VIX thoughts

The VIX index tracks implied volatility, using a basket of options with expirations closest to +30 days to compute an implied probability distribution for values of the SP500 30 days hence. The VIX is often referred to as a "fear gauge" because it is anticorrelated with market performance: when the SP goes up the implied vol goes down, and vice versa.

To characterize the prob. dist. with a single volatility value, one fits to a Gaussian. Historically we know that outlier events are much more likely than implied by a log normal distribution. Deep out of the money options are included in the VIX computation as long as there are nonzero bids (and no intervening zero bids at more probable strikes). Looking at the current prices I see this only goes out about 2 sigma into the tail, so the distortion from mispricing of rare events is small. I know Nassim Taleb (author of Fooled By Randomness) makes his living buying mispriced deep out of the money options - I assume he has to buy these directly by calling up market makers, since the widely traded options don't go too far out on the tail.

Why is the VIX anticorrelated with market moves? I can understand why options traders might be psychologically disposed to expect more vol in a down market, but does the observed, historical vol exhibit this anticorrelation? We could check by crunching the data looking for up/down moves to see if the variation in the following 30 days is correlated with the sign of the move. To put it very simply, are downward moves of the market choppier than upward moves? If not, can't I arbitrage by selling vol when the market goes down and buying it when the market moves up?