The Investment Horizon Problem: A Resolution
31 Pages Posted: 1 Nov 2009
Date Written: September 15, 2009
In the canonical model of investments, the optimal fractions in the risky assets do not depend on the time horizon. This is against empirical evidence, and against the typical recommendations of portfolio managers. We demonstrate that if the intertemporal coefficient of relative risk aversion is allowed to depend on time, or the age of the investor, the investment horizon problem can be resolved. Accordingly, the only standard assumption in applied economics/finance that we relax in order to obtain our conclusion, is the state and time separability of the intertemporal felicity index in the investor’s utility function. We include life and pension insurance, and we also demonstrate that preferences aggregate.
Keywords: investment horizon problem, complete markets, life and pension insurance, dynamic programming, Kuhn-Tucker, directional derivatives, time consistency, aggregation
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