This paper revisits the corner solution in classical portfolio choice theory in which risk-averse agents would all be optimally plungers rather than diversifiers. We examine the effect of higher-order moments of two-, three- and four-parameter density functions on the investor's decision to diversify in an expected utility framework. The empirical analysis provides estimates of four parametric and two semi-nonparametric densities for the S&P500 and concluded that allocation of all wealth in the risky asset would not have been optimal.