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庄园monar · 2022年10月08日

请问题目里不是说360吗？

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。

请问题目里不是说360吗？

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吴昊_品职助教 · 2022年10月09日

嗨，从没放弃的小努力你好：

题目现在要我们求的是BEY，而BEY是365天形式的add-on-yield。计算BEY时的计算公式是：【(FV-PV)/PV】×365/days，题中的360天用在discount rate中。

计算步骤如下：

1.题目给出了discount rate=4.25%，代入下图第一个公式，注意year要代入360。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（用下图第二个公式的变形）。BEY就是365天形式的add-on-yield，所以第二个公式中的year要代入365。

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