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

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  • 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.

Suggested Citation

  • Martin L. Weitzman, 2012. "Rare Disasters, Tail-Hedged Investments, and Risk-Adjusted Discount Rates," NBER Working Papers 18496, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:18496 Note: EEE
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    1. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    2. Maria Sandsmark & Haakon Vennemo, 2007. "A portfolio approach to climate investments: CAPM and endogenous risk," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 37(4), pages 681-695, August.
    3. Michael Greenstone & Elizabeth Kopits & Ann Wolverton, 2011. "Estimating the Social Cost of Carbon for Use in U.S. Federal Rulemakings: A Summary and Interpretation," NBER Working Papers 16913, National Bureau of Economic Research, Inc.
    4. Gollier, Christian & Weitzman, Martin L., 2010. "How should the distant future be discounted when discount rates are uncertain?," Economics Letters, Elsevier, vol. 107(3), pages 350-353, June.
    5. Robert J. Barro, 2006. "Rare Disasters and Asset Markets in the Twentieth Century," The Quarterly Journal of Economics, Oxford University Press, vol. 121(3), pages 823-866.
    6. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    7. Ian Martin, 2012. "On the Valuation of Long-Dated Assets," Journal of Political Economy, University of Chicago Press, vol. 120(2), pages 346-358.
    8. repec:hrv:faseco:33373345 is not listed on IDEAS
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    Citations

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    Cited by:

    1. Andersson , Henrik & Hultkrantz , Lars & Lindberg , Gunnar & Nilsson , Jan-Eric, 2017. "The role of economic analysis for investment priorities in Sweden’s transport sector," Working papers in Transport Economics 2017:12, CTS - Centre for Transport Studies Stockholm (KTH and VTI).
    2. Gollier, Christian, 2012. "Asset pricing with uncertain betas: A long-term perspective," IDEI Working Papers 752, Institut d'Économie Industrielle (IDEI), Toulouse.
    3. Gollier, Christian, 2012. "A theory of rational short-termism with uncertain betas," LERNA Working Papers 12.14.371, LERNA, University of Toulouse.
    4. Hultkrantz, Lars & A. Krüger, Niclas & Mantalos, Panagiotis, 2014. "Risk-adjusted long-term social rates of discount for transportation infrastructure investment," Research in Transportation Economics, Elsevier, vol. 47(C), pages 70-81.
    5. Giglio, Stefano & Maggiori, Matteo & Stroebel, Johannes, 2014. "Very long-run discount rates," Globalization and Monetary Policy Institute Working Paper 182, Federal Reserve Bank of Dallas.
    6. Christian Gollier, 2012. "Evaluation of Long-Dated Investments under Uncertain Growth Trend, Volatility and Catastrophes," CESifo Working Paper Series 4052, CESifo Group Munich.
    7. Isoré, Marlène & Szczerbowicz, Urszula, 2017. "Disaster risk and preference shifts in a New Keynesian model," Journal of Economic Dynamics and Control, Elsevier, vol. 79(C), pages 97-125.
    8. Hultkrantz, Lars & Mantalos, Panagiotis, 2016. "Estimating “Gamma” for Tail-hedge Discount Rates When Project Returns Are Co-integrated with GDP," Working Papers 2016:3, Örebro University, School of Business.
    9. Gollier, Christian, 2016. "Evaluation of long-dated assets: The role of parameter uncertainty," Journal of Monetary Economics, Elsevier, vol. 84(C), pages 66-83.
    10. Hultkrantz, Lars & Mantalos, Panagiotis, 2016. "Hedging with Trees: Tail-Hedge Discounting of Long-Term Forestry Returns," Working Papers 2016:2, Örebro University, School of Business.
    11. Corneo, Giacomo, 2015. "Volkswirtschaftliche Bewertung öffentlicher Investitionen," Discussion Papers 2015/12, Free University Berlin, School of Business & Economics.
    12. Rob Aalbers, 2013. "Optimal Discount Rates for Investments in Mitigation and Adaptation," CPB Discussion Paper 257, CPB Netherlands Bureau for Economic Policy Analysis.

    More about this item

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming

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