Pitfalls of Downside Performance Measures with Arbitrary Targets

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.