IDEAS home Printed from https://ideas.repec.org/p/fip/fednsr/723.html
   My bibliography  Save this paper

Nonlinearity and flight to safety in the risk-return trade-off for stocks and bonds

Author

Abstract

We document a highly significant, strongly nonlinear dependence of stock and bond returns on past equity market volatility as measured by the VIX. We propose a new estimator for the shape of the nonlinear forecasting relationship that exploits additional variation in the cross section of returns. The nonlinearities are mirror images for stocks and bonds, revealing flight to safety: expected returns increase for stocks when volatility increases from moderate to high levels, while they decline for Treasury securities. These findings provide support for dynamic asset pricing theories where the price of risk is a nonlinear function of market volatility.

Suggested Citation

  • Tobias Adrian & Richard K. Crump & Erik Vogt, 2015. "Nonlinearity and flight to safety in the risk-return trade-off for stocks and bonds," Staff Reports 723, Federal Reserve Bank of New York.
    • Handle: RePEc:fip:fednsr:723
    as

    Download full text from publisher

    File URL: https://www.newyorkfed.org/research/staff_reports/sr723.html
    File Function: Summary
    Download Restriction: no
    File URL: https://www.newyorkfed.org/medialibrary/media/research/staff_reports/sr723.pdf?la=en
    File Function: Full text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Martin Lettau & Stijn Van Nieuwerburgh, 2008. "Reconciling the Return Predictability Evidence," The Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1607-1652, July.
    2. Ricardo J. Caballero & Arvind Krishnamurthy, 2008. "Collective Risk Management in a Flight to Quality Episode," Journal of Finance, American Finance Association, vol. 63(5), pages 2195-2230, October.
    3. Abel, Andrew B, 1990. "Asset Prices under Habit Formation and Catching Up with the Joneses," American Economic Review, American Economic Association, vol. 80(2), pages 38-42, May.
    4. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2008. "Nonparametric Tests for Treatment Effect Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 389-405, August.
    5. Tobias Adrian & Nina Boyarchenko, 2012. "Intermediary leverage cycles and financial stability," Staff Reports 567, Federal Reserve Bank of New York.
    6. 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.
    7. Andrew Ang & Geert Bekaert, 2007. "Stock Return Predictability: Is it There?," The Review of Financial Studies, Society for Financial Studies, vol. 20(3), pages 651-707.
    8. Hui Guo & Robert F. Whitelaw, 2006. "Uncovering the Risk–Return Relation in the Stock Market," Journal of Finance, American Finance Association, vol. 61(3), pages 1433-1463, June.
    9. Lieven Baele & Geert Bekaert & Koen Inghelbrecht & Min Wei, 2020. "Flights to Safety," The Review of Financial Studies, Society for Financial Studies, vol. 33(2), pages 689-746.
    10. Gromb, Denis & Vayanos, Dimitri, 2002. "Equilibrium and welfare in markets with financially constrained arbitrageurs," Journal of Financial Economics, Elsevier, vol. 66(2-3), pages 361-407.
    11. John Y. Campbell & John H. Cochrane, 2000. "Explaining the Poor Performance of Consumption‐based Asset Pricing Models," Journal of Finance, American Finance Association, vol. 55(6), pages 2863-2878, December.
    12. Andrea M. Buffa & Dimitri Vayanos & Paul Woolley, 2022. "Asset Management Contracts and Equilibrium Prices," Journal of Political Economy, University of Chicago Press, vol. 130(12), pages 3146-3201.
    13. 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.
    14. Chen, Xiaohong & Christensen, Timothy M., 2015. "Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions," Journal of Econometrics, Elsevier, vol. 188(2), pages 447-465.
    15. John Y. Campbell & Stefano Giglio & Christopher Polk, 2013. "Hard Times," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 3(1), pages 95-132.
      • John Y. Campbell & Stefano Giglio & Christopher Polk, 2010. "Hard Times," NBER Working Papers 16222, National Bureau of Economic Research, Inc.
      • Campbell, John Y. & Giglio, Stefano & Polk, Christopher, 2013. "Hard Times," Scholarly Articles 12172786, Harvard University Department of Economics.
    16. Zhiguo He & Arvind Krishnamurthy, 2013. "Intermediary Asset Pricing," American Economic Review, American Economic Association, vol. 103(2), pages 732-770, April.
    17. Bekaert, Geert & Engstrom, Eric & Grenadier, Steven R., 2010. "Stock and bond returns with Moody Investors," Journal of Empirical Finance, Elsevier, vol. 17(5), pages 867-894, December.
    18. Chen, Xiaohong & Liao, Zhipeng & Sun, Yixiao, 2014. "Sieve inference on possibly misspecified semi-nonparametric time series models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 639-658.
