Question 4 [17 marks] Today is 15 September 2019. To construct a portfolio, Mike just purchased three different Treasury bonds, henceforth referred to as bond A, bond B and bond C. Assume the yield rate for all these financial instruments is j2 = 3.2% p.a. Bond A has a coupon rate of j2 = 3.25% p.a. and a face value of $100. The maturity date of this bond is 15 March 2021. Bond B has a coupon rate of j2 = 3.15% p.a. and a face value of $100. The maturity date of this bond is 15 April 2022. a. [3 marks] Calculate the duration and the modified duration of Treasury bond A. Give your answer in terms of years (rounded to three decimal places). b. [2 marks] Calculate the price Mike paid for bond A (rounded to three decimal places). c. [5 marks] Calculate Mike's purchase price of bond B by using the RBA ap- proach (rounded to three decimal places). d. [3 marks] Mike purchased 100 units of bond A and 205 units of bond B to establish his portfolio. Based on your results from part a, b and c above, calculate the duration of Mike's portfolio. Given that bond B has duration of 2.468 years. Give your answer in terms of years (rounded to two decimal places). e. [2 marks] Mike plans to use his portfolio to pay a future liability. Can he use the portfolio to immunise the interest rate risk of meeting this liability? Explain your answer. f. [2 marks] Mike also consider to purchase a bond C with the price of $99.782. Assume that this bond C has the duration of 1.478 years and the yield rate for this bond is j2 = 3.2% p.a. Without actually calculating the new price for bond c, use the price and the duration value to estimate (use the price sensitivity formula) the change in price of bond C that would result from an increase in yield rate (12) by 5 basis points. Round your answer to two decimal places. Question 4 [17 marks] Today is 15 September 2019. To construct a portfolio, Mike just purchased three different Treasury bonds, henceforth referred to as bond A, bond B and bond C. Assume the yield rate for all these financial instruments is j2 = 3.2% p.a. Bond A has a coupon rate of j2 = 3.25% p.a. and a face value of $100. The maturity date of this bond is 15 March 2021. Bond B has a coupon rate of j2 = 3.15% p.a. and a face value of $100. The maturity date of this bond is 15 April 2022. a. [3 marks] Calculate the duration and the modified duration of Treasury bond A. Give your answer in terms of years (rounded to three decimal places). b. [2 marks] Calculate the price Mike paid for bond A (rounded to three decimal places). c. [5 marks] Calculate Mike's purchase price of bond B by using the RBA ap- proach (rounded to three decimal places). d. [3 marks] Mike purchased 100 units of bond A and 205 units of bond B to establish his portfolio. Based on your results from part a, b and c above, calculate the duration of Mike's portfolio. Given that bond B has duration of 2.468 years. Give your answer in terms of years (rounded to two decimal places). e. [2 marks] Mike plans to use his portfolio to pay a future liability. Can he use the portfolio to immunise the interest rate risk of meeting this liability? Explain your answer. f. [2 marks] Mike also consider to purchase a bond C with the price of $99.782. Assume that this bond C has the duration of 1.478 years and the yield rate for this bond is j2 = 3.2% p.a. Without actually calculating the new price for bond c, use the price and the duration value to estimate (use the price sensitivity formula) the change in price of bond C that would result from an increase in yield rate (12) by 5 basis points. Round your answer to two decimal places
