Question

MLK Bank has an asset portfolio that consists of $220 million of 15-year, 7 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 9.7455 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? *Please show via financial calculator if possible*

Answer 1

Let's do the analysis for 1 bond with

Face Value, FV = $ 1,000

Payment per period = Annual Coupon = 7% x FV = 7% x 1,000 = 70

Period = time to maturity = 15 years

Since they are trading at par, yield of such bonds = coupon rate = 7%

Part a-1

If yield increases by 0.10%, yield = 7% + 0.10% = 7.10% = rate

Price of the bond can be calculated using the PV function.

Price, P = - PV(rate, period, payment, Future value) = - PV(7.10%, 15, 70, 1000) = $ 990.95

If yield decreases by 0.10%, yield = 7% - 0.10% = 6.90% = rate

Price of the bond can be calculated using the PV function.

Price, P = - PV(rate, period, payment, Future value) = - PV(6.90%, 15, 70, 1000) = $1,009.17

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Part a-2

If yield increases by 2.00%, yield = 7% + 2.00% = 9.00% = rate

Price of the bond can be calculated using the PV function.

Price, P = - PV(rate, period, payment, Future value) = - PV(9.00%, 15, 70, 1000) = $ 838.79

If yield decreases by 2.00%, yield = 7% - 2.00% = 5.00% = rate

Price of the bond can be calculated using the PV function.

Price, P = - PV(rate, period, payment, Future value) = - PV(5.00%, 15, 70, 1000) = $1,207.59

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Part b-1

D = Duration of these bonds = 9.7455 years

If yield increases by 0.10%, Price will decrease by D x 0.10% = 9.7455 x 0.10% = 0.97%

Hence, Price, P = 1,000 x (1 - 0.97%) = $ 990.25

If yield decreases by 0.10%, Price will increase by D x 0.10% = 9.7455 x 0.10% = 0.97%

Hence, Price, P = 1,000 x (1 + 0.97%) = $ 1,009.75

If yield increases by 2.00%, Price will decrease by D x 2.00% = 9.7455 x 2.00% = 19.49%

Hence, Price, P = 1,000 x (1 - 19.49%) = $ 805.09

If yield decreases by 2.00%, Price will increase by D x 2.00% = 9.7455 x 2.00% = 19.49%

Hence, Price, P = 1,000 x (1 + 19.49%) = $ 1,194.91

Part b-2

Let's summarise in the table below:

Situation	Actual market Price ($)	Price as predicted by duration theory ($)	Error ($)
	P	Pd	Pd - P
Increase in yield by 0.10%	990.95	990.25	(0.69)
Decrease in yield by 0.10%	1,009.17	1,009.75	0.58
Increase in yield by 2.00%	838.79	805.09	(33.70)
Decrease in yield by 2.00%	1,207.59	1,194.91	(12.68)