Question 4 (6 marks)

The following table gives monthly data (also provided in an Excel file) of the spot price and the futures price for commodities A and B respectively. A company expects to sell 100,000 units of commodity A in one month. The size of one futures contract on commodity B is 5,000 units. The company would like to hedge commodity A using commodity B futures contract.

(a) Use these data to calculate the minimum variance hedge ratio. (2 marks)

(b) What position should the company take (long vs. short and number of contracts)? (Round the number of contracts to the nearest integer). (2 marks)

(c) The 1-month futures price of the commodity is $12.4929 today. If the futures price two weeks from now (when the hedging position is closed out) is $12.5459 per unit and the spot price at the same time is $12.5549 per unit, what is the effective price (per unit) received by the company? (2 marks)

Month Futures price Spot price Month Futures price Spot price 1 12.6619 12.6199 12.6369 12.6179 12.5509 13 14 12.6979 12.6359 12.6619 12.5989 12.5909 12.6039 12.5629 OWN 15 16 17 12.5669 12.4919 12.5449 12.7409 12.6879 12.6499 12.5389 12.7019 12.6849 12.6279 12.5709 12.5139 12.4799 12.5279 18 19 12.5109 12.5189 7 8 12.6829 12.6539 20 12.6009 12.5989 9 10 12.6349 12.6799 21 22 12.6739 12.7219 12.6379 12.6809 12.6299 12.6509 12.6399 12.6599 11 12 12.6529 12.6719 23 24 12.7849 12.8149 12.7589 12.8089 Month Futures price Spot price Month Futures price Spot price 1 12.6619 12.6199 12.6369 12.6179 12.5509 13 14 12.6979 12.6359 12.6619 12.5989 12.5909 12.6039 12.5629 OWN 15 16 17 12.5669 12.4919 12.5449 12.7409 12.6879 12.6499 12.5389 12.7019 12.6849 12.6279 12.5709 12.5139 12.4799 12.5279 18 19 12.5109 12.5189 7 8 12.6829 12.6539 20 12.6009 12.5989 9 10 12.6349 12.6799 21 22 12.6739 12.7219 12.6379 12.6809 12.6299 12.6509 12.6399 12.6599 11 12 12.6529 12.6719 23 24 12.7849 12.8149 12.7589 12.8089