Question

Calculate the duration for a U.S. Treasury Bond issued in 2002 with an original 20-year maturity. The bond has a 6% coupon rate and will mature in 2022. The bond has four more coupon payments left (assume the first of these payment is exactly six months from now). The current required return for the bond is 1.00%.

Answer 1

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =2x2

Bond Price =∑ [(6*1000/200)/(1 + 1/200)^k]     +   1000/(1 + 1/200)^2x2

k=1

Bond Price = 1098.76

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1.098.76)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	30.00	1.01	29.85	29.85
2	30.00	1.01	29.70	59.40
3	30.00	1.02	29.55	88.66
4	1.030.00	1.02	1.009.65	4.038.62
			Total	4.216.54

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

=4216.54/(1098.76*2)

=1.918771

Modified duration = Macaulay duration/(1+YTM)

=1.92/(1+0.01)

=1.909225