The VIX index and futures are connected by a statistical relationship that depends on how fast the VIX tends to move toward its average level, the volatility of the index and how much time is left until expiration. Near expiration, the futures will be close to the index and move in tandem with it, while the long-term futures reflect the long-term expectation of VIX plus risk-premium.
VIX futures have a dynamic relationship with the index, just like options are related to their underlying stock by delta. Traders know that VIX futures do not always follow the index. However, because of the dynamic nature of this relationship, the correlation evolves over time and cannot be quantified with a single number.
Close to expiration, the futures will move right in sync with the index. When futures expire in a month (about 25 trading days), the futures will move about half as much as the index. Futures that expire in 125 trading days or more have virtually no correlation to the index. The exact relationship is, of course, dynamic and changes.
The relationship has other intuitive properties. For example, delta gets smaller as the index increases. This is the result of mean-reversion; futures will move up more when the VIX is below its long-term average and less if it is above it. If the parameters indicate that futures are strongly mean-reverting, the delta will be smaller because the current level matters less than its long-term level; if mean-reversion is weak, the delta will be greater because futures will be more sensitive to the current index level.
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