Pitfalls of Downside Performance Measures with Arbitrary Targets

Abstract

Downside performance measures relate above target returns with lower partial moments. They were developed to resolve restrictive assumptions of the classical Sharpe ratio. While the Sharpe ratio evaluates whether portfolios of a mutual fund and the risk‐free asset dominate passive portfolios of the benchmark and the risk‐free asset, this characteristic cannot be transferred to downside performance measures with arbitrary targets. We show that downside performance measures assign different values to passive benchmark strategies if the target differs from the risk‐free rate. This effect can lead to reverse rankings of financial assets. Therefore, downside performance measures are only applicable in asset management if the target is set equal to the risk‐free rate.

Statistically (optimal) estimators of semivariance: A correction of Josephy-Aczel’s proof

“…Therefore it is used in downside portfolio selection (pioneered by [Markowitz 1959;Jin, Markowitz, Zhou 2006]) for an overview of and further developments in downside portfolio selections, hedging [Demirer, Lien 2003;Cotter, Hanly 2006], downside asset pricing (pioneered by [Bawa, Lindenberg 1977;Ang, Chen, Xing 2006] for an overview of and further developments in downside betas), risk measurement in a regulatory context [Brooks, Persand 2003], and performance measurement (for stocks, e.g. [Hoechner, Reichling Schulze 2017], for the effects of environmental, social, and governance issues [Hoepner et al 2018], and for hedging [Lee, Chien 2010]. On the other hand, the formalism behind lower partial moments is identical to the computation of Conditional Value at Risk [Demirer, Lien, Shaffer 2005, p. 56] were the first to emphasize this connection -and stochastic dominance [Davidson, Duclas 2000, p. 1444.…”