## Understanding Volatility (the Vix)

Stock prices go up and down every day; volatility is an attempt to measure how much prices vary. In this article I explain the VIX

, a specific measure of market volatility. But first I will briefly review a little statistical theory (defining volatility) and then I address the specifics of the VIX (readers who understand the concecpt of standard deviation can skip the next two paragraphs).

Very brief review of statistics: Statisticians view data such as the change in stock prices as random numbers being generated by a statistical process such as an urn filled with balls with different stock returns (-7%, +9% and so on). A statistician can summarize a distribution with two measures

, the mean, or average change in stock prices and the standard deviation, which measures the spread of the data from the mean.

For the S&P 500, the average annual price change since 1928 is around 12% per year and the standard deviation is around 20%. Statistical theory tells us that roughly 2/3 of the time the price change will be within one standard deviations of the mean (or between -8% and +32%) and 95% of the time the price change will be within two standard deviations (or between -28% and +52%).

The VIX is called the market’s expectation of volatility over the next 30 days; the VIX is 100 times the standard deviation, so a VIX of 15 means that the market expects the standard deviation of the change in the S&P 500 should be 15%.

The details of the calculation of the VIX are beyond the scope of this site (see here)

, but the general idea is that volatility is an important determinant of the price of options to buy and sell the S&P 500, and by observing the prices of options one can infer the market’s estimate of volatility.

Options are the right to buy (or sell) something at a specific price in the future; for example, an S&P 500 1000 November call option allows the person who owns the option to buy the S&P 500 index at a price of 1000 in November. As I write, the S&P 500 is trading around 910; it does not take much complicated mathematics to see that the volatility of the S&P 500 will affect the value of the option. If the S&P 500 is unlikely to rise more than 10 or 20 points

, then there is little chance the price will be over 1000 and the option will most likely expire worthless, and the price will be very low; if the S&P 500 is very volatile, then there is a chance that the index will be, say, 1100, and the option to buy the index at 1000 will have significant value.

In general, if the market expects the S&P 500 to be volatile then the VIX will be high. Below is a chart of the VIX from the CBOE (CBOE VIX charts are available here). You can see that the VIX was mostly between 10 and 30

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, with occasional spikes to around 40 during periods of great turmoil.

Below you can see a chart of the VIX during 2008. During the financial crisis of the last few weeks the VIX reached levels of 60 or higher, as markets became more volatile than they had been in the past 20 years. Stock prices have been incredibly volatile in recent weeks, with markets swinging several percent every few hours.

One way to know how long the market expects the high VIX to last is to look at the price of VIX futures

, that is what the market expects the VIX to be in future months. As I write (October 23, 2008), the price of the VIX is 65.65, but the price of the November VIX is 47.81, the December VIX is 39.05 and the January VIX is 37.02. This means that the market expects the VIX to drop sharply in coming months but it expects that the VIX will still remain well above the average level of the 1990s for several months. Prices of VIX futures (delayed 15 minutes) are available here.