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Risk premium, variance premium and the maturity structure of uncertainty

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  • Feunou, Bruno
  • Fontaine, Jean-Sébastien
  • Taamouti, Abderrahim
  • Tédongap, Roméo

Abstract

Theoretical risk factors underlying time-variations of risk premium across asset classes are typically unobservable or hard to measure by construction. Important examples include risk factors in Long Run Risk [LRR] structural models (Bansal and Yaron 2004) as well as stochastic volatility or jump intensities in reduced-form affine representations of stock returns (Duffie, Pan, and Singleton 2000). Still, we show that both classes of models predict that the term structure of risk-neutral variance should reveal these risk factors. Empirically, we use model-free measures and construct the ex-ante variance term structure from option prices. This reveals (spans) two risk factors that predict the bond premium and the equity premium, jointly. Moreover, we find that the same risk factors also predict the variance premium. This important contribution is consistent with theory and confirms that a small number of factors underlies common time-variations in the bond premium, the equity premium and the variance premium. Theory predicts that the term structure of higher-order risks can reveal the same factors. This is confirmed in the data. Strikingly, combining the information from the variance, skewness and kurtosis term structure can be summarized by two risk factors and yields similar level of predictability (i.e., R2s). This bodes well for our ability to bridge the gap between the macro-finance literature, which uses very few state variables, and valuations in option markets.

Suggested Citation

  • Feunou, Bruno & Fontaine, Jean-Sébastien & Taamouti, Abderrahim & Tédongap, Roméo, 2011. "Risk premium, variance premium and the maturity structure of uncertainty," UC3M Working papers. Economics we1144, Universidad Carlos III de Madrid. Departamento de Economía.
  • Handle: RePEc:cte:werepe:we1144
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    Cited by:

    1. 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.
    2. Bruno Feunou & Mohammad R Jahan-Parvar & Cédric Okou, 2018. "Downside Variance Risk Premium," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 16(3), pages 341-383.
    3. 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.
    4. 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.
    5. 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.
    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. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Andreou, Panayiotis C. & Kagkadis, Anastasios & Philip, Dennis & Taamouti, Abderrahim, 2019. "The information content of forward moments," Journal of Banking & Finance, Elsevier, vol. 106(C), pages 527-541.
    13. Dotsis, George, 2017. "The market price of risk of the variance term structure," Journal of Banking & Finance, Elsevier, vol. 84(C), pages 41-52.
    14. Liu, Xiaochun, 2017. "Unfolded risk-return trade-offs and links to Macroeconomic Dynamics," Journal of Banking & Finance, Elsevier, vol. 82(C), pages 1-19.
    15. Cao, Charles & Simin, Timothy & Xiao, Han, 2020. "Predicting the equity premium with the implied volatility spread," Journal of Financial Markets, Elsevier, vol. 51(C).
    16. Cao, Charles & Simin, Timothy & Xiao, Han, 2019. "Predicting the equity premium with the implied volatility spread," MPRA Paper 103651, University Library of Munich, Germany.
    17. Mirco Rubin & Dario Ruzzi, 2020. "Equity Tail Risk in the Treasury Bond Market," Papers 2007.05933, arXiv.org.
    18. Schneider, Paul, 2019. "An anatomy of the market return," Journal of Financial Economics, Elsevier, vol. 132(2), pages 325-350.
    19. 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.

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    Keywords

    Equity premium;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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