Question 3
Collin is a fixed income portfolio manager. His current bond portfolio consists of the following corporate bonds:
Corporate Bond Corporate Rate Maturity Convexity Number of Bonds
A 6% 6 Months 0.50 600
B 7% 12 Months 1.42 900
C 8% 18 Months 3.40 800
D 9% 24 Months 4.46 1,000
All of Collin’s corporate bonds have a face value of $1,000 and pay coupons on a semiannual basis.
Collin is concerned how interest rate changes will affect the value of his portfolio. As part of his research, he has compiled the following information about the term structure of interest rates using government bonds.
Maturity Coupon Rate Yield
6 Months 0.0% 0.5%
12 Months 0.0% 1.0%
18 Months 2.5% 1.5%
24 Months 3.0% 1.8%
All the government bonds have a face value of $1,000 and also pay coupons on a semi-annual basis.
(a) Calculate all the implied forward rates beginning after 6 months up till 24 months.
(10 marks)
(b) Calculate the current value of Collin’s bond portfolio.
(10 marks)
(c) Calculate the duration of each of the bonds A, B, C and D.
(10 marks)
(d) Calculate the value of Collin’s bond portfolio using duration only; assuming interest rate has increased by 1.5%.
(10 marks)
(e) Calculate the value of Collin’s bond portfolio after 1 year using both duration and convexity; assuming interest rate has fallen by 1.2%.
(10 marks)