IDEAS home Printed from https://ideas.repec.org/p/bca/bocawp/12-11.html
   My bibliography  Save this paper

Risk Premium, Variance Premium and the Maturity Structure of Uncertainty

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.bankofcanada.ca/wp-content/uploads/2012/04/wp2012-11.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Mark Britten‐Jones & Anthony Neuberger, 2000. "Option Prices, Implied Price Processes, and Stochastic Volatility," Journal of Finance, American Finance Association, vol. 55(2), pages 839-866, April.
    2. Campbell, John Y. & Hentschel, Ludger, 1992. "No news is good news *1: An asymmetric model of changing volatility in stock returns," Journal of Financial Economics, Elsevier, vol. 31(3), pages 281-318, June.
    3. Tim Bollerslev & George Tauchen & Hao Zhou, 2009. "Expected Stock Returns and Variance Risk Premia," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4463-4492, November.
    4. Chamberlain, Gary, 1988. "Asset Pricing in Multiperiod Securities Markets," Econometrica, Econometric Society, vol. 56(6), pages 1283-1300, November.
    5. David Backus & Mikhail Chernov & Ian Martin, 2011. "Disasters Implied by Equity Index Options," Journal of Finance, American Finance Association, vol. 66(6), pages 1969-2012, December.
    6. John H. Cochrane & Monika Piazzesi, 2005. "Bond Risk Premia," American Economic Review, American Economic Association, vol. 95(1), pages 138-160, March.
    7. 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.
    8. George M. Constantinides & Anisha Ghosh, 2011. "Asset Pricing Tests with Long-run Risks in Consumption Growth," The Review of Asset Pricing Studies, Oxford University Press, vol. 1(1), pages 96-136.
    9. Chang, Bo Young & Christoffersen, Peter & Jacobs, Kris, 2013. "Market skewness risk and the cross section of stock returns," Journal of Financial Economics, Elsevier, vol. 107(1), pages 46-68.
    10. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    11. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
    12. Guo, Hui & Savickas, Robert, 2006. "Idiosyncratic Volatility, Stock Market Volatility, and Expected Stock Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 43-56, January.
    13. Andrew Ang & Robert J. Hodrick & Yuhang Xing & Xiaoyan Zhang, 2006. "The Cross‐Section of Volatility and Expected Returns," Journal of Finance, American Finance Association, vol. 61(1), pages 259-299, February.
    14. Ian W. Martin, 2013. "Consumption-Based Asset Pricing with Higher Cumulants," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(2), pages 745-773.
    15. Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
    16. Cook R.D. & Setodji C.M., 2003. "A Model-Free Test for Reduced Rank in Multivariate Regression," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 340-351, January.
    17. Peter Reinhard Hansen, 2008. "Reduced-Rank Regression: A Useful Determinant Identity," CREATES Research Papers 2008-02, Department of Economics and Business Economics, Aarhus University.
    18. Philippe Mueller & Andrea Vedolin & Hao Zhou, 2011. "Short Run Bond Risk Premia," FMG Discussion Papers dp686, Financial Markets Group.
    19. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    20. John H. Cochrane, 2011. "Presidential Address: Discount Rates," Journal of Finance, American Finance Association, vol. 66(4), pages 1047-1108, August.
    21. Gurdip Bakshi & Dilip Madan, 2006. "A Theory of Volatility Spreads," Management Science, INFORMS, vol. 52(12), pages 1945-1956, December.
    22. 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.
    23. Serge Darolles & Christian Gourieroux & Joann Jasiak, 2006. "Structural Laplace Transform and Compound Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(4), pages 477-503, July.
    24. Itamar Drechsler & Amir Yaron, 2011. "What's Vol Got to Do with It," Review of Financial Studies, Society for Financial Studies, vol. 24(1), pages 1-45.
    25. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    26. Ravi Bansal & Amir Yaron, 2004. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, August.
    27. Mueller, Philippe & Vedolin, Andrea & Zhou, Hao, 2011. "Short run bond risk premia," LSE Research Online Documents on Economics 119065, London School of Economics and Political Science, LSE Library.
    28. Bakshi, Gurdip & Panayotov, George & Skoulakis, Georgios, 2011. "Improving the predictability of real economic activity and asset returns with forward variances inferred from option portfolios," Journal of Financial Economics, Elsevier, vol. 100(3), pages 475-495, June.
    29. Bekker, Paul & Dobbelstein, Pascal & Wansbeek, Tom, 1996. "The APT Model as Reduced-Rank Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 199-202, April.
    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. Cao, Charles & Simin, Timothy & Xiao, Han, 2019. "Predicting the equity premium with the implied volatility spread," MPRA Paper 103651, University Library of Munich, Germany.
    2. Mirco Rubin & Dario Ruzzi, 2020. "Equity Tail Risk in the Treasury Bond Market," Papers 2007.05933, arXiv.org.
    3. 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.
    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. Liu, Xiaochun, 2017. "Unfolded risk-return trade-offs and links to Macroeconomic Dynamics," Journal of Banking & Finance, Elsevier, vol. 82(C), pages 1-19.
    6. 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.
    7. Schneider, Paul, 2019. "An anatomy of the market return," Journal of Financial Economics, Elsevier, vol. 132(2), pages 325-350.
    8. 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.
    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. 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.
    11. 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.
    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. 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.
    14. 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.
    15. Jianjian Jin, 2013. "Jump-Diffusion Long-Run Risks Models, Variance Risk Premium and Volatility Dynamics," Staff Working Papers 13-12, Bank of Canada.
    16. 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.
    17. 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.
    18. 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).
    19. 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.
    20. 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.
    21. Mueller, Philippe & Vedolin, Andrea & Yen, Yu-Min, 2012. "Bond variance risk premia," LSE Research Online Documents on Economics 119053, London School of Economics and Political Science, LSE Library.
    22. Dotsis, George, 2017. "The market price of risk of the variance term structure," Journal of Banking & Finance, Elsevier, vol. 84(C), pages 41-52.
    23. 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.
    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).

