Fin 445/545
Fall 2022
1. You are provided with the following Treasury Bond quotes:
Settlement date
Issue date
Maturity
Annual
Coupon rate
(coupons are
paid semiannually)
Bid
Asked
10/26/2021
11/15/2020
11/15/2044
3%
116.28
116.30
10/26/2021
5/15/2020
5/15/2046
2.5%
107.28
107.30
a) Compute the Modified duration of a portfolio of $10 million par of each of the above two
bonds. (10 points)
b) Compute the PVBP of a portfolio of $10 million par of each of the above two bonds. (10
points)
c) Compute the Duration of a portfolio of $10 million par of each of the above two bonds.
(10 points)
2. Bootstrap: You are given these prices for three Treasuries with semi-annual payments:
Bond
A
B
C
Maturity (Years)
0.5
1.0
1.5
Coupon Rate (%)
8.00
4.00
6.00
Price
97.561
90.703
80.496
a) Construct combinations, or portfolios, of these securities that replicate (mimic) zero
coupon bonds with maturities 0.5, 1.0, and 1.5 years. (10 points)
b) Use the synthetic zeros (coupon securities held in a portfolio that mimic zeros) to
compute their prices. (10 points)
c) Use the prices of zeros to compute spot rates and forward rates. (10 points)
3. Use Ch8_bootstrap.xlsm file and the matrix approach to do this problem. Example 8.2 in the
textbook will also help:
Use the following data for settlement date May 28, 2010 to answer the following
questions: (assume semi-annual payments, and par values of $100)
Coupon Rate (%)
1.25%
4.875%
4.5%
4.75%
3.375%
3.5%
2%
2.25%
2.125%
Maturity
11/30/2010
5/31/2011
11/30/2011
5/31/2012
11/30/2012
5/31/2013
11/30/2013
5/31/2014
11/30/2014
Price
100.550
104.513
105.856
107.966
105.869
106.760
101.552
101.936
100.834
a) Compute the annualized yield to maturity of the bonds given above. (10 points)
b) Estimate the term-structure of interest rates using the coupon bonds given above. (10
points)
c) Plot the yield curve and term structure on the same graph. (10 points)
d) Estimate the price of a 0.75%, November 30, 2011 maturity bond as of May 28, 2010.
(10 points)

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