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jvniki · 2024年02月10日

这道题在算pv的时候为什么会选择180而不是360。

NO.PZ2016031001000084

问题如下：

The bond equivalent yield of a 180-day banker’s acceptance quoted at a discount rate of 4.25% for a 360-day year is closest to:

选项：

A.

4.31%.

B.

4.34%.

C.

4.40%.

解释：

C is correct.

The bond equivalent yield is closest to 4.40%. The present value of the banker’s acceptance is calculated as:

$PV=FV\times{(1-\frac{Days}{Year}\times DR)}$

$PV=100\times{(1-\frac{Days}{Year}\times DR)}$

$PV=100\times{(1-\frac{180}{360}\times0.0425)}$

PV = 100 × (1 – 0.02125)

PV = 100 × 0.97875

PV = 97.875

The bond equivalent yield (AOR) is calculated as:

$AOR={(\frac{Year}{Days})}\times{(\frac{FV-PV}{PV})}$

$AOR={(\frac{365}{180})}\times{(\frac{100-PV}{PV})}$

$AOR={(\frac{365}{180})}\times{(\frac{100-97.875}{97.875})}$

AOR = 2.02778 × 0.02171

AOR = 0.04402, or approximately 4.40%

Note that the PV is calculated using an assumed 360-day year and the AOR (bond equivalent yield) is calculated using a 365-day year.

考点：Yield Measures

解析：考查的是discount yield和 add-on yield之间的转换。1.题目给出了discount rate=4.25%，可以算出PV=100×（1-180/360×4.25%）=97.875。2.然后通过计算出来的PV再计算BEY，BEY就是365天形式的add-on-yield，BEY=365/180×(100-97.875)/97.875=4.40%，故选项C正确。

这道题在算pv的时候为什么会选择180而不是360。

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吴昊_品职助教 · 2024年02月10日

嗨，从没放弃的小努力你好：

discount rate of 4.25%，这个利率形式是一个年化的概念，但是我们现在货币市场工具就只有180天，所以我们要去年化，4.25%×180/360，这样一来，discount rate就变成了半年的形式，从而计算出PV。

同理，当我们要计算BEY的时候，第二个括号算出来是180天的AOR，现在我们年化成365天的BEY，所以要在第二个括号的基础上×365/180。特别要注意的是BEY是365天的AOR。

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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