IDEAS home Printed from https://ideas.repec.org/a/spr/empeco/v44y2013i3p1291-1314.html
   My bibliography  Save this article

The risk-return relation and VIX: evidence from the S&P 500

Author

Listed:
  • Angelos Kanas

Abstract

A significantly positive risk-return relation for the S&P 500 market index is detected if the squared implied volatility index (VIX) is allowed for as an exogenous variable in the conditional variance equation of the parsimonious GARCH(1,1) model. This result holds for both daily and weekly observations, for extended conditional mean and variance specifications, and is robust to sub-samples. We show that the conditional variance obtained from the GARCH model with VIX has better predictive ability for realized volatility than the conditional variance from GARCH without VIX and VIX itself, thereby documenting an important information content of VIX for conditional variance. The results are interpreted as evidence that adding VIX squared in the conditional variance equation yields a better measure of conditional variance which, subsequently, uncovers a strong risk-return relation. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Angelos Kanas, 2013. "The risk-return relation and VIX: evidence from the S&P 500," Empirical Economics, Springer, vol. 44(3), pages 1291-1314, June.
    • Handle: RePEc:spr:empeco:v:44:y:2013:i:3:p:1291-1314
    DOI: 10.1007/s00181-012-0639-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00181-012-0639-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00181-012-0639-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Lamoureux, Christopher G & Lastrapes, William D, 1990. "Heteroskedasticity in Stock Return Data: Volume versus GARCH Effects," Journal of Finance, American Finance Association, vol. 45(1), pages 221-229, March.
    2. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    3. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    4. Koopman, Siem Jan & Jungbacker, Borus & Hol, Eugenie, 2005. "Forecasting daily variability of the S&P 100 stock index using historical, realised and implied volatility measurements," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 445-475, June.
    5. Li, Qi & Yang, Jian & Hsiao, Cheng & Chang, Young-Jae, 2005. "The relationship between stock returns and volatility in international stock markets," Journal of Empirical Finance, Elsevier, vol. 12(5), pages 650-665, December.
    6. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    7. Paul Harrison & Harold H. Zhang, 1999. "An Investigation Of The Risk And Return Relation At Long Horizons," The Review of Economics and Statistics, MIT Press, vol. 81(3), pages 399-408, August.
    8. Guo, Hui & Neely, Christopher J., 2008. "Investigating the intertemporal risk-return relation in international stock markets with the component GARCH model," Economics Letters, Elsevier, vol. 99(2), pages 371-374, May.
    9. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    10. Hui Guo & Robert F. Whitelaw, 2006. "Uncovering the Risk–Return Relation in the Stock Market," Journal of Finance, American Finance Association, vol. 61(3), pages 1433-1463, June.
    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. 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.
    13. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521424318.
    14. Hahn, Jaehoon & Lee, Hangyong, 2006. "Yield Spreads as Alternative Risk Factors for Size and Book-to-Market," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 41(2), pages 245-269, June.
    15. Canina, Linda & Figlewski, Stephen, 1993. "The Informational Content of Implied Volatility," The Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 659-681.
    16. Baillie, Richard T. & DeGennaro, Ramon P., 1990. "Stock Returns and Volatility," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(2), pages 203-214, June.
    17. Rabemananjara, R & Zakoian, J M, 1993. "Threshold Arch Models and Asymmetries in Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 31-49, Jan.-Marc.
    18. Harvey, Campbell R, 1991. "The World Price of Covariance Risk," Journal of Finance, American Finance Association, vol. 46(1), pages 111-157, March.
    19. 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.
    20. Campbell, John Y., 1987. "Stock returns and the term structure," Journal of Financial Economics, Elsevier, vol. 18(2), pages 373-399, June.
    21. 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.
