Question

a) Given the following information, please estimate the modified durations of the two bonds. Which one is riskier? (The coupon payment is made seminally. Par value is $1,000.) Time to maturity (years) Coupon Interest rate A. 20 8% 4% B. 30 10% 5%

b) If a bank expects the interest rate will rise, it should issue Bond A, given everything else equal. Do you agree? Why?

Answer 1

1. Price calculation of Bond A and Bond B

Bond A	Annual	Semiannual
Face value	1000	1000
Yield to Maturity or required rate of return	4.000%	2.00%
Maturity Period	20	40
Coupon Rate	8.00%	4.00%
Coupon paid	$80.00	$40.00
PV of coupon payments =	=	$                      1,094.22
PV of Maturity Value +	=	$                         452.89
Price of Bond =	=	$                      1,547.11
Bond B	Annual	Semiannual
Face value	1000	1000
Yield to Maturity or required rate of return	5.000%	2.50%
Maturity Period	30	60
Coupon Rate	10.00%	5.00%
Coupon paid	$100.00	$50.00
PV of coupon payments	=	$                      1,545.43
PV of Maturity Value	=	$                         227.28
Price of Bond	=	$                      1,772.72

Formulas used in excel calculation:

Formula to calculate modified duration

Modified duration = (Bond price when yield falls - Bond price when yield rises) / (2 * Current price of Bond * Change in yield in decimal)

Assume that the yield of bond is falls and rises by 1% or 0.01 (price can be calculated by above method by changing only the yield of the bond)

Then modified duration for Bond A

= ($1,747.90 - $1,376.54) / (2 * $1,547.11 * 0.01)

= $371.35 / (2 * $1,547.11 * 0.01)

= 12.00

The modified duration for Bond B

= ($2,042.83 - $1,553.51) / (2 * $1,772.72 * 0.01)

= $489.32 / (2 * $1,772.72 * 0.01)

= 13.80

As the modified duration is more for bond B therefore Bond B is riskier

2. If a bank expects the interest rate will rise, it should issue Bond A, given everything else equal.

Yes, bank should issue Bond A because bond with a shorter time to maturity will have shorter duration than a longer term bond. And if bond's duration rises, its interest rate risk also rises therefore bank should issue a bond with smaller duration.