It is March 9, and you have just entered into a short position in a soybean meal futures contract. The contract expires on July 9 and calls for the delivery of 100 tons of soybean meal. Further, because this is a futures position, it requires the posting of a $3000 initial margin and a $1500 maintenance margin for simplicity; however, assume that the account is marked to market on a monthly basis. Assume the following represent the contract delivery prices (in dollars per ton) that prevail on each settlement date:
Date price
March 9 (Initiation) $173.00
April 9 $179.75
May 9 $189.00
June 9 $182.50
July 9(Delivery) $174.25
a. Calculate the equity value of your margin account on each settlement date, including any additional equity required to meet a margin call. Also, compute the amount of cash that will be returned to you on July 9, and the gain or loss on your position expressed as a percentage of your initial margin commitment. [10 Marks]
b. Assuming that the underlying soybean meal investment pays no dividend and requires a storage cost of 1.5 percent (of current value), calculate the current (i.e., March 9) spot price for a ton of soybean meal and the implied May 9 price for the same ton. In your calculations, assume that an annual risk-free rate of 8 percent prevails over the entire contract life. [10 Marks]
c. Now suppose that on March 9 you also entered into a long forward contract for the purchase of 100 tons of soybean meal on July 9. Assume further that the July forward and futures contract prices always are identical to one another at any point in time. Calculate the cash amount of your gain or loss if you unwind both positions in their respective markets on May 9 and June 9, taking into account the prevailing settlement conditions in the two markets.