You are long a defence electronics stock that has no close listed peer. Given its betas, R-squared and residual volatility, how would you hedge it, how large is the hedge, and what risk is left?

Short about Rs 60 crore of sector index futures, 1.2 times the position, and accept that most of the risk stays. The hedge cancels the sector move, but with an R-squared of 0.35 it removes only 35% of the variance, cutting yearly risk from about Rs 17.4 crore to Rs 14.0 crore. What remains is Kavachdhar's own risk, which is the order thesis itself. Size the position for that residual, because no index can hedge it.

Think of a shopkeeper in a hill town who worries about tourist season. He can insure against a bad season for the whole town, but no policy covers his own shop losing customers to a new rival next door. A hedge removes the shared factor, the part of the stock's move that comes from its sector, and leaves the part that belongs to the company alone. Kavachdhar's sector explains 35% of its variance. The other 65% is order wins, delays, audits and management, which is exactly what the thesis is about and exactly what no index will offset.

Use the sector index, because it carries more of Kavachdhar's move than the market and already includes the market's influence. Hedging both would double count. The hedge ratio is the beta: Rs 50 crore times 1.2 is Rs 60 crore of sector futures sold. If the sector falls 10%, Kavachdhar's expected factor move is minus Rs 6 crore and the short futures gain Rs 6 crore, so the shared move nets to zero. A market hedge would be Rs 45 crore at a beta of 0.9, but it would leave the sector-specific swings of defence stocks in the position.

Rebuild the total from the pieces. If the residual is 28% and it is 65% of the variance, total volatility is 28% divided by the square root of 0.65, about 34.7%. Unhedged, the position carries about Rs 17.4 crore of one-standard-deviation risk a year; hedged, about Rs 14.0 crore, a cut of only 19%. Daily, the hedged risk is about Rs 0.88 crore. The hedge is worth doing, because it strips out a risk you are not paid for, but it does not make the position small.

Three things. A beta estimated with an R-squared of 0.35 is itself uncertain, so the true hedge ratio could plausibly sit anywhere from about 0.9 to 1.5. Re-estimate it over different windows and see how stable it is. Second, a single large index constituent can move the sector for reasons unrelated to Kavachdhar, adding noise to the hedge. Third, futures need rolling and margin, which costs money and cash. A custom basket of three or four companies exposed to the same defence budget might track better than the index; test that on history before using it.

Close with sizing, because that is where the residual risk is managed. If the fund can tolerate about Rs 10 crore of one-standard-deviation loss a year on this idea, the hedged position should be no larger than about Rs 36 crore, not Rs 50 crore. When a name cannot be hedged, the position size is the hedge.