Thursday, November 13, 2008

A look at volatility: Levels, Surprises, and History By Risk Metrics's Chris Finger

Doomed to Repeat it? Over at RiskMetrics, Chris Finger has examined the volatility of the US stock market for over one hundred years. While lacking any grand slam home runs, it is an interesting article for a number of reasons.

Short version:
It starts by breaking the time period into two periods (1940-1945, 1945 to present) and like other researchers the author shows that the volatility has in fact declined over time. Finger then makes forecasts of volatility and looks for surprise volatility events (that is when the forecast is off by a bunch). This is followed by an event study on volatility. True to form given the surprise definition the event study finds a "right angle" in increased volatility. And since volatility is not ever increasing, this spike in volatility declines back to the longer run average overtime. This may help to estimate the duration of current high volatility levels.

Some look-ins:
"the recent peak of 70% is extremely high, though lower than the spikes after the crashes in 1929 and 1987, when volatility jumped to 95% and almost 120%. Today’s level is comparable to what we saw in the early 1930s"
"With this large set of residuals...we choose a threshold, and compare how many residuals we actually see of this magnitude to what our assumed statistical distribution predicts. For instance, the t-distribution predicts that over the history in question (about 30,000 trading days), we should see between 29 and 49 days on which the market loss is a five-standard deviation event or greater; there are in fact 32 such days."
Because volatility had already been high (and high standard deviations of the residuals), this increase in volatility has not been that surprising since February 2007.
"Like these other crises, the current one seemed to have begun with a surprise—the 7.8-standard deviation loss in February 2007.....Since February 2007, however, despite all that has happened and the historic run-up in volatility, there have been no large surprises: the largest was the fall on September 29, 2008, the day the US Congress rejected the first bank bailout plan. This loss was one of the twenty largest ever, yet registered as only a 3.7-standard deviation event amid the already high volatility."
In other words, this increase in volatility has been more like a flood than a tsunami. It began raining in February 2007 has largely not stopped. While the author finds little evidence of similar patterns in the past [a very important fact given the difficulty/impossibility of forecasting off one data point], the one time this seemingly happened does not give great hope for a quick volatility decline:
"...volatility has risen in an orderly way, with no true surprises. The run-up in volatility in 1931 is the best example of this phenomenon, and in that case, volatility stayed elevated for quite a long time: it spent more sixteen months over 35%, during which time the index fell by 50%.
Good stuff. Go on and read the rest of it at RiskMetrics (and if you are in my class, be sure to note the figures too. A picture tells a thousand words and this may help you make sense of it quickly.)

No comments: