Robert Engle’s FT lectures on volatility, part 2

The most common way to measure volatility is to measure standard deviation over smaller periods of time—a week or a month. These measures of volatility are known as historical volatility. The problem is that if you use a short series you get a very noisy measure, and if you use a long series it’s so smooth that it doesn’t respond well to new information. So, as an alternative to historical volatility you can use ARCH: autoregressive conditional heteroskedasticity. ARCH is a very simple concept, but Engle got the Nobel Prize in 2003 for inventing this model.

ARCH uses a big window but weighted averages. That is, we’ll give more weight to recent information, less to those that happened a long time ago. You can estimate these weights using an econometric model.

In yellow is the 5-day moving average of the standard deviations. In red is the one-year standard deviation, and the green is a five-year standard deviation. If you give the same information to a GARCH program (generalized autoregressive conditional heteroskedasticity) such as MatLab it will calculate the best set of weights.

Another way to look at the same output is in terms of a confidence interval. Each day you can ask “How high or low do I expect the market to go?”

The GARCH bands are time-varying confidence intervals. For instance, at any one point in time you can say with confidence that the market isn’t going to be higher than the blue band or lower than the green band. 

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For the transcript of the original presentation go to the FT Business School - NYU Stern School of Business site.