    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. Mete Kilic & Ivan Shaliastovich, 2019. "Good and Bad Variance Premia and Expected Returns," Management Science, INFORMS, vol. 67(6), pages 2522-2544, June.
    2. Dufour, Jean-Marie & García, René & Taamouti, Abderrahim, 2008. "Measuring causality between volatility and returns with high-frequency data," UC3M Working papers. Economics we084422, Universidad Carlos III de Madrid. Departamento de Economía.
    3. Turan G. Bali & Hao Zhou, 2011. "Risk, uncertainty, and expected returns," Finance and Economics Discussion Series 2011-45, Board of Governors of the Federal Reserve System (U.S.).
    4. Bekaert, Geert & Hoerova, Marie, 2014. "The VIX, the variance premium and stock market volatility," Journal of Econometrics, Elsevier, vol. 183(2), pages 181-192.
    5. Ruan, Xinfeng & Zhang, Jin E., 2019. "Moment spreads in the energy market," Energy Economics, Elsevier, vol. 81(C), pages 598-609.
    6. Elyasiani, Elyas & Gambarelli, Luca & Muzzioli, Silvia, 2020. "Moment risk premia and the cross-section of stock returns in the European stock market," Journal of Banking & Finance, Elsevier, vol. 111(C).
    7. 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.
    8. 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.
    9. Agarwal, Vikas & Arisoy, Y. Eser & Naik, Narayan Y., 2017. "Volatility of aggregate volatility and hedge fund returns," Journal of Financial Economics, Elsevier, vol. 125(3), pages 491-510.
    10. Erik Vogt, 2014. "Option-implied term structures," Staff Reports 706, Federal Reserve Bank of New York.
    11. Ghosh, Anisha & Linton, Oliver, 2007. "Consistent estimation of the risk-return tradeoff in the presence of measurement error," LSE Research Online Documents on Economics 24506, London School of Economics and Political Science, LSE Library.
    12. Arash, Aloosh, 2011. "Variance Risk Premium Differentials and Foreign Exchange Returns," MPRA Paper 40829, University Library of Munich, Germany, revised 18 Aug 2012.
    13. 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.
    14. Bams, Dennis & Blanchard, Gildas & Honarvar, Iman & Lehnert, Thorsten, 2017. "Does oil and gold price uncertainty matter for the stock market?," Journal of Empirical Finance, Elsevier, vol. 44(C), pages 270-285.
    15. 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.
    16. Geert Bekaert & Eric Engstrom & Andrey Ermolov, 2023. "The Variance Risk Premium in Equilibrium Models," Review of Finance, European Finance Association, vol. 27(6), pages 1977-2014.
    17. Cathy Yi†Hsuan Chen & Thomas C. Chiang, 2016. "Empirical Analysis of the Intertemporal Relationship between Downside Risk and Expected Returns: Evidence from Time†varying Transition Probability Models," European Financial Management, European Financial Management Association, vol. 22(5), pages 749-796, November.
    18. 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.
    19. Bandi, Federico M. & Perron, Benoît, 2008. "Long-run risk-return trade-offs," Journal of Econometrics, Elsevier, vol. 143(2), pages 349-374, April.
    20. Dotsis, George, 2017. "The market price of risk of the variance term structure," Journal of Banking & Finance, Elsevier, vol. 84(C), pages 41-52.

    More about this item

    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

    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:bca:bocawp:12-11. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/bocgvca.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.