Investment Management

This document covers topics related to Investment Management including term-structure of interest rates, treasury bonds, and portfolio formation. It includes tables, graphs, and calculations related to bond yields, present value, and modified duration. The content is relevant for students studying finance and economics.

Running head: Investment Management
Investment Management
Name of the Student:
Name of the University:
Author’s Note:

1INVESTMENT MANAGEMENT
Table of Contents
In Response to Question 1..........................................................................................................2
In Response Question 2..............................................................................................................3
In Response to Question 3..........................................................................................................5

2INVESTMENT MANAGEMENT
In Response to Question 1
Treasury Bonds
Code Coupon PMT PMT Amt Maturity (years) N Face value
GSBE19 5.25% 2.63% 2.63 0.50 1.00 100
GSBS19 2.75% 1.38% 1.38 1.00 2.00 100
GSBG20 4.50% 2.25% 2.25 1.50 3.00 100
GSBU20 1.75% 0.88% 0.88 2.00 4.00 100
GSBI21 5.75% 2.88% 2.88 2.50 5.00 100
GSBW21 2.00% 1.00% 1.00 3.00 6.00 100
GSBM22 5.75% 2.88% 2.88 3.50 7.00 100
GSBU22 2.25% 1.13% 1.13 4.00 8.00 100
GSBG23 5.50% 2.75% 2.75 4.50 9.00 100
GSBG24 2.75% 1.38% 1.38 5.00 10.00 100
GSBG25 3.25% 1.63% 1.63 5.50 11.00 100
GSBG26 4.25% 2.13% 2.13 6.00 12.00 100
GSBG27 4.75% 2.38% 2.38 6.50 13.00 100
GSBU27 2.75% 1.38% 1.38 7.00 14.00 100
GSBI28 2.25% 1.13% 1.13 7.50 15.00 100
GSBG29 3.25% 1.63% 1.63 8.00 16.00 100
GSBU29 2.75% 1.38% 1.38 8.50 17.00 100
GSBG33 4.50% 2.25% 2.25 9.00 18.00 100
GSBK35 2.75% 1.38% 1.38 9.50 19.00 100
GSBK39 3.25% 1.63% 1.63 10.00 20.00 100
Term-structure of Interest Rates
Maturity (years) Zero-Coupon Yields I/Y Price YTM
0.50 1.470% 0.7350% -101.88 1.47%
1.00 1.540% 0.7700% -101.20 1.54%
1.50 1.650% 0.8250% -104.21 1.65%
2.00 1.760% 0.8800% -99.98 1.76%
2.50 1.880% 0.9400% -109.41 1.88%
3.00 1.980% 0.9900% -100.06 1.98%
3.50 2.060% 1.0300% -112.40 2.06%
4.00 2.130% 1.0650% -100.46 2.13%
4.50 2.190% 1.0950% -114.11 2.19%
5.00 2.230% 1.1150% -102.45 2.23%
5.50 2.270% 1.1350% -105.04 2.27%
6.00 2.300% 1.1500% -110.87 2.30%
6.50 2.330% 1.1650% -114.52 2.33%
7.00 2.360% 1.1800% -102.50 2.36%
7.50 2.390% 1.1950% -99.04 2.39%
8.00 2.410% 1.2050% -106.08 2.41%
8.50 2.440% 1.2200% -102.37 2.44%

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9.00 2.460% 1.2300% -116.38 2.46%
9.50 2.480% 1.2400% -102.27 2.48%
10.00 2.510% 1.2550% -106.51 2.51%
B) Plot the Curves
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
6.50
7.00
7.50
8.00
8.50
9.00
9.50
10.00
0.000%
1.000%
2.000%
3.000%
4.000%
5.000%
6.000%
Graphical Analysis
Zero-Coupon Yields YTM
C)
Particulars
Portfoli
o 5
2 Year ZCB
Time Period 2 Years
Face Value 100
Present Value 98
Required Rate 1.76%
PMT 0
Price -96.57
Portfolio will be formed by the allocation of each will be based on
20% weightage to per bond
The arbitrage portfolio will be considered after reconsidering the pricing and the yield
generated by the bond. The arbitrage portfolio will be created by the help of the bonds where

4INVESTMENT MANAGEMENT
bonds which provide a higher yield will be given a positive weight and bonds providing a
negative yield will be given a negative weight. In order to explore mispricing an earn profits.
In Response Question 2
Treasury Bonds
Code
Coupo
n PMT PMT Amt Maturity (years) N Face value
GSBI2
8 2.25%
1.13
% 1.13 7.50
15.0
0 100
0 BP 2.25%
1.13
% 1.13 7.50
15.0
0 100
25 BP 2.25%
1.13
% 1.13 7.50
15.0
0 100
50 BP 2.25%
1.13
% 1.13 7.50
15.0
0 100
75 BP 2.25%
1.13
% 1.13 7.50
15.0
0 100
100 BP 2.25%
1.13
% 1.13 7.50
15.0
0 100
0 BP 2.25%
1.13
% 1.13 7.50
15.0
0 100
25 BP 2.25%
1.13
% 1.13 7.50
15.0
0 100
50 BP 2.25%
1.13
% 1.13 7.50
15.0
0 100
75 BP 2.25%
1.13
% 1.13 7.50
15.0
0 100
100 BP 2.25%
1.13
% 1.13 7.50
15.0
0 100
Term-structure of Interest Rates
Maturity
(years)
Zero-Coupon
Yields I/Y Price YTM HPR
7.50 2.390%
1.1950
% -99.04 2.39%
0.00956
1
7.50 2.390%
1.1950
% -99.04 2.39% 0.96%
Decrease
in YTM
7.50 2.140%
1.0700
% -100.76 2.14% -0.76%
7.50 1.890%
0.9450
% -102.51 1.89% -2.51%
7.50 1.640%
0.8200
% -104.29 1.64% -4.29%
7.50 1.390%
0.6950
% -106.11 1.39% -6.11%

