IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/18411.html
   My bibliography  Save this paper

An Intertemporal CAPM with Stochastic Volatility

Author

Listed:
  • John Y. Campbell
  • Stefano Giglio
  • Christopher Polk
  • Robert Turley

Abstract

This paper studies the pricing of volatility risk using the first-order conditions of a long-term equity investor who is content to hold the aggregate equity market rather than tilting towards value stocks and other equity portfolios that are attractive to short-term investors. We show that a conservative long-term investor will avoid such tilts in order to hedge against two types of deterioration in investment opportunities: declining expected stock returns, and increasing volatility. Empirically, we present novel evidence that low-frequency movements in equity volatility, tied to the default spread, are priced in the cross-section of stock returns.

Suggested Citation

  • John Y. Campbell & Stefano Giglio & Christopher Polk & Robert Turley, 2012. "An Intertemporal CAPM with Stochastic Volatility," NBER Working Papers 18411, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:18411
    Note: AP
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w18411.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jagannathan, Ravi & Wang, Zhenyu, 1996. "The Conditional CAPM and the Cross-Section of Expected Returns," Journal of Finance, American Finance Association, vol. 51(1), pages 3-53, March.
    2. Arvind Krishnamurthy & Annette Vissing-Jorgensen, 2012. "The Aggregate Demand for Treasury Debt," Journal of Political Economy, University of Chicago Press, vol. 120(2), pages 233-267.
    3. Campbell, John Y. & Hentschel, Ludger, 1992. "No news is good news *1: An asymmetric model of changing volatility in stock returns," Journal of Financial Economics, Elsevier, vol. 31(3), pages 281-318, June.
    4. Hanno Lustig & Stijn Van Nieuwerburgh & Adrien Verdelhan, 2013. "The Wealth-Consumption Ratio," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 3(1), pages 38-94.
    5. Dew-Becker, Ian & Giglio, Stefano & Le, Anh & Rodriguez, Marius, 2017. "The price of variance risk," Journal of Financial Economics, Elsevier, vol. 123(2), pages 225-250.
    6. John Y. Campbell & Christopher Polk & Tuomo Vuolteenaho, 2010. "Growth or Glamour? Fundamentals and Systematic Risk in Stock Returns," The Review of Financial Studies, Society for Financial Studies, vol. 23(1), pages 305-344, January.
    7. Tobias Adrian & Joshua Rosenberg, 2008. "Stock Returns and Volatility: Pricing the Short‐Run and Long‐Run Components of Market Risk," Journal of Finance, American Finance Association, vol. 63(6), pages 2997-3030, December.
    8. Lars Peter Hansen & John C. Heaton & Nan Li, 2008. "Consumption Strikes Back? Measuring Long-Run Risk," Journal of Political Economy, University of Chicago Press, vol. 116(2), pages 260-302, April.
    9. John Y. Campbell & Robert J. Shiller, 1988. "Stock Prices, Earnings and Expected Dividends," Cowles Foundation Discussion Papers 858, Cowles Foundation for Research in Economics, Yale University.
    10. Larry G. Epstein & Emmanuel Farhi & Tomasz Strzalecki, 2014. "How Much Would You Pay to Resolve Long-Run Risk?," American Economic Review, American Economic Association, vol. 104(9), pages 2680-2697, September.
    11. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    12. Duffie, Darrell & Singleton, Kenneth J, 1997. "An Econometric Model of the Term Structure of Interest-Rate Swap Yields," Journal of Finance, American Finance Association, vol. 52(4), pages 1287-1321, September.
    13. Engsted, Tom & Pedersen, Thomas Q. & Tanggaard, Carsten, 2012. "Pitfalls in VAR based return decompositions: A clarification," Journal of Banking & Finance, Elsevier, vol. 36(5), pages 1255-1265.
    14. Lewellen, Jonathan & Nagel, Stefan & Shanken, Jay, 2010. "A skeptical appraisal of asset pricing tests," Journal of Financial Economics, Elsevier, vol. 96(2), pages 175-194, May.
    15. Campbell, John Y., 1987. "Stock returns and the term structure," Journal of Financial Economics, Elsevier, vol. 18(2), pages 373-399, June.
