IDEAS home Printed from https://ideas.repec.org/p/tse/wpaper/26543.html
   My bibliography  Save this paper

Asset pricing with uncertain betas: A long-term perspective

Author

Listed:
  • 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.

Suggested Citation

  • Gollier, Christian, 2012. "Asset pricing with uncertain betas: A long-term perspective," TSE Working Papers 12-354, Toulouse School of Economics (TSE).
  • Handle: RePEc:tse:wpaper:26543
    as

    Download full text from publisher

    File URL: http://www.tse-fr.eu/sites/default/files/medias/doc/wp/env/wp_tse_354.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    Other versions of this item:

    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.
    2. Gollier, Christian, 2010. "Ecological discounting," Journal of Economic Theory, Elsevier, vol. 145(2), pages 812-829, March.
    3. Roger Guesnerie, 2004. "Calcul économique et développement durable," Revue économique, Presses de Sciences-Po, vol. 55(3), pages 363-382.
    4. 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, June.
    5. Weitzman, Martin L., 2010. "Risk-adjusted gamma discounting," Journal of Environmental Economics and Management, Elsevier, vol. 60(1), pages 1-13, July.
    6. 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.
    7. 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.
    8. 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.
    9. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    10. John Y. Campbell, 1986. "Bond and Stock Returns in a Simple Exchange Model," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(4), pages 785-803.
    11. Ian W. Martin, 2013. "Consumption-Based Asset Pricing with Higher Cumulants," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(2), pages 745-773.
    12. Luc Baumstark & Pierre Ferry & Christian Gollier, 2011. "Le calcul du risque dans les investissements publics," Post-Print halshs-00958501, HAL.
    13. Traeger, Christian P., 2011. "Sustainability, limited substitutability, and non-constant social discount rates," Journal of Environmental Economics and Management, Elsevier, vol. 62(2), pages 215-228, September.
    14. 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.
    15. -, 2009. "The economics of climate change," Sede Subregional de la CEPAL para el Caribe (Estudios e Investigaciones) 38679, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    16. 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.
    17. Gollier, Christian, 2016. "Evaluation of long-dated assets: The role of parameter uncertainty," Journal of Monetary Economics, Elsevier, vol. 84(C), pages 66-83.
    18. Christian Gollier, 2008. "Discounting with fat-tailed economic growth," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 171-186, December.
    19. 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.
    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. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    22. Martin L. Weitzman, 2007. "Subjective Expectations and Asset-Return Puzzles," American Economic Review, American Economic Association, vol. 97(4), pages 1102-1130, September.
    23. 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.
    24. 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.
    25. Ian Martin, 2012. "On the Valuation of Long-Dated Assets," Journal of Political Economy, University of Chicago Press, vol. 120(2), pages 346-358.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Barahona, Ricardo & Driessen, Joost & Frehen, Rik, 2021. "Can unpredictable risk exposure be priced?," Journal of Financial Economics, Elsevier, vol. 139(2), pages 522-544.
    2. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gollier, Christian, 2012. "A theory of rational short-termism with uncertain betas," LERNA Working Papers 12.14.371, LERNA, University of Toulouse.
    2. Rick van der Ploeg, 2020. "Discounting and Climate Policy," CESifo Working Paper Series 8441, CESifo.
    3. Gollier, Christian, 2016. "Evaluation of long-dated assets: The role of parameter uncertainty," Journal of Monetary Economics, Elsevier, vol. 84(C), pages 66-83.
    4. Christian Gollier, 2012. "Evaluation of Long-Dated Investments under Uncertain Growth Trend, Volatility and Catastrophes," CESifo Working Paper Series 4052, CESifo.
    5. Lanlan Luo & Shou Chen & Ziran Zou, 2020. "Determining the Generalized Discount Rate for Risky Projects," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 77(1), pages 143-158, September.
    6. Frederick Ploeg, 2021. "Carbon pricing under uncertainty," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 28(5), pages 1122-1142, October.
    7. Kollenberg, Sascha & Taschini, Luca, 2016. "Emissions trading systems with cap adjustments," Journal of Environmental Economics and Management, Elsevier, vol. 80(C), pages 20-36.
    8. Gollier, Christian, 2019. "Valuation of natural capital under uncertain substitutability," Journal of Environmental Economics and Management, Elsevier, vol. 94(C), pages 54-66.
    9. Moritz Drupp & Mark Freeman & Ben Groom & Frikk Nesje, 2015. "Discounting disentangled: an expert survey on the determinants of the long-term social discount rate," GRI Working Papers 196a, Grantham Research Institute on Climate Change and the Environment.
    10. Gollier, Christian, 2016. "Gamma discounters are short-termist," Journal of Public Economics, Elsevier, vol. 142(C), pages 83-90.
    11. Kent D. Daniel & Robert B. Litterman & Gernot Wagner, 2016. "Applying Asset Pricing Theory to Calibrate the Price of Climate Risk," NBER Working Papers 22795, National Bureau of Economic Research, Inc.
    12. Hjort, Ingrid, 2016. "Potential Climate Risks in Financial Markets: A Literature Overview," Memorandum 01/2016, Oslo University, Department of Economics.
    13. van den Bergh, J.C.J.M. & Botzen, W.J.W., 2015. "Monetary valuation of the social cost of CO2 emissions: A critical survey," Ecological Economics, Elsevier, vol. 114(C), pages 33-46.
    14. Christian Gollier, 2019. "A Personal Biography of Marty Weitzman," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 74(3), pages 943-947, November.
    15. Moritz A. Drupp & Martin C. Hänsel, 2021. "Relative Prices and Climate Policy: How the Scarcity of Nonmarket Goods Drives Policy Evaluation," American Economic Journal: Economic Policy, American Economic Association, vol. 13(1), pages 168-201, February.
    16. Moritz A. Drupp, 2018. "Limits to Substitution Between Ecosystem Services and Manufactured Goods and Implications for Social Discounting," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 69(1), pages 135-158, January.
    17. Zhu, Xueqin & Smulders, Sjak & de Zeeuw, Aart, 2019. "Discounting in the presence of scarce ecosystem services," Journal of Environmental Economics and Management, Elsevier, vol. 98(C).
    18. Olijslagers, Stan & van der Ploeg, Frederick & van Wijnbergen, Sweder, 2023. "On current and future carbon prices in a risky world," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    19. Cameron Hepburn & Greer Gosnell, 2014. "Evaluating impacts in the distant future: cost–benefit analysis, discounting and the alternatives," Chapters, in: Giles Atkinson & Simon Dietz & Eric Neumayer & Matthew Agarwala (ed.), Handbook of Sustainable Development, chapter 9, pages 140-159, Edward Elgar Publishing.
    20. W. Botzen & Jeroen Bergh, 2014. "Specifications of Social Welfare in Economic Studies of Climate Policy: Overview of Criteria and Related Policy Insights," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 58(1), pages 1-33, May.

    More about this item

    Keywords

    asset prices; term structure; risk premium; certainty equivalent beta;
    All these keywords.

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tse:wpaper:26543. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/tsetofr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.