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Risk Premium, Variance Premium and the Maturity Structure of Uncertainty

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  • Bruno Feunou
  • Jean-Sébastien Fontaine
  • Abderrahim Taamouti
  • Roméo Tedongap

Abstract

Expected returns vary when investors face time-varying investment opportunities. Longrun risk models (Bansal and Yaron 2004) and no-arbitrage affine models (Duffie, Pan, and Singleton 2000) emphasize sources of risk that are not observable to the econometrician. We show that, for both classes of models, the term structure of risk implicit in option prices can reveal these risk factors ex-ante. Empirically, we construct the variance term structure implied in SP500 option prices. The variance term structure reveal two important drivers of the bond premium, the equity premium, and the variance premium, jointly. We also consider the term structure of higher-order risks as measured by skewness and kurtosis and still find that two factors are sufficient to summarize the information content from the term structure of risks. Overall, our results bode well for the ability of structural models to explain risk-returns trade-offs across different markets using only very few sources of risk.

Suggested Citation

  • Bruno Feunou & Jean-Sébastien Fontaine & Abderrahim Taamouti & Roméo Tedongap, 2012. "Risk Premium, Variance Premium and the Maturity Structure of Uncertainty," Staff Working Papers 12-11, Bank of Canada.
    • Handle: RePEc:bca:bocawp:12-11
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    Cited by:

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    2. Cao, Charles & Simin, Timothy & Xiao, Han, 2019. "Predicting the equity premium with the implied volatility spread," MPRA Paper 103651, University Library of Munich, Germany.
    3. Rombouts, Jeroen V.K. & Stentoft, Lars & Violante, Francesco, 2020. "Variance swap payoffs, risk premia and extreme market conditions," Econometrics and Statistics, Elsevier, vol. 13(C), pages 106-124.
    4. Mirco Rubin & Dario Ruzzi, 2020. "Equity Tail Risk in the Treasury Bond Market," Papers 2007.05933, arXiv.org.
    5. Konstantinidi, Eirini & Skiadopoulos, George, 2016. "How does the market variance risk premium vary over time? Evidence from S&P 500 variance swap investment returns," Journal of Banking & Finance, Elsevier, vol. 62(C), pages 62-75.
    6. Jianjian Jin, 2013. "Jump-Diffusion Long-Run Risks Models, Variance Risk Premium and Volatility Dynamics," Staff Working Papers 13-12, Bank of Canada.
    7. Xinglin Yang & Ji Chen, 2021. "VIX term structure: The role of jump propagation risks," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(6), pages 785-810, June.
    8. Jonathan Dark & Xin Gao & Thijs van der Heijden & Federico Nardari, 2022. "Forecasting variance swap payoffs," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(12), pages 2135-2164, December.
    9. Bruno Feunou & Mohammad R Jahan-Parvar & Cédric Okou, 2018. "Downside Variance Risk Premium," Journal of Financial Econometrics, Oxford University Press, vol. 16(3), pages 341-383.
    10. Wei Guo & Xinfeng Ruan & Sebastian A. Gehricke & Jin E. Zhang, 2023. "Term spreads of implied volatility smirk and variance risk premium," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(7), pages 829-857, July.
    11. Khalfaoui, Rabeh & Stef, Nicolae & Wissal, Ben Arfi & Sami, Ben Jabeur, 2022. "Dynamic spillover effects and connectedness among climate change, technological innovation, and uncertainty: Evidence from a quantile VAR network and wavelet coherence," Technological Forecasting and Social Change, Elsevier, vol. 181(C).
    12. Yaw‐Huei Wang & Kuang‐Chieh Yen, 2018. "The information content of option‐implied tail risk on the future returns of the underlying asset," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(4), pages 493-510, April.
    13. Benjamin A. Jansen, 2021. "Cash flow growth and stock returns," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 44(2), pages 371-402, June.
    14. Rubio, Gonzalo & Serrano, Pedro & Vaello-Sebastià, Antoni, 2023. "The international integration of the term structure of expected market risk premia," Finance Research Letters, Elsevier, vol. 58(PD).
    15. Mirco Rubin & Dario Ruzzi, 2020. "Equity tail risk in the treasury bond market," Temi di discussione (Economic working papers) 1311, Bank of Italy, Economic Research and International Relations Area.
    16. Philippe Mueller & Andrea Vedolin & Yu-min Yen, 2012. "Bond Variance Risk Premia," FMG Discussion Papers dp699, Financial Markets Group.
    17. Liu, Xiaochun, 2017. "Unfolded risk-return trade-offs and links to Macroeconomic Dynamics," Journal of Banking & Finance, Elsevier, vol. 82(C), pages 1-19.
    18. Yaw‐Huei Wang & Kuang‐Chieh Yen, 2019. "The information content of the implied volatility term structure on future returns," European Financial Management, European Financial Management Association, vol. 25(2), pages 380-406, March.
    19. Dotsis, George, 2017. "The market price of risk of the variance term structure," Journal of Banking & Finance, Elsevier, vol. 84(C), pages 41-52.
    20. Schneider, Paul, 2019. "An anatomy of the market return," Journal of Financial Economics, Elsevier, vol. 132(2), pages 325-350.
    21. Fabian Hollstein & Marcel Prokopczuk & Chardin Wese Simen, 2019. "The term structure of systematic and idiosyncratic risk," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(4), pages 435-460, April.
    22. Gomes, Pedro & Taamouti, Abderrahim, 2016. "In search of the determinants of European asset market comovements," International Review of Economics & Finance, Elsevier, vol. 44(C), pages 103-117.
    23. Liu, Xiaochun, 2017. "Can macroeconomic dynamics explain the time variation of risk–return trade-offs in the U.S. financial market?," The Quarterly Review of Economics and Finance, Elsevier, vol. 66(C), pages 275-293.
    24. Cao, Charles & Simin, Timothy & Xiao, Han, 2020. "Predicting the equity premium with the implied volatility spread," Journal of Financial Markets, Elsevier, vol. 51(C).

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    Keywords

    Asset Pricing; Financial services;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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