Is higher variance necessarily bad for investment?

We consider decision-making under risk in which random events affect the value of the portfolio multiplicatively, rather than additively. In this case, a higher variability in the rate of return not only is associated with a higher risk, a bad property, but also engenders a higher expected return, a good property. As a result, certain expected utility maximizing investors, namely those with the lowest risk aversion, will prefer some portfolios with higher variances in the rate of return over others with lower ones. This is demonstrated, and implications are considered. Copyright Springer Science+Business Media New York 2014