The Cost of Diversification Over Time, and a Simple Way to Improve Target-Date Funds

Diversification across time means changing the asset allocation from one period to another. We show that diversification across time is inferior to a portfolio with the same average asset allocation, held constant over time: it leads to a lower geometric mean, implying that in the long-run it almost-surely yields lower terminal wealth. Moreover, under mild conditions, time diversification yields a lower expected utility for all risk-averse investors and for all investment horizons. The welfare loss implied by diversification across time may be large. Target date funds help reduce the variation in the asset allocation throughout the lifecycle, by implicitly taking into account the reduction in human capital with age. However, their structure implies two systematic deviations from constant asset allocation. We suggest a simple way to correct these deviations, leading to a 10%-22% increase in welfare