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It is now Feb 1. A company expects to buy 100 million ounces of silver at the beginning of May. Assume that Silver futures contracts have delivery months in April, June, and August (Assume delivery on the first day of the delivery month). Each contract is for the delivery of 25 million ounces. Assume that the futures price on CME for silver equals its theoretical price. Storage costs will be continuously incurred at a rate of 2% per annum. The continuously compounded risk-free rate is 10% per annum. Spot price of silver on Feb 1 is $10/oz. Spot prices at the future dates will be as follows (we do not know these prices today):
April 1: $10.30/oz
May 1: $10.50/oz
June 1: $10.40/oz
July 1: $10.20/oz
Aug 1: $10.10/oz
(a) Should the company go short or long on silver futures? How many contracts? Which delivery month and why?
(b) Calculate the basis risk (per contract).
(c) Calculate the gain or loss on the futures position (per contract).
(d) Calculate the effective price received by the company (per contract) at the beginning of May
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