CFA Level I Derivatives practice questions
25 exam-style questions from across Derivatives, which is 6–9% of the Level I exam (roughly 11–16 of the 180 questions). Pick an answer to see whether you were right, why each option is right or wrong, and the lesson to go back to.
Module 1 Derivatives and Derivative Markets
-
1Which of the following is best described as a contingent claim?
Show the answer
The answer is B.
A. Both sides must settle, so it is a firm commitment. The fixed price only feels like a right. The trap
B. The buyer of the option chooses whether to exercise, so it is a contingent claim.
C. A swap obliges both sides to make the agreed payments: a firm commitment.
From the lesson What a derivative is
-
2Futures on coffee and live cattle are best described as derivatives on:
Show the answer
The answer is B.
A. Hard commodities are extracted resources, such as energy and metals. The trap
B. Coffee and cattle are agricultural products, so they are soft commodities.
C. A commodity future references a good, not a rate.
From the lesson What derivatives are written on: the main underlyings
-
3Compared with OTC derivatives, exchange-traded derivatives are most likely to have:
Show the answer
The answer is B.
A. Customized terms are the OTC feature; exchanges standardize contracts.
B. Standardization and trading volume lower costs.
C. This reverses the relationship. The exchange guarantees performance and requires margin. The trap
From the lesson OTC vs exchange-traded derivatives and central clearing
Module 2 Forwards, Futures, Swaps, Options and Credit Derivatives
-
4An investor is long one futures contract on 1,000 units with initial margin of EUR 6,000 and maintenance margin of EUR 4,400. The settlement price falls by EUR 1.80 on the first day. The variation margin the investor must deposit is closest to:
Show the answer
The answer is C.
A. Tops the account up to the maintenance margin only: 4,400 − 4,200. The trap
B. This is the gap between initial and maintenance margin, 6,000 − 4,400, which is not the amount needed.
C. Loss = 1.80 × 1,000 = 1,800, so the balance is 4,200, below 4,400. Restore to 6,000: 6,000 − 4,200 = 1,800.
On your calculator- 1.8×1000= loss 1800
- +|-+6000= balance 4200, below 4400
- 6000−4200= call 1800
+|- change sign
- 1.8ENTER1000× loss 1800
- CHS6000+ balance 4200, below 4400
- 6000ENTER4200− call 1800
ENTER enter (on the HP, puts the number on the stack) · CHS change sign
From the lesson Futures contracts, daily settlement and margin calls
-
5An investor buys a call with an exercise price of USD 105 for a premium of USD 6.40. At expiration the stock is USD 112. The investor's profit per share is closest to:
Show the answer
The answer is A.
A. Payoff = max(0, 112 − 105) = 7.00. Profit = 7.00 − 6.40 = 0.60.
B. This is the premium paid, not the profit.
C. This is the payoff. It ignores the premium. The trap
On your calculator- 112−105= payoff 7
- −6.4= 0.6
- 112ENTER105− payoff 7
- 6.4− 0.6
ENTER enter (on the HP, puts the number on the stack)
From the lesson Call and put options: payoff and profit at expiration
-
6Which position gains when the underlying price falls?
Show the answer
The answer is C.
A. A short put gains when the price rises, to a maximum of the premium. The trap
B. A long call gains when the price rises.
C. The short forward's payoff, F₀(T) − S_T, increases as S_T falls.
From the lesson Forward commitments vs contingent claims
Module 3 Derivative Benefits, Risks and Uses
-
7News breaks overnight while the stock exchange is closed, and equity index futures fall 1.5% in early trading. A portfolio manager uses that move to estimate where share prices will open. This is an example of:
Show the answer
The answer is B.
A. No risk moves from one party to another when someone only reads a price. The trap
B. Futures prices reveal information about where cash market prices are heading.
C. The manager is not saving cash or cost by trading a derivative, only reading the information in its price.
From the lesson Why use derivatives: the four benefits
-
8A fund hedges a portfolio of small-cap technology shares with futures on a broad large-cap index. The risk that the hedge gains less than the portfolio loses is best described as:
Show the answer
The answer is C.
