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Aliciaguo · 2022年02月20日

请问contribution of foreign currency 这个公式是怎么推导出来的？为什么asset return不考虑交currency的变动?

  1. CFA III
  2. Derivative

NO.PZ2018113001000083

问题如下：

Bevis is an adviser to WT, a fund management firm. WT's clients are all high-net-worth clients in the U.S. Bevis manages the account for Clare, one of his clients, which had a total return of 4.418% last year. Bevis wants to calculate the return due to the foreign currency contribution.

Exhibit 1 summarizes the investment information for Clare's account last year


Calculate the contribution of foreign currency to the total return.

选项：

解释：

Answer:

the Clare account’s total (US dollar) return of 4.418%.

The weighted asset return is equal to 1.8%, calculated as follows:

(60%×5%）+[ 40%×（-3%）] = 1.8%

The domestic-currency return is equal to the sum of the weighted asset return, the weighted currency return, and the weighted cross-product of the asset return and the currency return. The latter two terms explain the effects of foreign-currency movements.

Therefore, the contribution of foreign currency equals 2.618% = 4.418% - 1.8% .

中文解析：

本题考察的是外汇投资中return的计算。

要求解的“the contribution of foreign currency”是包含了两部分的，一是RFX，二是交叉项RFC ×RFX。

因此，在总的return中减掉RFC 后，剩下的return就是由foreign currency贡献的return了。

另外一种计算方法：

the contribution of foreign currency = wiRFX +wiRFCRFX

=0.6*0.02+0.4*0.035+0.6*0.05*0.02+0.4*0.035*(0.03)=2.618%

请问contribution of foreign currency 这个公式是怎么推导出来的？为什么asset return不考虑交currency的变动?

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1 个答案

Hertz_品职助教 · 2022年02月21日

嗨，努力学习的PZer你好：


同学你好~

1.     请问contribution of foreign currency 这个公式是怎么推导出来的？

关于为什么contribution of foreign currency是包含了解析中说的来给你两部分，我从两个角度来帮助同学理解下：

（1）     首先，我们需要明确的一点是收益率是没有货币单位的。比如你是个中国人，你可以投资美元资产，比如收益率是2%，如果你不打算把这个资产转成人民币，那么你获得的就是2%，跟买人民币资产获得的2%没什么不同，这个时候我们不需要考虑货币单位，收益率就是收益率，没有货币单位的。但是一旦我们要把这个资产换成人民币，那么就要考虑汇率问题了，获得总收益率就可能不是2%，那么这中间的差额就是contribution of foreign currency，也可以表述成contribution of exchange rate，是一个意思的哈，不必纠结。

（2）     或者我们可以这样思考，我们来比较两种情况：

①   不考虑foreign currency的问题，我们直接获得的就是asset return

②   考虑foreign currency，我们获得的是asset return + contribution of foreign currency

题目中问的便是②比①多的部分，就是wiRFX +wiRFCRFX，其中asset return指的是RFC。

2.     为什么asset return不考虑交currency的变动?

正如前面提到的，asset return指的是RFC，即投资外币资产本身的收益，是不会考虑外汇本身的变动的额，单纯考虑外币资产的收益其实是和考虑本币资产的收益没有区别的。

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