CFA Level II Derivatives Practice Questions
Question 1
An analyst explains why an American put on a non-dividend-paying stock can be rationally exercised early even though an American call on the same stock should not be. Which reason is most accurate?
- A. A put holder receives the stock's dividends, which exceed the option's time value
- B. A put's time value rises as it moves deeper into the money, making early exercise a way to realize that gain
- C. Put payoffs are unbounded as the stock falls, so exercising early locks in a larger payoff
- D. Maximum put payoff is capped at the strike, so receiving it early and earning interest can outweigh remaining time value when deep in the money
Show answer and explanation
Correct answer: D. Maximum put payoff is capped at the strike, so receiving it early and earning interest can outweigh remaining time value when deep in the money
A put's value cannot exceed X, and when the stock is near zero the put is worth almost its payoff. Exercising early lets the holder invest the strike proceeds at the risk-free rate, which can exceed the small remaining time value.
- A. The stock in this example pays no dividends, and put holders do not receive them in any case.
- B. Time value of a put shrinks as it goes deep in the money, which is why early exercise can be optimal.
- C. A put's payoff is bounded by the strike because the stock price cannot fall below zero.
- D. Correct: capped payoff plus interest on the strike can make early exercise optimal.
Question 2
Analyst Dana observes add-on reference rates on a 360-day basis: 3.00% for 180 days and 3.40% for 270 days. She wants the rate implied for a 90-day loan that begins in 180 days, which is the fair rate on a 6x9 forward rate agreement. What is it?
- A. 4.20%
- B. 3.80%
- C. 4.14%
- D. 3.40%
Show answer and explanation
Correct answer: C. 4.14%
Forward rate = [(1 + 0.034 x 270/360)/(1 + 0.03 x 180/360) - 1] x 360/90 = (1.0255/1.015 - 1) x 4 = 0.010345 x 4 = 4.14%. The longer deposit equals the shorter deposit rolled into the forward.
- A. Takes the difference in interest amounts (2.55% - 1.50%) without dividing by the growth factor of the shorter period.
- B. Extrapolates linearly (2 x 3.40% - 3.00%), which is not a no-arbitrage forward rate.
- C. Correct: (1.0255/1.015 - 1) x 4 = 4.14%.
- D. Reports the 270-day rate itself, ignoring the 180 days already covered.
Question 3
Investor Sam holds an American call with three months to expiration on a stock that pays no dividends. The stock has risen sharply and the call is deep in the money. Sam is tempted to exercise now to lock in the intrinsic value. What is the best assessment?
- A. Early exercise is preferred, since deep in-the-money options lose their time value to exercise
- B. Early exercise is preferred, because the stock could fall before expiry and erase the intrinsic value
- C. Early exercise is neutral, because the American call is worth the same as a European call after exercise
- D. Early exercise gives up time value and interest on the strike, so sell the call or hold it
Show answer and explanation
Correct answer: D. Early exercise gives up time value and interest on the strike, so sell the call or hold it
With no dividends, an American call is worth more unexercised than exercised: the call's price exceeds S - X, which includes the interest earned on the exercise price. Selling or holding captures that value; the American call equals its European value.
- A. Time value does not vanish through holding; exercise is what discards it.
- B. Selling the call also protects against a decline, and retains the time value.
- C. The values are equal before exercise, but exercise converts the option to intrinsic value only, which is less.
- D. Correct: exercising throws away time value and interest on the strike.
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A firm entered a swap two years ago as the fixed-rate receiver at 4.5% on a notional of USD 10 million, with annual payments and two years remaining. The current par swap rate for two years is 4.0%, and the discount factors are 0.9615 for one year and 0.9246 for two years. What is the swap's value to the firm?
- A. USD 100,000
- B. USD 94,305
- C. -USD 94,305
- D. USD 50,000
Show answer and explanation
Correct answer: B. USD 94,305
The firm receives 4.5% instead of the market 4.0%: value = (0.045 - 0.040) x 10,000,000 x (0.9615 + 0.9246) = 50,000 x 1.8861 = USD 94,305. Fixed receivers gain when swap rates fall.
- A. Sums the two annual 50,000 differences without discounting them.
- B. Correct: 50,000 x 1.8861 = 94,305.
- C. Has the sign wrong; the fixed receiver at an above-market rate holds an asset.
- D. Counts a single year of the rate difference.