IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v43y1997i3p371-385.html
   My bibliography  Save this article

Nonlinearities in the Relation Between the Equity Risk Premium and the Term Structure

Author

Listed:
  • Jacob Boudoukh

    (Stern School of Business, New York University, 44 W. 4th Street, New York, New York 10012)

  • Matthew Richardson

    (Stern School of Business, New York University, 44 W. 4th Street, New York, New York 10012)

  • Robert F. Whitelaw

    (Stern School of Business, New York University, 44 W. 4th Street, New York, New York 10012)

Abstract

This paper investigates the relation between the conditional expected equity risk premium and the slope of the term structure of interest rates. Theoretically, these variables are linked, the relation may be nonlinear, and negative risk premiums are consistent with equilibrium. Given these implications, we employ a nonparametric estimation technique to document the empirical relation between the risk premium and the slope of the term structure using almost two hundred years of data. Of particular interest, the risk premium is increasing in the term structure slope; however, for either small or negative slopes, the risk premium is much more sensitive to changes in interest rates. In addition, the empirical results imply negative expected equity risk premiums for some inverted term structures. Finally, variations in the risk premium do not appear to be related to variations in the variance of equity returns. We illustrate these features in a stylized consumption-based model, and provide the economic intuition behind the results.

Suggested Citation

  • Jacob Boudoukh & Matthew Richardson & Robert F. Whitelaw, 1997. "Nonlinearities in the Relation Between the Equity Risk Premium and the Term Structure," Management Science, INFORMS, vol. 43(3), pages 371-385, March.
  • Handle: RePEc:inm:ormnsc:v:43:y:1997:i:3:p:371-385
    DOI: 10.1287/mnsc.43.3.371
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.43.3.371
    Download Restriction: no

