Bond Portfolio Analysis

This assignment involves the analysis of a bond portfolio consisting of various securities. It requires calculating the Macaulay duration for each security to determine the average time it takes to recover the initial investment, assessing the investment amount needed to purchase both securities, and analyzing the present value of liabilities along with percentage changes in the bond portfolio under different interest rate scenarios.

INVESTMENT MANAGEMENT

TABLE OF CONTENTS
Question 1........................................................................................................................................1
(a)Calculating bond price............................................................................................................1
(B) Yield curve and explaination.................................................................................................1
© Arbitrage and dollar profit.......................................................................................................3
Question 2........................................................................................................................................4
(A)Computation of HPR..............................................................................................................4
© Risk in long and short trading strategy....................................................................................4
Question 3........................................................................................................................................5
(A)Maculay duration...................................................................................................................5
(B) Assessing investment amount...............................................................................................6
© Present value of liability and percentage change in bond portfolio.........................................6

Question 1
(a)Calculating bond price
Code Coupon
Face
value Yield
Years to
Maturity
GSBA18 5.50% 100 1.611% 0.5
GSBS18 3.25% 100 1.741% 1
GSBE19 5.25% 100 1.671% 1.5
GSBS19 2.75% 100 1.780% 2
GSBG20 4.50% 100 1.940% 2.5
GSBU20 1.75% 100 2.035% 3
GSBI21 5.75% 100 2.080% 3.5
GSBW2
1 2.00% 100 2.132% 4
Table 1Bond price
1 105.2132701
2 100
3 102.8466842
4 104.0786246
5 111.0293293
6 104.3409762
7 119.609293
8 106.9359346
(B) Yield curve and explaination
Table 2Calculation of ZYC
Face value Interest PV of interest
PV of Face
value PV of bond ZYC
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100 5.5 5.3515 97 102.3515 0.954050502
100 3.25 3.12 96 99.12 0.008878128
100 5.25 6.915948975 36.72048495
43.6364339
2 0.527775317
100 2.75 3.38267532 25.68277431
29.0654496
3 0.720255514
100 4.5 8.00079966 55.98941822
63.9902178
8 -0.374904457
100 1.75 3.051722537 50.66846062
53.7201831
5 -0.37950075
100 5.75 11.20993481 24.4781806
35.6881154
1 -0.199413355
100 2 3.871474954 19.443526
23.3150009
6 0.072271026
1 2 3 4 5 6 7 8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Chart Title
Figure 1Yield curve
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Curve shape is not stable as it can be seen that values are fluctuating at fast rate. Expectation theory state that expectation of rise in
short term interest rate create positive yield curve. In present case curve is positive and negative both and due to this reason theory
and curve does not match.
© Arbitrage and dollar profit
Code Coupon Face value Yield Years to Maturity
GSBE19 4.25% 130 1.671% 4
Bond value
132.733756
1
Number of units 3
Value
398.201268
2
Sale of one unit
132.733756
1
Value of bond
265.467512
1
Face
value Value of bond
Revised value of
bond Final value of bond
GSBA18 100 105.2132701 105.2132701
GSBS18 100 100 100
GSBE19 100 102.8466842 102.8466842
GSBS19 100 104.0786246 104.0786246
GSBG20 100 111.0293293 111.0293293
GSBU20 100 104.3409762 104.3409762
GSBI21 100 119.609293 239.2185861 358.8278791
GSBW21 100 106.9359346 106.9359346
800 854.0541121 1093.272698
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Profit 54.0541121 293.2726982
Arbitrage profit amount to 293 in case single unit of bond at 4.25% coupon rate will be sold in the market and same is invested
