A geometric property of indifference curves in the (mean-standard deviation) plane

Abstract

We prove that the slope of the indifference curve through point (m σ) of the (meanstandard deviation) plane must be smaller than the ratio (1+m)/σ. We show that the indifference curves corresponding to a quadratic utility function do actually satisfy that inequality; and prove, by the way, that these curves are not quarters of circles (as it is usually asserted), but smaller parts of them.