    16. James L. Davis & Eugene F. Fama & Kenneth R. French, 2000. "Characteristics, Covariances, and Average Returns: 1929 to 1997," Journal of Finance, American Finance Association, vol. 55(1), pages 389-406, February.
    17. John Y. Campbell, Robert J. Shiller, 1988. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," The Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 195-228.
    18. Hanno Lustig & Nikolai Roussanov & Adrien Verdelhan, 2011. "Common Risk Factors in Currency Markets," The Review of Financial Studies, Society for Financial Studies, vol. 24(11), pages 3731-3777.
    19. Kandel, Shmuel & Stambaugh, Robert F., 1991. "Asset returns and intertemporal preferences," Journal of Monetary Economics, Elsevier, vol. 27(1), pages 39-71, February.
    20. Martin Lettau & Sydney Ludvigson, 2001. "Consumption, Aggregate Wealth, and Expected Stock Returns," Journal of Finance, American Finance Association, vol. 56(3), pages 815-849, June.
    21. Ravi Bansal & Dana Kiku & Ivan Shaliastovich & Amir Yaron, 2014. "Volatility, the Macroeconomy, and Asset Prices," Journal of Finance, American Finance Association, vol. 69(6), pages 2471-2511, December.
    22. Calvet, Laurent E. & Fisher, Adlai J., 2007. "Multifrequency news and stock returns," Journal of Financial Economics, Elsevier, vol. 86(1), pages 178-212, October.
    23. Fernando Restoy & Philippe Weil, 2011. "Approximate Equilibrium Asset Prices," Review of Finance, European Finance Association, vol. 15(1), pages 1-28.
    24. Robert F. Engle & Eric Ghysels & Bumjean Sohn, 2013. "Stock Market Volatility and Macroeconomic Fundamentals," The Review of Economics and Statistics, MIT Press, vol. 95(3), pages 776-797, July.
    25. John Y. Campbell & Tuomo Vuolteenaho, 2004. "Bad Beta, Good Beta," American Economic Review, American Economic Association, vol. 94(5), pages 1249-1275, December.
    26. Charlotte Christiansen & Maik Schmeling & Andreas Schrimpf, 2012. "A comprehensive look at financial volatility prediction by economic variables," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 956-977, September.
    27. Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-1153, December.
    28. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    29. TallariniJr., Thomas D., 2000. "Risk-sensitive real business cycles," Journal of Monetary Economics, Elsevier, vol. 45(3), pages 507-532, June.
    30. Joshua D. Coval & Tyler Shumway, 2001. "Expected Option Returns," Journal of Finance, American Finance Association, vol. 56(3), pages 983-1009, June.
    31. Beeler, Jason & Campbell, John Y., 2012. "The Long-Run Risks Model and Aggregate Asset Prices: An Empirical Assessment," Critical Finance Review, now publishers, vol. 1(1), pages 141-182, January.
    32. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    33. Stefan Nagel, 2016. "The Liquidity Premium of Near-Money Assets," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(4), pages 1927-1971.
    34. Breeden, Douglas T., 1979. "An intertemporal asset pricing model with stochastic consumption and investment opportunities," Journal of Financial Economics, Elsevier, vol. 7(3), pages 265-296, September.
    35. Campbell, John Y & Shiller, Robert J, 1988. " Stock Prices, Earnings, and Expected Dividends," Journal of Finance, American Finance Association, vol. 43(3), pages 661-676, July.
    36. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    37. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-286, April.
    38. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    39. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    40. Christopher J. Malloy & Tobias J. Moskowitz & Annette Vissing‐Jørgensen, 2009. "Long‐Run Stockholder Consumption Risk and Asset Returns," Journal of Finance, American Finance Association, vol. 64(6), pages 2427-2479, December.
    41. Lars Peter Hansen, 2012. "Dynamic Valuation Decomposition Within Stochastic Economies," Econometrica, Econometric Society, vol. 80(3), pages 911-967, May.
