25721 Investment Management
Gender Diversity in Investment Management:
New Research for Practitioners on How to Close the Gender Gap.
ESG integration and the investment management process:
Answer:
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 |
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% |
|
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% |
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 |
|
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 | ||||||
|
Year |
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 | |
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 |
|
Year |
GSBE47 |
GSBG25 |
Cash Inflow |
0.00% |
0.25% |
0.50% |
0.75% |
1.00% |
|
1 |
3 |
3.25 |
(0.25) |
(0.2865) |
(0.2866) |
(0.2867) |
(0.2868) |
(0.2869) |
|
2 |
3 |
3.25 |
(0.25) |
(0.2822) |
(0.2823) |
(0.2824) |
(0.2824) |
(0.2825) |
|
3 |
3 |
3.25 |
(0.25) |
(0.2780) |
(0.2780) |
(0.2781) |
(0.2782) |
(0.2782) |
|
4 |
3 |
3.25 |
(0.25) |
(0.2738) |
(0.2738) |
(0.2739) |
(0.2740) |
(0.2740) |
|
5 |
3 |
103.25 |
(100.25) |
(108.1336) |
(108.1539) |
(108.1743) |
(108.1946) |
(108.2149) |
|
6 |
3 |
0 |
3.00 |
3.1873 |
3.1878 |
3.1883 |
3.1887 |
3.1892 |
|
7 |
3 |
0 |
3.00 |
3.1394 |
3.1398 |
3.1401 |
3.1405 |
3.1408 |
|
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 |
103.0000 |
103.0000 |
103.0000 |
103.0000 |
103.0000 |
|
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 |
|
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 | |
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 |
|
P1 |
90.65 |
|
Bond 2 | |
|
F |
100 |
|
c |
3.25% |
|
t |
5.00 |
|
C |
1.625 |
|
P1 |
100.49 |
|
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 |
|
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.
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.
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