题目
A fixed-income portfolio manager purchases a seasoned 5.5% agency mortgage-backed security with a weighted average loan age of 60 months. The current balance on the loans is USD 20 million, and the conditional prepayment rate is assumed to be constant at 0.4% per year. Which of the following is closest to the expected principal prepayment this month?
选项
A.USD 1,000
B.USD 7,000
C.USD 10,000
D.USD 70,000
答案
B
解析
SMM=1 – (1 – 0.004)^(1/12) = 0.0334%, N=60, I/Y=5.5/12, PV=-20,000,000, FV=0 ,CPT PMT=382,023.24. PRN=290,256.58. prePMT=(20,000,000 -290,356.58)× 0.0334%=6581.96第一步：由1-CPR=(1-SMM)^12，可得SMM=0.000334第二步：计算本月计划还的本金N=60，I/Y=5.5/12，PV=-20,000,000，FV=0，可得PMT=-382,023.24。利用计算器摊销功能，输入P1=1，P2=1，可得PRN=290,356.58。即本月计划还的本金=290,356.58。 第三步：由SMM=本月提前偿付的本金/(期初余额-本月计划还的本金)，可得本月提前偿付的本金=0.000334×（20,000,000-290,356.58）=6,583。