    42. Fu, Fangjian, 2009. "Idiosyncratic risk and the cross-section of expected stock returns," Journal of Financial Economics, Elsevier, vol. 91(1), pages 24-37, January.
    43. Long Chen & Xinlei Zhao, 2009. "Return Decomposition," The Review of Financial Studies, Society for Financial Studies, vol. 22(12), pages 5213-5249, December.
    44. Daniel, Kent & Titman, Sheridan, 1997. "Evidence on the Characteristics of Cross Sectional Variation in Stock Returns," Journal of Finance, American Finance Association, vol. 52(1), pages 1-33, March.
    45. Harvey, Campbell R., 1989. "Time-varying conditional covariances in tests of asset pricing models," Journal of Financial Economics, Elsevier, vol. 24(2), pages 289-317.
    46. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    47. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    48. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
    49. Paye, Bradley S., 2012. "‘Déjà vol’: Predictive regressions for aggregate stock market volatility using macroeconomic variables," Journal of Financial Economics, Elsevier, vol. 106(3), pages 527-546.
    50. Bjørn Eraker, 2008. "Affine General Equilibrium Models," Management Science, INFORMS, vol. 54(12), pages 2068-2080, December.
    51. Bansal, Ravi & Kiku, Dana & Yaron, Amir, 2012. "An Empirical Evaluation of the Long-Run Risks Model for Asset Prices," Critical Finance Review, now publishers, vol. 1(1), pages 183-221, January.
    52. Campbell, John Y, 1996. "Understanding Risk and Return," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 298-345, April.
    53. Jonathan B. Berk & Richard C. Green & Vasant Naik, 1999. "Optimal Investment, Growth Options, and Security Returns," Journal of Finance, American Finance Association, vol. 54(5), pages 1553-1607, October.
    54. Hull, John & Predescu, Mirela & White, Alan, 2004. "The relationship between credit default swap spreads, bond yields, and credit rating announcements," Journal of Banking & Finance, Elsevier, vol. 28(11), pages 2789-2811, November.
    55. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    56. Carhart, Mark M, 1997. "On Persistence in Mutual Fund Performance," Journal of Finance, American Finance Association, vol. 52(1), pages 57-82, March.
    57. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
    58. repec:hal:spmain:info:hdl:2441/8644 is not listed on IDEAS
    59. Garcia, Rene & Renault, Eric & Semenov, Andrei, 2006. "Disentangling risk aversion and intertemporal substitution through a reference level," Finance Research Letters, Elsevier, vol. 3(3), pages 181-193, September.
    60. Campbell, John Y, 1993. "Intertemporal Asset Pricing without Consumption Data," American Economic Review, American Economic Association, vol. 83(3), pages 487-512, June.
    61. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    62. Christie, Andrew A., 1982. "The stochastic behavior of common stock variances : Value, leverage and interest rate effects," Journal of Financial Economics, Elsevier, vol. 10(4), pages 407-432, December.
    63. Fama, Eugene F. & French, Kenneth R., 1989. "Business conditions and expected returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 25(1), pages 23-49, November.
    64. repec:hal:wpspec:info:hdl:2441/5l6uh8ogmqildh09h4838ip3n is not listed on IDEAS
    65. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    66. Daniel, Kent & Titman, Sheridan, 2012. "Testing Factor-Model Explanations of Market Anomalies," Critical Finance Review, now publishers, vol. 1(1), pages 103-139, January.
    67. repec:hal:spmain:info:hdl:2441/5l6uh8ogmqildh09h4838ip3n is not listed on IDEAS
    68. Harvey, Campbell R, 1991. "The World Price of Covariance Risk," Journal of Finance, American Finance Association, vol. 46(1), pages 111-157, March.
    69. Hansen, Lars Peter & Heaton, John & Lee, Junghoon & Roussanov, Nikolai, 2007. "Intertemporal Substitution and Risk Aversion," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 61, Elsevier.
    70. Eugene F. Fama & Kenneth R. French, 2016. "Dissecting Anomalies with a Five-Factor Model," The Review of Financial Studies, Society for Financial Studies, vol. 29(1), pages 69-103.
