NO.PZ2023032703000033
问题如下：
One year later, a duration gap exists between the liability and the immunization portfolio. The future liability now has a present value of USD 91,732,436 and a modified duration of 8.867. The immunization portfolio has a market value of USD 92,749,570 and a modified duration of 9.107.
Zerbe closes this duration gap using a US Treasury note futures contract in a derivatives overlay strategy. Based on the cheapest-to-deliver bond she determines the basis point value (BPV) for one futures contract is USD 71.32.
B. Determine whether Zerbe should take a long or short position in the futures contracts. Calculate the number of futures contracts required to close the duration gap. Show your calculations. (2018 Q7)
选项：
解释：
Determine whether Zerbe should take a long or short position in the futures contracts.
(circle one)
Long Short
Calculate the number of futures contracts required to close the duration gap.
To determine the number of futures contracts required to close the duration gap, compute the money durations for the liability and the immunization portfolio:
money duration = modified duration × market value
liability money duration = 8.867 × USD 91,732,436 = USD 813,391,510
immunization portfolio money duration = 9.107 × USD 92,749,570 = USD 844,670,334
The basis point values (BPVs) can then be calculated for the liability and the immunization portfolio:
BPV = money duration × 1 bp = money duration × 0.0001
liability BPV = USD 813,391,510 × 0.0001 = USD 81,339
immunization portfolio BPV = USD 844,670,334 × 0.0001 = USD 84,467
Calculate the number of futures contracts using the BPVs:
Nf ≈ 44 futures contracts
Since the money duration of the liability is less than that of the immunizing portfolio, Zerbe should short 44 futures contracts to close the duration gap.
老师好，题目中关于futures的CTD这样说的
Based on the cheapest-to-deliver bond she determines the basis point value (BPV) for one futures contract is USD 71.32.
这个是指BPVctd/CF了嘛？
