Question

Consider a zero coupon bond with three 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 =3

Bond Price =∑ [(0*1000/100)/(1 + 5/100)^k]     +   1000/(1 + 5/100)^3

k=1

Bond Price = 863.84

Period	Cash Flow	PV Cash Flow	Duration Calc
0	($863.84)
1	-	-	-
2	-	-	-
3	1,000.00	863.84	2,591.51
		Total	2,591.51

=2591.51/863.84 = 3

Modified duration = Macaulay duration/(1+YTM)

=3/(1+0.05) = 2.86

Percentage change in price for a 1% increase in the yield to maturity

= -Mod_Duration*Yield_Change

=-2.86*1=-2.86%