A. Liquidity risk is about the timing of cash flows, not the value of the hedge. The trap
B. Nobody is failing to pay in this scenario.
C. The index differs from the portfolio, so the values of hedge and exposure diverge. That is basis risk.
From the lesson Derivative risks: leverage, basis, liquidity, counterparty and systemic
-
9A company with fixed-rate bonds outstanding enters a swap to receive fixed and pay floating. Under hedge accounting this is most likely a:
Show the answer
The answer is C.
A. A cash flow hedge absorbs variable cash flows. Here the swap turns fixed payments into floating ones. The trap
B. No foreign operation is involved.
C. The swap offsets changes in the fair value of the fixed-rate debt.
From the lesson How companies use derivatives: hedge accounting
Module 4 Arbitrage, Replication and the Cost of Carry
-
10An arbitrage opportunity most likely exists when:
Show the answer
The answer is A.
A. Identical cash flows must sell for the same price. If they do not, buying the cheap one and shorting the dear one locks in a riskless profit.
B. A higher expected return is a reward for bearing risk. It is not riskless, so it is not an arbitrage.
C. With a positive risk-free rate, a forward price above spot is normal. It is the cost of carry, not a mispricing. The trap
From the lesson Arbitrage and the law of one price
-
11A share pays no dividends and trades at GBP 120. The risk-free rate is 5% a year. The no-arbitrage three-month forward price is closest to:
Show the answer
The answer is A.
A. 120 × 1.05^0.25 = 121.47.
B. Uses simple interest: 120 × (1 + 0.05 × 0.25). The convention is compounding. The trap
C. Compounds for a full year: 120 × 1.05. The contract runs only three months.
On your calculator- 1.05y^x0.25=×120= 121.4727
y^x power
- 1.05ENTER0.25y^x120× 121.4727
ENTER enter (on the HP, puts the number on the stack) · y^x power
From the lesson Replication and the no-arbitrage forward price
-
12A commodity trades at USD 80. The present value of storage costs for one year is USD 2 and the risk-free rate is 5%. The one-year no-arbitrage forward price is closest to:
Show the answer
The answer is C.
A. Ignores the storage cost: 80 × 1.05.
B. Adds the storage cost without compounding it: 80 × 1.05 + 2. The present value of the cost has to be inside the bracket. The trap
C. (80 + 2) × 1.05 = 86.10.
On your calculator- 80+2=×1.05= 86.1
- 80ENTER2+1.05× 86.1
ENTER enter (on the HP, puts the number on the stack)
From the lesson Cost of carry: income, storage and convenience yield
Module 5 Pricing and Valuing Forward Contracts and FRAs
-
13A one-year forward was agreed at F₀(T) = CHF 62.00. Three months later the spot price is CHF 63.10 and the risk-free rate is 4%. The asset pays no income and has no costs. The value of the long position is closest to:
Show the answer
The answer is B.
A. Uses the expiration formula, 63.10 − 62.00. Before expiry the forward price must be discounted.
B. Nine months remain: 63.10 − 62.00 × 1.04^−0.75 = 63.10 − 60.20 = 2.90.
C. Discounts the forward price over the full year, 62.00 × 1.04^−1 = 59.62. Only the remaining nine months count. The trap
On your calculator- 1.04y^x0.75+|-=×62= 60.20
- +|-+63.1= 2.90
y^x power · +|- change sign
- 1.04ENTER0.75CHSy^x62× 60.20
- CHS63.1+ 2.90
ENTER enter (on the HP, puts the number on the stack) · CHS change sign · y^x power
From the lesson Forward price vs forward value: at initiation, during the life, at expiry
-
14Two long forwards have the same forward price, the same expiration date and, today, the same spot price. The underlying of the first will pay a dividend before expiration; the underlying of the second pays no income. Compared with the second, the value of the first long position today is most likely:
Show the answer
The answer is A.
A. With S_t and F₀(T) equal, the only difference is −PV_t(I). The dividend still to come comes off the spot price, because the long will not receive it.
