Question

MLK Bank has an asset portfolio that consists of $170 million of 15-year, 9.5-percent-coupon, $1,000 bonds with annual coupon payments that sell at par.

a1.	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%	____

a2.	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%	_____

b1.	The duration of these bonds is 8.5719 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%	______

b2.	What is the amount of error between the duration prediction and the actual market values? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

	Amount of Error
At + 0.10%	_____$
At − 0.10%	_______
At + 2.0%	______
At − 2.0%	_______

Answer 1

(a1) Bond Par Value = $ 1000, Coupon Rate = 9.5 %, Tenure = 15 years, YTM = 9.5 % (as the bond sells at par)

+0.1% Change:

New YTM = 9.6 %

Annual Coupon = 0.095 x 1000 = $ 95

New Bond Price = 95 x (1/0.096) x [1-{1/(1.096)^(15)}] + 1000 / (1.096)^(15) = $ 992.2171 ~ $ 992.22

-0.1% Change:

New YTM = 9.4 %

Annual Coupon = 0.095 x 1000 = $ 95

New Bond Price = 95 x (1/0.094) x [1-{1/(1.094)^(15)}] + 1000 / (1.094)^(15) = $ 1007.8738 ~ $1007.87

(a2) + 2 % Change:

New YTM = 11.5 %

Annual Coupon = 0.095 x 1000 = $ 95

New Bond Price = 95 x (1/0.115) x [1-{1/(1.115)^(15)}] + 1000 / (1.115)^(15) = $ 860.07

- 2 % Change:

New YTM = 7.5 %

Annual Coupon = 0.095 x 1000 = $ 95

New Bond Price = 95 x (1/0.075) x [1-{1/(1.075)^(15)}] + 1000 / (1.075)^(15) = $ 1176.54

(b1) Duration (assumed to be Macaulay's Duration) = 8.5719 years (the duration provided seems to be Macaulay's Duration as assuming it to be a Modified Duration gives incorrect answers. Mention of the same would have been desirable)

Modified Duration = Macaulay's Duration = 8.5719 / (1+YTM) = 8.5719 / 1.095 = 7.828219

+ 0.1 % Change:

% Change in Bond Price = - (Duration) x (Change in YTM in BPS / 100) = -(7.828219) x (10/100) = - 0.7828219 %

Actual Bond Price = Par Value = $ 1000 (as bond sells at par)

New Bond Price = 1000 x [1- (0.7.828219/100)] = $ 992.1718

- 0.1 % Change:

% Change in Bond Price = - (Duration) x (Change in YTM in BPS / 100) = -(7.828219) x (-10/100) = 0.7828219 %

Actual Bond Price = Par Value = $ 1000 (as bond sells at par)

New Bond Price = 1000 x [1+ (0.7828219/100)] = $ 1007.828

+ 2 % Change:

% Change in Bond Price = - (Duration) x (Change in YTM in BPS / 100) = -(7.828219) x (200/100) = - 15.65644 %

Actual Bond Price = Par Value = $ 1000 (as bond sells at par)

New Bond Price = 1000 x [1- (15.65644 /100)] = $ 843.4356

- 2 % Change:

% Change in Bond Price = - (Duration) x (Change in YTM in BPS / 100) = -(7.828219) x (-200/100) = 15.65644 %

Actual Bond Price = Par Value = $ 1000 (as bond sells at par)

New Bond Price = 1000 x [1 + (15.65644 /100)] = $ 1156.564

(b2) +0.1 % Change:

Error = 992.1718 - 992.2171 = - $ 0.0453 ~ - $ 0.045 ~ - $ 0.04 (since the problem seems to be plagued by rounding errors try the last two values in the previous line from the right-hand side i.e - $ 0.045 or - $ 0.04. Same for the next error as well).

- 0.1 % Change:

Error = 1007.828 - 1007.8738 = $ 0.0456 ~ - $ 0.046 ~ - $ 0.05

+ 2 % Change:

Error = 843.4356 - 860.07 = - $ 16.63

- 2 % Change:

Error = 1156.564 - 1176.54 = - $ 19.98