S&P 500 – VIX Correlation And Selection Bias

An interesting article in Zero Hedge yesterday referred to a positive correlation between S&P 500 and VIX and pointed to several instances in the past when this signaled a major top or a large correction. Does this pattern have any significance?

This is what Zero hedge wrote:

The correlation between S&P and VIX is now +0.25 – the highest since 1998.

There was no mention whether the correlation was computed based on prices levels or returns and also of the number of days used in the computation. I had to try several alternatives and finally I think I came close to the results of the article after using price level correlation in a 30-day period rolling window. Below are the result:

In may be seen from the above chart that the 0-lag, 30-day correlation of S&P 500 and VIX price levels spiked above +0.25 before the 1998 correction, the 2000 top, the 2007 top and before the 2011 correction.

However, the correlation also spiked above +0.25 last March and in numerous occasions before 1998 and along the 1990s uptrend that were not shown on the Zero Hedge chart.

How significant are these signals?

Given that they are based on price level correlations they are quite ambiguous to start with. It is known that price levels overstate correlations and that there is high probability that two random walks have high correlation but the returns show no correlation.

Are these correlation patterns a result of data-mining? 

Probably they are. If one tries many different correlation periods, then one value may confirm some bias. For example, if the correlation period is increased to 120, the effect not only disappears but it seems that values of the correlation greater than +0.2 indicate a bear market bottom or a continuation of a bull market, as shown below.

There is selection bias involved when one chooses just a particular level of the correlation that supports a specific view without considering results for other values. I would be impressed if the 60-day correlation  between S&P 500 and VIX returns turned positive. This has not happened since VIX inception and may never happen but the 20-day price level correlation is more of a random pattern in my opinion.

Zero hedge article

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