Aarohan Textiles: Beta Hedging with Futures versus a Zero-Cost-Style Collar
Aarohan Textiles holds a ₹6 crore portfolio of twelve large-cap stocks with a beta of 1.20 against the Nifty 50. The promoter family cannot sell before a settlement nine months away because of capital gains tax and control issues, but has promised lenders that the portfolio will not fall more than about 8% over the next quarter. Nifty 50 spot is 24,000; the three-month futures contract trades at 24,180; lot size is 25. The treasury has two proposals. Proposal 1: sell Nifty futures to bring the effective beta down to 0.60. Proposal 2: buy Nifty puts struck at 22,800 and sell Nifty calls struck at 26,400 on the full portfolio notional, quoted at a net debit of ₹40 per unit. The CFO, who has never used futures, wants the downside arithmetic at a Nifty level of 21,000, a comparison of both proposals at 21,000, 24,000 and 27,000, and an explanation of what can go wrong with a hedge that is rolled every quarter.
1. Compute the number of Nifty futures contracts required to reduce the effective beta to 0.60 and evaluate the hedge if the Nifty falls to 21,000 at expiry.
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Hedge ratio
N = (β_target − β_portfolio) ÷ β_futures × (Portfolio value ÷ Contract value)
- Contract value at the futures price = 24,180 × 25 = ₹6,04,500
- N = (0.60 − 1.20) ÷ 1.00 × (6,00,00,000 ÷ 6,04,500)
- N = −0.60 × 99.256 = −59.55 → sell 60 contracts
If the Nifty falls to 21,000 (a 12.5% fall from spot)
- Expected portfolio return = −12.5% × 1.20 = −15.00% → loss of ₹90,00,000
- Futures gain = 60 × (24,180 − 21,000) × 25 = 60 × 79,500 = ₹47,70,000
- Net position = −90,00,000 + 47,70,000 = −₹42,30,000, i.e. −7.05%
Does it meet the 8% promise? Yes, with about 95 bps of headroom. The realised effective beta is 7.05 ÷ 12.5 = 0.564, marginally better than the 0.60 target because 59.55 contracts were rounded up to 60.
Two points the CFO must understand. First, the hedge is symmetric: at a Nifty level of 27,000 the portfolio gains 15% (₹90 lakh) but the futures lose 60 × (24,180 − 27,000) × 25 = ₹42.3 lakh, leaving +₹47.7 lakh. Upside is capped on the hedged 60% of beta, not on the whole portfolio. Second, the futures was sold at 24,180 rather than the spot 24,000 - a 0.75% premium that reflects cost of carry and is captured at expiry if the basis converges to zero, which is why the realised outcome is slightly better than the beta arithmetic predicts.
2. Evaluate Proposal 2: compute the number of contracts, the net premium, and the outcomes at Nifty levels of 21,000, 24,000 and 27,000. Compare it with the futures hedge on both downside and upside.
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Structure
- Contracts on full notional: 6,00,00,000 ÷ (24,000 × 25) = 100 contracts
- Net premium paid = ₹40 × 25 × 100 = ₹1,00,000 (₹1 lakh, 0.017% of portfolio)
- Payoff profile: protected below 22,800 (−5% from spot), fully exposed between 22,800 and 26,400, upside capped above 26,400 (+10%)
Outcomes (portfolio value ₹6 crore, beta 1.20)
| Nifty at expiry | Portfolio P&L | Option P&L | Premium | Net | % |
|---|---|---|---|---|---|
| 21,000 (−12.5%) | −₹90.0 lakh | Put +₹45.0 lakh | −₹1.0 lakh | −₹46.0 lakh | −7.67% |
| 24,000 (0%) | 0 | Nil | −₹1.0 lakh | −₹1.0 lakh | −0.17% |
| 27,000 (+12.5%) | +₹90.0 lakh | Call −₹15.0 lakh | −₹1.0 lakh | +₹74.0 lakh | +12.33% |
Comparison with 60 futures contracts
| Nifty | Futures hedge | Collar |
|---|---|---|
| 21,000 | −₹42.3 lakh (−7.05%) | −₹46.0 lakh (−7.67%) |
| 24,000 | +₹2.7 lakh (+0.45%) | −₹1.0 lakh (−0.17%) |
| 27,000 | +₹47.7 lakh (+7.95%) | +₹74.0 lakh (+12.33%) |
Judgement. Both satisfy the 8% floor, and the futures is marginally better on the downside. The collar is materially better in a rally because it caps upside 10% away, whereas selling 60 futures gives up upside on 60% of the portfolio from day one. The collar's cost is trivial relative to the protection it buys.
But the collar protects total return (it is a portfolio-level put on the index), while the futures hedge only re-scales beta - it does not stop a −7.67% outcome from becoming −12% if the twelve stocks underperform the Nifty. For a lender covenant expressed in rupees and not in beta, the collar is the more faithful instrument; the futures hedge is a de-risking, not an insurance policy.
3. The CFO asks what can go wrong with a hedge that is rolled every quarter over a nine-month horizon, and whether hedging is preferable to simply selling the shares.
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What can go wrong
- Basis risk. The twelve stocks are not the Nifty. If the portfolio's realised beta drifts (say to 1.35 after a sector re-rating), the hedge is under-sized and the 8% floor breaks. Beta must be re-estimated and the position rebalanced, and there is no guarantee the relationship holds in a crash.
- Rollover risk. The nine-month horizon requires three three-month rolls. Each roll involves a bid-ask spread (Nifty futures typically 0.05–0.10%), and in the final week before expiry the near month becomes illiquid. Three rolls could cost 20–30 bps of notional - roughly ₹1.2–1.8 lakh on ₹6 crore - on top of the ₹1 lakh collar premium.
- Roll cost/benefit in a backwardated or contangoed market. If the index is in contango, each roll sells low and buys high, bleeding carry; in backwardation the roll earns. This is not controllable and can turn a 0.60 beta into something quite different.
- Margin and liquidity. Futures require daily mark-to-market and SPAN plus exposure margin. A 12.5% index fall produces a ₹47.7 lakh variation margin inflow, which is fine - but a sharp rally produces a large outflow precisely when the family's liquidity may be stretched by the settlement. The collateral must be pre-arranged.
- Dividend yield. Index futures are priced off the spot index less expected dividends. A short futures position forgoes nothing directly, but the pricing already reflects the dividend, so the hedge captures slightly less than the beta arithmetic suggests.
- Accounting and disclosure. Hedge accounting under Ind AS 109 requires documented hedge relationships and effectiveness testing; the P&L will otherwise be volatile even though the economic exposure is hedged.
Hedge versus sell?
The tax and control reasons for not selling are real, but a hedge is not a substitute for a sale: it defers the disposal decision, not the exposure. The family should be told plainly that a nine-month hedge on a rising market costs them the upside above the cap, and that if they already intend to sell after the settlement, the hedge simply locks in today's value - which is an economically sensible outcome, not a tax trick. A cleaner structure is to hedge the value now and sell in tranches as the settlement approaches.