Investment Management: Bond Prices, Yield Curve, and Portfolio Construction

This article discusses bond prices, yield curve, and portfolio construction in investment management. It explains the relationship between HPR and changes in YTM and coupon rate. The article also provides solved assignments, essays, and dissertations on Investment Management available at Desklib.

Running head: INVESTMENT MANAGEMENT
Investment Management
Name of the Student:
Name of the University:
Authors Note:

INVESTMENT MANAGEMENT
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Table of Contents
Question 1:.................................................................................................................................2
a. Calculating bond prices and depicting yield curve:...............................................................2
b. Calculating Yield to maturity:................................................................................................3
c. Constructing arbitrage portfolio:............................................................................................5
Question 2:.................................................................................................................................5
a. Relationship between HPR and changes in the YTM:...........................................................5
b. Repeating the process with short sell:....................................................................................7
c. Relationship between HPR and changes in the Coupon rate:................................................8
Question 3:...............................................................................................................................10
a. Using present yield curve for detecting present value of the liability:.................................10
b. Calculating weights of the portfolio:....................................................................................10
c. Calculating PV of the liability and weights of the portfolio if yield curve shifts down size
by 100 basis points:..................................................................................................................11
References:...............................................................................................................................13

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Question 1:
a. Calculating bond prices and depicting yield curve:
Maturity (years) Market Price of Bond
0.50 100.69
1.00 103.34
1.50 100.80
2.00 102.47
2.50 99.67
3.00 103.55
3.50 103.43
4.00 103.08
4.50 100.25
5.00 100.65
5.50 101.56
6.00 102.00
6.50 100.00
7.00 99.50
7.50 100.47
8.00 101.54
8.50 99.74
9.00 100.68
9.50 100.13
10.00 99.76

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0.00 2.00 4.00 6.00 8.00 10.00 12.00
0.000%
0.500%
1.000%
1.500%
2.000%
2.500%
3.000%
3.500%
Yeild Curve
Zero-Coupon Yields
The general shape of the yield is approximately, as the above figure. However, the
curve is mainly smooth and tends to increase with tenure and decline after some years. The
change in bond prices and income tends to alter the YTM of the bond investment.
b. Calculating Yield to maturity:
Maturity (years) Semi-annually yield
0.50 0.24%
1.00 -0.71%
1.50 0.84%
2.00 1.00%
2.50 1.01%
3.00 1.66%
3.50 1.86%

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4.00 1.95%
4.50 1.32%
5.00 1.49%
5.50 1.83%
6.00 2.02%
6.50 1.37%
7.00 1.20%
7.50 1.56%
8.00 2.04%
8.50 1.41%
9.00 1.79%
9.50 1.61%
10.00 1.53%
0.00 2.00 4.00 6.00 8.00 10.00 12.00
-1.000%
-0.500%
0.000%
0.500%
1.000%
1.500%
2.000%
2.500%
3.000%
3.500%
Yeild Curve
Zero-Coupon Yields semi annualy yield

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c. Constructing arbitrage portfolio:
Bonds T FV Price Coupon rate Rate Duration Weights
GSBS18 0.50 100.00 100.69 3.25% 0.24% 0.49 20%
GSBE19 1.00 100.00 103.34 5.25% 0.71% 0.99 20%
GSBS19 1.50 100.00 100.80 2.75% 0.84% 1.47 20%
GSBG20 2.00 100.00 102.47 4.50% 1.00% 1.93 20%
Zero coupon bond 2.00 100.00 95.00 - 1.01% 2.00 20%
Portfolio Duration 1.38
With the use of equal weights, the portfolio duration calculated for the above arbitrage
position is mainly at the levels of 1.38. This mainly helps in understanding the minim tenure
which is used in deriving the returns from investment.
Question 2:
a. Relationship between HPR and changes in the YTM:
Bond Maturity (Years) Face Value Coupon YTM Bond price
GSBE47 10.00 100.00 3.00% 1.53% 99.76
Increase in YTM
Year Cash
Inflow
0.00% 0.25% 0.50% 0.75% 1.00%
1 3.00 3.4379 3.4391 3.4403 3.4414 3.4426
2 3.00 3.3863 3.3873 3.3883 3.3893 3.3904
3 3.00 3.3354 3.3363 3.3372 3.3380 3.3389

