Description
Answer the questions in the attached as word file. Notes are attached as zip folder.
Unformatted Attachment Preview
Part I:Please carry out the calculations using Excel.
You have Treasury bond quotes below. The dataset named the Project Data.xls. There are three
sets of the data: First set has 7 Treasury securities, second part has 3 Treasuries and third set has
2 Treasuries. Note that quoted prices are full prices.
A. For all Treasuries in the data (i.e. both first, second and third set Treasuries):
1. What are the bid and ask prices of the Treasuries for a $100 face value. (Note that
Treasury bills are quoted in discount yields. There is not adjustment needed for
Treasury notes and bonds.) Use ask prices for below questions.
B. For this part, use only the 7 bonds in the first set.
2. Using bootstrap method long way, extract zero coupon bonds
3.
a) Using short way of matrix inversion extract zero coupon bonds
b) Calculate spot rates of every six months up to 3.5 years
c) Plot the spot rate curve
C. For this part, use first and second set, i.e. total of 10 Treasuries
4.
a) Using regression methods, extract zero coupon bonds. (Note: Force the
intercept to zero in the regression).
b) Calculate 6 month spot rates
c) Plot the spot rate curve
d) Compare the spot rates with the ones you found by bootstrapping. Are
they different? Why? Why not?
D. For this part, use all 12 Treasuries, i.e. first, second, and third sets.
5. Using regression methods, find zeros for available maturities. (Note: Force the intercept
to zero in the regression).
6. Using polynomial spline method of order 3
a) Fit the zero curve to find the zero for year 4.
b) Calculate 6 month spot rates for 4.5 years and plot the spot rate curve
7. Using exponential spline method of order 3
a) Fit the zero curve to find the zero for year 4. Take initial values of , 1,
2, 3, and as 0.01 while using the Solver.
b) Calculate 6 month spot rate for 4.5 years and plot the spot rate curve
1
c) Using the zeros, find 6 month forward rates after 6 months, 1 year, 1.5
years, .. up to 3 years.
8. Using Nelson-Siegel method
a) Fit the spot curve to find the spot rate for year 4. Take initial values of ,
1, 2, and as 1 while using the Solver.
b) What are the 6 month spot rates for 4.5 years? What are the 6 months
zeros? Plot the spot rate curve.
9.
a) Using the zero coupons you have extracted by polynomial method, find
the price of a coupon bond X that pays 1% coupon semiannually and that
has time to maturity of 4.5 years. Take the face value of the bond as $1000.
b) Is it selling at premium or discount? Why?
c) Using the zeros you have extracted, find the Fisher-Weil duration and the
varying yield convexity of Bond X.
d) If the yield curve shifts up by 1 percent,
– What is the new price of Bond X? using only duration measure?
– What is the new price of Bond X? using duration and convexity
measure?
– Why did you get different answers with duration measure versus
duration and convexity measure?
(Hint: Use spot rate of 4.5 year as the yield.)
2
SET 1
Treasury Bill
Quotes are for transactions of $1 million or more.
Treasury-bill yields are in 100ths, all yields are to
maturity and based on the asked quote. Days to
maturity calculated from settlement date. Bid and ask
data are discounts from face value.
Asked
Maturity
8/15/2024
2/15/2025
Bid
0.07
0.1
Asked
0.065
0.09
Chg
.
.
yield
0.066
0.091
TreasuryNotes and Bonds
Treasury note and bond data are representative over-the-counter quotations
as of mid-afternoon based on transactions of $1 million or more. Figures
after colons in bid and ask quotes represent 32nds; 101:26 means 101
26/32, or 101.8125% of 100% face value; 99:01 means 99 1/32, or
99.03125% of face value. For notes and bonds callable prior to maturity,
yields are computed to the earliest call date for issues quoted above par and
to the maturity date for issues below par.
Asked
yield
Maturity
Coupon
Bid
Asked
Chg
8/15/2025
0.25 100.0625 100.0703
0.0156
0.202
2/15/2026
4.5 108.1953 108.2188
0.0313
0.311
8/15/2026
0.625 100.2734 100.3125
0.0469
0.498
2/15/2027
0.625 99.3891 99.4281
0.0781
0.684
8/15/2027
8.875 127.1484 127.1641
0.0781
0.905
SET 2
TreasuryNotes and Bonds
Maturity
2/15/2025
8/15/2025
2/15/2027
Coupon
Bid
Asked
4 103.7422
103.75
4.25 105.9453 105.9688
4.625 113.4609 113.4844
Chg
Asked
yield
.
-0.0078
0.0313
0.129
0.181
0.71
SET 3
TreasuryNotes and Bonds
Maturity
8/15/2028
8/15/2028
Coupon
Bid
Asked
4 111.6328 111.6641
1.5 100.5703 100.6172
Chg
0.2109
0.1719
Asked
yield
1.305
1.358
Purchase answer to see full
attachment
