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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.

Suggested Citation

  • Christian Gollier, 2013. "Asset Pricing with Uncertain Betas: A Long-Term Perspective," CESifo Working Paper Series 4072, CESifo Group Munich.
  • Handle: RePEc:ces:ceswps:_4072
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    References listed on IDEAS

    as
    1. Christian Gollier, 2012. "Evaluation of Long-Dated Investments under Uncertain Growth Trend, Volatility and Catastrophes," CESifo Working Paper Series 4052, CESifo Group Munich.
    2. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    3. 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.
    4. Gollier, Christian, 2010. "Ecological discounting," Journal of Economic Theory, Elsevier, vol. 145(2), pages 812-829, March.
    5. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    6. Davis, Morris A. & Heathcote, Jonathan, 2007. "The price and quantity of residential land in the United States," Journal of Monetary Economics, Elsevier, vol. 54(8), pages 2595-2620, November.
    7. Christian Gollier, 2008. "Discounting with fat-tailed economic growth," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 171-186, December.
    8. Roger Guesnerie, 2004. "Calcul économique et développement durable," Revue économique, Presses de Sciences-Po, pages 363-382.
    9. Ian W. Martin, 2013. "Consumption-Based Asset Pricing with Higher Cumulants," Review of Economic Studies, Oxford University Press, vol. 80(2), pages 745-773.
    10. Gollier, Christian, 2016. "Evaluation of long-dated assets: The role of parameter uncertainty," Journal of Monetary Economics, Elsevier, vol. 84(C), pages 66-83.
    11. Traeger, Christian P., 2011. "Sustainability, limited substitutability, and non-constant social discount rates," Journal of Environmental Economics and Management, Elsevier, pages 215-228.
    12. Weitzman, Martin L., 2010. "Risk-adjusted gamma discounting," Journal of Environmental Economics and Management, Elsevier, vol. 60(1), pages 1-13, July.
    13. Christian Gollier, 2012. "Pricing the Planet's Future: The Economics of Discounting in an Uncertain World," Economics Books, Princeton University Press, edition 1, number 9894, June.
    14. 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.
    15. 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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    17. 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.
    18. Martin L. Weitzman, 2009. "On Modeling and Interpreting the Economics of Catastrophic Climate Change," The Review of Economics and Statistics, MIT Press, pages 1-19.
    19. Philipp Krüger & Augustin Landier & David Thesmar, 2015. "The WACC Fallacy: The Real Effects of Using a Unique Discount Rate," Journal of Finance, American Finance Association, vol. 70(3), pages 1253-1285, 06.
    20. repec:hrv:faseco:33373344 is not listed on IDEAS
    21. Ian Martin, 2012. "On the Valuation of Long-Dated Assets," Journal of Political Economy, University of Chicago Press, vol. 120(2), pages 346-358.
    22. repec:hrv:faseco:33373345 is not listed on IDEAS
    23. Martin L. Weitzman, 2012. "Rare Disasters, Tail-Hedged Investments, and Risk-Adjusted Discount Rates," NBER Working Papers 18496, National Bureau of Economic Research, Inc.
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    Cited by:

    1. Katz, Yuri A., 2017. "Value of the distant future: Model-independent results," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 269-276.

    More about this item

    Keywords

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

    JEL classification:

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

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