Question

By calculating the duration for the following bonds decide which has a higher duration. The first bond is a 2 year $1000 zero coupon bond. The second is a 3 year $1000 bond that pays an annual coupon of 10%. Suppose the YTM is 8%

Answer 1

Duration for 0 bond is time to maturity = 2 for the 0 coupon bond

K = N

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

k=1

K =3

Bond Price =∑ [(10*1000/100)/(1 + 8/100)^k]     +   1000/(1 + 8/100)^3

k=1

Bond Price = 1051.54

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,051.54)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	100.00	1.08	92.59	92.59
2	100.00	1.17	85.73	171.47
3	1,100.00	1.26	873.22	2,619.65
			Total	2,883.71

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

=2883.71/(1051.54*1)

=2.74

3 yr bond has higher duration