    71. Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-455, July.
    72. repec:hal:wpspec:info:hdl:2441/8644 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    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. Stefan Nagel, 2013. "Empirical Cross-Sectional Asset Pricing," Annual Review of Financial Economics, Annual Reviews, vol. 5(1), pages 167-199, November.
    2. Roussanov, Nikolai, 2014. "Composition of wealth, conditioning information, and the cross-section of stock returns," Journal of Financial Economics, Elsevier, vol. 111(2), pages 352-380.
    3. Amit Goyal, 2012. "Empirical cross-sectional asset pricing: a survey," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 26(1), pages 3-38, March.
    4. Campbell, John Y., 2003. "Consumption-based asset pricing," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 13, pages 803-887, Elsevier.
    5. John Y. Campbell, 2000. "Asset Pricing at the Millennium," Journal of Finance, American Finance Association, vol. 55(4), pages 1515-1567, August.
    6. Ludvigson, Sydney C., 2013. "Advances in Consumption-Based Asset Pricing: Empirical Tests," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 799-906, Elsevier.
    7. Maio, Paulo & Santa-Clara, Pedro, 2012. "Multifactor models and their consistency with the ICAPM," Journal of Financial Economics, Elsevier, vol. 106(3), pages 586-613.
    8. John Y. Campbell & Tuomo Vuolteenaho, 2004. "Bad Beta, Good Beta," American Economic Review, American Economic Association, vol. 94(5), pages 1249-1275, December.
    9. Shen, Junyan & Yu, Jianfeng & Zhao, Shen, 2017. "Investor sentiment and economic forces," Journal of Monetary Economics, Elsevier, vol. 86(C), pages 1-21.
    10. Malamud, Semyon & Vilkov, Grigory, 2018. "Non-myopic betas," Journal of Financial Economics, Elsevier, vol. 129(2), pages 357-381.
    11. Sydney Ludvigson, 2008. "The Research Agenda: Sydney Ludvigson on Empirical Evaluation of Economic Theories of Risk Premia," EconomicDynamics Newsletter, Review of Economic Dynamics, vol. 9(2), April.
    12. Roh, Tai-Yong & Lee, Changjun & Min, Byoung-Kyu, 2019. "Consumption growth predictability and asset prices," Journal of Empirical Finance, Elsevier, vol. 51(C), pages 95-118.
    13. Neuhierl, Andreas & Varneskov, Rasmus T., 2021. "Frequency dependent risk," Journal of Financial Economics, Elsevier, vol. 140(2), pages 644-675.
    14. Michail Koubouros & Dimitrios Malliaropulos & Ekaterini Panopoulou, 2010. "Long-run cash flow and discount-rate risks in the cross-section of US returns," The European Journal of Finance, Taylor & Francis Journals, vol. 16(3), pages 227-244.
    15. Keunbae Ahn, 2021. "Predictable Fluctuations in the Cross-Section and Time-Series of Asset Prices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2021, March.
    16. Tim Bollerslev & George Tauchen & Hao Zhou, 2009. "Expected Stock Returns and Variance Risk Premia," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4463-4492, November.
    17. Cochrane, John H., 2005. "Financial Markets and the Real Economy," Foundations and Trends(R) in Finance, now publishers, vol. 1(1), pages 1-101, July.
    18. Bali, Turan G., 2008. "The intertemporal relation between expected returns and risk," Journal of Financial Economics, Elsevier, vol. 87(1), pages 101-131, January.
    19. Roméo Tédongap, 2015. "Consumption Volatility and the Cross-Section of Stock Returns," Review of Finance, European Finance Association, vol. 19(1), pages 367-405.
    20. Turan G. Bali & Hao Zhou, 2011. "Risk, uncertainty, and expected returns," Finance and Economics Discussion Series 2011-45, Board of Governors of the Federal Reserve System (U.S.).

    More about this item

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • N22 - Economic History - - Financial Markets and Institutions - - - U.S.; Canada: 1913-

    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:nbr:nberwo:18411. 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/nberrus.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.