B. Assumes the dividend no longer matters once the forward is agreed. Here both forwards share one price, so PV_t(I) is the only difference, and it lowers the first one's value. The trap
C. A dividend helps whoever owns the share, not the long forward, which does not receive it.
From the lesson Valuing a forward when the asset pays income or has costs
-
15The one-year spot rate is 2.5% and the two-year spot rate is 3.5%, both annually compounded. The one-year rate one year from now (1y1y) is closest to:
Show the answer
The answer is B.
A. Averages the two spot rates. A forward rate is not an average. The trap
B. 1.035² ÷ 1.025 − 1 = 1.071225 ÷ 1.025 − 1 = 4.51%.
C. Divides 1.035 by 1.025 and leaves out the second year of compounding in the two-year spot rate.
On your calculator- 1.035y^x2=÷1.025=−1= 0.0451
y^x power
- 1.035ENTER2y^x1.025÷1− 0.0451
ENTER enter (on the HP, puts the number on the stack) · y^x power
From the lesson Implied forward rates from spot rates
Module 6 Pricing and Valuing Futures Contracts
-
16Immediately after the daily settlement, the value of a long futures position is:
Show the answer
The answer is A.
A. Daily settlement pays the day's gain or loss into the margin account and re-sets the contract to the new settlement price, so its value is zero.
B. The cumulative gain has already been paid out through the margin account. It is not the contract's value.
C. That is the forward value formula. A forward is not settled until expiry, so it keeps accumulating value. The trap
From the lesson Futures price at inception and how daily settlement changes value
-
17If an asset's futures price is positively correlated with interest rates, compared with the forward price the futures price is most likely:
Show the answer
The answer is C.
A. Reverses the reinvestment logic. With positive correlation, futures gains come when rates are high and losses when rates are low, which favors the long. The trap
B. The prices are the same only when rates are constant or uncorrelated with the futures price.
C. Futures are more attractive to the long, and the more attractive contract has the higher price.
From the lesson Why forward and futures prices differ
Module 7 Pricing and Valuing Interest Rate Swaps
-
18A plain vanilla interest rate swap is best described as equivalent to:
Show the answer
The answer is B.
A. That describes a strip of at-market FRAs. Each would have zero value at the start, which is not true of the periods inside a swap. The trap
B. A swap applies one fixed rate to every period, so periods whose forward rate differs from it have non-zero value. Only the total is zero.
C. A swap has periodic settlements, not one settlement at maturity.
From the lesson A swap as a series of forwards: what is the same and what is different
-
19The one-year spot rate is 2% and the two-year spot rate is 3% (annual compounding). The two-year par swap rate (annual payments) is closest to:
Show the answer
The answer is B.
A. Averages the two spot rates. The swap rate comes from discount factors. The trap
B. DF₁ = 1 ÷ 1.02 = 0.98039 and DF₂ = 1 ÷ 1.03² = 0.94260. s₂ = (1 − 0.94260) ÷ (0.98039 + 0.94260) = 0.05740 ÷ 1.92299 = 2.985%.
C. The second-year forward rate, 1.03² ÷ 1.02 − 1 = 4.01%. The swap rate is a blend of the forwards for both years (2.00% and 4.01%), not the last one.
On your calculator- 1.021/xSTO1 0.98039
- 1.03y^x2=1/xSTO2 0.9426
- 1−RCL2=÷(RCL1+RCL2)= 0.029852
1/x reciprocal · STO store · y^x power · RCL recall a stored number
- 1.021/xSTO1 0.98039
- 1.03ENTER2y^x1/xSTO2 0.9426
- 1ENTERRCL2−RCL1RCL2+÷ 0.029852
1/x reciprocal · STO store · ENTER enter (on the HP, puts the number on the stack) · y^x power · RCL recall a stored number
From the lesson The swap price: solving for the par swap rate
Module 8 Pricing and Valuing Options
-
20A put has an exercise price of EUR 120, six months to expiry, and the risk-free rate is 3%. The underlying trades at EUR 112 and pays no income. The put trades at EUR 10.20. Its time value is closest to:
Show the answer
The answer is B.
