Assignment 7 finaincal analytics
xlsx
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School
University of South Florida, Tampa *
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Course
3320
Subject
Finance
Date
Feb 20, 2024
Type
xlsx
Pages
17
Uploaded by DoctorGalaxyWildcat25
Outline:
Bond Pricing
Duration and Convexity
Immunization Strategy
The Yield Curve - To price a bond and to determine forward rate
Input
Time to Maturity
5 This button doesn’t control the length of timeline, be careful
Payment Frequency
2
Face Value
$ 1,000.00 Coupon Rate
4.00%
400
YTM
3.48%
348
Period Of Maturity
10
Coupon Payment
$ 20.00 Period
0
1
2
3
4
Time (Years)
0
0.5
1
1.5
2
CFs
$ 20.00 $ 20.00 $ 20.00 $ 20.00 PVs of CFs
$19.66 $19.32 $18.99 $18.67 Bond Price
$1,023.68 Time to maturity spin button doesn’t control this result, be car
Bond Price (function)
$1,023.68 It does control this .
$1,023.68 Bond Price by YTM
1% 2% 3% Today, a 5-year Treasury Note with a face value of $1,000 a
to Maturity (YTM) of 3.48%. This bond makes 2 (semi-annu
periods until maturity. What is the price of this T-note? Add Spin Buttons to all the input variables to show how a c
Calculate the price using both a timeline and a function.
Create a graph to show bond price by YTM.
Create a graph to show bond price by Calendar time.
4% 5% 6% 7% 8% Calendar Time
Period to Maturity
$1,023.68 Bond Price by Calendar time
0
10 0.5
9 1
8 1.5
7 2
6 2.5
5 3
4 3.5
3 4
2 4.5
1 5
0
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5
6
7
8
9
10
2.5
3
3.5
4
4.5
5
$ 20.00 $ 20.00 $ 20.00 $ 20.00 $ 20.00 $ 1,020.00 $18.35 $18.03 $17.73 $17.42 $17.12 $858.39 reful
and an annual coupon rate of 4.00% has a Yield ual) coupon payments per year and thus has 10 change in input variable affects bond price.
0%
1%
2%
$- $2.00 $4.00 $6.00 $8.00 $10.00 $12.00 Bond
Bond Price
0
$- $2.00 $4.00 $6.00 $8.00 $10.00 $12.00 Bond Price
3%
4%
5%
6%
7%
8%
9%
d Price by YTM
YTM
1
2
3
4
5
6
Bond Price by Calendar Time
Calendar Time
Input
Time to Maturity
5 This button doesn’t control the length of timeline, be careful
Payment Frequency
2
Face Value
1,000.00 Coupon Rate
4.00%
400
YTM
3.48%
348
Period Of Maturity
10
Coupon Payment
$ 20.00 Period
0
1
2
3
4
5
6
Time (Years)
0
0.5
1
1.5
2
2.5
3
CFs
$ 20.00 $ 20.00 $ 20.00 $ 20.00 $ 20.00 $ 20.00 PVs of CFs
$19.66 $19.32 $18.99 $18.67 $18.35 $18.03 Bond Price
$1,023.68 Time to maturity spin button doesn’t control this result, be carefu
Bond Price (function)
$1,023.68 It does control this .
Weight
0.019203 0.018875 0.018552 0.018235 0.017923 0.017616
Weighted*Time
0.009602 0.018875 0.027828
0.03647 0.044807 0.052849
Duration (TimeLIne)
4.59
Duration (Function)
4.59
Modified Duration (Timeline)
4.51
Modified Duration (function
4.51 If interest raten increases by 1%, Bond Price decreases approxima
Weight*(Time^2+Time)
0.014402
0.03775
0.06957 0.109409 0.156826 0.211397
Convexity
26.78
Today, a 5-year Treasury Note with a face value of $1,000 and an annual co
to Maturity (YTM) of 3.48%. This T-Note makes 2 (semi-annual) coupon pay
10 periods until maturity. What is the Duration, Modified Duration, and Convexity of this bond?
Add Spin Buttons to all the input variables to show how a change in input v
Calculate duration and convexity using both a timeline and a function.
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Modify Duration + Convexity
-4.37%
7
8
9
10
3.5
4
4.5
5
$ 20.00 $ 20.00 $ 20.00 $ 1,020.00 $17.73 $17.42 $17.12 $858.39 ul
0.017315 0.017019 0.016728
0.8385336
0.060603 0.068076 0.075276
4.192668
ately by 4.51%
0.272713
0.34038 0.414016
25.156008
oupon rate of 4.00% has a Yield yments per year and thus has variable affects results.
