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

  • Martin L. Weitzman

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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 18496.

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Date of creation: Oct 2012
Date of revision:
Handle: RePEc:nbr:nberwo:18496
Note: EEE
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  1. Michael Greenstone & Elizabeth Kopits & Ann Wolverton, 2011. "Estimating the Social Cost of Carbon for Use in U.S. Federal Rulemakings: A Summary and Interpretation," Working Papers 1106, Massachusetts Institute of Technology, Center for Energy and Environmental Policy Research.
  2. Christian Gollier & Martin L. Weitzman, 2009. "How Should the Distant Future be Discounted when Discount Rates are Uncertain?," CESifo Working Paper Series 2863, CESifo Group Munich.
  3. Ian Martin, 2012. "On the Valuation of Long-Dated Assets," Journal of Political Economy, University of Chicago Press, vol. 120(2), pages 346 - 358.
  4. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
  5. Barro, Robert, 2006. "Rare Disasters and Asset Markets in the Twentieth Century," Scholarly Articles 3208215, Harvard University Department of Economics.
  6. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
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