Growth versus security tradeoffs indynamic investment analysis

Leonard MacLean and William Ziemba

Annals of Operations Research, 1999, vol. 85, issue 0, 193-225

Abstract: This paper presents an approach to the problem of optimal dynamic choice in discrete orcontinuous time where there is a direct tradeoff of growth versus security. In each period,the investor must allocate the available resources among various risky assets. The maximizationof the expected logarithm of the period‐by‐period wealth, called the capital growthor the Kelly criterion, has many desirable properties such as maximizing the asymptoticrate of asset growth. However, this strategy has low risk aversion and typically has verylarge wagers which yield high variance of wealth. With uncertain parameters, this can leadto overbetting and loss of wealth. Using fractional Kelly strategies leads to a less volatileand safer sequence of wealth levels with less growth. The investor can choose a desirabletradeoff of growth and security appropriate for the problem under consideration. Thisapproach yields simple two‐dimensional graphs analogous to static mean variance analysisthat capture the essence of the dynamic problem in a form useful for sound investmentanalysis. Use of the approach in practice is illustrated on favorable investments in blackjack,horse racing, lotto games, index and commodity futures and options trading. Copyright Kluwer Academic Publishers 1999

Date: 1999
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DOI: 10.1023/A:1018969727211

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