Question 2 (17 marks) a. Peter buys a 5% annual coupon bond with 4 years to maturity. The bond has a yield-to-maturity of 6%. The par value is $1,000. i. Calculate the duration and modified duration of the bond. (5 marks) 96,3489430 concept? ( 3 marks) b. At the end of next 3 years, you need to pay $50,000,$100,000 and $150,000 respectively. i. If the market interest rate is 5% per annum., what will be the duration of your payment obligation? ( 4 marks) ii. Suppose you plan to fully fund the obligation using both 6-month zero coupon bonds and perpetuities. Determine how much of each of these bonds (in market value) you will hold in the portfolio. (5 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 18,000 . The risk-free rate is 0.7% per month and dividend yield on the stock market index is 0.2% per month. The initial margin requirement is 10%. 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 2 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 19,500 after 1 month. 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 $1,600. The initial margin is $80,000 per contract and the maintenance margin is $70,000 per contrac What is the futures price that would lead to a margin call? ( 3 marks)