Doctor turned farmer, Victor Fischer, decides to hedge his crop of 10,000 bushel

Question

Doctor turned farmer, Victor Fischer, decides to hedge his crop of 10,000 bushels of corn by selling short European call options on that amount of corn. Currently, corn call options with a $1.60 strike price (per bushel) sell for $0.10 premium. Six month risk-free interest rate is 2%, and Dr. Fischer plans to close his position and sell his corn in six months. Spot price is $1.50 in six months. Dr. Fischer has to post a margin of $1500 at the onset of the transaction, and he does earn interest on that deposit. He does not, however, earn interest on the premium received for the options written, which is held by his broker until the transaction is closed in six months and then paid out to Dr. Fischer. Calculate Dr. Fischer’s effective annual rate of return on the entire hedging transaction (i.e., ignore the funds obtained from the sale of corn, as he would have sold the corn regardless of hedging).

A. 145.44% B. 254.22% C. 156.67% D. 56.67% E. 66.67%

Explanation / Answer

The premium on corn is 0.1*10000 = 1000

SInce the spot price reduced to 1.50 on expiry, these options will not be exercised

The margin of 1,500 will earn him an interest of 2% which is 0.02* 1500 = 30

He will also earn interest on the preimum received = 1000*0.02 = 20

Total profit = 1000 +30 + 20= 1050 for an investment of 1500

So the interest rate is for 6 months = 1050/1500 = 70%

So annual interest rate is (1+ 0.7)^2 -1 = 156.67%

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