Question

Consider a bond that has a coupon rate of 2%, five years to maturity, and is currently priced to yield 5%. Calculate the following:  Macaulay duration  Modified duration  Percentage change in price for a 1% increase in the yield to maturity

Answer 1

K = N

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

k=1

K =5

Bond Price =∑ [(2*1000/100)/(1 + 5/100)^k]     +   1000/(1 + 5/100)^5

k=1

Bond Price = 870.12

Period	Cash Flow	PV Cash Flow	Duration Calc
0	($870.12)
1	20.00	19.05	19.05
2	20.00	18.14	36.28
3	20.00	17.28	51.83
4	20.00	16.45	65.82
5	1,020.00	799.20	3,995.98
		Total	4,168.96

=4168.96/870.12

=4.79

Modified duration = Macaulay duration/(1+YTM) = 4.79/(1+0.05)

=4.56

for 1% increase in YTM

Modified duration prediction = -Mod_Duration*Yield_Change

=-4.56*1 = -4.56%