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4 3.00 3.2853 3.2860 3.2868 3.2875 3.2882
5 3.00 3.2359 3.2365 3.2371 3.2377 3.2384
6 3.00 3.1873 3.1878 3.1883 3.1887 3.1892
7 3.00 3.1394 3.1398 3.1401 3.1405 3.1408
8 3.00 3.0922 3.0925 3.0927 3.0929 3.0932
9 3.00 3.0458 3.0459 3.0460 3.0461 3.0462
10 103.00 103.0000 103.0000 103.0000 103.0000 103.0000
Total Payment 132.1455 132.1511 132.1567 132.1623 132.1679
Decrease in YTM
Yea
r
Cash Inflow 0.00% 0.25% 0.50% 0.75% 1.00%
1 3.00 3.4379 3.4368 3.4356 3.4345 3.4333
2 3.00 3.3863 3.3853 3.3842 3.3832 3.3822
3 3.00 3.3354 3.3345 3.3336 3.3328 3.3319
4 3.00 3.2853 3.2845 3.2838 3.2831 3.2823
5 3.00 3.2359 3.2353 3.2347 3.2341 3.2335
6 3.00 3.1873 3.1868 3.1863 3.1859 3.1854
7 3.00 3.1394 3.1390 3.1387 3.1383 3.1380
8 3.00 3.0922 3.0920 3.0918 3.0915 3.0913
9 3.00 3.0458 3.0457 3.0455 3.0454 3.0453
10 103.00 103.0000 103.0000 103.0000 103.0000 103.0000
Total Payment 132.1455 132.1399 132.1344 132.1288 132.1232

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The evaluation of above table mainly helps in understanding the relationship between
HPR and YTM. Therefore, any kind of increment or decline in YTM will directly affect the
end payment of the bond. Hence, it could be assumed that there is a direct relationship
between YTM and HPR (Van, Plantinga and Scholtens 2016).
b. Repeating the process with short sell:
Bond Maturity (Years) Face Value Coupon YTM Bond price
GSBE47 10.00 100.00 3.00% 1.53% 99.76
GSBG25 5.00 100.00 3.25% 1.49% 100.65
Ye
ar
GSBE
47
GSBG25 Cash
Inflow
0.00% 0.25% 0.50% 0.75% 1.00%
1 3 3.25
(0.25)
(0.2
865)
(0.2
866)
(0.2
867)
(0.2
868)
(0.2
869)
2 3 3.25
(0.25)
(0.2
822)
(0.2
823)
(0.2
824)
(0.2
824)
(0.2
825)
3 3 3.25
(0.25)
(0.2
780)
(0.2
780)
(0.2
781)
(0.2
782)
(0.2
782)
4 3 3.25
(0.25)
(0.2
738)
(0.2
738)
(0.2
739)
(0.2
740)
(0.2
740)
5 3 103.25 (
100.25)
(108.1
336)
(108.1
539)
(108.1
743)
(108.1
946)
(108.2
149)
6 3 0
3.00
3.
1873
3.
1878
3.
1883
3.
1887
3.
1892
7 3 0 3. 3. 3. 3. 3.

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3.00 1394 1398 1401 1405 1408
8 3 0
3.00
3.
0922
3.
0925
3.
0927
3.
0929
3.
0932
9 3 0
3.00
3.
0458
3.
0459
3.
0460
3.
0461
3.
0462
10 103.00 0
103.00
103.0
000
103.0
000
103.0
000
103.0
000
103.0
000
Total
Payment
6.
2107
6.
1912
6.
1718
6.
1523
6.
1328
c. Relationship between HPR and changes in the Coupon rate:
Bond Maturity (Years) Face Value Coupon YTM Bond price
GSBE47 10.00 100.00 0.03 0.02 99.76
Increase in Coupon rate
Year Cash
Inflow
0.00% 0.25% 0.50% 0.75% 1.00%
1 3.00 3.4379 3.4465 3.4551 3.4637 3.4723
2 3.00 3.3863 3.3948 3.4032 3.4117 3.4201
3 3.00 3.3354 3.3437 3.3521 3.3604 3.3688
4 3.00 3.2853 3.2935 3.3017 3.3099 3.3181
5 3.00 3.2359 3.2440 3.2521 3.2602 3.2683
6 3.00 3.1873 3.1953 3.2032 3.2112 3.2192
7 3.00 3.1394 3.1473 3.1551 3.1629 3.1708

