Pricing and Valuation of Futures Contracts

Derivatives. Worth 5 to 8 percent of the exam. One session: the lesson, the rules, the method, then the questions.

DerivativesPricing and Valuation of Futures Contracts
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The lesson

The video lesson for this unit is recorded and waiting to be published. Until it is, the rules and the method below carry everything this session needs; watching is a way of hearing it, not the only way of getting it.

The reading

Five to ten minutes on this one unit: what the exam wants, the idea in plain words, then straight into the trap and the practice.

The exam wants you to calculate the required deposit on a futures margin call, calculate basis using the CFA convention and describe convergence at expiration, describe why futures value resets toward zero daily while forward value accumulates, and compare the market and academic definitions of backwardation.

A futures contract is the standardized, exchange-traded version of a forward: fixed contract size, fixed delivery grade, fixed expiration, all set by the exchange rather than negotiated bilaterally. The single feature that drives almost everything else in this module is that a futures contract settles daily, through mark-to-market, rather than once at expiration. Immediately after each day's settlement, a futures position's carried-forward value resets to approximately zero, since every prior day's gain or loss has already been paid or collected in cash. A forward carries no such daily settlement, so its value, the same (Ft - F0) discounted figure from forward valuation, accumulates and can grow substantially away from zero well before the contract ever expires.

The margin call calculation is the most heavily tested numerical question in this module, and it runs in three fixed steps. First, calculate the new margin account balance after a loss. Second, check whether that new balance has fallen below the maintenance margin level; if so, a margin call is triggered. Third, the required deposit equals the initial margin minus the current balance, never the maintenance margin minus the current balance. Maintenance margin is only the alarm that triggers the call; initial margin is the full target level the account must be restored to.

Basis, under the CFA convention, is spot price minus futures price, never the reverse. When the futures price sits above spot, the normal condition for most financial assets once financing costs are built in, basis is negative, a condition called contango. When spot sits above the futures price, common for commodities carrying a high convenience yield, basis is positive, called backwardation in market terms. At expiration, basis must converge to exactly zero, enforced by arbitrage. If futures traded above spot right at expiration, buying spot and delivering against the futures would lock in a riskless profit. That opportunity disappears the instant the market notices it.

Backwardation carries two distinct definitions the exam tests separately. The market definition says futures prices sit below the current spot price. The academic, Keynes-Hicks definition compares the futures price to the expected future spot price instead, not the current one. Commodity producers, who are net short as hedgers, must set the futures price below the expected future spot price to attract speculators willing to go long. That gap compensates those speculators for bearing the risk. A question that names an expected future spot price is testing the academic definition. One that only references the current spot price and the shape of the futures curve is using the market definition instead.

Under constant, deterministic interest rates, the no-arbitrage forward price and futures price on the same underlying and the same maturity come out equal. The timing of daily settlement cash flows makes no financial difference when the financing rate never changes. Forward and futures prices diverge specifically once interest rates become stochastic and move together with the underlying's own price, not from any difference in credit risk or contract structure between the two instrument types.

Worked in full

A trader holds a long futures position with an initial margin of $12,000 and a maintenance margin of $9,000. The account balance currently stands at $9,500. The position loses $1,200 the next trading day. Is a margin call triggered, and if so, how much must be deposited? New balance = $9,500 - $1,200 = $8,300. Since $8,300 is below the $9,000 maintenance margin, a margin call is triggered. Required deposit = initial margin - new balance = $12,000 - $8,300 = $3,700. The trader must deposit $3,700 to restore the account to the full initial margin level, not merely back up to $9,000.

The same problem, one step removed

Same account: initial margin $12,000, maintenance margin $9,000, balance $9,500 before a $1,200 loss. Compute the new balance, confirm whether it triggers a call, then find the required deposit yourself.

The trap

A margin call restores the account to the full initial margin level, not merely up to the maintenance margin threshold; maintenance margin is only the trigger that sets off the call, and depositing just enough to reach maintenance margin again is the exam's standard wrong-answer choice.

What this unit turns on

Read these before the questions, not after them. Everything here traces to this module's own lesson and to the 2026 outline.

Daily mark-to-market resets a futures contract's value to zero, while a forward's value accumulates unrealized until expiration

A futures contract settles its gain or loss in cash every trading day, so immediately after each daily settlement its value is reset to approximately zero; the contract carries forward no unrealized gain or loss from prior days. A forward contract has no such daily cash settlement, so its value, Vt = (Ft - F0) discounted back to today, accumulates and can grow substantially away from zero well before expiration, only settling in full at the end. The two instruments can have identical prices at initiation and still carry very different values partway through their lives, precisely because of this settlement mechanics difference.