    19. John H. Cochrane & Monika Piazzesi, 2005. "Bond Risk Premia," American Economic Review, American Economic Association, vol. 95(1), pages 138-160, March.
    20. 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.
    21. Dimitri Vayanos & Paul Woolley, 2013. "An Institutional Theory of Momentum and Reversal," The Review of Financial Studies, Society for Financial Studies, vol. 26(5), pages 1087-1145.
    22. 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.
    23. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    24. Bekaert, Geert & Hoerova, Marie, 2014. "The VIX, the variance premium and stock market volatility," Journal of Econometrics, Elsevier, vol. 183(2), pages 181-192.
    25. Pierre-Olivier Weill, 2007. "Leaning Against the Wind," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(4), pages 1329-1354.
    26. Adrian, Tobias & Crump, Richard K. & Moench, Emanuel, 2013. "Pricing the term structure with linear regressions," Journal of Financial Economics, Elsevier, vol. 110(1), pages 110-138.
    27. Tobias Adrian & Erkko Etula & Tyler Muir, 2014. "Financial Intermediaries and the Cross-Section of Asset Returns," Journal of Finance, American Finance Association, vol. 69(6), pages 2557-2596, December.
    28. Markus K. Brunnermeier & Lasse Heje Pedersen, 2009. "Market Liquidity and Funding Liquidity," The Review of Financial Studies, Society for Financial Studies, vol. 22(6), pages 2201-2238, June.
    29. John Y. Campbell & John Cochrane, 1999. "Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," Journal of Political Economy, University of Chicago Press, vol. 107(2), pages 205-251, April.
    30. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    31. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2005. "There is a risk-return trade-off after all," Journal of Financial Economics, Elsevier, vol. 76(3), pages 509-548, June.
    32. Tobias Adrian & Nina Boyarchenko, 2012. "Intermediary leverage cycles and financial stability," Staff Reports 567, Federal Reserve Bank of New York, revised 01 Feb 2015.
    33. Alessandro Beber & Michael W. Brandt & Kenneth A. Kavajecz, 2009. "Flight-to-Quality or Flight-to-Liquidity? Evidence from the Euro-Area Bond Market," The Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 925-957, March.
    34. repec:bla:jfinan:v:43:y:1988:i:3:p:661-76 is not listed on IDEAS
    35. Hodrick, Robert J, 1992. "Dividend Yields and Expected Stock Returns: Alternative Procedures for Inference and Measurement," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 357-386.
    36. Sundaresan, Suresh M, 1989. "Intertemporally Dependent Preferences and the Volatility of Consumption and Wealth," The Review of Financial Studies, Society for Financial Studies, vol. 2(1), pages 73-89.
    37. Vayanos, Dimitri, 2004. "Flight to quality, flight to liquidity, and the pricing of risk," LSE Research Online Documents on Economics 456, London School of Economics and Political Science, LSE Library.
    38. Tobias Adrian & Emanuel Moench & Hyun Song Shin, 2010. "Financial intermediation, asset prices, and macroeconomic dynamics," Staff Reports 422, Federal Reserve Bank of New York.
    39. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, February.
    40. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    41. Bollerslev, Tim & Osterrieder, Daniela & Sizova, Natalia & Tauchen, George, 2013. "Risk and return: Long-run relations, fractional cointegration, and return predictability," Journal of Financial Economics, Elsevier, vol. 108(2), pages 409-424.
    42. Ghysels, Eric & Guérin, Pierre & Marcellino, Massimiliano, 2014. "Regime switches in the risk–return trade-off," Journal of Empirical Finance, Elsevier, vol. 28(C), pages 118-138.
    43. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    44. M. Hashem Pesaran & Davide Pettenuzzo & Allan Timmermann, 2006. "Forecasting Time Series Subject to Multiple Structural Breaks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(4), pages 1057-1084.
    45. Bali, Turan G. & Engle, Robert F., 2010. "The intertemporal capital asset pricing model with dynamic conditional correlations," Journal of Monetary Economics, Elsevier, vol. 57(4), pages 377-390, May.
    46. Harry Mamaysky, 2002. "Market Prices of Risk and Return Predictability in a Joint Stock-Bond Pricing Model," Yale School of Management Working Papers ysm297, Yale School of Management, revised 01 Oct 2002.
    47. Min Wei & Jonathan H. Wright, 2013. "Reverse Regressions And Long‐Horizon Forecasting," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(3), pages 353-371, April.
    48. Markus K. Brunnermeier & Yuliy Sannikov, 2014. "A Macroeconomic Model with a Financial Sector," American Economic Review, American Economic Association, vol. 104(2), pages 379-421, February.
