## Friday, October 1, 2010

### Robert Engle’s FT lectures on volatility, part 4: long run risk

When we are measuring volatility using the GARCH model we’re using high frequency data. This measures only short-term volatility—over the next few days, for instance. The options market, using implied volatility, estimates volatility over various time horizons.

The two-year volatility measured in red versus the one-month volatility measured in blue oscillate—sometimes short-term volatility is predicted to be higher than long-term volatility, sometimes lower.

The above graph shows the period between 2004 and 2005. Here the long-horizon volatility in red is much higher than short-horizon volatility. This disparity is even more pronounced if you look at longer-term options which are traded only OTC.

What is the implication of having long-run volatility so much higher than short-run volatility? For one thing, the sophisticated investor is not going to put money into the market under these conditions because the odds of losing money in a higher volatility environment are greater.