Tracy Alloway points us to another fun indicator:
GP on your Bloomberg.
You’ll get a chart that looks like this:
It’s the CBOE’s S&P 500 Implied Correlation Index — based on options expiring in January 2011. It’s a basic measure of the correlation of stocks within the S&P 500, and you can see that it’s been approaching the end of day record it hit back in July.
Unfortunately, I do not have a Bloomberg terminal. But my Goog-Fu is strong, so I bring you the free version:
The basic idea is this. According to the standard Black-Scholes options pricing model, option prices depend on the “volatility” of the underlying asset’s price. By examining option prices and then inverting the Black-Scholes formula, you can infer the market’s estimate of the volatility of the underlying. This is called the “implied volatility”.
Now, options trade not only on individual stocks, but also on indices. (You may have heard of the VIX). Since an index is just a basket of stocks, there should be some relationship between the volatility implied by an option on an index and the volatilities implied by options on the stocks in the index.
And there is. For example, suppose you have two stocks with equal volatilities and you construct a portfolio containing those two stocks in equal weight. Then the volatility of the portfolio — aka. “the standard deviation of the average of two random variables” — will be 1/sqrt(2) times the volatility of either stock.
…if the stocks are totally uncorrelated, that is. If instead the stocks are perfectly correlated — i.e., they move together exactly all the time — then the volatility of the portfolio will obviously be identical to the volatility of either stock. And if, say, the stocks are perfectly anti-correlated — i.e., they move exactly opposite to each other all the time — then the volatility of the portfolio will obviously be zero, since the portfolio’s value will never change.
In other words, by examining the implied volatility of an index and comparing it to the implied volatility of the stocks in the index, we can deduce the market’s implied correlation for the stocks in the index. The math for more than two stocks and unequal weights is a little more complicated, but should be familiar if you ever took an undergraduate class in statistics; see the white paper for details.
(The correlation between two random variables is quantified by their “correlation coefficient”. Perfectly correlated variables have a correlation coefficient of 1; perfectly anti-correlated, -1; totally uncorrelated, 0. This index calculates the implied average correlation coefficient for the S&P 500.)
One caveat: The CBOE implied correlation index only examines the implied volatility of the top 50 stocks in the S&P 500. From the white paper:
On May 29, 2009, the total capitalization of the 50-stock basket was $4.15 trillion. The weight of Exxon Mobil Corp (XOM), the largest component in the 50-stock basket, was 8.3% ($343 billion / $4.15 trillion), compared to 4.3% in the S&P 500 Index.
Which is a convoluted way of saying the top 50 stocks represent 4.3/8.3 = 52% of the market cap of the entire S&P 500. If for some reason the correlation of those stocks is not representative of all of the stocks in the index, the implied correlation calculation could give the wrong answer. (I have not yet tried to quantify this. Maybe later.)
Summary: This indicator provides the market’s expectation for the correlation of S&P 500 stocks between now and Jan 2011. And it has been spiking recently, which means the market is expecting everything to move together, one way or another…
She was always using the word “infer”
When she obviously meant “imply”
And I know some guys would put up with that kind of thing
But frankly, I can’t imagine why
– W.A. Yankovic