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Asset Pricing with Uncertain Betas: A Long-Term Perspective

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  • Christian Gollier

Abstract

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 investments. We define the notion of a certainty equivalent beta. 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. If current beliefs concerning the asset’s beta are represented by a normal distribution, the certainty equivalent beta becomes infinite for finite maturities.

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Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 4072.

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Date of creation: 2013
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Handle: RePEc:ces:ceswps:_4072

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Keywords: asset prices; term structure; risk premium; certainty equivalent beta;

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References

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  1. Ian Martin, 2010. "The Valuation of Long-Dated Assets," NBER Working Papers 16219, National Bureau of Economic Research, Inc.
  2. Roger Guesnerie, 2004. "Calcul économique et développement durable," Revue économique, Presses de Sciences-Po, vol. 55(3), pages 363-382.
  3. Martin L. Weitzman, 2007. "Subjective Expectations and Asset-Return Puzzles," American Economic Review, American Economic Association, vol. 97(4), pages 1102-1130, September.
  4. Gollier, Christian, 2012. "Evaluation of long-dated investments under uncertain growth trend, volatility and catastrophes," TSE Working Papers 12-361, Toulouse School of Economics (TSE).
  5. Weitzman, Martin L., 2009. "On Modeling and Interpreting the Economics of Catastrophic Climate Change," Scholarly Articles 3693423, Harvard University Department of Economics.
  6. Martin L. Weitzman, 2012. "Rare Disasters, Tail-Hedged Investments, and Risk-Adjusted Discount Rates," NBER Working Papers 18496, National Bureau of Economic Research, Inc.
  7. Jonathan Heathcote & Morris Davis, 2004. "The Price and Quantity of Residential Land in the United States," 2004 Meeting Papers 32, Society for Economic Dynamics.
  8. Gollier, Christian, 2009. "Ecological Discounting," TSE Working Papers 09-062, Toulouse School of Economics (TSE).
  9. Martin L. Weitzman, 2009. "Risk-Adjusted Gamma Discounting," NBER Working Papers 15588, National Bureau of Economic Research, Inc.
  10. Christian Gollier, 2008. "Discounting with fat-tailed economic growth," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 171-186, December.
  11. Krüger, Philipp & Landier, Augustin & Thesmar, David, 2011. "The WACC Fallacy: The Real Effects of Using a Unique Discount Rate," IDEI Working Papers 629, Institut d'Économie Industrielle (IDEI), Toulouse.
  12. Ian W. Martin, 2013. "Consumption-Based Asset Pricing with Higher Cumulants," Review of Economic Studies, Oxford University Press, vol. 80(2), pages 745-773.
  13. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
  14. 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.
  15. Gollier, Christian & Weitzman, Martin, 2009. "How Should the Distant Future be Discounted When Discount Rates are Uncertain?," IDEI Working Papers 588, Institut d'Économie Industrielle (IDEI), Toulouse.
  16. Traeger, Christian P., 2008. "Sustainability, Limited Substitutability and Non-Constant Social Discount Rates," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt10d7d7n4, Department of Agricultural & Resource Economics, UC Berkeley.
  17. 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.
  18. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  19. 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.
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