Tilting safety first and the Sharpe portfolio

Haley and Whiteman [2005. Manuscript. University of Iowa] demonstrate that the performance portfolio index from Stutzer [May/June 2000. Financial Analyst Journal, 52-61] and the decay-rate maximizing criterion from Stutzer [2003. Journal of Econometrics 116, 365-386] are closely related to their generalized safety first rule, and that all three methods sort portfolios using a mean-constrained Kullback-Leibler divergence. This paper extends their results by demonstrating that the safety first and Sharpe ratio rules sort portfolios using a mean-constrained sum-of-squared-deviations divergence. The end result is an ability to interpret all these seemingly disparate portfolio selection rules criteria through the single lens of underperformance minimization and minimum-disparity optimization.