Anytime we want to talk about “deconstructing” something, it helps to know what that something is. Here’s a good definition. Probably the key concept is that index options are sampled and calculations based on them become the VIX. This is also a good definition link because it includes the misnomer “investor fear gauge.”

I had been having a conversation with Bill Luby of VIX and More about this topic. My distaste for using the VIX can be summed up by its easy model-ability based on price action; if we already have price action in our model, VIX adds comparatively little useful information. VIX, regardless of actual construction methodology, can be described in terms of three contributors:

1) Actual, historical volatility
2) Some predictable measure of fear/greed resulting from recent price momentum
3) An error term.

NOW we might have something interesting. If we assume that a modeled VIX (based on volatility and momentum in the index) contains no useful information outside of that in the price data itself, then the deviation of actual from expected VIX could be said to contain “pure sentiment data” that corresponds to the pricing biases of market participants.

It’s a fairly simple process to work through, but time-consuming if one wants to optimize the formulae.

The first step is to date-match the data so that VIX and SPX data coincide; from 1/2/1990, I have three more days of SPX data than I do VIX data, probably because of different days the different exchanges were open – I discarded the three extra days in my data set, but you may choose to do something different.

The second step is to determine what “historical volatility” is. One could choose to use a standard deviation of the closing prices over some time period (what time period?), or use “typical prices” (average of Open/High/Low/Close? Ignore the Open?) over some time period, or use the Average True Range over some time period, etc. This choice could be done with single-variable analysis, or one could choose multiple definitions of “historical volatility” and run several multi-variate regressions in combination with the other variable …

Which is the third step, determine what measure of price momentum best predicts the level of fear/greed in the marketplace. This should probably be a timeframe that corresponds with a high level of mean reversion in the marketplace, so it could be a percentage MACD (PPO) of some length, a rate-of-change (ROC) calculation of the closes, or even! a 2-period RSI range.

Step four is to start running regressions. One could, of course, have run single-variable regressions to determine the highest correlation of VIX to various “historical volatility” measures and the optimum mean-reverting measure of price momentum, or one could merely run bunches of regressions, one against every possible pairing of measures, in a surfait of brute force calculations. Booyah!

Now that we have a good, bivariate regression formula that predicts VIX very well, using only historical volatility in price and recent momentum, we can compare this value to the actual VIX and see what the error term is.

Only when we have this “error term” do we have a true, unique measure of sentiment. VIX, in and of itself, is impure, i.e., it is mostly comprised of data that can be obtained from the movement of the SPX itself. If the VIX is high, does it really mean there’s inordinate fear in the market? I would suggest that the valid comparison is most likely “is the VIX high (low) compared to what I would expect given recent volatility and returns?” and not “is the VIX high (low) compared to historical or recent norms?” The “error term” between modeled and actual VIX is apt to give us better insight than just the VIX itself.

The penultimate step in the puzzle would be to compare this “error term” to various future returns on the SPX (2-, 5-, 10-day returns?) and find which ones were best predicted by the use of sentiment. The final step would be to compare the modeled result to other trading plans for the SPX to see if this work not only yielded something trade-able, but profitable enough to be worth the effort.

More on this later.