Implied Volatility Index as a predictor of Historical Volatility 

Continued from "Implied Volatility Index and related indicators: How you can use them in trading & risk management, part V" 
In our previous newsletters we mentioned that IV Index might be considered as an estimate of future Realized (or Historical) Volatility. Based on this assertion, IV Index to HV ratio (or, Relative Volatility) is frequently used for different stock and option trading strategies. Now we are trying to understand how good IV Index is as such a predictor. 
Lagged Correlation indicatorIn fact, if you are using our Advanced Historical Data service http://www.ivolatility.com/adv_hist_data/ivx.j , you are able to see the quality of HV prediction by IVX. The value of Lagged Correlation shows how the IVX 30 value (shifted one month back) is correlated with 20 trading days HV. IVX term 30 is chosen as it is most liquid, and therefore the most relevant one, as usual; 20 trading days taken for HV, are most close to 30 calendar ones, used for IVX. The correlation itself is calculated by one month period. The 100 % value of Lagged Correlation means that IV Index is an exact predictor of HV, and it grows when an increase in HV is expected. The value of 100 % still means that IVX exactly predicts HV value, but declines when HV would be increasing. In practice, values of Lagged Correlation of � 3050 % (and sometimes even less) are considered to be sufficiently good for the prediction. The value of zero or close to it would mean that there is no simple linear dependence between Lagged IVX and HV  the worst case that can be expected. The typical chart for Microsoft Corp. (MSFT:NASDAQ) is shown below.
As you can see, the behavior of Lagged Correlation is much more interesting than simply "always good" or "always bad". Rather, the periods of quite significant positive correlation are interleaved by periods of comparably significant negative correlation (that is, higher IVX level forecasts lower HV and vice versa). The picture is quite regular, with the period of about 1.5 months  this pattern is considerably violated only near the end of year 2003. Broader look on the date range of 2 years shows that this oscillating picture was in place for quite a while  though IVX was working a bit better "on average" before the end of year 2002.
As our brief investigation shows, this picture is quite typical for all the US stock market  that is, quite high positive correlation is quickly replaced with negative one, and then not only for this particular equity. What forces are in place here ? We are not sure, but the situation is far from disappointing in our opinion. Indeed, if there is a regular relation between IV Index and HV, it can be used for options cost estimate and risk/reward evaluation of most of the options strategies (straddles and strangles come to mind first here). Even if this relation is far from "always good/bad"  well, there should be a way to exploit it!
A couple of concluding remarks: 1) Mind, that Lagged Correlation, which is high now, means that IVX was a good predictor of HV 1 month ago. It is a realized value and does not estimate how good the current IV Index will predict the future HV! So, in any case one needs to investigate the Lagged Correlation entire pattern, to estimate future Realized Volatility. 2) At any particular moment, IVX and HV seem to be fairly well correlated  the higher the IVX, the higher the HV (see Chart 3 below). This does not contradict the picture of Lagged Correlation we've seen above. This is so, because the Lagged Correlation value unveils the dynamics of dependence of HV on IVX, rather than connection between snapshot values.