A. Uses X instead of PV(X): exercise value 120 − 112 = 8.00, and 10.20 − 8.00 = 2.20. The trap
B. PV(X) = 120 × 1.03^−0.5 = 118.24. Exercise value = 118.24 − 112 = 6.24. Time value = 10.20 − 6.24 = 3.96.
C. This is the exercise value, not the time value.
On your calculator- 1.03y^x0.5+|-=×120= 118.24
- −112= 6.24
- +|-+10.2= 3.96
y^x power · +|- change sign
- 1.03ENTER0.5CHSy^x120× 118.24
- 112− 6.24
- CHS10.2+ 3.96
ENTER enter (on the HP, puts the number on the stack) · CHS change sign · y^x power
From the lesson Exercise value, moneyness and time value
-
21All else equal, an increase in the risk-free rate will most likely:
Show the answer
The answer is A.
A. A higher rate lowers PV(X). That helps the payer of X (call) and hurts the receiver of X (put).
B. Reverses the PV(X) logic. The trap
C. Both rising is the volatility effect, not the rate effect.
From the lesson Six factors that move an option's value
Module 9 Put–Call Parity and Option Replication
-
22A share trades at USD 100. A one-year European put with an exercise price of USD 95 costs USD 3.20, and the risk-free rate is 5%. The share pays no income. The price of the European call with the same exercise price and expiry is closest to:
Show the answer
The answer is B.
A. Uses X instead of PV(X): 100 + 3.20 − 95. The trap
B. PV(X) = 95 ÷ 1.05 = 90.48. c = S + p − PV(X) = 100 + 3.20 − 90.48 = 12.72.
C. Subtracts the put instead of adding it: 100 − 3.20 − 90.48. Keep the put on the share's side: S + p = c + PV(X).
On your calculator- 95÷1.05= 90.48
- +|-+100+3.2= 12.72
+|- change sign
- 95ENTER1.05÷ 90.48
- CHS100+3.2+ 12.72
ENTER enter (on the HP, puts the number on the stack) · CHS change sign
From the lesson Put–call parity: fiduciary call = protective put
-
23A long put option is equivalent to:
Show the answer
The answer is B.
A. That mixes up the signs: long share, long call and short bond is not a put. The trap
B. Parity gives p = c + PV(X) − S: buy the call, buy the bond, sell the share short.
C. Long share, short call and short bond is S − c − PV(X), which is a short put, the opposite of the target.
From the lesson Building synthetic positions with put–call parity
Module 10 The One-Period Binomial Model
-
24A share at USD 40 will be USD 48 or USD 36 in one period. A call with an exercise price of USD 40 pays USD 8 or zero. The hedge ratio is closest to:
Show the answer
The answer is B.
A. Divides the up payoff by the share price today: 8 ÷ 40. The denominator is the spread of share prices at expiry.
B. (8 − 0) ÷ (48 − 36) = 8 ÷ 12 = 0.67.
C. Turns the ratio upside down: 12 ÷ 8. It is the spread of option payoffs over the spread of share prices. The trap
On your calculator- 8÷(48−36)= 0.6667
- 8ENTER48ENTER36−÷ 0.6667
ENTER enter (on the HP, puts the number on the stack)
From the lesson The one-period binomial tree and the hedge ratio
-
25A share is EUR 40. In one year it will rise 20% or fall 10%, and the risk-free rate is 4%. The risk-neutral probability of an up move is closest to:
Show the answer
The answer is B.
A. Leaves the risk-free rate out of the top: (1 − 0.90) ÷ 0.30. The top is 1 + r − R_d.
B. π = (1.04 − 0.90) ÷ (1.20 − 0.90) = 0.14 ÷ 0.30 = 0.467.
C. Assumes equal odds. The risk-neutral probability comes from the tree and r, not from a guess. The trap
On your calculator- 1.04−0.9=÷(1.2−0.9)= 0.4667
- 1.04ENTER0.9−1.2ENTER0.9−÷ 0.4667
ENTER enter (on the HP, puts the number on the stack)
From the lesson Pricing calls and puts with risk-neutral probabilities
Keep going
Study the topic module by module in the Derivatives lessons, look up a word in the Level I glossary, or run a timed practice set that tracks your score by topic.