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The Cross-Sectional Intrinsic Entropy. A Comprehensive Stock Market Volatility Estimator

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  • Claudiu Vinte
  • Marcel Ausloos

Abstract

To take into account the temporal dimension of uncertainty in stock markets, this paper introduces a cross-sectional estimation of stock market volatility based on the intrinsic entropy model. The proposed cross-sectional intrinsic entropy (CSIE) is defined and computed as a daily volatility estimate for the entire market, grounded on the daily traded prices: open, high, low, and close prices (OHLC), along with the daily traded volume for all symbols listed on The New York Stock Exchange (NYSE) and The National Association of Securities Dealers Automated Quotations (NASDAQ). We perform a comparative analysis between the time series obtained from the CSIE and the historical volatility as provided by the estimators: close-to-close, Parkinson, Garman-Klass, Rogers-Satchell, Yang-Zhang, and intrinsic entropy (IE), defined and computed from historical OHLC daily prices of the Standard & Poor's 500 index (S&P500), Dow Jones Industrial Average (DJIA), and the NASDAQ Composite index, respectively, for various time intervals. Our study uses approximately 6000 day reference points, starting on 1 Jan. 2001, until 23 Jan. 2022, for both the NYSE and the NASDAQ. We found that the CSIE market volatility estimator is consistently at least 10 times more sensitive to market changes, compared to the volatility estimate captured through the market indices. Furthermore, beta values confirm a consistently lower volatility risk for market indices overall, between 50% and 90% lower, compared to the volatility risk of the entire market in various time intervals and rolling windows.

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  • Claudiu Vinte & Marcel Ausloos, 2022. "The Cross-Sectional Intrinsic Entropy. A Comprehensive Stock Market Volatility Estimator," Papers 2205.00104, arXiv.org.
    • Handle: RePEc:arx:papers:2205.00104
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    References listed on IDEAS

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    1. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    2. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January.
    3. John Y. Campbell & Martin Lettau & Burton G. Malkiel & Yexiao Xu, 2001. "Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk," Journal of Finance, American Finance Association, vol. 56(1), pages 1-43, February.
    4. Garman, Mark B & Klass, Michael J, 1980. "On the Estimation of Security Price Volatilities from Historical Data," The Journal of Business, University of Chicago Press, vol. 53(1), pages 67-78, January.
    5. Ang, Andrew & Hodrick, Robert J. & Xing, Yuhang & Zhang, Xiaoyan, 2009. "High idiosyncratic volatility and low returns: International and further U.S. evidence," Journal of Financial Economics, Elsevier, vol. 91(1), pages 1-23, January.
    6. Yang, Dennis & Zhang, Qiang, 2000. "Drift-Independent Volatility Estimation Based on High, Low, Open, and Close Prices," The Journal of Business, University of Chicago Press, vol. 73(3), pages 477-491, July.
    7. 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.
    8. Zhanhui Chen & Ralitsa Petkova, 2012. "Does Idiosyncratic Volatility Proxy for Risk Exposure?," The Review of Financial Studies, Society for Financial Studies, vol. 25(9), pages 2745-2787.
    9. Aabo, Tom & Pantzalis, Christos & Park, Jung Chul, 2017. "Idiosyncratic volatility: An indicator of noise trading?," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 136-151.
    10. Pietro Coretto & Michele La Rocca & Giuseppe Storti, 2020. "Improving Many Volatility Forecasts Using Cross-Sectional Volatility Clusters," JRFM, MDPI, vol. 13(4), pages 1-23, March.
    11. Fama, Eugene F, 1990. "Stock Returns, Expected Returns, and Real Activity," Journal of Finance, American Finance Association, vol. 45(4), pages 1089-1108, September.
    12. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    13. Sanjay Sehgal & Vidisha Garg, 2016. "Cross-sectional Volatility and Stock Returns: Evidence for Emerging Markets," Vikalpa: The Journal for Decision Makers, , vol. 41(3), pages 234-246, September.
    14. Byun, Sung Je, 2016. "The usefulness of cross-sectional dispersion for forecasting aggregate stock price volatility," Journal of Empirical Finance, Elsevier, vol. 36(C), pages 162-180.
    15. William Day & Herbert Edelsbrunner, 1984. "Efficient algorithms for agglomerative hierarchical clustering methods," Journal of Classification, Springer;The Classification Society, vol. 1(1), pages 7-24, December.
    16. Barinov, Alexander, 2012. "Aggregate volatility risk: Explaining the small growth anomaly and the new issues puzzle," Journal of Corporate Finance, Elsevier, vol. 18(4), pages 763-781.
    17. Tarnopolski, Mariusz, 2016. "On the relationship between the Hurst exponent, the ratio of the mean square successive difference to the variance, and the number of turning points," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 662-673.
    18. Patro, Dilip K. & Qi, Min & Sun, Xian, 2013. "A simple indicator of systemic risk," Journal of Financial Stability, Elsevier, vol. 9(1), pages 105-116.
    19. González-Urteaga, Ana & Rubio, Gonzalo, 2016. "The cross-sectional variation of volatility risk premia," Journal of Financial Economics, Elsevier, vol. 119(2), pages 353-370.
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