ON THE INEFFICIENCY OF BANG-BANG AND STOP-LOSS PORTFOLIO STRATEGIES

We show in this article that bang-bang portfolio strategies where the investor is alternatively 100% in equity and 100% in cash are dynamica lly inefficient. Our proof of this result is based on a simple second- order stochastic dominance (SSD) argument. It implies that this is tru e for any decision criterion that satisfies SSD, not necessarily expec ted utility. We also examine the stop-loss strategy in which the inves tor is 100% in equity as long as the value of the portfolio exceeds a lower limit where the investor switches to 100% in cash. Again, we sho w that this strategy is inefficient under second-order risk aversion. However, a slight modification of it-in which all wealth exceeding a m inimum reserve is invested in equity-is shown to be an efficient dynam ic portfolio strategy. This strategy is optimal for investors with a n ondifferentiable utility function.