__Forecasting Volatility using GARCH for the SPY__

Most traders and investors spend the majority of their time trying to forecast the direction of a stock or the market in general. Many seasoned option professionals don’t bother predicting market direction, but instead use market neutral or ‘delta’ neutral strategies and try to forecast volatility instead. There are different types of volatility; we are going to focus on implied volatility and statistical volatility. Implied volatility is the volatility priced into an option and derived from an option pricing model. Statistical volatility is the actual volatility of the underlying investment. With the different types of volatility, you may find yourself wondering how and why one should have a forecast of future historical or implied volatility. Followers of the buy and hold “random walk” theory know that the market has a strong upside bias over long time periods and will buy low cost index funds and hold them indefinitely. Most investors will buy a stock thinking that over time it will appreciate in price and maybe pay some nice dividends along the way. Technical analysts will devote time to studying charts, looking at things like moving averages, stochastics and other indicators to attempt to forecast a future price or at least the direction of the price in the future. Fundamental analysts will study earnings reports, the trend of the reported earnings and use things like PE multiples and book values to determine the future value of a stock. Traders and investors devote the vast majority of their analytical efforts in studying company reports or charts of past price action to determine the future price of a stock or index. So why would anyone be interested in forecasting the future volatility of a stock?

The first reason is that the volatility of a stock or index generally has an inverse relationship to its price. That is because prices have a tendency to fall faster than they rise. So, if the volatility is increasing, the price is usually declining and if the volatility is falling, the price is generally rising. So, if we could forecast volatility accurately, that would also tell us something about the likely future direction of the stock. There is a great deal of statistical evidence that stock prices do follow a random walk. In other words the current price reflects all of the known information about the company and there is no correlation between past prices and prices in the future.

The second reason is because volatility can be possible to forecast. When analyzing volatility we do find that there is a serial correlation between returns. Volatility has a tendency to manifest itself in clusters. If you look at a chart of price of a stock it goes up or down and may show signs of trending predominately in one direction or another, but the price movements are random. If you study a chart of the volatility of a stock you’ll immediately notice that there are distinct periods of high and low volatility and that the periods of high volatility are followed by periods of lower volatility and that the periods of low volatility are interrupted by high volatility periods. There’s a simple reason for the clustering of volatility. In the absence of significant news a stock may quietly drift higher for a long period of time. If some news like a potential lawsuit, a product recall, or a new product announcement by a competitor comes out, the stock may sell off quite rapidly until the news is fully digested by the investing public. These short term sell offs can be considered to be buying opportunities for investors wishing to accumulate shares of the stock. When we chart the volatility of the stock these news events will show brief spikes in the volatility that typically persist for short periods of time, then return to normal. At times like this the future price direction may not be simple to forecast, but the volatility can be because it is a very good assumption that the volatility will eventually revert to the mean or return to a more normal level. The tactical option investor will utilize periods of high volatility to produce more income or do some share accumulation.

Serious academics have devoted thousands of hours researching volatility. There is a wealth of information available on the internet. GARCH (Generalized Auto-Regressive Conditional Heteroskcedasticity) models and variants of the GARCH model seem to produce the best results. Traders and investors don’t have to have PHD’s in mathematics to learn how to apply volatility forecasting. There’s software available to run the calculations and all the investor needs is an understanding of how to apply the forecasting mathematics to their trading methods.

Below is a table as of Friday January 6

^{th}, 2012 for the SPY that show various volatility forecasts from different variations of GARCH. It is interesting to note that all of the long term forecasts are currently predicting rising volatility for the future.

__SPY__

__CURRENT__

__1 WEEK__

__1 MONTH__

__6 MONTHS__

__1 YEAR__GARCH 18.06 18.09 18.20 18.77 19.18

AGARCH 17.75 18.10 19.20 22.75 23.95

EGARCH 15.49 15.57 15.86 16.94 17.37

APARCH 15.22 15.37 15.87 17.96 18.92

GJRGARCH 15.28 15.32 15.45 16.03 16.33

**Disclosure:**I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.