I thought that now would be a suitable time to take an aside and look at the long term volatility of major market indices. Many market participants use the term "volatility" to mean "large losses" and so, in current times, we are hearing the term frequently.

I use a simple GARCH model to forecast volatility for the Dow Jones Industrial Average. Although many professional money managers dismiss the Dow, I like to look at it because: a, it is what the media and public talk about when they talk about "the market;" and b, it is equal weighted rather than "cap. weighted" so it represents a more efficient variance reduction than cap. weighting (which over emphasizes the largest companies and so represents the economy and not the market).

The chart above shows the level, and volatility of the Dow, since 1995. The volatility model was fitted on data from 2000 to 2003 and is out-of-sample prior to 2000 and from 2003 to date. (For clarity of exposition, I'm presenting the volatility as a daily point volatility.) We see that the volatility has fallen precipitously from the extreme levels at the end of the prior year.

The innovations are well described by the generalized error distribution, and no severe shocks seem to have occurred since the beginning of 2007 (which was associated by the Jerome Kervial panic liquidation by Societe Generale).