Does portfolio optimization pay?

All HARA-utility investors with the same exponent invest in a single risky fund and the risk-free asset. In a continuous time-model stock proportions are proportional to the inverse local relative risk aversion of the investor (1/gamma-rule). This paper analyses the conditions under which the optimal buy and holdportfolio of a HARA-investor can be approximated by the optimal portfolio of an investor with some low level of constant relative risk aversion using the 1/gamma-rule. It turns out that the approximation works very well in markets without approximate arbitrage opportunities. In markets with high equity premiums this approximation may be of low quality