Question

You have two bonds (A and B) with a (modified) duration of 4.3. Bond A is a coupon bond with a semi-annual coupon of SEK 75 and Bond B is a zero coupon bond.
a) How much does the value of each bonds change if the interest rate changes by 0.1%-unit.
b) What is the time to maturity for the zero coupon bond?
c) Which bond has the longest time to maturity?
d) Calculate the accrued interest of the coupon bond if you buy the bond 1 September year 2 and the coupons are paid out 1 January and 1 July.

Answer 1

a)

Percentage change in value of bond A = Percentage change in interest rate*Modified duration 

                                                                     = 0.1%*4 

                                                                     = 0.4%

 

Percentage change in value of bond B = Percentage change in interest rate*Modified duration 

                                                                     = 0.1%*3 

                                                                     = 0.3%

 

b)

Duration of bond B = 3 years

For zero-coupon bond, duration is same as its time to maturity.

Therefore, time to maturity for the zero coupon bond is 3 years

 

c)

Bond A is coupon paying bond. Hence, its time to maturity, TA will be higher than its duration, DA.

Therefore, TA > DA

Time to maturity of bond B, TB = Duration of bond B, DB = 3

 

Since bond A has higher duration than bond B, it implies that

TA > DA > DA = TB

or, TA > TB

Hence, bond A has higher maturity than bond B

 

d)

Buy date = 1 September

Last coupon payment date = 1 July

Assuming 30/360 days convention, time elapsed since last coupon payment, n = Number of days between 1 July and 1 September = 30+30

                                       = 60

 

Semi-annual period, T = 180 days

Therefore, accrued interest = Coupon payment*n/T 

                                                  = 75*60/180

                                                  = 25

 

Hence, accrued interest is SEK 25.

a. Percentage change in value of bond A is 0.4%.

Percentage change in value of bond B is 0.3%.