Many different investment objectives and criteria have been suggested for choosing investment strategies. In a static setting, Markowitz  suggests the mean-variance approach. Economic theory more formally postulates that an individual investor would choose an investment strategy to maximize expected utility of wealth and or consumption. In other settings, other criteria might be more relevant. Rather than maximizing utility, investors in certain circumstances might be more concerned about minimizing the probability of a shortfall, where the shortfall is measured relative to a target return or a specific investment goal. Roy  suggests this criterion in a static (one-period) framework and applies Chebyshev's inequality to obtain a criterion that is closely related to the mean-variance framework of Markowitz. Investment strategies that minimize the probability of a shortfall can be more optimistically referred to as probability-maximizing strategies, in that they maximize the probability of reaching the investment goal. We consider the performance and implementation of such strategies in a dynamic multiperiod setting. We show that dynamic probability-maximizing investment strategies have a variety of positive features that are attractive in a variety of economic settings, although there is also substantial investment risk.
Browne, Sid. "The Risks and Rewards of Minimizing Shortfall Probability." Journal of Portfolio Management 25, no. 4 (Summer 1999): 76-85.
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