By analyzing the portfolio allocations of target date funds (TDFs), we document that the observed durations of TDF portfolios are inconsistent with the durations predicted by classical portfolio theory. We call this stylized fact the duration puzzle. We investigate to what extent several extensions of classical portfolio theory can explain the duration puzzle. More specifically, we consider the impact of human capital, inflation risk, and portfolio restrictions on the duration of the optimal portfolio. We find that it is difficult to explain the duration puzzle, especially for individuals aged between 35 and 65 years.

This paper explores the optimal consumption and investment behavior of an individual who derives utility from the ratio between his consumption and an endogenous habit. We obtain closed-form policies under general utility functionals and stochastic investment opportunities by developing a nontrivial linearization to the budget constraint. This enables us to explicitly characterize how habit formation affects the marginal propensity to consume and optimal stock–bond investments. We also show that in a setting that combines habit formation with Epstein–Zin utility, consumption no longer grows at unrealistically high rates at high ages and investments in risky assets decrease.