A fund sells Satpura 50 index variance at 16 and buys variance on its ten equal-weight constituents at 28. Realised comes in at 14 for the index and 30 for each stock. What correlation was implied, what was realised, and where did the P&L come from?

The strikes implied an average correlation of about 0.25; the market realised about 0.13, and the trade made about Rs 39 lakh. The short index leg earned Rs 18.8 lakh because the index realised below 16, and the ten long stock legs earned Rs 20.7 lakh because each stock realised above 28. Both legs paid for the same reason: the stocks moved apart more than the index price assumed. A dispersion trade is a short correlation position.

Think of ten people walking: if they all step the same way together the group moves a lot; if they step in random directions the group barely moves, though each person walks just as far. An index is the group. For ten equal-weight stocks of the same volatility, index variance equals stock variance times one tenth plus correlation times nine tenths. The one tenth is the floor the index keeps even at zero correlation, and it is the piece that trips people. At the strikes, 16 squared over 28 squared is 0.327; subtract 0.1 and divide by 0.9 to get an implied average correlationHow much the stocks move together. One means they move in step; zero means their moves are unrelated. of 0.25. Realised: 14 squared over 30 squared is 0.218, so realised correlation was 0.13.

Convert each vega notional into a variance notionalThe amount paid per point of variance. Vega notional divided by twice the strike, so the swap pays about the vega notional per volatility point near the strike. by dividing by twice the strike. The index leg, short at 16 with Rs 10 lakh of vega, is Rs 31,250 per variance point; realised 14 squared is 196 against a strike of 256, so the short earns 60 points, Rs 18.8 lakh. Each stock leg, long at 28 with Rs 1 lakh of vega, is Rs 1,786 per point; realised 900 against 784 earns 116 points, Rs 2.07 lakh, and ten of them make Rs 20.7 lakh. The total is Rs 39.5 lakh, and both legs are in profit.

Here is the test. Suppose the stocks had realised exactly 28, their strike, and correlation had still fallen to 0.13. The index would then have realised about 13.1, below 16, so the index leg would still have paid while the stock legs broke even. Run it the other way: stocks at 30 but correlation at the implied 0.25 puts the index at about 17.1, above 16, so the index leg loses roughly what the stock legs make. Single-stock volatility cancels across the two legs when they are sized to match; what is left is correlation, and the trade earns when stocks move apart more than the index price assumed. That is why dealers quote dispersion as a correlation level rather than as two volatilities.

Say the limits. The equal-weight, equal-volatility index is a classroom simplification; a real index needs each stock's weight and its own strike, and the vega sizing then has to be chosen, vega-flat as here or correlation-weighted, which changes how clean the cancellation is. The legs also do not cancel day by day: ten long variance swaps at 28 carry far more gross exposure than one short at 16, so the position has a large positive theta bill and a large gain in a crash on the stock legs. And the implied correlation of 0.25 embeds a premium: index variance usually trades rich to the single names precisely because index protection is what people buy, which is the structural reason the trade exists and the reason it bleeds when a crash lifts correlation towards one.