Term structures of discount rates for risky investments

Résumé

There is still much confusion about which discount rates should be used to evaluate actions having long-lasting impacts, as in the contexts of climate change, social security reforms or large public infrastructures for example. Contrary to the existing literature that focuses on the discount rate for safe projects, this paper characterizes the term structure of discount rates for investment projects and assets with a non-zero beta. We assume that the growth rate of aggregate consumption follows a Brownian motion with uncertain parameters. We show that the term structures of the risk free discount rate and of the aggregate risk premium are respectively decreasing and increasing. Overall, the slope of term structure to be used for a specific project depends upon whether its beta is smaller or larger than half the index of relative risk aversion. We also argue that the beta of actions to mitigate climate change is relatively large around 1.3, so that the term structure of the associated real discount rates is increasing, from 1.3% for short maturities to 4.6% for extra-long ones, given the current low growth of the economy.