natural Log Utility theory to revise the expected value based on a corporate risk tolerance to determine the risk adjusted value (RAV), and the present author previously provided an additional method to directly calculate the Optimum Working Interest in an investment or a series of investments with a constrained budget. The difficulty in this task is deciding on an appropriate amount of risk tolerance. The present author provided some insight by suggesting a formula for Apparent Risk Tolerance of past investments but even with this information the amount of risk tolerance is uncertain.

The Kelly Criterion does not use risk tolerance or utility theory so it requires fewer input variables. The rest of the required data are the same as the data required for determining RAV, Cost at Risk, Chance of Success, and Present Value of Success. The results of a simple comparison of four investment scenarios are surprisingly similar. The Kelly Criterion recommends a slightly larger Optimum Working Interest. These approaches suggest a practical, understandable quick look alternative to more sophisticated, data intensive portfolio optimization techniques. As with all investment approaches, a multi-year study of results versus forecasts is needed to comprehend the long term applicability of these approaches.