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Asset pricing with uncertain betas: A long-term perspective

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  • Gollier, Christian

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 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
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Handle: RePEc:ide:wpaper:26544

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

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  1. 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.
  2. 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.
  3. Gollier, Christian, 2010. "Ecological discounting," Journal of Economic Theory, Elsevier, vol. 145(2), pages 812-829, March.
  4. 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.
  5. Gollier, Christian, 2012. "Evaluation of long-dated investments under uncertain growth trend, volatility and catastrophes," IDEI Working Papers 754, Institut d'Économie Industrielle (IDEI), Toulouse.
  6. Martin L. Weitzman, 2009. "Risk-Adjusted Gamma Discounting," NBER Working Papers 15588, National Bureau of Economic Research, Inc.
  7. 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.
  8. Roger Guesnerie, 2004. "Calcul économique et développement durable," DELTA Working Papers 2004-02, DELTA (Ecole normale supérieure).
  9. 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.
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  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. 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.
  14. 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.
  15. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  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, 2008. "Discounting with fat-tailed economic growth," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 171-186, December.
  18. Martin L. Weitzman, 2012. "Rare Disasters, Tail-Hedged Investments, and Risk-Adjusted Discount Rates," NBER Working Papers 18496, National Bureau of Economic Research, Inc.
  19. Martin L. Weitzman, 2007. "Subjective Expectations and Asset-Return Puzzles," American Economic Review, American Economic Association, vol. 97(4), pages 1102-1130, September.
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