HHK Inc. has an asset portfolio that consists of $220 million of 15-year, 7 percent coupon,...

HHK Inc. 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 when 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?

Solutions

Expert Solution

Formula to calculate price of bond
Price of bond	Coupon amountPVIFA(r,n) + Face valuePV(r,n)

a-1
Calculation of price of bond if market yield falls by 0.10 percent
New yield	6.90%	7%-0.10%

PVIFA	(1-((1.069)^(-15)))/0.069
PVIFA	9.165721311

Price of bond	(2207%)9.165721+(220*(1/(1.069^15))
Price of bond	(15.409.165721)+(2200.367565)
Price of bond	$222.02	million

Calculation of price of bond if market yield increase by 0.10 percent
New yield	7.10%	7%+0.10%

PVIFA	(1-((1.0710)^(-15)))/0.0710
PVIFA	9.05066494

Price of bond	(2207%)9.165721+(220*(1/(1.071^15))
Price of bond	(15.409.050665)+(2200.367565)
Price of bond	$218.01	million

a-2.
Calculation of price of bond if market yield falls by 2 percent
New yield	5.00%	7%-2%

PVIFA	(1-((1.05)^(-15)))/0.05
PVIFA	10.37965804

Price of bond	(2207%)10.37966+(220*(1/(1.05^15))
Price of bond	(15.4010.37966)+(2200.481017)
Price of bond	$265.67	million

Calculation of price of bond if market yield increase by 2 percent
New yield	9.00%	7%+2%

PVIFA	(1-((1.09)^(-15)))/0.09
PVIFA	8.06068843

Price of bond	(2207%)8.060688+(220*(1/(1.09^15))
Price of bond	(15.408.060688)+(2200.274538)
Price of bond	$184.53	million

b-1
% change in price of bond = -Duration*Change in yield
Calculation of price of bond if market yield falls by 0.10 percent
% change in price of bond	-9.7455*(-0.10%)
% change in price of bond	0.97%

Price of bond	220*(1+0.0097)
Price of bond	$222.14

Calculation of price of bond if market yield increase by 0.10 percent
% change in price of bond	-9.7455*(0.10%)
% change in price of bond	-0.0097455

Price of bond	220*(1-0.0097)
Price of bond	$217.86

Calculation of price of bond if market yield falls by 2 percent
% change in price of bond	-9.7455*(-2%)
% change in price of bond	0.19491

Price of bond	220*(1+0.19491)
Price of bond	$262.88

Calculation of price of bond if market yield increase by 2 percent
% change in price of bond	-9.7455*(2%)
% change in price of bond	-0.19491

Price of bond	220*(1-0.19491)
Price of bond	$177.12

Calculation of error between duration prediction and actual market data
	Decrease by 0.10%	Increase by 0.10%	Decrease by 2%	Increase by 2%
Duration prediction	$222.14	$217.86	$262.88	$177.12
Actual market	$222.02	$218.01	$265.67	$184.53
Error	$0.13	-$0.15	-$2.79	-$7.41

jeff jeffy answered 2 weeks ago

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