NO.PZ2023091701000170
问题如下:
1.1 A fixed-income portfolio manager is using discount factors to price a sovereign bond. The bond is a coupon bond with the following cash flows:
- 3 months from today: USD 67,500
- 6 months from today: USD 67,500
- 9 months from today: USD 4,567,500
The manager observes the following market price quotes for three zero-coupon bonds issued by the same country:
Based on the discount factors of the zero-coupon bonds, what is the present value of the cash flows from the sovereign coupon bond?
选项:
A.USD 3,728,209
B.USD 4,059,055
C.USD 4,349,780
D.USD 4,436,915
解释:
C is correct. First, the discount factors for the zero-coupon bonds must be calculated:
- 3-month bond: 97.8012/100 = 0.978012
- 6-month bond: 95.2375/100 = 0.952375
- 9-month bond: 92.3805/100 = 0.923805
These are then applied to the corresponding cash flows from the coupon-paying bond:
- 3-month CF: 67,500 * 0.978012 = 66,015.81
- 6-month CF: 67,500 * 0.952375 = 64,285.31
- 9-month CF: 4,567,500 * 0.923805 = 4,219,479.34
The present value of the bonds cash flows is therefore 66,015.81 + 64,285.31 + 4,219,479.34 = 4,349,780.46.
A is incorrect. This adjusts each of the discount factors from the zero-coupon bonds by raising them to the power of the respective number of quarterly periods to maturity, before applying them to the coupon paying bond’s cash flows:
- 3-month adjusted factor: 0.978012^1 = 0.978012
- 6-month adjusted factor: 0.952375^2 = 0.907018
- 9-month adjusted factor: 0.923805^3 = 0.788390
B is incorrect. This adjusts each of the discount factors from the zero-coupon bonds by progressively multiplying all of the previous factors, before applying them to the coupon paying bond’s cash flows:
- 3-month adjusted factor: 0.978012
- 6-month adjusted factor: 0.978012 * 0.952375 = 0.931434
- 9-month adjusted factor: 0.978012 * 0.952375 * 0.923805 = 0.860464
D is incorrect. This uses the correct discount factors from the zero-coupon bonds, but then raises them to the power of the respective portion of 1 year when computing the coupon paying bond’s cash flows:
- 3-month CF: 67,500 * 0.978012^(3/12) = 67,125.85
- 6-month CF: 67,500 * 0.952375^(6/12) = 65,873.05
- 9-month CF: 4,567,500 * 0.923805^(9/12) = 4,303,916.01
这样算哪里有问题?这样貌似选A