Growth versus security tradeoffs in dynamic investment analysis

This paper presents an approach to the problem of optimal dynamic choice in discrete or continuous 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 maximization of the expected logarithm of the period-by-period wealth, called the capital growth or the Kelly criterion, has many desirable properties such as maximizing the asymptotic rate of asset growth. However, this strategy has low risk aversion and typically has very large wagers which yield high variance of wealth. With uncertain parameters, this can lead to overbetting and loss of wealth. Using fractional Kelly strategies leads to a less volatile and safer sequence of wealth levels with less growth. The investor can choose a desirable tradeoff of growth and security appropriate for the problem under consideration. This approach yields simple two-dimensional graphs analogous to static mean variance analysis that capture the essence of the dynamic problem in a form useful for sound investment analysis. Use of the approach in practice is illustrated on favorable investments in blackjack, horse racing, lotto games, index and commodity futures and options trading.