Rare Disasters, Tail-Hedged Investments, and Risk-Adjusted Discount Rates

What is the best way to incorporate a risk premium into the discount rate schedule for a real investment project with uncertain payo¤s? 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 payo¤s 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 e¤ective discount rate schedule that declines over time from the standard CAPM formula down to the riskfree rate alone. Some simple numerical examples are given. Iimplications are noted for discounting long-term public investments and calculating the social cost of carbon in climate change.