Hi I have 4 finance questions related to futures contracts. Thank you.

1c. One futures contract on orange juice is equal to 15,000 lbs. of juice. Recently, the contract was trading at around $ 1.46/lb. The initial margin for an orange juice contract is $1,320, approximately what is the leverage an investor enjoys by trading this commodity? 2a. On Nov. 28, 2016, the nearby S&P 500 contract closed at 2200.80. What was the total value represented by one S&P contract as of the day of that close? 2c. Assume that in two weeks, the contract closes at 2250. What would be the dollar amount of your profit or loss, given the action you answered for part b? Explain how you arrived at your answer. 2d. Currently, the initial margin requirement for an S&P futures contract is $28,125, and the maintenance margin requirement is $22,500. Given the profit you found in part c, calculate your percentage profit on the trade, given what you had invested (the initial margin requirement). 2e. Assume now that the trade went against you, i.e., the price of the contract goes down instead of up. At what contract price would you have gotten a margin call? Explain. How much additional margin will you need to deposit in your account? Question 1c One futures contract on orange juice is equal to 15,000 lbs. of juice. Recently, the contract was trading at around $1.46/lb. The initial margin for an orange juice contract is $1,320, approximately what is the leverage an investor enjoys by trading this commodity? Solution The value of the underlying asset on one futures contract is Value of underlying asset per futures contract = 15, 000 $1.46 = $21, 900 (1) Thus the leverage amount in trading one futures contract is Leverage amount = Value of underlying asset per futures contract Initial margin = $21, 900 $1, 320 = $20, 580 (2) Expressing the leverage as a percentage of the value of the underlying asset: Leverage amount Value of underlying asset per futures contract $20, 580 = = 93.97% $21, 900 Leverage = (3) Question 2a On Nov. 28, 2016, the nearby S&P 500 contract closed at 2200.80. What was the total value represented by one S&P contract as of the day of that close? Solution In what follows, I assume that the multiplier on the S&P futures contract is 250, identical to that applicable to the S&P futures traded by the CME Group. The total value of one futures contract is Value = Multiplier Futures price = 250 2, 200.80 = $550, 200 (4) Question 2c Assume that in two weeks, the contract closes at 2,250. What would be the dollar amount of your profit or loss, given the action you answered for part b? Explain how you arrived at your answer. Solution Since I bought the futures, i.e. I am long, my profit is: Profit = Change in futures price multiplier = (2, 250 2, 200.80) 250 = $12, 300 1 (5) Question 2d Currently, the initial margin requirement for an S&P futures contract is $28,125, and the maintenance margin requirement is $22,500. Given the profit you found in part c, calculate your percentage profit on the trade, given what you had invested (the initial margin requirement). Solution The percentage profit is computed below Profit Initial margin $12, 300 = 43.73% = $28, 125 Percentage profit = (6) Question 2e Assume now that the trade went against you, i.e., the price of the contract goes down instead of up. At what contract price would you have gotten a margin call? Explain. How much additional margin will you need to deposit in your account? Solution I get a margin call if I incur a loss equal to the variation margin, which is: Variation margin = Initial margin Maintenance margin = $28, 125 $22, 500 = $5, 625 (7) Let F denote the futures price that triggers the margin call. This can be derived from the following relationship. Profit = Change in futures price multiplier = $5, 625 = (F 2, 200.80) 250 = $5, 625 5, 625 + 2, 200.80 = 2, 178.30 F = 250 (8) The additional margin I need to deposit if the futures price drops to 2,178.30 corresponds to the variation margin, which is $5,625. 2