Time-Inconsistent Risk Preferences and the Term Structure of Dividend Strips

Recent empirical research finds that the term structures of risk premia, return volatilities and Sharpe ratios on dividend strips are all downward-sloping (van Binsbergen et al. (2012)), but these observations cannot be explained by most asset-pricing theories. In this paper, I resolve this discrepancy using time-inconsistent risk preferences: agents' risk aversion differs in the short-run from the long-run. I solve three variants of the model: i) I allow the agent to commit to her future plan; assuming committing is not possible, I consider ii) a naive agent unaware of her time inconsistency, and iii) a sophisticated agent aware of it. I show that the naive agent case generates a flat term structure when endowment growth is i.i.d., as with standard time-consistent preferences. In the commitment and sophisticated agent cases, the term structures are downward-sloping when the agent is less averse to immediate risks than to future risks. The reasoning is that time inconsistency makes the state prices depend on the current state of the economy. If the agent is less averse to immediate risk, one-period future consumption is valued less if the current state is the good state than if it is the bad state, which causes the payoff structure of long-maturity dividend strips to become less risky than short-maturity dividend strips, leading to a downward-sloping term structure