in exisitng portfolio. Hence, dollar profit on arbitrage is equal to 293. Arbitrage is possible in this case because single security is
purchased and then sold. Received proceeds are again invested in portfolio and in this way gain is made.
Question 2
(A)Computation of HPR
Table 3Computation of HPR
ZYC Semi annual ZYC PV Net gain/Loss
0.07 0.04 100.1446204 0.145%
Facts are revealing that gain of 0.14% can be made on security as HPR. HPR is ensured because for long duration bond will trade in
the exchange.
(B)
Table 4Computation of HPR
ZYC Redued ZYC PV Net gain/Loss
0.072271026 0.07 100.2693557 0%
HPR can not be guaranteed because already ZYC reduced by some points. Hence, HRC value also get reduced as can be seen from
table that gain amount is 0% and same is high equal to 0.145% in above case. Thus, HPR can not be guarantted in this case.
© Risk in long and short trading strategy
Table 5HPR at different rates
ZYC New PV Net gain/Loss HPR ZYC New PV Net gain/Loss HPR
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ZYC ZYC
0.07227
1
0.06727
1
99.7313
7 0.268632174 0.26%
0.07227
1
0.07227
1 99.71143745 -$0.29 0.28%
There is heavy risk associated with HPR in case of long and short strategy. This is because in case of long strategy one have to
buy position and in short same need to be sold. It is very difficult task to keep close eye on open long and short positions closely.
Hence, there is heavy risk in long short strategy then former one.
Question 3
(A)Maculay duration
Table 6Calculation of Macuclary duration
5.50
%
Pe
rio
d
X
ca
sh
flo
w
PV at
5.50
%
3.25
%
Perio
d X
cash
flow
PV at
3.25
%
5.25
%
Perio
d X
cash
flow
PV at
5.25
%
2.7
5%
Peri
od
X
cas
h
flo
w
PV at
2.75
%
4.5
0%
Peri
od
X
cas
h
flo
w
PV at
4.50
%
0
.
5
0.97
358
48
5.
5
5.354
7162
19 1
0.968
5230
02 3.25
3.147
6997
58 1
0.950
1187
65 5.25
4.988
1235
15 1
0.9
732
36
2.7
5
2.676
3990
27 1
0.9
569
38 4.5
4.306
2200
96
1
0.50
669
22 0 2
0.258
0590
01 0
1
.
5
0.367
2048
49 5.25
1.927
8254
6 2
0.2
568
28
2.7
5
0.706
2762
93 2
0.2
611
23 4.5
1.175
0557
45
3
0.29
236
57
105.3
5471
62 3
0.502
2234
32
103.1
4769
98 2
0.534
9741
77
106.9
1594
9 3
0.5
037
01
103.3
8267
53
2
.
5
0.5
598
94 4.5
2.519
5238
2
4
0.35
847
46 100 4
0.196
3640
01 100 3
0.276
5010
46 100 4
0.1
955
93 100 3
0.2
634
6
108.0
0079
97
5 0.21 M 1.053 5 0.408 MD 1.031 4 0.376 MD 1.069 5 0.4 MD 1.033 4 0.3 100
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614
36 D
5471
62
0217
54
4769
98
6303
38
1594
9
093
38
8267
53
924
23
6
0.30
909
41 6
0.128
3346
15 5
0.202
2615
44 6
0.1
276
17 5
0.1
910
49 MD
1.080
0079
97
7
0.15
177
63 7
0.429
4717
66 6
0.331
1358
98 7
0.4
313
89 6
0.3
502
86
8
0.32
289
03 8
0.057
3581
78 7
0.135
0340
31 8
0.0
567
46 7
0.1
221
86
9
0.08
059
08 9
0.605
3420
51 8
0.363
0186
51 9
0.6
085
03 8
0.3
976
33
1
0
0.46
066
73
1
0
0.008
7967
89 9
0.061
5862
57
1
0
0.0
086
25 9
0.0
491
43
3.67
227
96
3.562
4945
89
0.744
0939
15
3.598
4655
57
0.766
4167
32
3.5
715
77
0.7
440
94
3.5
441
34
0.7
664
17
Maculay duration is 7.4 which means that in order to earn return one have to make investment for 7 years and 4 month.
(B) Assessing investment amount
Investment of 100 need to be made to make purchase of both securities which is GSBU20 and GSB121. Maculay duration is
2.13 which means that investment can be covered in 2 year and 13 month.
© Present value of liability and percentage change in bond portfolio
Table 7Percentage change in liability and bond portofolio
Face value
Interes
t
PV of
interest PV of Face value PV of bond
12500000 687500 668937.5 12125000 12793937.5
12500000 406250 390000 12000000 12390000
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12500000 656250 864919.2107 4586872.27
5451791.48
1
12500000 343750 422834.415 3210346.788
3633181.20
3
12500000 562500 1000152.984 6999016.349
7999169.33
2
12500000 218750 381487.5968 6333932.982
6715420.57
9
12500000 718750 1401798.227 3057728.925
4459527.15
2
12500000 250000 483955.8322 2430247.508 2914203.34
10000000
0 PV of liability
56357230.5
9
Percentage change in liability or bond
portfolio -44%
Percentage change in liability or bond value will be -44% which means that with decline in interest rate liability and portfolio value
which change by -44%.
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