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FRM Part I · FRM Exam Part I

Using Futures for Hedging: FRM Part I Chapter Guide

Hedging with futures means taking a futures position that offsets the price risk of an asset you hold or will trade. You size it with the hedge ratio h* = ρ × σS ÷ σF, then N* = h* × QA ÷ QF contracts. Basis risk is what remains after the hedge.

What this chapter covers

This chapter shows how a firm or portfolio manager uses futures to reduce price risk. You start with the basic idea: a short hedge protects a holder of an asset, and a long hedge protects a future buyer. Then you see why hedges are rarely perfect. The gap between spot and futures prices, called the basis, can change, and that leaves basis risk.

The quantitative core is the minimum variance hedge ratio. You use the correlation between spot and futures price changes and their standard deviations to choose the best hedge size. This links directly to the Quantitative Analysis topic, where you study correlation, variance and regression. The hedge ratio is also the slope of a regression of spot changes on futures changes, and the effectiveness of the hedge is ρ².

The last topics apply the same logic to equity portfolios and to real-world frictions. With stock index futures you adjust portfolio beta using the number of contracts needed. Tailing and rolling deal with daily settlement and with contracts that expire before the hedge ends. The chapter connects to the pricing of futures in Financial Markets and Products and to risk measurement in Valuation and Risk Models.

Hedging questions are calculation-heavy and predictable in form, so they reward practice. A hedge ratio, a contract count or a beta-adjustment problem can be solved in under two minutes once you know the formula. The conceptual questions on basis risk and rolling are also common and test whether you understand why hedges fail. Since all 100 questions carry equal weight, the fast, reliable marks here help you save time for harder questions elsewhere in the paper.

Using Futures for Hedging: topics in the order to study them

  1. 1Basic Principles of Hedging with FuturesStart here to learn short and long hedges, and what a hedge can and cannot achieve, before any formulas.
  2. 2Basis RiskBasis risk is why hedges are imperfect. Basis risk and a hedge ratio below or above 1 can both arise when you hedge with a different but related asset. The minimum variance hedge ratio, in the next topic, is how you choose the hedge size given that risk.
  3. 3Minimum Variance Hedge RatioThis is the core formula, h* = ρ × σS ÷ σF, and everything later builds on it.
  4. 4Stock Index Futures and Beta HedgingThis applies the hedge ratio idea to equity portfolios. The portfolio's beta relative to the index sizes the hedge, in the same spirit as the minimum variance hedge ratio, because beta is the slope of a regression of portfolio returns on index returns.
  5. 5Tailing the Hedge and Rolling Hedges ForwardStudy this last because it adds refinements and practical limits on top of a hedge you already understand.

How to prepare Using Futures for Hedging

Treat this chapter as a formula chapter with a conceptual layer. Learn the logic first, then drill numbers until the steps are automatic.

  1. Read the basic hedge setup and write down in your own words when you use a short hedge and when a long hedge.
  2. Define basis as spot price − futures price. A strengthening basis (spot rises relative to futures) benefits a short hedger, and a weakening basis benefits a long hedger. Work through a case of each and check who gains. Note that basis risk is why hedges are imperfect.
  3. Learn h* = ρ × σS ÷ σF and N* = h* × QA ÷ QF. Note that h* differs from 1 when ρ < 1 or σS ≠ σF, which can happen for the same reason basis risk arises: hedging with a different but related asset. Solve at least five problems, writing the formula, the numbers and the answer each time.
  4. Practise beta hedging. Use N = (β* − β) × P ÷ A, where P is portfolio value and A is the value of one futures contract (index level × multiplier). Check that the sign tells you whether to go long or short.
  5. Learn tailing: it adjusts the contract count by the ratio of the spot value of the exposure to the value of one futures contract. Use N* = h* × VA ÷ VF, where VA = QA × S is the spot value of the exposure and VF = QF × F is the value of one futures contract. This equals h* × QA ÷ QF × (S ÷ F) and reflects daily settlement. Then read how rolling a hedge adds basis risk at each roll.
  6. Finish with a mixed timed set of questions, and review every error by naming the formula or concept you missed.

Common mistakes in Using Futures for Hedging

  • Mixing up the inputs in h* = ρ × σS ÷ σF

    Fix: Remember the spot is what you hedge, so σS sits on top. Check the result: if σF is much larger than σS, h* should be small.

  • Forgetting to convert h* into a number of contracts

    Fix: Always multiply by QA ÷ QF. For example, h* = 0.8, exposure 1,000,000 units and contract size 100,000 gives N* = 0.8 × 1,000,000 ÷ 100,000 = 8 contracts.

  • Getting the direction of the beta adjustment wrong

    Fix: Compute (β* − β). If it is negative, sell futures; if positive, buy futures. Then confirm the direction makes sense.

  • Treating a hedge as eliminating all risk

    Fix: Remember basis risk, imperfect correlation and mismatched maturities. Only when ρ = 1 and ratios match is variance removed completely.

  • Using the wrong contract value in beta hedging

    Fix: Futures value A = index level × multiplier. Write it as a separate line before computing N.

  • Confusing the meaning of rolling and tailing

    Fix: Link tailing to daily settlement and the size of the position. Link rolling to hedge horizons that are longer than the contract life.

Last-day revision: Using Futures for Hedging

  • A short hedge protects an asset you own or will sell; a long hedge protects a future purchase.
  • Basis = spot price − futures price; a hedger is exposed to changes in basis. A strengthening basis benefits a short hedger; a weakening basis benefits a long hedger.
  • Basis risk arises when the asset hedged differs from the futures asset or the dates do not match. It is why hedges are imperfect. Hedging with a different but related asset can also make h* differ from 1.
  • Minimum variance hedge ratio: h* = ρ × σS ÷ σF.
  • h* differs from 1 when ρ < 1 or σS ≠ σF.
  • Number of contracts: N* = h* × QA ÷ QF.
  • Hedge effectiveness equals ρ², the share of spot variance removed.
  • h* is the slope from regressing spot price changes on futures price changes.
  • If ρ = 1 and σS = σF, then h* = 1.
  • Beta hedge contracts: N = (β* − β) × P ÷ A; a negative result means sell futures.
  • To take beta to zero, sell β × P ÷ A contracts.
  • Tailing adjusts the contract count by the ratio of the spot value of the exposure to the value of one futures contract: N* = h* × VA ÷ VF, where VA = QA × S and VF = QF × F. This equals h* × QA ÷ QF × (S ÷ F) and reflects daily settlement. The count falls when the futures price exceeds the spot price.
  • Rolling a hedge forward adds basis risk at each roll date.

Using Futures for Hedging practice questions

Using Futures for Hedging in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Using Futures for Hedging: frequently asked questions

What is the minimum variance hedge ratio in FRM Part I?

It is the hedge ratio that minimises the variance of the hedged position. It equals ρ × σS ÷ σF, where ρ is the correlation between spot and futures price changes. It is also the slope of a regression of spot changes on futures changes.

How do I calculate the number of futures contracts for a hedge?

First find h*. Then compute N* = h* × QA ÷ QF, where QA is the size of the exposure and QF is the size of one futures contract. Round to the nearest whole contract if the question asks for it.

How do I hedge a stock portfolio with index futures?

Use N = (β* − β) × P ÷ A, where β* is the target beta, β is the current beta, P is the portfolio value and A is the value of one futures contract. A negative answer means you sell contracts.

Does a good hedge remove basis risk?

No. A hedge can reduce price risk, but changes in the basis still affect the result. Basis risk is larger when the hedged asset differs from the futures asset or when the hedge ends at a different date than contract expiry.