Question

Consider the following.

a. What is the duration of a four-year Treasury bond with a 10.5 percent semiannual coupon selling at par?
b. What is the duration of a three-year Treasury bond with a 10.5 percent semiannual coupon selling at par?
c. What is the duration of a two-year Treasury bond with a 10.5 percent semiannual coupon selling at par?
  
(For all requirements, do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

a. Duration of the bond _______ years
b. Duration of the bond _______ years
c. Duration of the bond _______ years

Answer 1

a

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,000.00)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	52.50	1.05	49.88	49.88
2	52.50	1.11	47.39	94.79
3	52.50	1.17	45.03	135.09
4	52.50	1.23	42.78	171.13
5	52.50	1.29	40.65	203.24
6	52.50	1.36	38.62	231.73
7	52.50	1.43	36.69	256.86
8	1,052.50	1.51	698.95	5,591.59
			Total	6,734.31

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

=6734.31/(1000*2)

=3.37

b

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,000.00)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	52.50	1.05	49.88	49.88
2	52.50	1.11	47.39	94.79
3	52.50	1.17	45.03	135.09
4	52.50	1.23	42.78	171.13
5	52.50	1.29	40.65	203.24
6	1,052.50	1.36	774.26	4,645.59
			Total	5,299.72

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

=5299.72/(1000*2)

=2.65

c

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,000.00)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	52.50	1.05	49.88	49.88
2	52.50	1.11	47.39	94.79
3	52.50	1.17	45.03	135.09
4	1,052.50	1.23	857.70	3,430.79
			Total	3,710.54

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

=3710.54/(1000*2)

=1.86