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

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  • 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
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    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. Piotr Płuciennik, 2012. "The Impact of the World Financial Crisis on the Polish Interbank Market: A Swap Spread Approach," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 4(4), pages 269-288, December.
    7. 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.
    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. Osman Kilic & Joseph M. Marks & Kiseok Nam, 2022. "Predictable asset price dynamics, risk-return tradeoff, and investor behavior," Review of Quantitative Finance and Accounting, Springer, vol. 59(2), pages 749-791, August.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Khoa Hoang & Robert Faff, 2021. "Is the ex‐ante equity risk premium always positive? Evidence from a new conditional expectations model," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 61(1), pages 95-124, March.
    15. Ross McCown, James, 2001. "Yield curves and international equity returns," Journal of Banking & Finance, Elsevier, vol. 25(4), pages 767-788, April.
    16. 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.
    17. 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.
    18. 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.
    19. Chelikani, Surya & Marks, Joseph M. & Nam, Kiseok, 2024. "State-dependent intertemporal risk-return tradeoff: Further evidence," Journal of Economics and Business, Elsevier, vol. 130(C).
    20. 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.
    21. 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.
    22. Jaewon Choi & Matthew P. Richardson & Robert F. Whitelaw, 2014. "On the Fundamental Relation Between Equity Returns and Interest Rates," NBER Working Papers 20187, National Bureau of Economic Research, Inc.
    23. Chelikani, Surya & Marks, Joseph M. & Nam, Kiseok, 2023. "Volatility feedback effect and risk-return tradeoff," The Quarterly Review of Economics and Finance, Elsevier, vol. 92(C), pages 49-65.
    24. 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.
    25. 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.

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