Question

Consider the following.

a. What is the duration of a four-year Treasury bond with a 7 percent semiannual coupon selling at par?
b. What is the duration of a three-year Treasury bond with a 7 percent semiannual coupon selling at par?
c. What is the duration of a two-year Treasury bond with a 7 percent semiannual coupon selling at par?

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	35.00	1.04	33.82	33.82
2	35.00	1.07	32.67	65.35
3	35.00	1.11	31.57	94.70
4	35.00	1.15	30.50	122.00
5	35.00	1.19	29.47	147.35
6	35.00	1.23	28.47	170.84
7	35.00	1.27	27.51	192.57
8	1,035.00	1.32	785.99	6,287.93
			Total	7,114.54

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

=7114.54/(1000*2)

=3.557272

b

Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
($1,000.00)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
35.00	1.04	33.82	33.82
35.00	1.07	32.67	65.35
35.00	1.11	31.57	94.70
35.00	1.15	30.50	122.00
35.00	1.19	29.47	147.35
1,035.00	1.23	841.97	5,051.84
		Total	5,515.05

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

=5515.05/(1000*2)

=2.757526

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	35.00	1.04	33.82	33.82
2	35.00	1.07	32.67	65.35
3	35.00	1.11	31.57	94.70
4	1,035.00	1.15	901.94	3,607.77
			Total	3,801.64

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

=3801.64/(1000*2)

=1.900818