Non-Myopic Portfolio Choice with Unpredictable Returns: The Jump-to-Default Case

If a risky asset is subject to a jump-to-default event, the investment horizon affects the optimal portfolio rule, even if the asset returns are unpredictable. The optimal rule solves a non-linear differential equation that, by not depending on the investor's pre-default value function, allows for its direct computation. Importantly for financial planners offering portfolio advice for the long term, tiny amounts of constant jump-to-default risk induce marked time variation in the optimal portfolios of long-run conservative investors. Our results are robust to the introduction of multiple non-defaultable risky assets.