Abstract
Mean-variance portfolio optimization is more popular than optimization procedures that employ downside risk measures such as the semivariance, despite the latter being more in line with the preferences of a rational investor. We describe strengths and weaknesses of semivariance and how to minimize it for asset allocation decisions. We then apply this approach to a variety of simulated and real data and show that the traditional approach based on the variance generally outperforms it. The results hold even if the CVaR is used, because all downside risk measures are difficult to estimate. The popularity of variance as a measure of risk appears therefore to be rationally justified.