A derivative security pays $100 if the Dow Jones Industrial Average shows a 15% return over the next year and does not pay anything of the return is lower. If the security costs $45 and its expected return is 30%, what's the probability that the Dow Jones return will exceed 15%?
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A. B. C. D.B
If p is the probability of the Dow Jones return exceeding 15%, then the expected total return on the derivative security is (p * 100 + (1-p)*0)/45 = 2.222p. Since the expected return is given to be 30%, we get 2.22p = 1.3. Therefore, p = 1.3/2.222 = 58.51%