Time to MaturityPayment freqPeriods
Coupon Rate YTM
Face Value
Bond #1
2
2
4
4.63%
3.88%
1000
Bond #2
5
2
10
4%
3.48%
1000
Liability
3.50%
Period
0
1
2
3
4
5
Year
0
0.5
1
1.5
2
2.5
Cf of Liability
0
0
0
0
0
0
PV of CF
$0.00 $0.00 $0.00 $0.00 $0.00 Pv of Liability
$3,604,570.17 Weight
0
0
0
0
0
Weight*Time
0
0
0
0
0
Duration of Liability
3
Bond 1 CF
49207.53565 49207.5357 49207.5357 2174803.02826
0
Bond 2 CF
28301.52499
28301.525
28301.525 28301.5249857
28301.525
PV of Bond 1
$48,271.08 $47,352.44 $46,451.28 $2,013,916.28 $0.00 PV of Bond 2
$27,817.50 $27,341.75 $26,874.14 $26,414.53 $25,962.78 PV of assets
$3,604,570.17 Weight
0.021108918 0.02072208 0.02034235 0.56603997531 0.00720274
Weight*Time
0.010554459 0.02072208 0.03051353 1.13207995062 0.01800685
Duration of assets
2.999999
Diff of PV
$0.00 Needs to be 0
Diff of Duration
0.00 Needs to be 0
Suppose that an insurance company sells a guaranteed investment con
in 3 years. The company wishes to construct a portfolio of assets to co
against interest rate risk right now.
The company is considering investing in two bonds:
(1) A 2-year Treasury bond with a face value of $1,000 and an annual c
(2) A 5-year Treasury bond with a face value of $1,000 and an annual c
Both bonds make 2 (semi-annual) coupon payments per year. Thus the
maturity, repsectively.
How many 2-year and 5-year Treasury Notes should the insurance com
immunized against interest rate risk right now?
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Coupon Payment
# of Bonds to Buy
23.15
2125.595492603
20
1415.076249285
6
7
8
9
10
3
3.5
4
4.5
5
4,000,000
0
0
0
0
$3,604,570.17 $0.00 $0.00 $0.00 $0.00 1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
28301.5249857
28301.525
28301.5249857
28301.525 1443377.77427
$0.00 $0.00 $0.00 $0.00 $0.00 $25,518.75 $25,082.32 $24,653.35 $24,231.72 $1,214,682.24 0.007079554897 0.00695848 0.006839470602
0.0067225 0.33698393452
0.021238664691 0.02435467 0.027357882408 0.03025125 1.68491967259
ntract (GIC) to make a $4,000,000 lump-sum payment over this single liability, such that it is immunized coupon rate of 4.63%. Its yield is 3.88%.
coupon rate of 4%. Its yield is 3.48%.
ey have 4 periods until maturity and 10 periods until mpany buy in order to fully fund the liability and be
Time to maturiuty
5
Date
1 Mo
2 Mo
3 Mo
4 Mo
Face Value
1000
10/25/2023
5.56%
5.57%
5.59%
5.61%
Coupon Rate
5%
Coupon of Payment
25
Period
0
1
2
3
4
5
6
7
Year
0
0.5
1
1.5
2
2.5
3
3.5
CF
$ 25.00 $ 25.00 $ 25.00 $ 25.00 $ 25.00 $ 25.00 $ 25.00 Yeild Curve for Rates
5.57%
5.43%
5.26%
5.08%
5.03%
4.98%
4.96%
PV of CFS
$24.32 $23.70 $23.13 $22.61 $22.08 $21.57 $21.06 Bond Price
$1,004.18 Implied Ytm
4.9%
Obtain current US Treasury Yield Curve Rates from Department of Treasur
website.
Create the yield curve graph. Use the yield curve information to price a 5-year bond. Consider a coupon
has a face value of $1,000, an annual coupon rate of 5%, makes 2 (semiann
coupon payemnts per year, and 10 periods to maturity (5 years to maturity
What is price and YTM of this coupon bond?
Use the yield curve information to calculate the implied forward rates at al
maturities. Add forward rates on the yield curve graph.