    49. 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.
    50. John H. Cochrane, 2011. "Presidential Address: Discount Rates," Journal of Finance, American Finance Association, vol. 66(4), pages 1047-1108, August.
    51. Constantinides, George M, 1990. "Habit Formation: A Resolution of the Equity Premium Puzzle," Journal of Political Economy, University of Chicago Press, vol. 98(3), pages 519-543, June.
    52. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, Decembrie.
    53. Francis A. Longstaff, 2004. "The Flight-to-Liquidity Premium in U.S. Treasury Bond Prices," The Journal of Business, University of Chicago Press, vol. 77(3), pages 511-526, July.
    54. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    55. repec:bla:jfinan:v:59:y:2004:i:4:p:1481-1509 is not listed on IDEAS
    56. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    57. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    58. Lundblad, Christian, 2007. "The risk return tradeoff in the long run: 1836-2003," Journal of Financial Economics, Elsevier, vol. 85(1), pages 123-150, July.
    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. 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.
    2. Hui Chen & Scott Joslin & Sophie X. Ni, 2019. "Demand for Crash Insurance, Intermediary Constraints, and Risk Premia in Financial Markets," NBER Working Papers 25573, National Bureau of Economic Research, Inc.
    3. Tobias Adrian & Nellie Liang, 2018. "Monetary Policy, Financial Conditions, and Financial Stability," International Journal of Central Banking, International Journal of Central Banking, vol. 14(1), pages 73-131, January.
    4. Tobias Adrian & Emanuel Moench & Hyun Song Shin, 2013. "Dynamic Leverage Asset Pricing," Staff Reports 625, Federal Reserve Bank of New York.
    5. He, Zhiguo & Kelly, Bryan & Manela, Asaf, 2017. "Intermediary asset pricing: New evidence from many asset classes," Journal of Financial Economics, Elsevier, vol. 126(1), pages 1-35.
    6. Tyler Muir, 2017. "Financial Crises and Risk Premia," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(2), pages 765-809.
    7. Engsted, Tom & Hyde, Stuart & Møller, Stig V., 2010. "Habit formation, surplus consumption and return predictability: International evidence," Journal of International Money and Finance, Elsevier, vol. 29(7), pages 1237-1255, November.
    8. 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.
    9. Kargar, Mahyar, 2021. "Heterogeneous intermediary asset pricing," Journal of Financial Economics, Elsevier, vol. 141(2), pages 505-532.
    10. Peter Van Tassel & Erik Vogt, 2016. "Global variance term premia and intermediary risk appetite," Staff Reports 789, Federal Reserve Bank of New York.
    11. 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.
    12. Committee, Nobel Prize, 2013. "Understanding Asset Prices," Nobel Prize in Economics documents 2013-1, Nobel Prize Committee.
    13. Timmer, Yannick, 2018. "Cyclical investment behavior across financial institutions," Journal of Financial Economics, Elsevier, vol. 129(2), pages 268-286.
    14. Ye Li & Chen Wang, 2023. "Valuation Duration of the Stock Market," Papers 2310.07110, arXiv.org.
    15. Malamud, Semyon & Vilkov, Grigory, 2018. "Non-myopic betas," Journal of Financial Economics, Elsevier, vol. 129(2), pages 357-381.
    16. Geert Bekaert & Eric C. Engstrom & Nancy R. Xu, 2022. "The Time Variation in Risk Appetite and Uncertainty," Management Science, INFORMS, vol. 68(6), pages 3975-4004, June.
    17. João M. Sousa & Ricardo M. Sousa, 2019. "Asset Returns Under Model Uncertainty: Evidence from the Euro Area, the US and the UK," Computational Economics, Springer;Society for Computational Economics, vol. 54(1), pages 139-176, June.
    18. Okou, Cédric & Jacquier, Éric, 2016. "Horizon effect in the term structure of long-run risk-return trade-offs," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 445-466.
    19. Grishchenko, Olesya V., 2010. "Internal vs. external habit formation: The relative importance for asset pricing," Journal of Economics and Business, Elsevier, vol. 62(3), pages 176-194, May.
    20. 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.

    More about this item

    Keywords

    flight to safety; risk-return trade-off; dynamic asset pricing; volatility; nonparametric estimation and inference; intermediary asset pricing; asset management;
    All these keywords.

    JEL classification:

    • G01 - Financial Economics - - General - - - Financial Crises
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

    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:fip:fednsr:723. 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: Gabriella Bucciarelli (email available below). General contact details of provider: https://edirc.repec.org/data/frbnyus.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.