Question

Consider the following.

a. What is the duration of a four-year Treasury bond with a 7.5 percent semiannual coupon selling at par?

b. What is the duration of a three-year Treasury bond with a 7.5 percent semiannual coupon selling at par?

c. What is the duration of a two-year Treasury bond with a 7.5 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))

Answer 1

• In all the cases the bonds are selling at par, ie; Coupon rate = YTM
• Since the bond makes semiannual interest payments, total no. of period is multiplied by 2, cashflow per period and YTM are divided by 2.
• It is general practice to take $1,000 as face value when no details are given.

Answer a

Time	Cashflow	[email protected]%	Present Value (Cashflow*PVF)	Weight based on present value	Time*Weight
1	37.5	0.964	36.14	0.0361	0.04
2	37.5	0.929	34.84	0.0348	0.07
3	37.5	0.895	33.58	0.0336	0.10
4	37.5	0.863	32.37	0.0324	0.13
5	37.5	0.832	31.20	0.0312	0.16
6	37.5	0.802	30.07	0.0301	0.18
7	37.5	0.773	28.98	0.0290	0.20
8	1037.5	0.745	772.83	0.7728	6.18

Duration of Semi annual bond= Time*Weight/2

= 7.06/2

= 3.53

Answer b

Time	Cashflow	[email protected]%	Present Value (Cashflow*PVF)	Weight based on present value	Time*Weight
1	37.5	0.964	36.14	0.0361	0.04
2	37.5	0.929	34.84	0.0348	0.07
3	37.5	0.895	33.58	0.0336	0.10
4	37.5	0.863	32.37	0.0324	0.13
5	37.5	0.832	31.20	0.0312	0.16
6	1037.5	0.802	831.88	0.8319	4.99

Duration of Semi annual bond= Time*Weight/2

= 5.48/2

= 2.74

Answer c

Time	Cashflow	[email protected]%	Present Value (Cashflow*PVF)	Weight based on present value	Time*Weight
1	37.5	0.964	36.14	0.0361	0.04
2	37.5	0.929	34.84	0.0348	0.07
3	37.5	0.895	33.58	0.0336	0.10
4	1037.5	0.863	895.44	0.8954	3.58

Duration of Semi annual bond= Time*Weight/2

= 3.79/2

= 1.89