How to read it
Two ends and a point between
Take the 50 stocks with their weights and at the money IVs. If no two of them ever moved together, the index would be as volatile as the root of the sum of squared weighted vols. If all of them always moved together, it would be as volatile as their weighted average. The index IV sits somewhere between, and where it sits is the correlation.
One number for every pair
The formula assumes the same correlation between every pair of stocks. The real matrix has high pairs, such as two large private banks, and low ones, so the number is an average. It is the figure that makes the weighted stocks add up to the index, not a measured pair.
Realised, on the same formula
Replace each implied vol with the stock's realised vol over a window, and the index IV with the index's realised vol over the same window. The same formula then gives a realised correlation. The tool shows the 20 and 60 sessions before the date, which were known, and the sessions up to the expiry, which were not.
Why one vol point matters so much
The index IV is squared in the numerator and the gap between the two ends is small next to it. The sensitivity table shows it: a vol point on the index moves the correlation by a visible amount. The implied correlation module builds the formula, the dispersion module covers how a correlation view becomes a position and the correlation risk premium module looks at implied against realised.
What it leaves out
Each stock is represented by its at the money IV, so skew is left out, and index options carry a steeper skew than most stocks, which pulls the two sides apart in ways one number cannot show. The weights are the month end holdings of a fund that tracks the Nifty 50, multiplied by closing prices on the day: close to the index, not the index provider's own weights. Index and stock options expire together here, but they are separate markets with their own liquidity, and a settlement price on a thin strike is partly a model price. Stock dividends and corporate actions sit inside the prices. The realised figure over the option's life covers only a few sessions. A Nifty Bank version is not offered: no weights file for its twelve stocks is in the data. None of this is a forecast or a signal.