Question 3 (13 marks) a. The maturity of a futures contract on a stock market index is 6 months. The multiplier for the futures contract $50. The current level of the index is 20,000 . The risk-free rate is 0.6% per month and dividend yield on the stock market index is 0.3% per month. The initial margin requirement is 20%. i. What is the parity value of the futures price now? (3 marks) ii. Assume the futures contract is fairly priced. How much initial margin you need to deposit if you long 3 contracts? ( 2 marks) iii. Calculate the one-month holding-period return for your long position in the futures contract if the stock market index increases to 22,000 after 1month. Assume the futures contract keeps being priced fairly. ( 5 marks) b. Peter buys five December futures contracts on gold. Each contract is for the delivery of 100 Troy ounces of gold. The current futures price is $1,900. The initial margin is $90,000 per contract and the maintenance margin is $70,000 per contract. What is the futures price that would lead to a margin call? ( 3 marks)