Question

Consider a 3-year maturity annual 9% coupon paying bond with a YTM of 12%.

a. What is the Duration of this bond?

b. What will be the predicted price of this bond if the market yield increases by 100 basis points. [Remember, 100 basis points = 1% point]? You must use the duration (calculated in the part above) to get full points for this question.

Answer 1

a). Given about a bond,

Face value = $1000

coupon rate = 9% annual

annual coupon = $90

YTM = 12%

duration is calculated in below table:

here PV of PMT = PMT/(1+YTM)^year

Price = sum of all PVs = $927.95

Weight = PV of pmt/total PV

duration of coupon = weight*year

Duration of bond = sum of duartion of all coupons = 2.75 years

Year	PMT	PV of PMT PMT/(1+rate/2)^year	weight = PV of PMT/total PV	Duration of coupon
1	$         90.00	$                 80.36	0.086596875	0.086597
2	$         90.00	$                 71.75	0.077318639	0.154637
3	$   1,090.00	$               775.84	0.836084486	2.508253
	Price	$               927.95	Duration	2.749488

b). if yield increases by 100 basis point

dy = 0.01

P = 927.95

change in price using duration formula is

dP = -D*P*dy

where D = modified duration

Duration we calculated above is Macaulay duration = 2.75 years

So, modified duartion D = Macaulay duration/(1+YTM) = 2.75/1.12 = 2.45 years

So, now dP = -2.45*927.95*0.01 = $-22.78

So new predicted price = 927.95 - 22.78 = $905.16