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Realized Daily Variance of S&P 500 Cash Index: A Revaluation of Stylized Facts

Author

Listed:
  • Shirley J. Huang

    (Lee Kong Chian School of Business, Singapore Management University)

  • Qianqiu Liu

    (College of Business Administration, University of Hawaii)

  • Jun Yu

    (School of Economics and Social Sciences, Singapore Management University)

Abstract

In this paper the realized daily variance is obtained from intraday transaction prices of the S&P 500 cash index over the period from January 1993 to December 2004. When constructing realized daily variance, market microstructure noise is taken into account using a technique proposed by Zhang, Mykland and Ait-Sahalia (2005). The time series properties of realized daily variance are compared with those of variance estimates obtained from parametric GARCH and stochastic volatility models. Unconditional and dynamic properties concerning the realized daily variance are examined, the relationship between realized variance and returns is investigated, and the stylized facts concerning realized daily variance are reevaluated with this long dataset. While many properties are similar to what have been reported based on artificially constructed five-minute returns, three distinct results stand out in our empirical analysis. First, we find evidence that both the realized standard deviation and the realized log variance are not covariance stationary, but nonetheless have memory parameter less than unity. Second, we document a positive and statistically significant risk-return trade-off. Finally, we find a monotonically decreasing news impact function.

Suggested Citation

  • Shirley J. Huang & Qianqiu Liu & Jun Yu, 2007. "Realized Daily Variance of S&P 500 Cash Index: A Revaluation of Stylized Facts," Annals of Economics and Finance, Society for AEF, vol. 8(1), pages 33-56, May.
  • Handle: RePEc:cuf:journl:y:2007:v:8:i:1:p:33-56
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    References listed on IDEAS

    as
    1. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    2. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    3. Daniel B. Nelson, 1994. "Asymptotic Filtering Theory for Multivariate ARCH Models," NBER Technical Working Papers 0162, National Bureau of Economic Research, Inc.
    4. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    5. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-417, October.
    6. repec:bla:restud:v:65:y:1998:i:3:p:361-93 is not listed on IDEAS
    7. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
    8. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
    9. Peter C. B. Phillips, 2005. "Jackknifing Bond Option Prices," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 707-742.
    10. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, pages 307-327.
    11. Robert F. Engle & Joshua Rosenberg, 1994. "Hedging Options in a GARCH Environment: Testing the Term Structure of Stochastic Volatility Models," NBER Working Papers 4958, National Bureau of Economic Research, Inc.
    12. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2005. "There is a risk-return trade-off after all," Journal of Financial Economics, Elsevier, pages 509-548.
    13. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    14. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
    15. Aït-Sahalia, Yacine & Mykland, Per A. & Zhang, Lan, 2011. "Ultra high frequency volatility estimation with dependent microstructure noise," Journal of Econometrics, Elsevier, pages 160-175.
    16. Renate Meyer & Jun Yu, 2000. "BUGS for a Bayesian analysis of stochastic volatility models," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 198-215.
    17. Yacine Aït-Sahalia, 2005. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 351-416.
    18. Engle, Robert F & Ng, Victor K, 1993. " Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    19. Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January.
    20. Berg, Andreas & Meyer, Renate & Yu, Jun, 2004. "Deviance Information Criterion for Comparing Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 107-120, January.
    21. Ronald J. Mahieu & Peter C. Schotman, 1998. "An empirical application of stochastic volatility models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(4), pages 333-360.
    22. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201.
    23. Daniel B. Nelson, 1994. "Asymptotically Optimal Smoothing with ARCH Models," NBER Technical Working Papers 0161, National Bureau of Economic Research, Inc.
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    Citations

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    Cited by:

    1. Symeonidis, Lazaros & Daskalakis, George & Markellos, Raphael N., 2010. "Does the weather affect stock market volatility?," Finance Research Letters, Elsevier, vol. 7(4), pages 214-223, December.

    More about this item

    Keywords

    High frequency data; Integrated variance; Microstructure noise; GARCH; Stochastic volatility; Long range dependence; Intertemporal CAPM;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General

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