Free CFA Level I Derivatives Practice Questions

A derivative is a financial instrument whose value depends on (is derived from) the value of an underlying asset, rate, or index. Choice A describes equity securities such as common stock, not derivatives. Choice C describes bonds, which are primary securities rather than derivatives.

Cash-and-carry arbitrage is used when the forward price exceeds its theoretical no-arbitrage value. The trader buys the spot asset (carrying it to delivery), borrows funds to finance the purchase, and simultaneously shorts the overpriced forward. At delivery, the forward proceeds repay the loan plus interest, with a riskless profit remaining. Choice C describes reverse cash-and-carry, used when the forward is underpriced, not overpriced. Choice B describes a swap position motivated by rate expectations, which is speculation rather than a no-arbitrage strategy.

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 = $100 * 1.44 =$144, Sud = $100 * 1.02 =$102, Sdd = $100 * 0.7225 =$72.25. Put payoffs: Puu = 0, Pud = 0, Pdd = 95 - 72.25 = $22.75. Period-1 down node: Pd = (0.5714 * 0 + 0.4286 * 22.75) / 1.05 = 9.751 / 1.05 =$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. Choice A uses pi_u = 0.4286, which is the down probability mistakenly used as the up probability, overstating the chance of down moves and inflating the put value. Choice B uses the correct pi_u but makes an error in the period-1 node calculation, double-counting the Pdd payoff.