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8 3.00 3.0922 3.1000 3.1077 3.1154 3.1232
9 3.00 3.0458 3.0534 3.0610 3.0686 3.0762
10 3.00 103.0000 103.0075 103.0150 103.0225 103.0300
Total Payment 132.1455 132.2259 132.3063 132.3866 132.4670
Decrease in Coupon rate
Year Cash
Inflow
0.00% 0.25% 0.50% 0.75% 1.00%
1 3.00 3.4379 3.4293 3.4208 3.4122 3.4036
2 3.00 3.3863 3.3778 3.3694 3.3609 3.3524
3 3.00 3.3354 3.3271 3.3187 3.3104 3.3020
4 3.00 3.2853 3.2771 3.2689 3.2606 3.2524
5 3.00 3.2359 3.2278 3.2197 3.2116 3.2036
6 3.00 3.1873 3.1793 3.1714 3.1634 3.1554
7 3.00 3.1394 3.1316 3.1237 3.1159 3.1080
8 3.00 3.0922 3.0845 3.0768 3.0690 3.0613
9 3.00 3.0458 3.0382 3.0305 3.0229 3.0153
10 3.00 103.0000 102.9925 102.9850 102.9775 102.9700
Total Payment 132.1455 132.0652 131.9848 131.9044 131.8241

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Question 3:
a. Using present yield curve for detecting present value of the liability:
Liability
F(L) 100,000,000
t 1
Yield 2.62%
PV(L) 97,451,639.62
b. Calculating weights of the portfolio:
Bond 1
F 100
c 2.75%
t 4.50
C 1.375
P
1
90.65
Bond 2
F 100
c 3.25%
t 5.00
C 1.625
P1 100.49

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Cash Flow
Time (year) B1 B2 L checking
4.50 101.375 1.625 0 0
5.00 0 101.625 100,000,000 100,000,000
Bond Portfolio No of bond bond price $ invest
B1 -15773.27734 90.65410927 -1429912.407
B2 984009.8401 100.4883773 98881552.03
B 97451639.62 97451639.62
c. Calculating PV of the liability and weights of the portfolio if yield curve shifts down
size by 100 basis points:
Liability
F(L) 100,000,000
t 1
PV(L) 97,476,480.14
Bond 1
F 100
c 2.75%
t 4.50
C 1.375
P1 90.75

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Bond 2
F 100
c 3.25%
t 5.00
C 1.625
P1 100.52
Cash Flow
Time (year) B1 B2 L checking
4.50 101.375 1.625 0 0
5.00 0 101.625 100,000,000 100,000,000
Bond Portfolio No of bond bond price $ invest
B1 -15773.27734 90.75425759 -1431492.075
B2 984009.8401 100.52 98907972.22
B 97,476,480 97,476,480
From the overall evaluation, it could be identified that the hedge was held effectively,
where the losses from the bond hedge was minimised from the portfolio weights. This might
help in minimising the risk from changing YTM rates. In this context, Fender et al. (2016)
stated that with the use of hedging measures investors are able to minimise the risk from
investment and maximise their profitability.

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References:
Fender, R., Adams, R., Barber, B. and Odean, T., 2016. Gender Diversity in Investment
Management: New Research for Practitioners on How to Close the Gender Gap. Research
Foundation Briefs, 5(1), pp.1-16.
van Duuren, E., Plantinga, A. and Scholtens, B., 2016. ESG integration and the investment
management process: Fundamental investing reinvented. Journal of Business Ethics, 138(3),
pp.525-533.