Portfolio Choice for HARA Investors: When Does 1/γ (not) Work?

In the continuous time-Merton-model the instantaneous stock proportions are inversely proportional to the investor’s local relative risk aversion γ. This paper analyses the conditions under which a HARA-investor can use this 1/γ-rule to approximate her optimal portfolio in a finite time setting without material effects on the certainty equivalent of the portfolio payoff. The approximation is of high quality if approximate arbitrage opportunities do not exist and if the investor’s relative risk aversion is higher than that used for deriving the approximation portfolio. Otherwise, the approximation quality may be bad.