The Sign of Risk for Present Value of Future Losses

TL;DR

This paper demonstrates that risk in the valuation of future losses can only be incorporated through a lower discount rate, challenging the notion that higher rates can account for risk.

Contribution

It provides a formal proof that risk considerations in present value calculations necessitate a lower discount rate, clarifying a key debate in climate economics.

Findings

Risk can only be represented by a lower discount rate

Challenges the idea that higher discount rates account for risk

Clarifies the relationship between risk and discount rate choice

Abstract

In the ongoing debate over discount rates and climate change, William Nordhaus has championed a higher discount rate to account for risk. Nicholas Stern has championed a lower rate. Here we prove that in the case of a stream of future losses, risk can only be represented by a lower discount rate, never a higher one.