The Risk and Rewards of Minimizing Shortfall Probability

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Abstract
Dynamic investment strategies that minimize the probability of a shortfall relative to a given target return or other investment goal are useful in a variety of economic and risk management settings, but the author argues that some properties of these strategies are misunderstood. For example, some advocate minimizing shortfall probability as a risk management tool by claiming that it reduces investment risk. This is not always the case, and, indeed, the author shows that dynamic strategies, and for those who do wish to take the associated risks, the author argues that there is a very simple way to implement that dynamic strategy, namely, by purchasing a digit option with a specific set of parameters. This result allows a decision-maker to make some definitive quantitative comparisons that are in the understanding of risk.