The correlation of the returns of the market (specifically the S&P 500 Index) and the VIX is large and negative, sampling in the region −85% to −100%. Without the results of the prior post, we are forced to seek a behavioural root for this observation:

demand for hedging instruments increases when the market is falling, increasing implied volatilities as the price of put options increases beyond fair value.

i.e. We have ascribed the observed covariance as a consequence of market participants' irrationality, as they believe that it's worth hedging only after they've lost money. However, Completely Asymmetric GARCH, such as that exhibited in the prior post, describes a process in which increases in future actual volatilities are only due to downwards moves and volatilities decrease after upwards moves. This linkage describes negative correlation between the returns of the index and future volatility and also describes a process which cannot crash upwards, as many commentators observe that the market does not do.

Why is this important? Well, consider if one believes that the increase in options prices on a down day is due to market participants situational bias. i.e. Their irrational belief that because the market is falling today then it is more likely to fall tomorrow. Under this scenario, the observed phenomenology represents an alpha or a predictable conditional mean for the future distribution of option trading profits. However, if the observations are consistent with the actual empirical price process — that down days do tend to increase future volatility — then there is no alpha. The increased prices represent an increase in fair value.

Under the first scenario, the right thing to do is to sell options; whereas, under the second, the right thing to do is to buy options.