Our New Volatility Laboratory

Recent turmoil in the financial markets has been accompanied by daily volatility reaching unprecedented levels. (The chart DJIA Volatility illustrates the daily point volatility for the DJIA estimated from a simple GARCH model. n.b. This chart was prepared during the day, so the "current" levels indicated numerically do not represent the "end of day" levels.)

The level of volatility enters into our trading strategy in several places. Firstly, if we are risk averse, then our asset price change forecasts must be weighed against a risk metric when we decide whether or not to trade. Most likely this risk metric will scale in some way with the level of volatility. If we do not dynamically alter our risk metric to take account of the current levels of volatility then we will fail to maintain the same risk/reward ratio (or signal-to-noise ratio) in volatilite times that we have in quiescent times. This will act to deteriorate the Sharpe Ratio of the trading strategy. To pick a guady metaphore, when one hears the noise of the waterfall ahead one should start to paddle less swiftly.

Secondly, if our forecasting procedure involves variables in lagged returns; or, cross-sectional dispersive measures; or, implied volatilities; or such like factors; then, our alpha itself will scale in some way with the level of volatility and so it itself will become larger in magnitude during volatile times.

Canonical "Modern Portfolio Theory" explicitly specifies that the ideal portfolio should be linear in the product of the inverse of the covariance matrix into the vector of forecasts. This quantity, whether expressed in price change space or return space or some other manner, is not dimensionless (it has the dimension of quantity/forecast e.g. contracts/dollar) and will therefore scale inversely with the level of volatility.

So theory often tells risk averse traders to take some account of volatility when making their trade decision. However, in practice I've often found it difficult to show the actual benefit of such considerations as an empirical reality. But one problem with econometric analysis of financial markets is that the data does not do a good job of exploring the available ranges of empirically important variables. Interest rates, for example, can stay in a similar range for years. This, as we see from the DJIA chart referenced above, is also true for volatility.

Now, in stark contrast, volatility has broken into a wholly new region of phase space. Now we can actually compare decisions made in times of radically high volatility with those made in more quiet times. Of course, this analysis still has a temporal bias --- for we only have one such region of high volatility and during that time the markets fell dramatically --- so we must maintain caution as to what we do with this dataset but, nevertheless, we have a new volatility laboratory to work in.