Under constant, deterministic interest rates, the no-arbitrage forward price and futures price on the same underlying and maturity are equal

When the risk-free rate is known and unchanging over the life of the contract, the sequence of daily settlement cash flows on a futures position can be reinvested or financed at exactly the same rate regardless of when they occur, so there is no financial advantage to receiving cash flows daily (as with futures) versus receiving the full amount at expiration (as with a forward). Under this assumption, the no-arbitrage pricing logic that determines the forward price applies equally to the futures price, and the two prices coincide.

Forward and futures prices diverge specifically when interest rates are stochastic and correlated with the underlying's price movements

If interest rates vary unpredictably and move in the same direction as the underlying asset's price, a long futures position's daily mark-to-market gains, received exactly when the underlying is rising, tend to be reinvested at a higher rate at those same moments, and its losses, incurred when the underlying is falling, tend to be financed at a lower rate; this systematic reinvestment advantage (or, for negative correlation, disadvantage) has no equivalent in a forward contract, whose single terminal payoff is not exposed to interim reinvestment risk at all. This interest-rate-correlation effect, not any difference in credit risk or contract structure, is the specific, examinable reason forward and futures prices can differ.

The trick

Futures value resets to zero every day; forward value accumulates until expiration

Immediately after daily settlement a futures position's carried-forward value is approximately zero; a forward's unrealized value can be large right up until the moment it finally settles.

Forward price equals futures price only under one specific assumption: constant, deterministic interest rates

This equality is not automatic or a given; the exam tests the precise condition under which it holds, and the precise condition under which it breaks.

Price divergence comes from the correlation between interest rates and the underlying, not from credit risk or contract structure

A candidate who answers a forward-versus-futures price divergence question by citing counterparty credit risk or margin has answered a different, related question; the specific driver here is the reinvestment effect of daily settlement under stochastic, correlated rates.

The method

The order to work a question of this type in, every time, before you touch the numbers.

  1. For a value-comparison question, remember futures value resets to approximately zero at each daily settlement, while forward value accumulates unrealized until expiration.
  2. For a price-equality question, check whether the question specifies constant or deterministic interest rates; if so, forward price and futures price are equal.
  3. For a price-divergence question, look for stochastic interest rates correlated with the underlying's price as the specific driver, not credit risk, margin, or contract standardization.

Two worked examples, then you are on your own

The first is worked in full. The second gives you the setup and stops. After that the questions give you nothing, which is the point: the help fades on purpose, so the last thing you practise is the thing the exam actually asks of you.

Worked in full

An investor enters a long futures contract when the futures price is $1,050. The following day, the futures price rises to $1,060. Which of the following best describes the settlement that occurs?

Answer A. Futures contracts use daily mark-to-market settlement. When the price rises by $10, the long position gains $10 per unit of underlying, and this amount is credited to the long's margin account by the clearinghouse. The short's margin account is debited $10. This is variation margin. Distinct from initial margin. Settlement is through the clearinghouse, not directly between counterparties. The gain is realized daily, not at expiration.

Your turn, setup given

A trader enters a short futures position on crude oil. Initial margin is $5,000 and maintenance margin is $3,750. After three days, cumulative losses total $1,500. Which of the following best describes the required action?

For a value-comparison question, remember futures value resets to approximately zero at each daily settlement, while forward value accumulates unrealized until expiration.

The practice run

Pick an answer, say how sure you are, then reveal. Being sure and wrong is the most useful thing that can happen in a session, so answer honestly: it sends the unit back to learning and puts it at the front of your revision queue.

Question 1Exam level

At futures contract expiration, which of the following is most accurate regarding the relationship between the futures price and the spot price?

How sure are you?

Correct: A. At expiration, the futures price must converge to the spot price. This is enforced by arbitrage: if the futures price differed from the spot price at expiration, traders could simultaneously transact in both markets for a risk-free profit until prices converge. This convergence means basis (= spot price - futures price, using CFA convention) equals zero at expiration. Answer D is wrong because the futures price changes daily via mark-to-market; it is NOT the original agreed price at expiration.
B. You might be thinking that convenience yield makes futures prices lower than spot prices, but this confuses the role of convenience yield in creating a premium for holding the physical asset, not a discount; at expiration, convergence ensures futures and spot prices align.
C. You might be tempted to choose C because it seems logical that prices would stay fixed as agreed, but futures prices adjust daily based on market conditions, not the initial agreement, unlike forward contracts which lock in a price at initiation.