    22. Blair, Bevan J. & Poon, Ser-Huang & Taylor, Stephen J., 2001. "Forecasting S&P 100 volatility: the incremental information content of implied volatilities and high-frequency index returns," Journal of Econometrics, Elsevier, vol. 105(1), pages 5-26, November.
    23. Banerjee, Prithviraj S. & Doran, James S. & Peterson, David R., 2007. "Implied volatility and future portfolio returns," Journal of Banking & Finance, Elsevier, vol. 31(10), pages 3183-3199, October.
    24. Konstantinidi, Eirini & Skiadopoulos, George & Tzagkaraki, Emilia, 2008. "Can the evolution of implied volatility be forecasted? Evidence from European and US implied volatility indices," Journal of Banking & Finance, Elsevier, vol. 32(11), pages 2401-2411, November.
    25. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    26. Lundblad, Christian, 2007. "The risk return tradeoff in the long run: 1836-2003," Journal of Financial Economics, Elsevier, vol. 85(1), pages 123-150, July.
    27. Lin Peng & Turan G. Bali, 2006. "Is there a risk-return trade-off? Evidence from high-frequency data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(8), pages 1169-1198.
    28. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, vol. 50(2), pages 125-150, November.
    29. Amit Goyal & Pedro Santa-Clara, 2003. "Idiosyncratic Risk Matters!," Journal of Finance, American Finance Association, vol. 58(3), pages 975-1008, June.
    30. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521370905.
    31. Kalev, Petko S. & Liu, Wai-Man & Pham, Peter K. & Jarnecic, Elvis, 2004. "Public information arrival and volatility of intraday stock returns," Journal of Banking & Finance, Elsevier, vol. 28(6), pages 1441-1467, June.
    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. Anupam Dutta & Elie Bouri & David Roubaud, 2021. "Modelling the volatility of crude oil returns: Jumps and volatility forecasts," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(1), pages 889-897, January.
    2. Dutta, Anupam & Bouri, Elie & Saeed, Tareq, 2021. "News-based equity market uncertainty and crude oil volatility," Energy, Elsevier, vol. 222(C).
    3. Singh, Mahendra Kumar & Lence, Sergio H., 2023. "Market Stress in Agricultural Markets: Can Alternative Implied Volatility Measures Predict It?," 2023 Annual Meeting, July 23-25, Washington D.C. 335789, Agricultural and Applied Economics Association.
    4. Chang, C-L. & Hsieh, T-L. & McAleer, M.J., 2016. "How are VIX and Stock Index ETF Related?," Econometric Institute Research Papers EI2016-07, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. Suzanne G. M. Fifield & David G. McMillan & Fiona J. McMillan, 2020. "Is there a risk and return relation?," The European Journal of Finance, Taylor & Francis Journals, vol. 26(11), pages 1075-1101, July.
    6. Nkwoma John Inekwe, 2016. "Financial uncertainty, risk aversion and monetary policy," Empirical Economics, Springer, vol. 51(3), pages 939-961, November.
    7. Liu, Jingzhen, 2019. "Impacts of lagged returns on the risk-return relationship of Chinese aggregate stock market: Evidence from different data frequencies," Research in International Business and Finance, Elsevier, vol. 48(C), pages 243-257.
    8. Chia-Lin Chang & Tai-Lin Hsieh & Michael McAleer, 2016. "Connecting VIX and Stock Index ETF," Tinbergen Institute Discussion Papers 16-010/III, Tinbergen Institute, revised 23 Jan 2017.
    9. Chia-Lin Chang & Tai-Lin Hsieh & Michael McAleer, 2018. "Connecting VIX and Stock Index ETF with VAR and Diagonal BEKK," JRFM, MDPI, vol. 11(4), pages 1-25, September.
    10. Patrizia Perras & Niklas Wagner, 2020. "On the pricing of overnight market risk," Empirical Economics, Springer, vol. 59(3), pages 1307-1327, September.
    11. Just, Małgorzata & Echaust, Krzysztof, 2020. "Stock market returns, volatility, correlation and liquidity during the COVID-19 crisis: Evidence from the Markov switching approach," Finance Research Letters, Elsevier, vol. 37(C).
    12. John Nkwoma Inekwe, 2020. "Market uncertainty, risk aversion, and macroeconomic expectations," Empirical Economics, Springer, vol. 59(4), pages 1977-1995, October.
    13. Mollick, André Varella & Sakaki, Hamid, 2019. "Exchange rates, oil prices and world stock returns," Resources Policy, Elsevier, vol. 61(C), pages 585-602.
    14. Nektarios Aslanidis & Charlotte Christiansen & Christos S. Savva, 2021. "Quantile Risk–Return Trade-Off," JRFM, MDPI, vol. 14(6), pages 1-14, June.

