Working Paper: NBER ID: w18496
Authors: Martin L. Weitzman
Abstract: What is the best way to incorporate a risk premium into the discount rate schedule for a real investment project with uncertain payoffs? The standard CAPM formula suggests a beta-weighted average of the return on a safe investment and the mean return on an economy-wide representative risky investment. Suppose, though, that the project constitutes a tail-hedged investment, meaning that it is expected to yield positive payoffs in catastrophic states of nature. Then the model of this paper suggests that what should be combined in a weighted average are not the two discount rates, but rather the corresponding two discount factors. This implies an effective discount rate schedule that declines over time from the standard CAPM formula down to the riskfree rate alone. Some simple numerical examples are given. Implications are noted for discounting long-term public investments and calculating the social cost of carbon in climate change.
Keywords: risk-adjusted discount rates; tail-hedged investments; social cost of carbon; climate change
JEL Codes: E43; G11; G12; Q54
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| tail-hedged investments (G11) | appropriate method for discounting future payoffs (D15) |
| declining discount rate (E43) | accurately reflecting the value of investments in projects with long-term payoffs (H43) |
| risk associated with catastrophic outcomes (G22) | greater reliance on the risk-free rate (G19) |
| time-dependent discount rate (rt) (H43) | converges towards the risk-free rate (r1) as time approaches infinity (G19) |
| traditional constant discount rates (H43) | bias against long-term investments (G31) |