How Does the Fortune’s Formula Kelly CapitalGrowth Model Perform?

William Poundstone’s book, Fortune’s Formula, brought the Kelly capital growth criterion to the attention of investors. But how do full and fractional Kelly strategies perform in practice? The authors study three simple investment situations and simulate the behavior of these strategies over medium-term horizons using a large number of scenarios. The results show 1) the great superiority of full Kelly and close-to-full Kelly strategies over longer horizons in that they earn very large gains a large fraction of the time, 2) the very risky short-term performance of Kelly and high-fractional Kelly strategies, 3) a consistent trade-off of growth versus security as a function of the bet size determined by the various strategies, and 4) no matter how favorable the investment opportunities are, or how long the finite horizon is, a sequence of bad scenarios can lead to very poor final wealth outcomes with a loss of most of the investor’s initial capital. Hence, in practice, financial engineering is important for dealing with the short-term volatility and long-run situations in a sequence of bad scenarios. Properly used, however, the strategy has much to commend it, especially in trading with many repeated investments.

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