Question

A bond pays annual interest. Its coupon rate is 9%. Its value at maturity is $1,000. It matures in 4 years. Its yield to maturity (YTM) is currently 6%.

a. Calculate the Macaulay's duration.

b. Calculate the modified duration

c. Calculate the percentage change in bond price if YTM increases by 1%

Answer 1

K = N

Bond Price =∑ [( Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =4

Bond Price =∑ [(9*1000/100)/(1 + 6/100)^k]     +   1000/(1 + 6/100)^4

k=1

Bond Price = 1103.95

a

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,103.95)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	90.00	1.06	84.91	84.91
2	90.00	1.12	80.10	160.20
3	90.00	1.19	75.57	226.70
4	1,090.00	1.26	863.38	3,453.53
			Total	3,925.33

Macaulay duration =(∑ Duration calc)/(bond price*number of coupon per year)

=3925.33/(1103.95*1)

=3.555714

b

Modified duration = Macaulay duration/(1+YTM)

=3.56/(1+0.06)

=3.354447

c

Using only modified duration

Mod.duration prediction = -Mod. Duration*Yield_Change*Bond_Price

=-3.35*0.01*1103.95

=-37.03

%age change in bond price=Mod.duration prediction/bond price

=-37.03/1103.95

=-3.35%