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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?

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  • $\begingroup$ The SP500 is calculated assuming dividend reinvestment, while volatility is not. Have you tried correlating excluding dividend reinvestment? (not saying you'll get vastly different results, just curious). $\endgroup$ – barrycarter Feb 1 '11 at 3:20
  • $\begingroup$ @barrycarter Really? Are dividends (and reinvestment) included in the S&P500 calculation? I thought Standard and Poors just calculated an average price weighted by market capitalization. Did something change? $\endgroup$ – pteetor Feb 3 '11 at 1:30
  • $\begingroup$ @pteetor You're right, I'm wrong. I didn't realize until now that the S&P500 excluded dividend reinvestment. I'm now going w/ my comment on quant.stackexchange.com/questions/9/… (basically, markets crash hard, but rebound soft) $\endgroup$ – barrycarter Feb 3 '11 at 8:22
  • $\begingroup$ On the topic of dividends reinvested in the index, S&P generates it in both flavors. If you wanted a version that includes it, click through to the Export button at us.spindices.com/indices/equity/sp-500 $\endgroup$ – vwood May 23 '13 at 23:10
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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.

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  • $\begingroup$ should there be an observable volume effect because of this? for example, should this imply a spike in trading volume or interest when volatility spikes up? $\endgroup$ – shabbychef Feb 1 '11 at 5:25
  • $\begingroup$ @arjen-kruithof Thanks, Arjen. Your answer is far more eloquent than mine! $\endgroup$ – pteetor Feb 3 '11 at 16:05
  • $\begingroup$ "Since long positions outweigh short positions in the market as a whole"???? What about futures markets? $\endgroup$ – RockScience Apr 1 '11 at 2:11
  • $\begingroup$ to @RockScience, yes, that's what I'm thinking ... $\endgroup$ – TMS Sep 6 '12 at 22:49
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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.

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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.

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    $\begingroup$ It doesn't matter if the demand is for calls or for puts. Due to put/call parity, demand for either drives up the implied vol for both. $\endgroup$ – pteetor Feb 3 '11 at 17:11
  • $\begingroup$ @pteetor -- good catch! SPX is a euro option so put-call parity should be exact. $\endgroup$ – Richard Herron Feb 3 '11 at 19:01
  • $\begingroup$ @pteetor -- thinking on this more, I guess it really doesn't matter if American options have a dead band for put-call parity, does it? We're talking big jumps in implied vol, the call has to move, also. Do you think the demand for calls is one-for-one with the demand for puts during these down markets? I always thought the puts were causing the change. In other words, are a lot of people buying calls during a down market? $\endgroup$ – Richard Herron Feb 3 '11 at 19:27
  • $\begingroup$ In my experience, put/call parity can get out of whack (if only because of frictional costs) when demand for one side exceeds the other. I've seen the imp vols eventually converge, despite the demand imbalance, so IV rises. This is anecdotal, however. I've no hard evidence here. $\endgroup$ – pteetor Feb 3 '11 at 20:28
  • $\begingroup$ In the formula for VIX, the puts have a much larger weighting than calls, so the discussion here (as interesting as it is) is probably moot. $\endgroup$ – Chan-Ho Suh Dec 12 '16 at 13:50
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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.

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  • $\begingroup$ This is the best explanation I've had so far. $\endgroup$ – Contango May 22 '11 at 8:56
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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).

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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.

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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.

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