A Rs 300 crore portfolio has a beta of 0.9 to the broad index and 0.5 to the bank index in a two-factor regression. Hedge both factors with index futures, and show why hedging only with the broad index leaves a bank bet.

Sell about 2,455 Satpura 50 contracts and 2,083 Satpura Bank contracts; the broad-only hedge leaves a Rs 150 crore bet on banks. Each Satpura 50 contract covers Rs 11 lakh and each bank contract Rs 7.2 lakh. The 0.9 beta is Rs 270 crore of broad exposure, 2,454.5 contracts; the 0.5 beta is Rs 150 crore of bank exposure, 2,083.3 contracts. With only the first hedge on, a 6% fall in bank stocks still costs about Rs 9 crore.

A household that spends on rent and on fuel has two bills that rise for different reasons; fixing the rent does nothing about fuel. A two-factor regression gives two separate exposures, and each needs its own hedge sized in rupees of index. The broad exposure is 0.9 times Rs 300 crore, Rs 270 crore. A Satpura 50 contract is 22,000 times 50, Rs 11 lakh, so the hedge is 270 crore over 11 lakh, 2,454.5, rounded to 2,455 contracts sold. The bank exposure is 0.5 times 300, Rs 150 crore; a bank contract is 48,000 times 15, Rs 7.2 lakh, so the hedge is 2,083.3, rounded to 2,083 contracts sold.

Because the 0.9 was estimated holding banks fixed. The regression has already split the book's market risk into a broad part and a bank part, so hedging the broad part alone leaves the bank part exactly where it was: Rs 150 crore of exposure to the bank index. When everything falls 4%, the broad hedge saves Rs 10.8 crore of the Rs 16.8 crore loss but the fund still loses Rs 6.0 crore. When banks alone fall 6%, the broad hedge does nothing and the loss is Rs 9.0 crore. The analyst's hedge looks complete on a day when the two indices move together and fails on exactly the day the fund manager feared, a sector-specific shock.

A tempting shortcut is to regress the book on the broad index alone. Because banks are a large part of the broad index and move with it, that single beta would come out well above 0.9, perhaps around 1.2, and the fund would sell more Satpura 50 futures. That over-hedges the broad market and still leaves a residual bank exposure: the part of bank returns not explained by the broad index. On a day when banks fall and the rest of the market rises, the single-beta hedge loses on both legs. Two factors that overlap must be hedged together, using the betas from the regression that contains both.

Four things, and the portfolio manager should hear all of them. The betas are estimates and drift; a month is long enough for them to move. The contracts must be resized as index levels and the book's value change. The hedge removes factor risk only, so stock-specific risk, which is what the fund wants to keep, now drives the whole P&L, including any single name that blows up. And the futures carry basis risk, the gap between futures and index, plus a roll at expiry. Selling about 4,500 contracts also ties up margin, which should be sized before the trade, not after.