In: Finance
MLK Bank has an asset portfolio that consists of $230 million of
15-year, 8 percent coupon, $1,000 bonds with annual coupon payments
that sell at par.
a-1. What will be the bonds’ new prices if market
yields change immediately by ± 0.10 percent?
a-2. What will be the new prices if market yields
change immediately by ± 2.00 percent?
b-1. The duration of these bonds is 9.2442 years.
What are the predicted bond prices in each of the four cases using
the duration rule?
b-2. What is the amount of error between the
duration prediction and the actual market values?
Complete this question by entering your answers in the tabs below.
What will be the bonds’ new prices if market yields change immediately by ± 0.10 percent? (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))
|
What will be the new prices if market yields change immediately by ± 2.00 percent? (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))
|
The duration of these bonds is 9.2442 years. What are the predicted bond prices in each of the four cases using the duration rule? (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))
|
Answer-a-1
Bond price = PV of the annual cashflows discounted at market yield.
FV = $1000
Coupon rate = 8%
Annual coupon = $1000*8%= $80
if yield has increased by +0.10 % or if yield is 8.10% | |||||
1 | 2 | 3 | 4 | 5 | 2*5 |
year | cash flow | nature | market yield | PVF@Market yield=(1/(1+yield)^t) |
PV of cash flows |
1 | $80 | coupon | 8.10% | 0.9250693802 | $74.006 |
2 | $80 | coupon | 8.10% | 0.8557533582 | $68.460 |
3 | $80 | coupon | 8.10% | 0.7916312287 | $63.330 |
4 | $80 | coupon | 8.10% | 0.7323138101 | $58.585 |
5 | $80 | coupon | 8.10% | 0.6774410824 | $54.195 |
6 | $80 | coupon | 8.10% | 0.6266800022 | $50.134 |
7 | $80 | coupon | 8.10% | 0.5797224812 | $46.378 |
8 | $80 | coupon | 8.10% | 0.5362835164 | $42.903 |
9 | $80 | coupon | 8.10% | 0.4960994601 | $39.688 |
10 | $80 | coupon | 8.10% | 0.4589264201 | $36.714 |
11 | $80 | coupon | 8.10% | 0.424538779 | $33.963 |
12 | $80 | coupon | 8.10% | 0.3927278252 | $31.418 |
13 | $80 | coupon | 8.10% | 0.3633004858 | $29.064 |
14 | $80 | coupon | 8.10% | 0.3360781552 | $26.886 |
15 | $1,080 | coupon+Face value | 8.10% | 0.3108956108 | $335.767 |
Total bond price | $991.49 |
if yield has decreased by -0.10 % or if yield is 7.90% | |||||
1 | 2 | 3 | 4 | 5 | 2*5 |
year | cash flow | nature | market yield | PVF@Market yield=(1/(1+yield)^t) |
PV of cash flows |
1 | $80 | coupon | 7.90% | 0.9267840593 | $74.143 |
2 | $80 | coupon | 7.90% | 0.8589286926 | $68.714 |
3 | $80 | coupon | 7.90% | 0.7960414204 | $63.683 |
4 | $80 | coupon | 7.90% | 0.737758499 | $59.021 |
5 | $80 | coupon | 7.90% | 0.6837428165 | $54.699 |
6 | $80 | coupon | 7.90% | 0.633681943 | $50.695 |
7 | $80 | coupon | 7.90% | 0.5872863234 | $46.983 |
8 | $80 | coupon | 7.90% | 0.5442876028 | $43.543 |
9 | $80 | coupon | 7.90% | 0.504437074 | $40.355 |
10 | $80 | coupon | 7.90% | 0.4675042391 | $37.400 |
11 | $80 | coupon | 7.90% | 0.4332754764 | $34.662 |
12 | $80 | coupon | 7.90% | 0.4015528049 | $32.124 |
13 | $80 | coupon | 7.90% | 0.3721527385 | $29.772 |
14 | $80 | coupon | 7.90% | 0.3449052257 | $27.592 |
15 | $1,080 | coupon+Face value | 7.90% | 0.3196526651 | $345.225 |
Total bond price | $1,008.61 |
