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Clarifying Correlation


When investors become concerned with systematic risk, correlation starts to rise between stocks.

Yesterday I made some comments about the correlation between stocks and the implication it brings to volatility and possible direction. It all has to do with sentiment. Scott describes the ebbs and flows of the market in terms of the amount of risk investors are willing to take. It's the same thing.

The accompanying chart shows the implied correlation (the square of the correlation coefficient) of all S&P 500 (SPX) stocks against the price of the SPX over the last few years.

To understand correlation, pretend the SPX had only two stocks in it. If one stock goes up exactly as much as another goes down, the correlation number will be near zero and will imply a very low volatility for the index (one stock up, one stock down, index unchanged). Conversely, if both stocks move in the same direction, the correlation number would be near 1 (1998 it got as high as 0.98) and it would imply a very high volatility for the index (both stocks down index down). When we calculate the correlation between many stocks, we normalize all this and measure the cross-correlation.

When investors become concerned with systematic risk (macro risk not associated with an individual stock, but the market itself) correlation starts to rise between stocks. This makes intuitive sense: a holder of Johnson & Johnson (JNJ) stock sees nothing wrong with the company itself, but begins to worry it will go down with the rest of the market because of some extraneous factor (which could be as simple as the desire to reduce risk). The investor begins to sell JNJ just because the market is going down. The investor is reducing risk as the rest of the market does. It then makes sense why correlation increases usually when markets are going down. This is what happened in 1998.

When markets begin to rise, perceived systematic risk is declining. At first, all stocks may rise together and correlation can stay high for some time, but eventually correlation begins to break down as investors discriminate between the valuation of stocks as they rise (no one is really concerned about valuation when stocks are going down (except savvy insiders who actually increase their risk when others are decreasing it).

So let's look at this chart. Nothing is perfect, but the probabilities of movements do increase and decrease based on volatility and correlation because both are measures of the risk investors want to take.

Notice when implied correlation (and by definition volatility) is very low, it is normally after a rally when investors are discriminating between stocks and the risk they are taking is therefore high. They are not worried about systematic risk at all. This leaves them exposed. As the market begins to decline, correlation and volatility rise. There may or may not be any other reason than risk is being reduced. At market lows the opposite is occurring: correlation is very high because worry is very high about systematic risk and no one is discriminating between "good" stocks and "bad" ones. One reason correlation will increase is that these investors usually buy index puts as the market declines. This forces increased correlation: the sellers of index puts sell futures and the buyers of futures sell stocks indiscriminately.

These two statistics, correlation and volatility, are mostly set up high probabilities at extremes, as they are now. Low correlation, low volatility indicates complacency while high correlation, high volatility indicates fear. The unwind of both of these tend to drive things in the other direction.
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Position in JNJ, SPX

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