    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. Kanas, Angelos, 2012. "Modelling the risk–return relation for the S&P 100: The role of VIX," Economic Modelling, Elsevier, vol. 29(3), pages 795-809.
    2. Salvador, Enrique & Floros, Christos & Arago, Vicent, 2014. "Re-examining the risk–return relationship in Europe: Linear or non-linear trade-off?," Journal of Empirical Finance, Elsevier, vol. 28(C), pages 60-77.
    3. Wu, Shue-Jen & Lee, Wei-Ming, 2015. "Intertemporal risk–return relationships in bull and bear markets," International Review of Economics & Finance, Elsevier, vol. 38(C), pages 308-325.
    4. 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.
    5. Chiang, Thomas C. & Li, Huimin & Zheng, Dazhi, 2015. "The intertemporal risk-return relationship: Evidence from international markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 39(C), pages 156-180.
    6. Bali, Turan G., 2008. "The intertemporal relation between expected returns and risk," Journal of Financial Economics, Elsevier, vol. 87(1), pages 101-131, January.
    7. Chiang, Thomas C., 2019. "Empirical analysis of intertemporal relations between downside risks and expected returns—Evidence from Asian markets," Research in International Business and Finance, Elsevier, vol. 47(C), pages 264-278.
    8. Thomas C. Chiang & Jiandong Li, 2012. "Stock Returns and Risk: Evidence from Quantile," JRFM, MDPI, vol. 5(1), pages 1-39, December.
    9. 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.
    10. Kim, Eung-Bin & Byun, Suk-Joon, 2021. "Risk, ambiguity, and equity premium: International evidence," International Review of Economics & Finance, Elsevier, vol. 76(C), pages 321-335.
    11. Hui Guo & Robert F. Whitelaw, 2006. "Uncovering the Risk–Return Relation in the Stock Market," Journal of Finance, American Finance Association, vol. 61(3), pages 1433-1463, June.
    12. Bali, Turan G. & Engle, Robert F., 2010. "The intertemporal capital asset pricing model with dynamic conditional correlations," Journal of Monetary Economics, Elsevier, vol. 57(4), pages 377-390, May.
    13. Jin, Xiaoye, 2017. "Time-varying return-volatility relation in international stock markets," International Review of Economics & Finance, Elsevier, vol. 51(C), pages 157-173.
    14. Jiranyakul, Komain, 2011. "On the Risk-Return Tradeoff in the Stock Exchange of Thailand: New Evidence," MPRA Paper 45583, University Library of Munich, Germany.
    15. Lundblad, Christian, 2007. "The risk return tradeoff in the long run: 1836-2003," Journal of Financial Economics, Elsevier, vol. 85(1), pages 123-150, July.
    16. Bali, Turan G. & Cakici, Nusret & Chabi-Yo, Fousseni, 2015. "A new approach to measuring riskiness in the equity market: Implications for the risk premium," Journal of Banking & Finance, Elsevier, vol. 57(C), pages 101-117.
    17. Keunbae Ahn, 2021. "Predictable Fluctuations in the Cross-Section and Time-Series of Asset Prices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2021.
    18. Angelos Kanas, 2014. "Uncovering a positive risk-return relation: the role of implied volatility index," Review of Quantitative Finance and Accounting, Springer, vol. 42(1), pages 159-170, January.
    19. Bai, Jennie & Bali, Turan G. & Wen, Quan, 2021. "Is there a risk-return tradeoff in the corporate bond market? Time-series and cross-sectional evidence," Journal of Financial Economics, Elsevier, vol. 142(3), pages 1017-1037.
    20. 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.

    More about this item

    Keywords

    S&P 500; VIX; GARCH-M; Risk-return relation; Predictive ability; G12; C22;
    All these keywords.

    JEL classification:

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

    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:spr:empeco:v:44:y:2013:i:3:p:1291-1314. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.