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Question 2Exam level

The spot price of gold is $1,900/oz and the 3-month futures price is $1,930/oz. The basis using the CFA Institute convention is closest to:

How sure are you?

Correct: B. The CFA Institute defines basis as: Basis = Spot Price - Futures Price. Therefore: $1,900 - $1,930 = -$30. Negative basis (basis = -$30) is the normal condition for financial assets and storable commodities under contango. The futures price exceeds the spot price because of carrying costs (storage, financing). This is called a negative basis or inverse basis. A positive basis (spot > futures) is called a normal basis or backwardation. Candidates who define basis as futures minus spot get the sign convention backwards.
A. You might be tempted to choose +$30 if you mistakenly subtract the spot price from the futures price, but the CFA Institute defines basis as spot price minus futures price, making +$30 incorrect and violating the proper sign convention for basis calculation.
C. Choosing +$1,900 might tempt you if you mistakenly added the spot price to the difference between the futures and spot prices, but the basis calculation strictly requires subtracting the futures price from the spot price, making +$1,900 an incorrect representation of the basis.

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Question 3Exam level

Which of the following is most likely the most significant difference between a futures contract and a forward contract from a credit risk perspective?

How sure are you?

Correct: A. The daily mark-to-market mechanism is the key credit risk differentiator. In a forward contract, gains and losses accumulate unrealized throughout the contract life. Creating large bilateral credit exposure by expiration. In a futures contract, gains and losses are settled daily in cash, so the maximum credit exposure at any time is limited to one day's price move. The clearinghouse acts as central counterparty, but the daily settlement mechanism is what eliminates the accumulation of credit exposure. Answer A is correct but describes standardization (a different distinction). Answer C is backwards. Futures require margin, forwards typically do not.
B. You might be misled by the idea that forwards, being less standardized, require margin to mitigate risk, but in reality, futures require margin to support daily mark-to-market settlements, whereas forwards typically do not require margin, thus accumulating credit risk over time.
C. You might be tempted by choice C because it sounds like exchanges provide a blanket guarantee, but exchanges act as intermediaries through clearinghouses, not as insurers against default, which is different from the daily mark-to-market mechanism that actually limits credit exposure in futures.

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Question 4Exam level

A corn farmer wants to hedge a harvest in 4 months using CME corn futures. She enters a short futures position. At expiration, the local elevator price is $4.20/bushel but the CME futures settlement price is $4.35/bushel. The farmer originally entered the short futures at $4.40/bushel. Her effective selling price per bushel is closest to:

How sure are you?

Correct: B. The effective selling price = local spot price received + gain/loss on futures. Futures gain (short position): $4.40 - $4.35 = +$0.05/bushel (she shorted at $4.40, futures settled at $4.35. Short gains when price falls). Effective price = $4.20 (local spot) + $0.05 (futures gain) = $4.25. She expected $4.40 but received $4.25 due to basis risk: the local price ($4.20) did not equal the CME settlement price ($4.35). The basis at initiation was $4.20 - $4.40 = -$0.20; at expiration, basis was $4.20 - $4.35 = -$0.15. The basis strengthened (became less negative), which benefits the short hedger. This $0.05 improvement = the effective price improvement over local spot.
A. Choosing $4.35 might seem logical if you think the futures settlement price directly determines the effective selling price, but this overlooks the impact of the local elevator price and the gain from the futures position, which together adjust the effective price to $4.25.
C. Choosing $4.20 might seem logical if you only consider the local elevator price, but this overlooks the gain from the futures market; the effective price must include the $0.05 gain from the short futures position, making $4.20 too low.

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Question 5Harder

In a normal market (contango), which of the following statements about the term structure of futures prices is most accurate?

How sure are you?

Correct: A. Contango describes a market where futures prices are higher for longer-dated contracts. The primary driver is the cost of carry: to hold the underlying asset until delivery, the holder incurs financing costs (the risk-free rate applied to the spot price) plus storage costs, less any convenience yield or dividends. These carrying costs cause futures prices to exceed near-term spot prices and to be higher for more distant contracts. This is the 'normal' state for financial assets and most storable commodities. Answer D describes a relationship between futures and expected future spot (which defines normal backwardation/contango in the Keynes-Hicks theory). Different from the cost-of-carry contango.
B. Choosing B might seem logical if you assume that futures prices should mirror the current spot price, but this ignores the cost of carry that causes futures prices to rise with longer expiration times, directly contradicting the concept of contango.
C. Choosing C might seem logical if you think futures prices always exceed what the market expects the future spot price to be, but this overlooks the cost-of-carry model, which explains why futures prices increase with time to expiration due to carrying costs rather than solely reflecting expectations of future spot prices.

