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CFA Level I · CFA Level I Exam · Valuing a Derivative Using a One-Period Binomial Model

A stock trades at 50. After one period it will be either 60 or 40. A call option with an exercise price of 50 expires at the end of the period. The hedge ratio (number of shares per call) is closest to:

The hedge ratio is 0.50. The call's payoff difference between states is 10 (10 minus 0), and the stock's price difference is 20 (60 minus 40). Dividing 10 by 20 gives 0.50 shares of stock per call option.

  1. A0.25
  2. B0.50Correct
  3. C1.00

Explanation

Call payoffs are 10 in the up state and 0 in the down state. Hedge ratio = (10 - 0)/(60 - 40) = 0.50. A ratio of 1.00 would wrongly treat the option as moving one-for-one with the stock; 0.25 divides by an incorrect spread.

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