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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 a strike of 50 expires at that time. The hedge ratio of the call is closest to:

The hedge ratio is 0.50. The call pays 10 in the up state and 0 in the down state, a spread of 10, while the stock moves between 60 and 40, a spread of 20. Dividing 10 by 20 gives 0.50 shares per call.

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

Explanation

Call payoffs: up = 60 − 50 = 10, down = 0. Stock spread = 60 − 40 = 20. Hedge ratio = (10 − 0)/20 = 0.50. Choice 0.25 wrongly divides by 40 (the stock price level difference misused), and 1.00 is the ratio for a deep in-the-money call.

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