Question

We have a bond with a coupon rate of 12% paid annually, 3 years to maturity, a par value of $1,000, and the yield to maturity of 1$0%.

1. Figure out the duration of the bond.

  

2. You believe that the Fed is about to increase interest rates by 60 basis points (0.6%). Figure out the percentage change in the bond price using the duration. (If you cannot figure out the duration above, please use a duration of 3.)

Answer 1

Given about a 3-year bond,

Face value = $1000

Coupon rate = 12% annually

coupon = 12% of 1000 = $12

Yield to maturity = 10%

Duration is calculated as below table:

here, since it is a semiannual bond, discount factor = 1/(1+YTM)^year

PV of coupon = discount factor * coupon

Price = sum of all PV = $1049.74

weight = PV of coupon/price

duration of each coupon = year*weight

duration of the bond = sum of all duration = 2.70 years

Year	Coupon	PV of Cash flow=Coupon/(1+r)^period	weight = PV of coupon/Price	Duration = weight*year
1	$             120.00	$             109.09	0.1039	0.1039
2	$             120.00	$                99.17	0.0945	0.1889
3	$          1,120.00	$             841.47	0.8016	2.4048
	Price	$          1,049.74	Duration	2.70

So, Macaulay duration of the bond = 2.70

Modified duration D = Macaulay duration/(1+YTM) = 2.7/1.1 =  2.45 years

Interest rate increase by 0.6%

=> dy = 0.6%

So, percentage change in price (dP/P) = -D*dy = -2.45*0.006 = -1.47%

So, percentage change in price = -1.47%