Cross hedge
Hedging 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.
In plain language
The ideal hedge uses a futures contract on exactly the thing you own. Often there isn't one.
The workbook defines a cross hedge for that situation: when a futures contract on an asset is not available, market participants look for an asset that is closely associated with their underlying and trade in the futures market of that associated asset, for hedging purposes. They trade futures on the related asset to protect the value of their actual asset.
Its example is jet fuel. If futures on jet fuel are not available, hedgers may use contracts on other energy products such as crude oil, heating oil or gasoline, because of their close association with jet fuel.
Closer to this paper's subject, the workbook adds that "in a crude sense", using index futures to hedge the market risk of a portfolio is essentially a cross hedge, because the exact underlying is not being used to hedge the risk.
How it works
Same-asset hedge first. When a stock has its own futures, the hedge ratio is 1:1. The workbook's investor holds 550 shares of HDFC Bank; the contract size is 550, so one contract hedges her holding.
Why a cross hedge is needed. Futures contracts "are available only on a limited set of stocks", so the workbook says index futures can be used to hedge the remaining stocks that do not have their own futures contracts.
Why the ratio is not 1:1. The portfolio being hedged is different from the hedging instrument. A 10-stock portfolio hedged with a futures contract on a 30- or 50-stock index is not a perfect hedge, and the portfolio's beta may differ from the index's. So the number of contracts is:
Number of contracts = Vp × βp ÷ Vi
where Vi is the value of one index futures contract (futures index level × contract multiplier), and the beta of the futures index against the spot index is taken as one.
What can go wrong. The hedge depends on the relationship between the portfolio and the index, measured by beta. A portfolio has a different relationship with each index, so the hedge ratio changes when the index changes. And the calculation assumes the past relationship will continue, which "may result in some difference between actual and expected numbers".
A worked example
Illustrative portfolio; Nifty futures price and lot size are the workbook's Chapter 3 figures.
Anil holds Rs 32,50,000 of mid-sized stocks, none of which has its own futures contract. Their portfolio beta is 1.5. He fears a market fall over the next month and cross hedges with Nifty futures at 25,006.60, lot size 65.
Vi = 25,006.60 × 65 = Rs 16,25,429
Contracts = 32,50,000 × 1.5 ÷ 16,25,429 = 48,75,000 ÷ 16,25,429 = 3.0 → short 3 lots
If the relationship holds. The Nifty falls 4%, the futures fall with it, and the portfolio falls 4% × 1.5 = 6%.
Loss on portfolio = 6% × 32,50,000 = Rs 1,95,000
Gain on futures = 25,006.60 × 4% × 65 × 3 = 1,000.26 × 195 = Rs 1,95,051
Net ≈ Rs 0
If it does not. Same 4% fall in the Nifty, but Anil's stocks fall 8%, because mid-sized stocks sold off harder than the index this time.
Loss on portfolio = 8% × 32,50,000 = Rs 2,60,000
Gain on futures = Rs 1,95,051
Unhedged loss = Rs 64,949
Nothing was wrong with the arithmetic. The cross hedge protected the part of the risk that moves with the Nifty; the rest was the difference between his stocks and the index.
Why NISM asks about it
Chapter 3, section 3.9 (Uses of futures), defines the cross hedge under "Important terms in hedging", alongside long hedge, short hedge and hedge contract month, with the jet fuel example and the remark that index futures hedges are crude cross hedges. The same section gives the 1:1 stock futures hedge, the Vp × βp ÷ Vi formula and its limitations. Expect a definition question, the jet fuel illustration, and a hedge ratio calculation.
Common exam traps
- A cross hedge uses futures on a related asset, not on the asset itself. Hedging HDFC Bank shares with HDFC Bank futures is not a cross hedge.
- Index futures hedges of a portfolio are cross hedges "in a crude sense" — the workbook's words.
- The hedge ratio is Vp × βp ÷ Vi, not 1:1, whenever the portfolio differs from the index.
- Changing the index changes the hedge ratio, because beta is measured against a specific index.
- A cross hedge is imperfect by construction; beta is historical and may not hold.
- The jet fuel example uses crude oil, heating oil or gasoline futures — all named in the workbook.
Where this is taught
Free preparation for NISM Series V-DRelated 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.
- Hedge ratioThe 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.
- HedgingTaking a derivative position that moves opposite to an exposure you already have, so gains on one offset losses on the other and the future rate is locked in at a known level.
- 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.
- Basis riskThe risk left over after hedging, because the exposure and the contract used to hedge it do not move identically — in size, in expiry date, or in what they are written on.
- 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.
- 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.
- Portfolio betaThe weighted average of the betas of the holdings in a portfolio — the measure of its systematic, non-diversifiable risk used in CAPM, the Treynor ratio and market-neutral strategies.
- 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.