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不拉不拉123 · 2019年11月01日

问一道题:NO.PZ2015121801000039 [ CFA I ]

问题如下图:

选项:

A.

B.

C.

解释:

我的计算方式有点不一样,我是用(1+ear/365)^146/365=1+4.61%。没搞清楚。为什么不用除以365。

1 个答案

星星_品职助教 · 2019年11月01日

同学你好,

题干中给出的return已经是期间利率的概念了,或者说是HPR。即4.61%就是146天的利率,而不是名义利率为4.61%,如果这道题要求算名义利率,在这里应该是4.61%* (365/146)。

正因为4.61%本身就是期间利率的概念,所以算EAR时,要看这4.61%在一年内复利了几次(也就是“滚了几圈”),由于一共滚了365/146这么多圈,所以就是答案解析中的算法(1+4.61%)^(365/146)。这种算法实际上是(1+4.61%)^(365/146)=1+EAR。

所以如果用你的算法的那个角度,应该是1+EAR=(1+4.61%)^(365/146),等式左侧是按照有效实际年利率计息的一年的本息和,右侧是按照期间利率4.61%滚了365/146这么多圈后的本息和,两者相等。

除以365的方法的目的是将名义的“假的”年利率转化为真的期间利率。所以这时候等式左侧的EAR(已经是真实的年利率了)就不用再除以365了,加油

treepple · 2019年11月28日

我想请问一下,按照这种算法,实际业务场景是怎样的?比如假设此笔存款存在银行,银行是在每第146天支付利息,然后利息和本金再按此循环计息?在第一个146天的时候,假设本金1元,那利息如何计算?

星星_品职助教 · 2019年11月28日

呃....CFA是纯理论。如果是实务的话,需要看银行具体条款是怎么规定的。没法直接套用。例如存款,银行往往会在3,6,9,12的20/21日支付利息,不大可能在具体的多少天。

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