Hedge ratio
The number of futures (or options) needed to hedge a position. For one stock with its own futures it is 1:1; for a portfolio against index futures it is portfolio value × beta ÷ contract value.
In plain language
A hedge only works if it is the right size. Too small and part of the risk is left open; too large and you have turned a hedge into a bet in the other direction. The hedge ratio answers "how many contracts?"
The workbook treats two cases:
Hedging a single stock with its own stock futures. The futures contract moves with the very stock you hold, so the hedge ratio is 1:1 — match the shares to the lot size.
Hedging a portfolio with index futures. Now the hedge instrument is different from what you hold. Your ten stocks are not the index's thirty or fifty, and your portfolio may be more or less volatile than the index. A 1:1 ratio is not appropriate. You scale by beta, the measure of how much the portfolio moves when the index moves.
In Chapter 4 the workbook also notes that an option's delta is often called the hedge ratio — a separate use of the phrase for options.
How it works
Portfolio beta is the weighted average of the stocks' betas, weights summing to 1. Beta above 1 is an aggressive portfolio; below 1, conservative.
Contract value = futures index level × contract multiplier. For simplicity, the beta of the futures index relative to the spot index is taken as one.
The workbook's cautions (Chapter 3, section 3.9):
- A portfolio has a different beta against different indices, so the hedge ratio changes with the index used.
- Beta is historical; the hedge assumes the past relationship continues, so actual results may differ.
- Index futures hedge systematic risk only. Stock-specific risk is not hedged.
For options (Chapter 4, section 4.7): with a portfolio of n shares, n ÷ delta gives the number of calls to write for a delta-neutral hedge.
The formula
Single stock: Contracts = Shares held / Lot size (1:1)
Portfolio: Contracts = (Vp × βp) / Vi
Vp = portfolio value, βp = portfolio beta
Vi = futures index level × contract multiplier
Portfolio beta βp = W1β1 + W2β2 + … + Wnβn
A worked example
1. Portfolio beta (Chapter 3). Four stocks with betas 0.5, 1.1, 1.3 and 0.9, weights 35%, 15%, 20% and 30%:
βp = 0.5×0.35 + 1.1×0.15 + 1.3×0.20 + 0.9×0.30
= 0.175 + 0.165 + 0.260 + 0.270 = 0.87
A conservative portfolio.
2. Contracts to short (Chapter 5). Portfolio value Rs 90,00,000, beta 1.3, index futures 17,700, lot size 50.
Vi = 17,700 × 50 = Rs 8,85,000
Contracts = (90,00,000 × 1.3) / 8,85,000
= 1,17,00,000 / 8,85,000 = 13.22
Short 13 index futures contracts.
3. Single stock (Chapter 3). An investor holds 550 HDFC Bank shares; the futures lot is 550. Hedge ratio 1:1 → 1 contract.
Notice what beta does in example 2. Without it, the answer would be 90,00,000 / 8,85,000 = 10.17 contracts — about three contracts short of a full hedge for a portfolio that moves 1.3 times the index.
Why NISM asks about it
Chapter 3, section 3.9 (Uses of index futures), explains beta, portfolio beta, the 1:1 ratio for stock futures and the beta-based formula for index futures. Chapter 5, section 5.1, applies it to a Rs 90 lakh portfolio. Chapter 4, section 4.7, calls delta the hedge ratio for options. Calculation questions on the number of contracts are frequent.
Common exam traps
- Multiply by beta; do not divide. A high-beta portfolio needs more contracts.
- Vi is the contract value, futures level × lot size — not the index level alone.
- 1:1 works only when the futures are on the same stock. For a portfolio against an index, it does not.
- Round sensibly: 13.22 contracts means 13 in the workbook.
- Beta is historical and index-specific. Change the index and the hedge ratio changes.
- In options, "hedge ratio" means delta — keep the two uses apart.
Where this is taught
Free preparation for NISM Series XVIRelated terms
- BetaHow sharply a share moves relative to the market index — beta 1 moves with the index, above 1 amplifies it, below 1 dampens it. The standard measure of systematic risk.
- Systematic riskThe part of an investment's risk that comes from economy-wide forces moving every asset at once — it cannot be diversified away, and it is the only risk the market pays you to carry.
- DeltaThe change in an option's premium for a one-rupee change in the underlying — the first and most used Greek, and the hedge ratio that says how much underlying to hold against an option position.
- Long hedgeA hedge made by buying futures to protect against a price rise before a planned future purchase — the gain on futures offsets the higher cash price, locking in roughly the futures price.
- Short hedgeA hedge made by selling futures to protect an existing holding or a planned sale against a price fall — the futures gain offsets the lower cash price, locking in roughly the futures price.
- Cross hedgeHedging an exposure with futures on a different but closely associated asset, because no futures contract exists on the asset itself — for example, hedging a stock portfolio with index futures.
- Delta hedgingOffsetting an option position's delta with the underlying or futures so the combined delta is zero, then buying or selling as delta changes to keep it there — the option trader's way of managing risk.
- Contango and backwardationThe two shapes a commodity futures curve can take — contango when the futures price is above spot, backwardation when it is below.
- Risk transferThe economic function by which commodity price risk moves off the hedger, who does not want it, onto the speculator, who is willing to carry it for a return.
- Hedging disclosure normsSEBI's requirement, dated 15 November 2018, that a listed company disclose its commodity risk policies and, for each commodity, its exposure and the extent hedged in domestic and international markets.
- Naturally longThe position every business holds in its finished goods — it gains when their prices rise and loses when they fall, which is why finished goods are hedged by selling futures.
- Naturally shortThe position every business holds in its raw materials — it must buy them in future, so a price rise hurts it exactly as a short position would, and a long hedge cancels the exposure.
- Offsetting hedgeA hedge undertaken to offset price risk that has arisen from a physical market activity already carried out — one of the workbook’s two basic hedging strategies, the other being locking in a price.
- Hedge effectivenessThe degree to which changes in the fair value or cash flows of a hedged item, attributable to the hedged risk, are offset by changes in the fair value or cash flows of the hedging instrument.
- Effective priceThe rate a hedger actually ends up with: the price realised or paid in the spot market, adjusted by the payoff on the hedge — added for a receiver, subtracted for a payer.
- Index derivativesDerivative contracts — chiefly index futures and index options — that have a stock index as the underlying asset. In India they are cash settled and used to hedge market risk.