a) An HSBC bond has a face value of 1000, a coupon rate of 8%, 3 years until maturity and a yield to maturity of 7%. Calculate bond duration. D= ? *[cash flowt/(1+YTM)t]}/price of bond where t is time to maturity and YTM stands for yield to maturity. N.B: You need to show how you have calculated duration. A single value will not suffice.
b) HSBC has issued a 9-year bond with YTM of 10% and duration of 7.194 years. If the market yield changes by 0.5% what is the percentage change in the bond’s price? Use modified duration to do your calculations.
c) HSBC has issued a 6% coupon paying bond with modified duration of 10 years, convexity of 120 and YTM of 8%. If YTM changes to 9.5% what is the percentage change in price? d) You are the manager of a bond portfolio which is worth £10 million. You have liabilities with duration of 10 years and you have two choices to match that duration. You can choose to buy a zero coupon bond with maturity of 5 years or buy a perpetuity. The bond and the perpetuity have a yield of 4%. Find how much of the bond and the perpetuity will you hold in your portfolio to match that duration?