This paper investigates some implications of empirically observed stochastic properties of stock returns for asset allocation problems. For that purpose, decisions of representative investors for different utility functions are compared. Actual returns are assumed to have time-varying first and second order moments. Investors have different (false and correct) assumptions about the stochastic properties of returns. Consequences of their decisions are expressed in terms of ex post utility and converted to monetary units. Two main results are obtained: (a) there are almost no gains when GARCH properties of returns are correctly taken into account. (b) correct assumptions about time-variation in expected returns lead to significant gains for short investment horizons.