Abstract
We show in this article that bang-bang portfolio strategies where the investor is alternatively 100% in equity and 100% in cash are dynamically inefficient. Our proof of this result is based on a simple second-order stochastic dominance (SSD) argument. It implies that this is true for any decision criterion that satisfies SSD, not necessarily expected utility. We also examine the stop-loss strategy in which the investor is 100 percent in equity as long as the value of the portfolio exceeds a lower limit where the investor switches to 100 percent in cash. Again, we show that this strategy is inefficient under second-order risk aversion. However, a slight modification of it–in which all wealth exceeding a minimum reserve is invested in equity–is shown to be an efficient dynamic portfolio strategy. This strategy is optimal for investors with a nondifferentiable utility function.
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Gollier, C. On the Inefficiency of Bang-Bang and Stop-Loss Portfolio Strategies. Journal of Risk and Uncertainty 14, 143–154 (1997). https://doi.org/10.1023/A:1007725428360
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DOI: https://doi.org/10.1023/A:1007725428360