Case 042Hedging a bookWarm up
An asset manager wants to hedge a high-beta equity portfolio with index futures. Size the hedge, then show what happens when the index falls 8% and the portfolio falls 12%.
1The situation
Morvani Asset Managers runs a Rs 300 crore equity portfolio with a beta of 1.3 against the index: historically it has moved 1.3% for every 1% move in the index. Ahead of an uncertain month, the chief investment officer asks for the market risk to be hedged with index futures, each with a notional value of Rs 15 lakh.
During the month the index falls 8% and the portfolio falls 12%.
2Your task
How many futures should Morvani sell, what does each leg make or lose, and what risk is left after the hedge?
Quick check
How many index futures does Morvani need to sell?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
Sell 2,600 contracts. After the fall, Morvani loses Rs 4.8 crore instead of Rs 36 crore. The hedge covers beta times value, Rs 390 crore, so an 8% index fall pays Rs 31.2 crore on the futures. The portfolio fell 12%, more than the 10.4% beta predicts, and that extra Rs 4.8 crore is stock-specific. A beta hedge removes market risk and leaves exactly that residual.
Step 1How do you size the hedge?
An umbrella sized for one person leaves a tall friend's shoulders wet. The hedge has to cover how much the portfolio moves, not what it is worth. Market exposure is value times beta, Rs 300 crore x 1.3 = Rs 390 crore, and Rs 390 crore over Rs 15 lakh per contract is 2,600 contracts. Selling only 2,000 contracts, matching the Rs 300 crore value, would leave about a quarter of the market move unhedged, because the portfolio exaggerates every index move by 30%.
Step 2What does each leg do when the index falls 8%?
The futures position is short Rs 390 crore of index. An 8% fall pays 8% of Rs 390 crore, Rs 31.2 crore, which is exactly what beta predicted the portfolio would lose: 1.3 x 8% = 10.4% of Rs 300 crore. The portfolio actually fell 12%, Rs 36 crore. The extra 1.6 points, Rs 4.8 crore, came from Morvani's stocks doing worse than their beta implied: company news, sector moves or plain bad luck. That part the index hedge cannot touch.
| Rs crore | Unhedged | Hedged |
|---|---|---|
| Portfolio, down 12% | (36.0) | (36.0) |
| Short 2,600 futures, index down 8% | none | 31.2 |
| Result | (36.0) | (4.8) |
Step 3What risks does the hedge leave or create?
Three, and a risk manager should name all of them. First, idiosyncratic riskThe part of a portfolio return that comes from its particular stocks rather than the market as a whole. An index hedge cannot remove it.: the Rs 4.8 crore could as easily have been a gain; the hedge leaves the manager's stock picks fully exposed, which is usually the point. Second, beta is an estimate from past data and drifts; if the true beta were 1.2, the hedge would be too big. Third, cash: futures are settled daily, so in a rally the short futures lose money every day and need margin, even though the portfolio is gaining on paper. A hedge that the fund cannot fund through a rally is a hedge that gets closed at the worst moment.
Where candidates lose it
The common error is to hedge the value, 2,000 contracts, rather than the beta-weighted exposure. That under-hedges by 30% and leaves Rs 9.4 crore of the fall uncovered.
The second is to call the remaining Rs 4.8 crore a hedging failure. The hedge did exactly its job, removing the market part; the rest belongs to the stocks the manager chose.
What the interviewer asks next
- The index rises 8% instead and the portfolio rises 9%. What is the hedged result?
- How would you hedge only half the market risk, and why might a CIO want that?
- Beta was estimated over a calm year. How would you check it before relying on it?
Company names and figures are illustrative.