Equity Risk: Measuring Return Volatility Using Historical High-Frequency Data

Open access

Abstract

Market Volatility has been investigated at great lengths, but the measure of historical volatility, referred to as the relative volatility, is inconsistent. Using historical return data to calculate the volatility of a stock return provides a measure of the realized volatility. Realized volatility is often measured using some method of calculating a deviation from the mean of the returns for the stock price, the summation of squared returns, or the summation of absolute returns. We look to the stocks that make up the DJIA, using tick-by-tick data from June 2015 - May 2016. This research helps to address the question of what is the better measure of realized volatility? Several measures of volatility are used as proxies and are compared at four estimation time intervals. We review these measures to determine a closer/better fit estimator to the true realized volatility, using MSE, MAD, Diebold-Mariano test, and Pitman Closeness. We find that when using a standard deviation based on transaction level returns, shorter increments of time, while containing some levels of noise, are better estimates of volatility than longer increments.

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  • Anderson T. Bollerslev T. Diebold F. & Ebens H. (2001). The distribution of realized stock return volatility Journal of Financial Economics 61 43 – 76.

  • Anderson T. & Bollerslev T. (1998). Answering the skeptics: Yes standard volatility models do provide accurate forecasts* International Economic Review 39:(4) 885 – 905.

  • Barron O. (1995). Trading volume and belief revisions that differ among individual analysts The Accounting Review 70:4 581-597.

  • Christoffersen P. Diebold F.X. and Schuermann T. (1998). Horizon problems and extreme events in financial risk management. Economic Policy Review FRBNY.

  • Danielsson J. and Zigrand J.P. (2006). On time-scaling of risk and the square-root-of-time rule. Journal of Banking & Finance 30(10) 2701-2713.

  • Diebold F. and Mariano R. (1995). Comparing predictive accuracy Journal of Business & Economic Statistics 13(3) 253 – 263.

  • Ghysels E. and Sinko A. (2011). Volatility forecasting and microstructure noise Journal of Econometrics 160 257 – 271.

  • Hansen P.R. and Lunde A. (2005). A forecast comparison of volatility models: Does anything beat a GARCH (11)? Journal of Applied Econometrics 20 873 – 889.

  • Hsieh D. (1991). Chaos and nonlinear dynamics: Application to financial markets Journal of Finance 46 1839 – 1877.

  • Koopman S. Jungbacker B. and Hol E. (2005). Forecasting daily variability of the S&P 100 stock index using historical realized and implied volatility measurements. Journal of Empirical Finance 12 445 – 475.

  • Liu L. Patton A. & Sheppard K. (2015). Does anything beat 5-minute RV? A comparison of realized measures across multiple asset classes Journal of Econometrics 187 293 – 311.

  • Morgan J.P. (1996). RiskMetrics – Technical document fourth ed. Morgan Guaranty Company New York.

  • Ñíguez T.M. (2016). Evaluating monthly volatility forecasts using proxies at different frequencies Finance Research Letters 17 41 – 47.

  • Schwert G. (1989). Why does stock market volatility change over time? Journal of Finance 44 1115 – 1153.

  • Schwert G. (1990a). Stock volatility and the crash of ‘87 Review of Financial Studies 3 77 – 102.

  • Schwert. G. (1990b). Stock market volatility Financial Analysts Journal 46: 23 – 34.

  • Schwert G. & Seguin P. (1990). Heteroskedasticity in stock returns Journal of Finance 45 1129 – 1155.

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