Bonds new price | |
at +0.10% | $991.49 |
at -0.10% | $1,008.61 |
--------------------------------------------------------------------------------------------------------------------------------------------
Answer-a-2
if yield has increased by +2.0 % or if yield is 10% | |||||
1 | 2 | 3 | 4 | 5 | 2*5 |
year | cash flow | nature | market yield | PVF@Market yield=(1/(1+yield)^t) |
PV of cash flows |
1 | $80 | coupon | 10.00% | 0.9090909091 | $72.727 |
2 | $80 | coupon | 10.00% | 0.826446281 | $66.116 |
3 | $80 | coupon | 10.00% | 0.7513148009 | $60.105 |
4 | $80 | coupon | 10.00% | 0.6830134554 | $54.641 |
5 | $80 | coupon | 10.00% | 0.6209213231 | $49.674 |
6 | $80 | coupon | 10.00% | 0.5644739301 | $45.158 |
7 | $80 | coupon | 10.00% | 0.5131581182 | $41.053 |
8 | $80 | coupon | 10.00% | 0.4665073802 | $37.321 |
9 | $80 | coupon | 10.00% | 0.4240976184 | $33.928 |
10 | $80 | coupon | 10.00% | 0.3855432894 | $30.843 |
11 | $80 | coupon | 10.00% | 0.3504938995 | $28.040 |
12 | $80 | coupon | 10.00% | 0.3186308177 | $25.490 |
13 | $80 | coupon | 10.00% | 0.2896643797 | $23.173 |
14 | $80 | coupon | 10.00% | 0.2633312543 | $21.067 |
15 | $1,080 | coupon+Face value | 10.00% | 0.2393920494 | $258.543 |
Total bond price | $847.88 |
if yield has decreased by -2.0 % or if yield is 6% | |||||
1 | 2 | 3 | 4 | 5 | 2*5 |
year | cash flow | nature | market yield | PVF@Market yield=(1/(1+yield)^t) |
PV of cash flows |
1 | $80 | coupon | 6% | 0.9433962264 | $75.472 |
2 | $80 | coupon | 6% | 0.88999644 | $71.200 |
3 | $80 | coupon | 6% | 0.839619283 | $67.170 |
4 | $80 | coupon | 6% | 0.7920936632 | $63.367 |
5 | $80 | coupon | 6% | 0.7472581729 | $59.781 |
6 | $80 | coupon | 6% | 0.7049605404 | $56.397 |
7 | $80 | coupon | 6% | 0.6650571136 | $53.205 |
8 | $80 | coupon | 6% | 0.6274123713 | $50.193 |
9 | $80 | coupon | 6% | 0.5918984635 | $47.352 |
10 | $80 | coupon | 6% | 0.5583947769 | $44.672 |
11 | $80 | coupon | 6% | 0.5267875254 | $42.143 |
12 | $80 | coupon | 6% | 0.4969693636 | $39.758 |
13 | $80 | coupon | 6% | 0.4688390222 | $37.507 |
14 | $80 | coupon | 6% | 0.4423009644 | $35.384 |
15 | $1,080 | coupon+Face value | 6% | 0.4172650607 | $450.646 |
Total bond price | $1,194.25 |
Bonds new price | |
at +2% | $847.88 |
at -2% | $1,194.25 |
-----------------------------------------------------------------------------------------------------------------------------------
Answer-B-1
effect on bond price due to change in interest rate can be calculated by dollar duration of the bond
Dollar Duration = Duration* ( change in yield/ (1+yield)) * price of bond
Effect on bond price | formula | Old price | new price(old+effect) | |
at +0.10% | -8.56 | [-9.2442*(0.001/1.08)*1000] | 1000 | 991.44 |
at -0.10% | 8.56 | [9.2442*(0.001/1.08)*1000] | 1000 | 1008.56 |
at +2% | -171.19 | [-9.2442*(0.02/1.08)*1000] | 1000 | 828.81 |
at -2% | 171.19 | [9.2442*(0.02/1.08)*1000] | 1000 | 1171.19 |
-----------------------------------------------------------------------------------------------------------------------
answer-b-2
price as per Duration prediction(A) | actual market prices(B) |
amount of error(A-B) |
|
at +0.10% | 991.44 | 991.49 | -0.05 |
at -0.10% | 1008.56 | 1,008.61 | -0.05 |
at +2% | 828.81 | 847.88 | -19.07 |
at -2% | 1171.19 | 1,194.25 | -23.06 |