GROWTH VERSUS SECURITY IN DYNAMIC INVESTMENT ANALYSIS

L. C. Maclean, W. T. Ziemba and G. Blazenko

Chapter 24 in The Kelly Capital Growth Investment Criterion:Theory and Practice, 2011, pp 331-354 from World Scientific Publishing Co. Pte. Ltd.

Abstract: This paper concerns the problem of optimal dynamic choice in discrete time for an investor. In each period the investor is faced with one or more risky investments. The maximization of the expected logarithm of the period by period wealth, referred to as the Kelly criterion, is a very desirable investment procedure. It has many attractive properties, such as maximizing the asymptotic rate of growth of the investor's fortune. On the other hand, instead of focusing on maximal growth, one can develop strategies based on maximum security. For example, one can minimize the ruin probability subject to making a positive return or compute a confidence level of increasing the investor's initial fortune to a given final wealth goal. This paper is concerned with methods to combine these two approaches. We derive computational formulas for a variety of growth and security measures. Utilizing fractional Kelly strategies, we can develop a complete tradeoff of growth versus security. The theory is applicable to favorable investment situations such as blackjack, horseracing, lotto games, index and commodity futures and options trading. The results provide insight into how one should properly invest in these situations.

Keywords: Kelly Criterion; Dynamic Investment Analysis; Capital Growth Theory; Sports Betting; Hedge Fund Strategies; Speculative Investing; Fortune 's Formula (search for similar items in EconPapers)
Date: 2011
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