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Asset pricing with uncertain betas: A long-term perspective

  • Gollier, Christian

How should one evaluate investment projects whose CCAPM betas are uncertain? This question is particularly crucial for projects yielding long-lasting impacts on the economy, as is the case for example for many green investment projects. We defined the notion of a certainty equivalent beta. We characterize it as a function of the characteristics of the uncertainties affecting the asset’s beta and the economy as a whole. We show that its term structure is not constant and that, for short maturities, it equals the expected beta. If the expected beta is larger than a threshold (which is negative and large in absolute value in all realistic calibrations), the term structure of the certainty equivalent beta is increasing and tends to its largest plausible value. In the benchmark case in which the asset’s beta is normally distributed, the certainty equivalent beta becomes infinite for finite maturities.

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Paper provided by Institut d'Économie Industrielle (IDEI), Toulouse in its series IDEI Working Papers with number 752.

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Date of creation: Nov 2012
Date of revision:
Handle: RePEc:ide:wpaper:26544
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  1. Krüger, Philipp & Landier, Augustin & Thesmar, David, 2011. "The WACC Fallacy: The Real Effects of Using a Unique Discount Rate," TSE Working Papers 11-222, Toulouse School of Economics (TSE).
  2. Gollier, Christian, 2012. "Evaluation of long-dated assets : The role of parameter uncertainty," TSE Working Papers 12-361, Toulouse School of Economics (TSE), revised Sep 2015.
  3. Christian Gollier, 2008. "Discounting with fat-tailed economic growth," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 171-186, December.
  4. Martin L. Weitzman, 2007. "Subjective Expectations and Asset-Return Puzzles," American Economic Review, American Economic Association, vol. 97(4), pages 1102-1130, September.
  5. Christian Gollier, 2012. "Evaluation of Long-Dated Investments under Uncertain Growth Trend, Volatility and Catastrophes," CESifo Working Paper Series 4052, CESifo Group Munich.
  6. Weitzman, Martin L., 1998. "Why the Far-Distant Future Should Be Discounted at Its Lowest Possible Rate," Journal of Environmental Economics and Management, Elsevier, vol. 36(3), pages 201-208, 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. 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.
  9. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  10. Davis, Morris & Heathcote, Jonathan, 2005. "The Price and Quantity of Residential Land in the United States," CEPR Discussion Papers 5333, C.E.P.R. Discussion Papers.
  11. Traeger, Christian P, 2007. "Sustainability, limited substitutability and non-constant social discount rates," CUDARE Working Paper Series 1045, University of California at Berkeley, Department of Agricultural and Resource Economics and Policy.
  12. Ekaterini Panopoulou & Ben Groom & Phoebe Koundouri & Theologos Pantelidis, 2004. "An Econometric Approach To Estimating Long-Run Discount Rates," Royal Economic Society Annual Conference 2004 70, Royal Economic Society.
  13. Gollier, Christian, 2009. "Ecological Discounting," IDEI Working Papers 524, Institut d'Économie Industrielle (IDEI), Toulouse.
  14. Weitzman, Martin L., 2010. "Risk-adjusted gamma discounting," Journal of Environmental Economics and Management, Elsevier, vol. 60(1), pages 1-13, July.
  15. Martin L. Weitzman, 2009. "On Modeling and Interpreting the Economics of Catastrophic Climate Change," The Review of Economics and Statistics, MIT Press, vol. 91(1), pages 1-19, February.
  16. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
  17. Christian Gollier, 2012. "Pricing the Planet's Future: The Economics of Discounting in an Uncertain World," Economics Books, Princeton University Press, edition 1, volume 1, number 9894.
  18. Roger Guesnerie, 2004. "Calcul économique et développement durable," Revue économique, Presses de Sciences-Po, vol. 55(3), pages 363-382.
  19. Thomas Sterner & U. Martin Persson, 2008. "An Even Sterner Review: Introducing Relative Prices into the Discounting Debate," Review of Environmental Economics and Policy, Association of Environmental and Resource Economists, vol. 2(1), pages 61-76, Winter.
  20. Martin L. Weitzman, 2012. "Rare Disasters, Tail-Hedged Investments, and Risk-Adjusted Discount Rates," NBER Working Papers 18496, National Bureau of Economic Research, Inc.
  21. Ian W. Martin, 2013. "Consumption-Based Asset Pricing with Higher Cumulants," Review of Economic Studies, Oxford University Press, vol. 80(2), pages 745-773.
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