Why the VIX Often Rises When the Stock Market Falls

# Why does the VIX index have *any* correlation to the market?


# Why does the VIX index have *any* correlation to the market?












It appears that the log 'returns' of the VIX index have a (negative) correlation to the log 'returns' of e.g. the S&P 500 index. The r-squared is on the order of 0.7. I thought VIX was supposed to be a measure of volatility, both up and down. However, it appears to spike up when the market spikes down, and has a fairly strong negative correlation to the market (in fact, the correlation is much stronger than e.g. for your garden variety tech stock).

Can anyone explain why? The mean 'returns' of both indices are accounted for in this correlation, so this is not a result of the expectation of the market to increase at ~7% p.a.

Is there a more pure volatility index or instrument?

## Answer by Joseph Tanenbaum (score 15, accepted)

https://quant.stackexchange.com/a/54

Increased volatility (high VIX) signifies more risk. To keep their portfolio in line with their risk preferences, market participants deleverage. Since long positions outweigh short positions in the market as a whole, deleveraging entails a lot of selling and less buying. The relative increase in selling causes downward pressure on stocks.

## Answer by pteetor (score 9)

https://quant.stackexchange.com/a/136

Technically, yes, the VIX is a measure of implied volatility. But practically speaking, it is a measure of market uncertainty: when market participants are uncertain of the future, they buy options to protect their positions, driving up option premiums and increasing implied volatility.

The broader market hates uncertainty, however, so that same uncertainty drives some participants to sell off their holdings or, at least, stop buying. That drives down market prices, creating a correlation between rising implied volatility and falling prices.

If you want a "more pure" volatility index, perhaps realized variance could be useful to you. That is a backward-looking measure, of course, but any forward-looking measure will inevitably be tainted by people's emotions and, hence, less pure.

## Answer by Richard Herron (score 7)

https://quant.stackexchange.com/a/137

VIX is mechanically determined from the price of S&P500 call and put options. So if the demands for S&P500 calls/puts rise, then the prices rise, then the implied vol from these options rises. During a down market there's a lot of demand for portfolio protection. If you're diversified, then S&P500 puts are good protection, so the prices for puts rise and the implied vol from puts rises. The vol rise from puts drives the VIX up. In most cases the implied vol from calls probably contributes, too, but it's the puts driving VIX.

## Answer by Keith A. Lewis (score 7)

https://quant.stackexchange.com/a/871

Richardh is spot on. The price of the VIX option is a weighted sum of put (strikes < forward) and call (strikes > forward) options on the S&P 500. The weights are proportional to 1/strike^2. As the S&P goes down the out of the money puts become more valuable and those have the highest weights.

I will leave arguments about the market as a whole to fuzzy headed pundits.

## Answer by Tal Fishman (score 4)

https://quant.stackexchange.com/a/2025

This phenomenon is known as the "leverage effect." It was first pointed out by Black (1976) ["Studies of Stock Price Volatility Changes"]. It was studied in slightly greater detail by Schwert (1989). A (relatively) more recent reference is Figlewski and Wang (2000).

## Answer by goric (score 1)

https://quant.stackexchange.com/a/48

Markets seem to have a bias against being bearish. Lower stock prices are perceived as more risky, and as risk increases so does implied volatility. For example, as the market decreases there will generally be more demand for puts, causing higher prices and higher implied volatility. An up market will imply less volatility for the same reason.

## Answer by demully (score 0)

https://quant.stackexchange.com/a/47120

There is no theoretical reason why any volatility index should be directionally correlated to its underlying asset. However, the VIX is indeed negatively correlated to the S&P. And if you look across FX markets, you will find similar, including opposite (ie price up = vol up), effects priced into their risk-reversal curves.

Theory in the sense of the Black-Scholes framework assumes a default lognormal return distribution. If any market exhibits significantly skewed and kurtic returns in reality, then the probability of a major decline, slight decline, slight appreciation and major apprecation will not be in balance. A decline or an appreciation will then be more or less likely to be either slight or major in scale.

This produces the vol-smile seen in these markets. And when spot moves, measures like the VIX will shift to give a greater or lesser weight to different strikes along the curve, which have different associated volatilities. S&P down moves the move to weight lower stikes, that have higher vols, more heavily. And vice versa.

Short answer: vol-spot correlation is a function of skew and kurtosis in the return distribution of the underlying market that the vol series is tracking.