Question

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MLK Bank has an asset portfolio that consists of $230 million of 15-year, 8 percent coupon,...

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.

  • Required A1
  • Required A2
  • Required B1
  • Required B2

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))

Bonds’ New Price
At + 0.10%
At − 0.10%
  • Required A1
  • Required A2
  • Required B1
  • Required B2

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))

Bonds’ New Price
At + 2.0%
At − 2.0%
  • Required A1
  • Required A2
  • Required B1
  • Required B2

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))

Bonds’ New Price
At + 0.10%
At − 0.10%
At + 2.0%
At − 2.0%

Solutions

Expert Solution

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

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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

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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

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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

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