Mining Firm Derivative Security: Probability of Metal Price Remaining Above $2 per Pound

Probability Calculation: Mining Firm Derivative Security

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Question

A mining firm has purchased a derivative security to partially hedge itself against the losses caused by fluctuations in a base metal price. The security pays a million dollars if the metal price falls below $2 per pound. Otherwise, it pays $100,000. If the expected rate of return on the security is 21% and the security costs

$400,000, what is the probability that the metal price will remain above $2 per pound?

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A. B. C. D.

C

If p is the probability of the metal price remaining above $2/pound, then the expected total return on the derivative security is (p * 100,000 + (1-p)

*1,000,000)/400,000 = (10-9p)/4. Since the expected return is given to be 21%, we get (10-9p)/4 = 1.21. Therefore, p = 57.33%.