The cost of diversification over time, and a simple way to improve target-date funds

Diversification across time means changing the asset allocation over time. We show that under mild conditions diversification across time is inferior for all risk-averters and for all investment horizons, relative to a portfolio with the same average asset allocation, held constant over time. Target-date funds help reduce the variation in the asset allocation throughout the lifecycle, by implicitly considering the reduction in human capital with age. However, their structure implies two systematic deviations from constant asset allocation. We suggest a simple correction leading to a typical increase of 5%-22% in welfare.