Free CFA Level I Derivatives Practice Questions
Derivatives on the CFA Level I exam cover forward contracts, futures, options, and swaps, from basic payoff structures to introductory pricing and hedging strategies. Weighted 5-8% (CFA Institute).
Sample Questions
Question 1
Easy
Which of the following best describes a derivative security?
Solution
C is correct.
A derivative is a financial instrument whose value depends on (is derived from) the value of an underlying asset, rate, or index.
A derivative is a financial instrument whose value depends on (is derived from) the value of an underlying asset, rate, or index.
Question 2
Medium
A synthetic long forward position can be created using options by combining which of the following positions with the same strike K and expiration?
Solution
B is correct.
A synthetic long forward = long call + short put with the same strike K and expiration. At expiration: if S > K, the long call pays S - K and the short put expires worthless, net payoff = S - K. If S < K, the long call expires worthless and the short put pays -(K - S), net payoff = -(K - S) = S - K. In both cases, the payoff equals S - K, identical to a long forward with delivery price K.
A synthetic long forward = long call + short put with the same strike K and expiration. At expiration: if S > K, the long call pays S - K and the short put expires worthless, net payoff = S - K. If S < K, the long call expires worthless and the short put pays -(K - S), net payoff = -(K - S) = S - K. In both cases, the payoff equals S - K, identical to a long forward with delivery price K.
Question 3
Hard
In a two-period binomial model, a stock is priced at 100, u = 1.20, d = 0.85, and the risk-free rate is 5% per period. Using risk-neutral pricing, what is the value today of a European put option with a strike price of 95?
Solution
C is correct.
Pi_u = (1 + r - d) / (u - d) = (1.05 - 0.85) / (1.20 - 0.85) = 0.20 / 0.35 = 0.5714. pi_d = 0.4286. Period-2 stock prices: Suu = 144, Sud = 102, Sdd = 72.25. Put payoffs: Puu = 0, Pud = 0, Pdd = 95 - 72.25 = 9.287. Period-1 up node: Pu = 0. Put value today: P0 = (0.5714 * 0 + 0.4286 * 9.287) / 1.05 = 3.982 / 1.05 = 3.79.
Pi_u = (1 + r - d) / (u - d) = (1.05 - 0.85) / (1.20 - 0.85) = 0.20 / 0.35 = 0.5714. pi_d = 0.4286. Period-2 stock prices: Suu = 144, Sud = 102, Sdd = 72.25. Put payoffs: Puu = 0, Pud = 0, Pdd = 95 - 72.25 = 9.287. Period-1 up node: Pu = 0. Put value today: P0 = (0.5714 * 0 + 0.4286 * 9.287) / 1.05 = 3.982 / 1.05 = 3.79.