Unit: pricing-and-valuation-of-futures-contracts

Question 6Exam level

A trader holds a long futures position. The initial margin is $8,000, the maintenance margin is $6,000, and the current margin account balance is $6,500. The next day, the position loses $700. Which of the following best describes what happens?

How sure are you?

Correct: B. Step 1: New balance = $6,500 - $700 = $5,800. Step 2: $5,800 < $6,000 maintenance margin threshold. Margin call triggered. Step 3: Amount to deposit = initial margin - current balance = $8,000 - $5,800 = $2,200. The key rule: a margin call always requires restoration to the INITIAL margin level, not the maintenance margin level. The maintenance margin is simply the trigger; the initial margin is the target. This is the most tested numerical question type on futures margin.
A. 5,800 is below the $6,000 maintenance margin, which is exactly the trigger for a margin call. Being positive is not enough; the balance must stay at or above the maintenance level.
C. A margin call requires restoring the account to the INITIAL margin level ($8,000), not simply replacing the day's loss. The required deposit is $8,000 minus the new balance ($5,800) = $2,200, not the $700 loss itself.

Unit: pricing-and-valuation-of-futures-contracts

Question 7Exam level

Which of the following most likely explains why futures contracts have essentially no credit risk while forward contracts do carry significant credit risk?

How sure are you?

Correct: B. Credit risk in derivatives arises from the accumulation of unrealized gains over the life of the contract. If the counterparty defaults after a large favorable price move, you lose those gains. In forwards, this accumulation is unrestricted over the entire contract life (often months or years). Futures eliminate this through daily settlement: each day's gain or loss is paid in cash, resetting the accumulated unrealized exposure to near zero each day. The maximum loss to default is therefore one day's price move, not the full contract life. Margin (answer D) is a mechanism, but it is the daily settlement that actually eliminates credit risk accumulation.
A. You might be tempted by choice A because exchange-traded futures are indeed more liquid than forwards, but liquidity does not address credit risk; instead, it is the daily mark-to-market settlement that minimizes credit risk by preventing large unrealized losses from accumulating.
C. You might think initial margin protects against credit risk by ensuring funds are available, but initial margin only covers a portion of potential losses and does not prevent the accumulation of unrealized losses over time, unlike daily mark-to-market settlement which resets exposure daily.

Unit: pricing-and-valuation-of-futures-contracts

Question 8Harder

A futures price is in backwardation. Which of the following is most consistent with this description (using the CFA Institute definition)?

How sure are you?

Correct: A. Under the CFA Institute's academic definition (Keynes-Hicks normal backwardation theory): backwardation occurs when the futures price is BELOW the expected future spot price. The rationale: commodity producers (e.g., farmers, oil companies) are net short futures as hedgers. To attract speculators to take the other side (go long), the futures price must be set below the expected future spot. Giving speculators an expected profit as compensation for bearing price risk. As expiration approaches, the futures price rises toward the expected spot (and ultimately the spot itself), rewarding the long speculator. This is distinct from 'inverted market' where futures < current spot.
B. Choosing B might seem logical if you think higher futures prices indicate backwardation, but this actually describes contango, where the futures price exceeds the expected future spot price, contrary to backwardation where the futures price is below the expected future spot price.
C. Choosing C might be tempting if you think that futures prices always equal spot prices at expiration, but this overlooks the dynamics of backwardation where the futures price is specifically below the expected future spot price, not equal to it at any time before expiration.

Unit: pricing-and-valuation-of-futures-contracts

Question 9Exam level

An investor enters a long futures position at $100. Over the next three days, the settlement prices are: Day 1: $104, Day 2: $99, Day 3: $106. The total gain or loss from daily settlement over the three days is closest to:

How sure are you?

Correct: A. Daily settlement credits/debits: Day 1: +$4 ($104 - $100), Day 2: -$5 ($99 - $104), Day 3: +$7 ($106 - $99). Total = +$4 - $5 + $7 = +$6. This equals the difference between the final settlement price and the entry price: $106 - $100 = $6. This confirms that daily settlement produces the same total P&L as a single settlement at expiration. The mechanism differs, not the outcome. The total gain is $6, regardless of path.
B. You might be tempted to add up the absolute values of daily changes, thinking each day's movement contributes positively to the total gain, but this approach ignores the fact that price declines reduce your overall gain, as seen on Day 2 when the price dropped from $104 to $99, resulting in a net debit of $5 that must be accounted for in the total P&L calculation.
C. You might be tempted to choose a gain of $2 if you mistakenly sum the daily changes without considering the cumulative effect of each day's settlement, leading to an incorrect total; this violates the concept of daily settlement where each day's gain or loss is based on the previous day's settlement price, not the initial entry price.

