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

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  • 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
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    3. 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.
    4. 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.
    5. Zhang, Lei & Chen, Yan & Bouri, Elie, 2024. "Time-varying jump intensity and volatility forecasting of crude oil returns," Energy Economics, Elsevier, vol. 129(C).
    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. 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).
    10. 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.
    11. Nektarios Aslanidis & Charlotte Christiansen & Christos S. Savva, 2021. "Quantile Risk–Return Trade-Off," JRFM, MDPI, vol. 14(6), pages 1-14, June.
    12. 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.
    13. Patrizia Perras & Niklas Wagner, 2020. "On the pricing of overnight market risk," Empirical Economics, Springer, vol. 59(3), pages 1307-1327, September.
    14. John Nkwoma Inekwe, 2020. "Market uncertainty, risk aversion, and macroeconomic expectations," Empirical Economics, Springer, vol. 59(4), pages 1977-1995, October.
    15. Mollick, André Varella & Sakaki, Hamid, 2019. "Exchange rates, oil prices and world stock returns," Resources Policy, Elsevier, vol. 61(C), pages 585-602.

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    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

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