1. A Consider a portfolio consisting of the following bonds:
Bond No Face value Maturity Coupon Frequency Yield
Bond A 500 $2,000 2 Years 2% Q 1.75%
Bond B 1000 $1,000 5 Years 4% S 4.5 %
Bond C 1500 $1,000 10 Years 5% S 5.25%
a. What is the price of each bond?
b. What is the value of the portfolio?
c. What is the duration and modified duration of each bond?
d. What is the modified duration of the portfolio using the weighted average method?
e. What is the duration of the portfolio using numerical method?
f. If the yield of the bonds increase by 0.05% determine the value of the portfolio by calculating the new prices of the bonds.
g. If the yield of the bonds increase by 0.05% determine the value of the portfolio using duration of the portfolio calculated by weighted average method.
h. If the yield of the bonds increase by 0.05% determine the value of the portfolio using duration of the portfolio calculated by numerical method.
2. A portfolio of bonds is valued at $12,750,000. The yield of each bonds falls by 0.025% and the value of portfolio becomes $12,762,500.
a. What is the Duration of the portfolio?
b. What is the value of the portfolio if the rates increase by 0.03%?
3. Two portfolios of bonds are worth $5,000,000 each. Duration of portfolio A is 2.5 years and duration portfolio B is 4.77 years.
c. If you think interest rates will rise, which of the two portfolios will you choose? Why?
d. Suppose the rates rise by 0.05% what will be the value of the portfolios?
e. If you think interest rates will fall, which of the two portfolios will you choose? Why?
f. Suppose the rates fall by 0.03% what will be the value of the portfolios?