Practice: Pricing and Valuation of Futures Contracts
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DerivativesPricing and Valuation of Futures Contracts
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Question 1Exam level
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?
How sure are you?
Correct: 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.
B. You might be thinking that direct payments are made between the parties involved, but futures contracts settle through a clearinghouse, not directly between counterparties, so you would not pay $10 directly to the counterparty.
C. You might think that a rise in futures price requires additional margin, but initial margin is a fixed amount set at the beginning and does not change daily with price fluctuations; instead, daily price changes affect the variation margin, which is credited or debited to your margin account.
Unit: pricing-and-valuation-of-futures-contracts
Question 2Exam level
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?
How sure are you?
Correct: B. When a margin account falls below the maintenance margin level (here $5,000 - $1,500 = $3,500, which is below $3,750 maintenance), a margin call is triggered. The critical CFA exam point: when a margin call is received, the trader must restore the account to the INITIAL margin level ($5,000), not merely the maintenance margin level. This is the #1 exam trap on this topic. Answer B is wrong because it describes restoring to maintenance margin, which is incorrect for futures.
A. Choosing A might seem logical if you think maintaining the minimum required balance is sufficient, but this overlooks the rule that a margin call requires you to restore the account to the initial margin level of $5,000, not just the maintenance level.
C. You might be thinking that exchanges automatically close positions to prevent further losses, but this confuses futures trading rules with some spot market practices; in futures, a margin call requires you to top up the account to the initial margin level rather than having the position closed automatically by the exchange.
Unit: pricing-and-valuation-of-futures-contracts
Question 3Exam 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.
Unit: pricing-and-valuation-of-futures-contracts
Question 4Exam 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.
Unit: pricing-and-valuation-of-futures-contracts
Question 5Exam 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.
Unit: pricing-and-valuation-of-futures-contracts
Question 6Exam 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.
Unit: pricing-and-valuation-of-futures-contracts
Question 7Harder
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 8Exam 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 9Exam 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 10Harder
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 11Exam 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 12Exam 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 13Above 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 14Above 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.