6 Mo
1 Yr
2 Yr
3 Yr
5 Yr
7 Yr
10 Yr
20 Yr
30 Yr
5.57%
5.43%
5.08%
4.98%
4.89%
4.98%
4.95%
5.27%
5.09%
8
9
10
4
4.5
5
$ 25.00 $ 25.00 $ 1,025.00 4.94%
4.91%
4.89%
$20.57 $20.10 $805.04 ry n bond nual) y). ll
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Date
1 Mo
2 Mo
3 Mo
4 Mo
6 Mo
1 Yr
10/2/2023
5.56
5.6
5.62
5.62
5.58
5.49
10/3/2023
5.55
5.6
5.62
5.62
5.58
5.49
10/4/2023
5.56
5.58
5.61
5.62
5.57
5.42
10/5/2023
5.57
5.59
5.61
5.62
5.56
5.39
10/6/2023
5.59
5.6
5.63
5.64
5.59
5.43
10/10/2023
5.6
5.61
5.61
5.63
5.57
5.37
10/11/2023
5.58
5.59
5.61
5.63
5.56
5.38
10/12/2023
5.61
5.59
5.63
5.63
5.58
5.43
10/13/2023
5.6
5.58
5.62
5.62
5.57
5.41
10/16/2023
5.57
5.58
5.61
5.63
5.58
5.42
10/17/2023
5.58
5.58
5.62
5.64
5.6
5.48
10/18/2023
5.57
5.56
5.61
5.62
5.58
5.47
10/19/2023
5.58
5.57
5.6
5.62
5.56
5.44
10/20/2023
5.56
5.56
5.58
5.61
5.54
5.41
10/23/2023
5.57
5.57
5.58
5.59
5.56
5.42
10/24/2023
5.57
5.57
5.58
5.6
5.57
5.41
10/25/2023
5.56
5.57
5.59
5.61
5.57
5.43
2 Yr
3 Yr
5 Yr
7 Yr
10 Yr
20 Yr
30 Yr
5.12
4.88
4.72
4.73
4.69
5
4.81
5.15
4.95
4.8
4.84
4.81
5.13
4.95
5.05
4.85
4.72
4.75
4.73
5.05
4.87
5.03
4.82
4.68
4.73
4.72
5.06
4.89
5.08
4.87
4.75
4.79
4.78
5.13
4.95
4.96
4.74
4.62
4.66
4.66
5.03
4.85
4.99
4.73
4.59
4.61
4.58
4.92
4.73
5.06
4.82
4.69
4.73
4.7
5.05
4.86
5.04
4.8
4.65
4.66
4.63
4.97
4.78
5.09
4.87
4.72
4.74
4.71
5.06
4.87
5.19
5.01
4.86
4.88
4.83
5.14
4.94
5.19
5.03
4.92
4.95
4.91
5.2
5
5.14
5.01
4.95
5
4.98
5.3
5.11
5.07
4.93
4.86
4.93
4.93
5.27
5.09
5.05
4.89
4.81
4.87
4.86
5.19
5.01
5.02
4.91
4.82
4.86
4.83
5.15
4.96
5.08
4.98
4.89
4.98
4.95
5.27
5.09
Time to maturiuty
10
Face Value
1000
Date
1 Mo
2 Mo
3 Mo
4 Mo
6 Mo
Coupon Rate
4%
###
5.56%
5.57%
5.59%
5.61%
5.57%
Coupon of Payment
20
Period
1
2
3
4
5
6
7
8
year
0.5
1
1.5
2
2.5
3
3.5
4
Cf
20
20
20
20
20
20
20
20
Yield of Curve
5.57%
5.43%
5.26%
5.08%
5.03%
4.98%
4.96%
4.94%
PV of CFS
$19.46 $18.96 $18.50 $18.09 $17.66 $17.26 $16.85 $16.46 Bond Price
$925.56 Implied Ytm
5%
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1 Yr
2 Yr
3 Yr
5 Yr
7 Yr
10 Yr
20 Yr
30 Yr
5.43%
5.08%
4.98%
4.89%
4.98%
4.95%
5.27%
5.09%
9
10
11
12
13
14
15
16
17
18
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
20
20
20
20
20
20
20
20
20
20
4.91%
4.89%
4.91%
4.94%
4.96%
4.98%
4.92%
4.94%
4.97%
4.95%
$16.08 $15.71 $15.31 $14.93 $14.55 $14.17 $13.89 $13.53 $13.18 $12.88
19
20
9.5
10
20
1020
4.95%
4.95%
$12.57 $625.52
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12.00%
ΥTM
2.000% 3.908% 5.840% 5.783%
a) Determine the yield to maturity of a two-year zero-coupon bond.
b) What is the zero-coupon yield curve for years 1 through 4.
c) What is the forward rate for year 3 (short rate from end of year 2 until end of year 3).
d) What should have been the zero-coupon yield for year 4 so that the forward rate in year 4 is
the same than year 3.
Problem 2 Currently the yield curve observed in the market is as follows: y1 = 7%, y2 = 8%, and
Y3 = 9%. You are choosing between a two-year and three-year maturity bonds all paying annual
coupons
of 8%, once a year. You strongly believe that at the end of year the yield curve will become
flat at 9%. Which bond should you buy if you plan to close out your position in one year right
after receiving the coupon payment?
Problem 3 Your…
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