Gaussian and logistic adaptations of smoothed safety first

In one model of portfolio choice, dating to the Safety First principle, the investor is assumed to select assets to minimize the probability of realizing a portfolio return below some pre-determined target or benchmark rate of return. This paper builds on a recent refinement of Safety First—Smoothed Safety First—but is distinct in that it uses Gaussian and logistic distributions instead of the extreme value type-I distribution. Empirical and simulation results suggest that these alternative smoothing functions perform very much like the original formulation, suggesting that smoothing is robust to the choice of smoothing function for suitably large samples. For smaller samples, both Smoothed Safety First and the standard normal-based smoothing function appear to deliver portfolios with slightly smaller shortfall probabilities than the logistic-based approach. Copyright Springer-Verlag Berlin Heidelberg 2014