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Time Diversification: Definitions and Some Closed-Form Solutions

We establish general conditions under which younger investors should invest a larger proportion of their wealth in risky assets than older ones. In the finite horizon dynamic setting, we show that such phenomenon, known as time diversification, can occur in the presence of human wealth, target consumption, or mean-reverting stock returns. We formalize two alternative notions of time diversification commonly confounded in the literature. Analytic solutions are provided for both time-series and cross-sectional forms of time diversification. To our best knowledge, this paper is the first to solve in closed-form the hedging demand for a CARA investor with inter-temporal consumption and a finite horizon, facing mean-reverting expected returns.