5INVESTMENT MANAGEMENT
7.50 2.390%
1.1950
% -99.04 2.39% 0.96%
Increase
in YTM
7.50 2.640%
1.3200
% -97.36 2.64% 2.64%
7.50 2.890%
1.4450
% -95.71 2.89% 4.29%
7.50 3.140%
1.5700
% -94.09 3.14% 5.91%
7.50 3.390%
1.6950
% -92.51 3.39% 7.49%
0 BP 25 BP 50 BP 75 BP 100 BP
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
Decrease in YTM
1 2 3 4 5 6 7 8 9 10 11
-8.00%
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
YTM AND ZCB
YTM HPR

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In Response to Question 3
a) Summarize the Present value of the Fund
Particulars 1 2 3 4 5 6 7 8 9 10
Liabilility
Amt 2,50,000 2,50,000 2,50,000 2,50,000 2,50,000 2,50,000 2,50,000 2,50,000 2,50,000 2,50,000
Yeld Curve 0.7350% 0.7700% 0.8250% 0.8800% 0.9400% 0.9900% 1.0300% 1.0650% 1.0950% 1.1150%
Present
VALUE 248175.9 248089.7 247954.4 247819.2 247671.9 247549.3 247451.3 247365.6 247292.2 247243.2
Sum Total 3465170
b) The calculation of the Modified Duration was done after calculating he duration of
each of the Treasury Bond Taken below :
 The treasury bond taken was one was of 3 Years which a coupon rate of 9%
payable semi-annually and the price for the same is trading at 96.2$. The
YTM calculated for the Bond was around 5.25%.
 The second bond had a face value of 100 with a coupon rate of 10% payable,
3year semi-annually and the price for the same was trading at 98.79. The
YTM calculated for the bond was around 5.25%.
Calculation of D (Duration)
Bond 1
Present Value 96.2
Modified
Duration Duration/(1+ Periodic R)
PMT (Coupon) 4.5
YTM
(Calculated) 5.25%
Face Value 100
Annual
Duration
2.68810
1
Period (Semi Annually) 12
Modified
Duration
2.55401
5
Period In 6 months
Cash
Flow
P.V @
5.25% Weights
Weights*Perio
d
1 4.5
4.27553444
2
0.04443
3 0.044433381
2 4.5
4.06226550
3
0.04221
7 0.084433978
3 4.5
3.85963468
2
0.04011
1 0.12033346

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4 4.5
3.66711133
7 0.03811 0.152441438
5 4.5
3.48419129
4
0.03620
9 0.181046839
6
104.
5
76.8747406
1
0.79891
9 4.793512497
Total Price
96.2234778
7
Duratio
n 5.376201593
Calculation of D (Duration)
Bond 2
Present Value
98.7
9
Modified
Duration Duration/(1+ Periodic R)
PMT (Coupon) 5
YTM
(Calculated) 5.25%
Face Value 100
Annual
Duration 2.73194
Period (Semi Annually) 12
Modified
Duration
2.59566
8
Period In 6 months
Cash
Flow
P.V @
5.25% Weights
Weights*Perio
d
1 5
4.75059382
4 0.04937 0.049370423
2 5
4.51362833
7
0.04690
8 0.093815531
3 5 4.28848298
0.04456
8 0.133703845
4 5
4.07456815
2
0.04234
5 0.169379376
5 5 3.87132366
0.04023
3 0.201163154
6 105
77.2425623
4
0.80274
1 4.816447963
Total Price
98.7411592
9 Duration 5.463880292

8INVESTMENT MANAGEMENT
Modified Duration: Duration in Year/ (1+ Periodic r)
Modified Duration for the portfolio calculated was done by taking the weight in each of the
bond as 50% and the annual duration of the bond was calculated for bond 1 and 2
respectively.
The modified duration for the portfolio was calculated as 2.71%, which implies that if the
YTM of the Bond that is 10.5% changes by 1% the value of the portfolio is expected to
change by 2.71% in the opposite direction ignoring convexity.
The reason for selecting the Treasury bond was the liquidity factor present in this bond.
c) After setting up the hedge, if the entire yield curve shifts down by 25 basis points then
the recalculation of the Modified duration will be done by using the approx. formula
taking a 25 basis point shock in the YTM.
Modified Duration Approx.: P2-P1(2P0*YTM)
Calculation of P2
So new YTM = 10.5-0.25 = 10.25 annually.
i.e., YTM semi-annually = 5.125% for 6 months.
The new price of the bond 1 will be:
4.5PMT (Coupon Payment)
12 N=Time period
100 Face Value.
5.125% I/Y
Equals: Present Value: $96.22856
Calculation of P2
So new YTM = 10.5-0.25 = 10.25 annually.

9INVESTMENT MANAGEMENT
i.e., YTM semi-annually = 5.125% for 6 months.
The new price of the bond 2 will be:
5 PMT (Coupon Payment)
12 N=Time period
100 Face Value.
5.125% I/Y
Equals: Present Value: $98.74680803
Yes the bond portfolio is a perfectly hedged portfolio as the interest rate charged by
negative 25 basis point and the value of the bond portfolio increased.