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anyewumian · 2021年04月19日

问一道题:NO.PZ2016082402000008 [ FRM I ]

问题如下:

Suppose the face value of a three-year option-free bond is USD 1,000 and the annual coupon is 10%. The current yield to maturity is 5%. What is the modified duration of this bond?

选项:

A.

2.62

B.

2.85

C.

3.00

D.

2.75

解释:

ANSWER: A

As in Table below, we lay out the cash flows and find

Duration is then 2.75, and modified duration 2.62.

老师,能详细解释一下这道题吗

1 个答案

小刘_品职助教 · 2021年04月19日

同学你好,

这道题先求的Mac.D

麦考利久期的定义是:债券在未来产生现金流的时间的加权平均,其权重是各期现值在债券价格中所占的比重。

所以,本题中 Mac.D=1*95.24/1136.16+2*90.71/1136.16+3*950.22/1136.16=2.75 years


modified D =Mac.D / 1+y=2.62

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