    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Fama, Eugene F., 1986. "Term premiums and default premiums in money markets," Journal of Financial Economics, Elsevier, vol. 17(1), pages 175-196, September.
    3. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-396, March.
    4. Hansen, Lars Peter & Singleton, Kenneth J, 1983. "Stochastic Consumption, Risk Aversion, and the Temporal Behavior of Asset Returns," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 249-265, April.
    5. Whitelaw, Robert F, 1994. "Time Variations and Covariations in the Expectation and Volatility of Stock Market Returns," Journal of Finance, American Finance Association, vol. 49(2), pages 515-541, June.
    6. Aman Ullah, 1988. "Non-parametric Estimation of Econometric Functionals," Canadian Journal of Economics, Canadian Economics Association, vol. 21(3), pages 625-658, August.
    7. Ferson, Wayne E & Harvey, Campbell R, 1991. "The Variation of Economic Risk Premiums," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 385-415, April.
    8. Backus, David K & Gregory, Allan W, 1993. "Theoretical Relations between Risk Premiums and Conditional Variances," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 177-185, April.
    9. Campbell, John Y., 1987. "Stock returns and the term structure," Journal of Financial Economics, Elsevier, vol. 18(2), pages 373-399, June.
    10. 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.
    11. Foster, F Douglas & Smith, Tom & Whaley, Robert E, 1997. "Assessing Goodness-of-Fit of Asset Pricing Models: The Distribution of the Maximal R-Squared," Journal of Finance, American Finance Association, vol. 52(2), pages 591-607, June.
    12. Boudoukh, Jacob, et al, 1997. "Pricing Mortgage-Backed Securities in a Multifactor Interest Rate Environment: A Multivariate Density Estimation Approach," Review of Financial Studies, Society for Financial Studies, vol. 10(2), pages 405-446.
    13. Fama, Eugene F, 1991. "Efficient Capital Markets: II," Journal of Finance, American Finance Association, vol. 46(5), pages 1575-1617, December.
    14. John Y. Campbell, 1986. "Bond and Stock Returns in a Simple Exchange Model," The Quarterly Journal of Economics, Oxford University Press, vol. 101(4), pages 785-803.
    15. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    16. Keim, Donald B. & Stambaugh, Robert F., 1986. "Predicting returns in the stock and bond markets," Journal of Financial Economics, Elsevier, vol. 17(2), pages 357-390, December.
    17. Cecchetti, Stephen G & Lam, Pok-sang & Mark, Nelson C, 1990. "Mean Reversion in Equilibrium Asset Prices," American Economic Review, American Economic Association, vol. 80(3), pages 398-418, June.
    18. Gallant, A. Ronald, 1982. "Unbiased determination of production technologies," Journal of Econometrics, Elsevier, vol. 20(2), pages 285-323, November.
    19. Estrella, Arturo & Hardouvelis, Gikas A, 1991. "The Term Structure as a Predictor of Real Economic Activity," Journal of Finance, American Finance Association, vol. 46(2), pages 555-576, June.
    20. Harvey, Campbell R., 1988. "The real term structure and consumption growth," Journal of Financial Economics, Elsevier, vol. 22(2), pages 305-333, December.
    21. Siegel, Jeremy J., 1992. "The real rate of interest from 1800-1990 : A study of the U.S. and the U.K," Journal of Monetary Economics, Elsevier, vol. 29(2), pages 227-252, April.
    22. Chen, Nai-Fu, 1991. "Financial Investment Opportunities and the Macroeconomy," Journal of Finance, American Finance Association, vol. 46(2), pages 529-554, June.
    23. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
    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. Jose Soares da Fonseca, 2010. "The performance of the European stock markets: a time-varying Sharpe ratio approach," The European Journal of Finance, Taylor & Francis Journals, vol. 16(7), pages 727-741.
    2. Hong, Seok Young & Linton, Oliver, 2020. "Nonparametric estimation of infinite order regression and its application to the risk-return tradeoff," Journal of Econometrics, Elsevier, vol. 219(2), pages 389-424.
    3. Deng, Yongheng & Gabriel, Stuart A. & Sanders, Anthony B., 2011. "CDO market implosion and the pricing of subprime mortgage-backed securities," Journal of Housing Economics, Elsevier, vol. 20(2), pages 68-80, June.
    4. Leonid Kogan & Raman Uppal, "undated". "Risk Aversion and Optimal Portfolio Policies in Partial and General Equilibrium Economies," Rodney L. White Center for Financial Research Working Papers 13-00, Wharton School Rodney L. White Center for Financial Research.
    5. Ludvigson, Sydney C. & Ng, Serena, 2007. "The empirical risk-return relation: A factor analysis approach," Journal of Financial Economics, Elsevier, vol. 83(1), pages 171-222, January.
    6. Kiseok Nam & Joshua Krausz & Augustine C. Arize, 2014. "Revisiting the intertemporal risk-return relation: asymmetrical effect of unexpected volatility shocks," Quantitative Finance, Taylor & Francis Journals, vol. 14(12), pages 2193-2203, December.
    7. Hong, S-Y. & Linton, O., 2018. "Nonparametric estimation of infinite order regression and its application to the risk-return tradeoff," Cambridge Working Papers in Economics 1877, Faculty of Economics, University of Cambridge.
    8. Robert F. Whitelaw, 1997. "Time-Varying Sharpe Ratios and Market Timing," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-074, New York University, Leonard N. Stern School of Business-.
    9. Kothari, S. P. & Shanken, Jay, 1997. "Book-to-market, dividend yield, and expected market returns: A time-series analysis," Journal of Financial Economics, Elsevier, vol. 44(2), pages 169-203, May.
    10. Gupta, Rangan & Risse, Marian & Volkman, David A. & Wohar, Mark E., 2019. "The role of term spread and pattern changes in predicting stock returns and volatility of the United Kingdom: Evidence from a nonparametric causality-in-quantiles test using over 250 years of data," The North American Journal of Economics and Finance, Elsevier, vol. 47(C), pages 391-405.
    11. Eleswarapu, Venkat R. & Thompson, Rex, 2007. "Testing for negative expected market return premia," Journal of Banking & Finance, Elsevier, vol. 31(6), pages 1755-1770, June.
    12. Wonsup Shin & Seok-Jun Bu & Sung-Bae Cho, 2019. "Automatic Financial Trading Agent for Low-risk Portfolio Management using Deep Reinforcement Learning," Papers 1909.03278, arXiv.org.
    13. Ross McCown, James, 2001. "Yield curves and international equity returns," Journal of Banking & Finance, Elsevier, vol. 25(4), pages 767-788, April.
    14. Robert J Bianchi & Adam E Clements & Michael E Drew, 2009. "HACking at Non-linearity: Evidence from Stocks and Bonds," School of Economics and Finance Discussion Papers and Working Papers Series 244, School of Economics and Finance, Queensland University of Technology.
    15. Wang, Zijun & Khan, M. Moosa, 2017. "Market states and the risk-return tradeoff," The Quarterly Review of Economics and Finance, Elsevier, vol. 65(C), pages 314-327.
    16. Yacine AÏT‐SAHALI & Michael W. Brandt, 2001. "Variable Selection for Portfolio Choice," Journal of Finance, American Finance Association, vol. 56(4), pages 1297-1351, August.
    17. Doron Avramov, "undated". "Stock-Return Predictability and Model Uncertainty," Rodney L. White Center for Financial Research Working Papers 12-00, Wharton School Rodney L. White Center for Financial Research.
    18. Ostdiek, Barbara, 1998. "The world ex ante risk premium: an empirical investigation," Journal of International Money and Finance, Elsevier, vol. 17(6), pages 967-999, December.
    19. Angelos Kanas, 2009. "The relation between the equity risk premium and the bond maturity premium in the UK: 1900–2006," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 33(2), pages 111-127, April.
    20. Angelos Kanas, 2010. "A note on the relation between the equity risk premium and the term structure," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 34(1), pages 89-95, January.

