Hedging versus Insurance: Long-Horizon Investing with Short-Term Constraints

We solve for the optimal long-term portfolio strategy in the presence of a stochastic opportunity set, and short-term performance constraints with a stochastic floor. We show that the resulting strategy is of the Option-Based Portfolio Insurance type, and combines a procyclical aspect, coming from the portfolio insurance technique, and a counter-cyclical aspect, which arises because of the predictability in stock returns. This result allows us to provide a formal analysis of the much debated perceived conflict between long-term objectives and short-term constraints. In an empirical analysis, we show that using sub-optimal strategies to respect short-term constraints, namely a fixedmix or a Constant Proportion Portfolio Insurance, carries a substantial opportunity cost.
Keywords: Performance constraints; Portfolio insurance; Stochastic risk premium.
JEL codes: G11