Unit: pricing-and-valuation-of-futures-contracts

Question 10Exam level

A hedger uses futures contracts to hedge a commodity position but finds that the hedge is not perfect at expiration. The imperfection arises because the local cash price moved differently from the futures settlement price. This risk is most likely described as:

How sure are you?

Correct: B. Basis risk is the risk that the relationship between the local cash (spot) price and the futures price changes unexpectedly. Since futures contracts are standardized (standard delivery location, grade, quantity), the local price a hedger actually transacts at may differ from the futures settlement price. This difference (basis = local spot - futures) can narrow or widen unpredictably, causing the hedge to be imperfect. A perfect hedge would require zero basis risk. This meaning local spot price tracks futures exactly. In practice, basis risk is unavoidable and is the primary residual risk in commodity hedging programs.
A. You might be tempted by liquidity risk because it involves the ease of entering and exiting positions, but liquidity risk pertains to the market's ability to handle large transactions without price impact, not the difference between local cash and futures prices like basis risk does.
C. Answer A (counterparty credit risk) is eliminated by daily settlement. Answer D (mark-to-market risk) is not a standard term. It describes the daily settlement mechanism, not a risk category. Basis risk is the correct term for imperfect hedge outcomes.

Unit: pricing-and-valuation-of-futures-contracts

Question 11Above the exam

An investor holds a long futures position on a commodity. Over three consecutive days, the settlement prices are: Day 1 close $52.00 (entered at $50.00), Day 2 close $49.50, Day 3 close $51.00. Combining the mechanics of daily mark-to-market settlement with a margin account that started at the $4,000 initial margin (1 contract, 100 units), the investor's margin account balance after Day 3 settlement, ignoring any margin calls or withdrawals, is closest to:

How sure are you?

Correct: A. Daily settlement gains/losses (per unit): Day 1: 52.00 - 50.00 = +2.00; Day 2: 49.50 - 52.00 = -2.50; Day 3: 51.00 - 49.50 = +1.50. Net cumulative change = +2.00 - 2.50 + 1.50 = +1.00 per unit, x100 units = +$100. Margin balance = $4,000 + $100 = $4,100. Daily settlement means each day's gain or loss is settled in cash to the margin account immediately, based on the change from the PRIOR day's settlement price, not the original entry price each time.
B. $4,300 would result from comparing only the final settlement price to the original entry price (51.00 - 50.00 = 1.00 x 100 = $100 gain, then possibly double counting or misapplying an intermediate figure); daily settlement requires summing each DAY'S incremental gain/loss, not just the net change from entry to the final price treated with a different multiplier.
C. $3,700 would result from applying the Day 2 loss without correctly offsetting it with both the Day 1 and Day 3 gains, understating the account's true cumulative position after all three days of mark-to-market settlement.

Unit: pricing-and-valuation-of-futures-contracts

Question 12Above the exam

A futures contract on a dividend-paying stock index is priced using the cost-of-carry model. The risk-free rate rises while the index's expected dividend yield stays the same. Combining the cost-of-carry components (financing cost minus dividend yield benefit), the no-arbitrage futures price relative to the spot index should most likely:

How sure are you?

Correct: A. The cost-of-carry model for a futures price on a dividend-paying index is approximately F0 = S0 x (1 + r - dividend yield)^T (or the continuous-compounding equivalent): the NET cost of carrying the underlying is financing cost MINUS the dividend income received while holding it. If the risk-free rate rises while the dividend yield is unchanged, the net carry cost increases, which raises the no-arbitrage futures price relative to the spot index.
B. This conflates the general effect of interest rates on asset VALUATIONS with the specific cost-of-carry relationship between a futures price and its OWN underlying spot price; within the cost-of-carry framework, a higher risk-free rate raises the futures price relative to spot, it does not lower it.
C. The risk-free rate is just as much a component of the cost-of-carry formula as the dividend yield; both financing cost and dividend yield jointly determine the futures-to-spot relationship, so a change in the risk-free rate alone does affect the result.

Unit: pricing-and-valuation-of-futures-contracts