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Dr. Alex Castaldo

11/08/05
Review: Predicting volatility using intraday data (Forsberg and Ghysels)

"Why do absolute returns predict volatility so well?" by L. Forsberg and E. Ghysels, August 2004

The problem studied is the prediction of volatility of S&P500 for the next 1 day, 1 week, 2, 3 and 4 weeks using intraday data (specifically 5 minute returns). After a theoretical and empirical analysis of several alternatives, the authors come to the following conclusions:

1. As dependent variable it is best to use ln(RV) i.e., the log of the Realized Variance. This outperforms both the RV itself as well as sqrt(RV) i.e., the volatility. This idea of using a logarithmic transformation had been suggested before. The authors show that even if one is ultimately interested in volatility, it is advantageous to run the regression in terms of logs, make the forecast and then transform back to a vol.
2. As independent variables it is best notto use RV or a transformation thereof and instead use RAV or Realized Absolute Values. Recall that RV over a period (such as 1 day) is the sum of the squared returns over the subperiods (i.e., 5 minutes). RAV on the other hand is the sum of absolute values of the returns. The RAV are better behaved statistically (less sampling error) and more appropriate to use when the stochastic process for prices includes jumps, the authors show. This result is somewhat counterintuitive: since we are trying to predict RV, it would seem reasonable to use past RVs on the right side of the equation as well; but the authors show otherwise.
3. A reasonable specification is the so-called HAR (Heterogenous autoregressive) model of Corsi (2003):

ln(RV_future) = b0 + bd*RAV_today +bw*RAV_week + bm*RAV_four_weeks

where the coefficients b0, bd, bw, bm are estimated by regression. The three independent variables are the RAV's of today, of the past week (5 trading days) and the last month (actually the last 20 trading days, for simplicity). This model gave reasonable results in an out of sample test (the model was estimated for 1985 to 2001 and tested from January 2, 2002 to October 29, 2003). It was superior or comparable to any other model the authors tried.

Yesterday I spoke with a hedge fund manager who tried to impress me with a description of his very fancy proprietary econometric techniques for estimating vol. But I wonder if they are truly superior to published, well documented approaches like this one.

Alessandro Castaldo, CFA, is a researcher and trader for Manchester Trading. Dr. Castaldo wrote his PhD dissertation on stock market volatility at the City University of New York, and taught courses in finance and options to undergraduates at Baruch College (CUNY) from 1998-2001. He has been associated with Circle T Partners, LP, a \$400 million equity hedge fund; and Willowbridge Associates, a \$1 billion-plus commodities trading adviser, where his responsibilities included the ongoing refinement of a market-neutral statistically based ("stat-arb") stock selection model.  Dr. Castaldo holds a B.S. in electrical engineering/computer science and an M.S. in management from the Massachusetts Institute of Technology, and worked as a software engineer at SEI Corporation/TMI Systems, Software Research Corp. and Systems Constructs Inc. before entering the finance profession.

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