# When the Inverse Correlation between the SPX and VIX breaks down

As we all know the S&P and its implied vol, the VIX, generally move in opposite direction. To a large extent, the correlations makes sense. IV is one of the main drivers of the price of options, going long options is also going long IV. When the market drops, option prices, adjusted for the drop in the the S&P price, experience a further appreciation, the extra appreciation o the options above and beyond the the price movement can be attributed to an increase in IV. My question is when IV(the VIX) and SPX correlation breakdown from its usual inverse relationship( corr=-.95), what do you think this implies about future returns? Why does these instances occur? There are many times when the correlations drops to 0 and becomes positive!

Below is a picture with the 20 day correlation between the two indices.

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like all observations of "realized" metrics, realized correlation tells you something about data points that lie in the past not what the market implies about the future. Thus, trying to draw conclusions from a breakdown in realized correlations about future investor behavior looks to be a futile endeavor. – Matt Wolf May 19 '13 at 1:44

If you look at tick data, you will probably get an even better analysis. However, vix correlation tends to be negative with spx but remember that this is generally more true for when spx tanks. When spx goes up, the correlation isn't as strong. Why? People panic after a drop, therefore leading to people buying options. They don't care about black scholes delta hedging etc. They only want to hedge their position. However, when spot is going up, vix doesn't necessarily have to go down because if it does go down quite a bit, you buy the option, and just delta hedge and collect the difference between realized and implied volatility.

Another thing that you can also look at is the skew in the options market. When correlation between spot and vol is very high, you tend find a much steeper skew and vice versa.

spx is cash settled so there is no physical to deliver. and spx is so liquid that it is nearly impossible for any individual to move the market. we know that market impact is proportional to sigma * sqrt( (order size) / (average volume) ). on any given day, spx and spy trades at least 2 million contracts. for a big player to move the market, you will literally need to trade at least half a billion which I've personally never seen.

You should do an analysis of realized volatility during the previous 20 days as well. If the realized volatility during the previous 20 days was .16, and the implied volatility was .12, you will still buy the option even if markets were going up no? since you can make a profit from delta hedging.

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That is true. The correlation does break down when the SPX is on the up move. However I wonder what one can infer if the SPX are moving in the same direction (positive correlated). IS this a warning a sign of future price drops? Could it be some big player moving the market with a big order? Could it be because of folks selling calls, buying position in the physical to deliver because of a squeeze? – jessica May 18 '13 at 21:54
message too long, look at edited post – Andrew May 18 '13 at 22:54
@Andrew, having traded for many years various volatility products I can advise to be very careful when drawing conclusions from all such observations ("such", as in investors delta hedge to take advantage of realized vs implied vol differentials [which in itself is hard to impossible to do profitably over the long-term], or your observation of the skew vs correlation relationships). Such observations are anything but stable and thus a very bad recipe for building trading strategies around. – Matt Wolf May 19 '13 at 1:50
@jessica, re your first comment, no, its not a warning sign of anything, maybe one time yes, the other 99 times not. There is no repeated pattern that would give you an edge that can be exploited. You most often cannot take advantage of realized vs implied vol differentials, such differentials can widen out another couple orders of magnitude or can stay out for months/years. All that this correlation breakdown tells you is that traders do not sell as much implied vol as a rising cash market suggests, nothing else. Many buy side PMs have an allergy against being short wings. – Matt Wolf May 19 '13 at 1:54
@jessica, a long straddle is long iVol, and my implication was that many PMs on the buy side do not look to sell or be net-short implied vol products. So when a cash market trades higher, cash equity returns correlate less negatively with changes in implied volatility. But my overall point is that you are most likely wasting your time by trying to model future investor behavior on realized vol or realized correlation data points. To answer your last question: you are looking at relationships that existed in the past and that you observe changed. – Matt Wolf May 19 '13 at 2:26