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Here are the prices of three bonds with 10-year maturities:
Bond coupon (%) Price (%)
2 81.62
4 98.39
8 133.42

If coupons are paid annually, which bond offered the highest yieldto maturity? Which had the lowest? Which bonds had the longest andshortest durations?

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Lelia Lubowitz
Lelia LubowitzLv2
30 Sep 2019

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Assume coupons are paid annually. Here are the prices of three bonds with 10-year maturities:

Bond Coupon % Price %
2 83
4 102
8 133

What is the duration of each bond?

3. Key rate duration I have a portfolio of two fixed rate bonds. Bond A is a 2 year, $100 par value US govt bond, coupon=5% (per annum), payable annually. Bond B is a 4 year, $100 par value US govt bond, coupon=6% (per annum), payable annually. Assume the relevant term structure from the price of US government STRIPS is : d(1Y)=0 .95 d(2Y)=0.91 d(3Y)= 0.87 d(4Y)= 0.83

a. What are the relevant nonzero key rate durations for Bond A ?

b. What are the relevant nonzero key rate durations for Bond B ?

c. What are the relevant nonzero key rate durations for the entire portfolio ? Note: You may need to refer to the result for Fisher-Weil duration of a portfolio of bonds in question 4 below, and make an educated guess here.

d. What is the Fisher-Weil duration Bond A, Bond B, and the entire portfolio ?

You want to make a 5-year investment on bonds, and if you buy bonds with longer period of maturity, they will be sold at the prevailing market price at the end of the fifth year. All coupons will be reinvested. You forecast that the rates are going to change after you purchase the bonds. Now you have three bonds with same initial YTM to consider: A. 5-year maturity, 6% coupon paid annually, YTM=9% B. 10-year maturity, 8% coupon paid annually, YTM=9% C. 15-year maturity, 4% coupon paid annually, YTM=9% To pick the best one, you want to calculate the following:

1) What are the current prices of three bonds based on the initial YTM given? [2 points]Current prices of all bonds are shown below Bond 1: n=5; PMT = 6; YTM = 9%; FV = 100; PV=calculate = 88.33 It can be calculated by putting the values in the financial calculator OR by using the PV formule in excel which is =PV(9%,5,6,100) Bond 2 n=10; PMT = 8; YTM = 9%; FV = 100; PV=calculate = 93.58 Bond 3 n=15; PMT = 4; YTM = 9%; FV = 100; PV=calculate = 59.7

2) If the coupon payments are reinvested at the prevailing market rate (7% for the coming 5 years), what are the future values (at the end of the fifth year) of all five coupon payments for three bonds respectively? [3 points]

3) What are the selling prices of three bonds at the end of the fifth year, given that the prevailing market rate is 8% at that time? (For bond A, use its par value as the final selling price, as it will mature in 5 years). [2 points]

4) What are the HPRs for the three bonds? [2 points] 5) What’s your recommendation? [1 point]

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