Dynamic Choice and Risk Aversion

This paper explicitly solves a dynamic portfolio choice problem in which an investor allocates his wealth between a riskless and a risky asset. The solution shows that insights gained from studying static portfolio choice problems do not necessarily carry over to dynamic choice settings. For example, even though the risk premium of the risky asset in the problem presented here is strictly positive, holdings of that risky asset might increase with risk aversion. More surprisingly, a risk-averse investor might take a short position in the risky asset. The findings suggest that using stock holdings as a proxy for risk aversion may be inappropriate. Finally, I show that volatility might not prevent a risk averse investor from holding an infinite amount of a risky asset, contrary to Harry Markowitz’s insights on the static portfolio choice