    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. 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.
    2. Kirby, Chris, 1998. "The Restrictions on Predictability Implied by Rational Asset Pricing Models," Review of Financial Studies, Society for Financial Studies, vol. 11(2), pages 343-382.
    3. Robert F. Whitelaw, 1997. "Time-Varying Sharpe Ratios and Market Timing," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-074, New York University, Leonard N. Stern School of Business-.
    4. Campbell, John Y, 1996. "Understanding Risk and Return," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 298-345, April.
    5. John Y. Campbell, 2000. "Asset Pricing at the Millennium," Journal of Finance, American Finance Association, vol. 55(4), pages 1515-1567, August.
    6. Turan Bali & Kamil Yilmaz, 2009. "The Intertemporal Relation between Expected Return and Risk on Currency," Koç University-TUSIAD Economic Research Forum Working Papers 0909, Koc University-TUSIAD Economic Research Forum, revised Nov 2009.
    7. Hardouvelis, Gikas A. & Kim, Dongcheol & Wizman, Thierry A., 1996. "Asset pricing models with and without consumption data: An empirical evaluation," Journal of Empirical Finance, Elsevier, vol. 3(3), pages 267-301, September.
    8. Mika Vaihekoski, 1998. "Short-term returns and the predictability of Finnish stock returns," Finnish Economic Papers, Finnish Economic Association, vol. 11(1), pages 19-36, Spring.
    9. Chrétien, Stéphane, 2012. "Bounds on the autocorrelation of admissible stochastic discount factors," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 1943-1962.
    10. Ľluboš Pástor & Robert F. Stambaugh, 2001. "The Equity Premium and Structural Breaks," Journal of Finance, American Finance Association, vol. 56(4), pages 1207-1239, August.
    11. 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.
    12. Hui Guo & Zijun Wang & Jian Yang, 2006. "Does aggregate relative risk aversion change countercyclically over time? evidence from the stock market," Working Papers 2006-047, Federal Reserve Bank of St. Louis.
    13. Guo, Hui & Savickas, Robert & Wang, Zijun & Yang, Jian, 2009. "Is the Value Premium a Proxy for Time-Varying Investment Opportunities? Some Time-Series Evidence," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 44(1), pages 133-154, February.
    14. Yueh-Neng Lin & Ken Hung, 2008. "Is Volatility Priced?," Annals of Economics and Finance, Society for AEF, vol. 9(1), pages 39-75, May.
    15. Yacine AÏT‐SAHALI & Michael W. Brandt, 2001. "Variable Selection for Portfolio Choice," Journal of Finance, American Finance Association, vol. 56(4), pages 1297-1351, August.
    16. Juan Carlos Escanciano & Juan Carlos Pardo-Fernández & Ingrid Van Keilegom, 2017. "Semiparametric Estimation of Risk–Return Relationships," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 40-52, January.
    17. Lo, Andrew W. & Mackinlay, A. Craig, 1997. "Maximizing Predictability In The Stock And Bond Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 1(1), pages 102-134, January.
    18. Antonis Demos & George Vasillelis, 2007. "U.K. Stock Market Inefficiencies and the Risk Premium," Multinational Finance Journal, Multinational Finance Journal, vol. 11(1-2), pages 97-122, March-Jun.
    19. David Rey, 2005. "Market Timing And Model Uncertainty: An Exploratory Study For The Swiss Stock Market," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 19(3), pages 239-260, October.
    20. Bali, Turan G., 2008. "The intertemporal relation between expected returns and risk," Journal of Financial Economics, Elsevier, vol. 87(1), pages 101-131, January.

    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:inm:ormnsc:v:43:y:1997:i:3:p:371-385. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Matthew Walls). General contact details of provider: http://edirc.repec.org/data/inforea.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.