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Chartered Financial Analyst · Level I

CFA L1 Derivatives and Risk Management: practice questions with answers

6 free exam-style questions on Derivatives and Risk Management for CFA L1 Level I. Try each one, then open the answer to read the explanation. Fincora has 52 original questions on this syllabus area.

Question 1

A trader goes long one futures contract on 100 units of a commodity at a futures price of USD 250.00 per unit. The initial margin is USD 2,000 per contract and the maintenance margin is USD 1,500 per contract. Settlement prices are USD 247.00 at the end of day 1 and USD 244.00 at the end of day 2. The variation margin the trader must deposit at the end of day 2 is closest to:

  1. A USD 100
  2. B USD 300
  3. C USD 600
Show the answer

Answer: C. Each USD 1.00 move in price changes the account by 100 × 1.00 = USD 100. Day 1: price falls 3.00, loss = 300, balance = 2,000 - 300 = 1,700 (above 1,500, no call). Day 2: price falls another 3.00, loss = 300, balance = 1,400. This is below the maintenance margin of 1,500, so a margin call is issued and the trader must deposit variation margin to restore the balance to the initial margin: 2,000 - 1,400 = USD 600.

Question 2

A non-dividend-paying share trades at EUR 42.00. A six-month European call option on the share with an exercise price of EUR 40.00 costs EUR 5.20. The risk-free rate is 3% per year with annual compounding. Using put-call parity, the price of a six-month European put option with the same exercise price is closest to:

  1. A EUR 2.61
  2. B EUR 3.20
  3. C EUR 7.79
Show the answer

Answer: A. Put-call parity: S0 + p0 = c0 + X / (1 + r)^T (a fiduciary call equals a protective put). Rearranging: p0 = c0 - S0 + X / (1 + r)^T. PV of X = 40.00 / 1.03^0.5 = 39.41. p0 = 5.20 - 42.00 + 39.41 = EUR 2.61.

Question 3

Yesterday a trader went long one equity index futures contract at a price of 1,412.50, with a multiplier of USD 50 per index point. Yesterday's settlement price was 1,418.00, and the trader's account was marked to market at that price. Today, before the daily settlement, the futures price is 1,409.25. The value of the trader's futures contract at this moment is closest to:

  1. A -USD 437.50
  2. B -USD 162.50
  3. C USD 0
Show the answer

Answer: A. Marking to market settles the gain or loss each day and effectively resets the contract price to the settlement price.
- Yesterday: gain of (1,418.00 - 1,412.50) x 50 = USD 275 credited to the account; contract value reset to zero.
- Now, before today's settlement: value = (current futures price - last settlement price) x multiplier = (1,409.25 - 1,418.00) x 50 = -USD 437.50.
At today's settlement this amount will be paid and the value will again be zero.

Question 4

Eight months ago, Caradoc Partners entered into a short forward contract to sell a share in one year at USD 85.00. The share now trades at USD 88.00, and it will pay a dividend of USD 1.50 in two months, before the forward expires in four months. The risk-free rate is 4.8% per year with annual compounding. The value of the forward contract to Caradoc today is closest to:

  1. A -USD 4.32
  2. B -USD 2.83
  3. C USD 2.83
Show the answer

Answer: B. During its life, the value of a long forward on a share with a dividend is:
V_t(long) = S_t - PV(dividends before expiration) - F0 / (1 + r)^(T - t)
- PV of dividend = 1.50 / 1.048^(2/12) = 1.4883
- PV of forward price = 85.00 / 1.048^(4/12) = 83.6820
- V(long) = 88.00 - 1.4883 - 83.6820 = 2.8297
The value to the short is the negative: -USD 2.83. The share price has risen above the level implied by the contract price, so Caradoc, which has agreed to sell at USD 85.00, has lost value.

Question 5

All options below are European options on the same non-dividend-paying share, with exercise price X and the same expiration date, and the bond is a risk-free zero-coupon bond that pays X at expiration. Which portfolio replicates the payoff at expiration of a long put option?

  1. A Long call, short share, long bond
  2. B Long call, long share, short bond
  3. C Short call, long share, long bond
Show the answer

Answer: A. Put-call parity: S0 + p0 = c0 + X / (1 + r)^T (protective put = fiduciary call).
Rearranging: p0 = c0 - S0 + X / (1 + r)^T.
So a synthetic long put = long call + short share + long risk-free bond paying X.
Check at expiration: if S_T < X, payoff = 0 - S_T + X = X - S_T; if S_T >= X, payoff = (S_T - X) - S_T + X = 0. Both match a put.

Question 6

A futures contract was entered into two days ago. Immediately after today's daily settlement (marking to market), the value of the contract to the long position is:

  1. A equal to the cumulative change in the futures price since the contract was entered, multiplied by the contract size.
  2. B the present value of the difference between today's futures price and the original futures price.
  3. C zero.
Show the answer

Answer: C. Between settlements, a futures contract's value is the change in the futures price since the last settlement, times the contract size. At each daily settlement this gain or loss is credited or debited to the margin account and the contract is effectively re-struck at the new settlement price, so its value goes back to zero. A forward contract, by contrast, builds up value over its life, equal to the present value of the difference between the current forward price and the contract price.

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