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moon · 2022年02月22日

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NO.PZ201601050100001201

问题如下:

Calculate the contribution of foreign currency to the Bhatt account’s total return. Show your calculations.

选项:

解释:

Currency movements contributed 1.5% to the account’s 7.0% total (US dollar) return, calculated as follows:

The domestic-currency return (RDC ) on a portfolio of multiple foreign assets is


Where RFC ,i is the foreign-currency return on the ith foreign asset, RFX ,i is the appreciation of the ith foreign currency against the domestic currency, and Éi is the weight of the asset as a percentage of the aggregate domestic-currency value of the portfolio. This equation can be rearranged as


Therefore, 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 on the Bhatt account’s total (US dollar) return of 7.0%.

The weighted asset return is equal to 5.5%, calculated as follows:

(0.50 × 10.0%) + (0.25 × 5.0%) + [0.25 × (–3.0%)] = 5.5%.

The weighted currency return is equal to 1.5% calculated as follows:

(0.50 × 0.0%) + (0.25 × 2.0%) + (0.25 × 4.0%) = 1.5%.

The weighted cross-product is equal to –0.005%, calculated as follows:

[0.50 × (10.0% × 0.0%)] + [0.25 × (5.0% × 2.0%)] + [0.25 × (–3.0% × 4.0%)] = –0.005%.

Therefore, the contribution of foreign currency equals 1.5%, calculated as the 7.0% total (US dollar) return less the 5.5% weighted asset return. Alternatively, the contribution of foreign currency to the total return can be calculated as the sum of the weighted currency return of 1.5% and the weighted cross-product of –0.005%:

1.5% + (–0.005%) = 1.495%, which rounds to 1.5%.

中文解析:

本题考察的是外汇投资中return的计算。

表格中给到的currency return是对应单个资产的,而本题中是投资了三个外币资产,因此是一个资产组合,所以涉及到加权平均的过程。

另外需要注意的是“the contribution of foreign currency”是包含了交叉项部分的return的。


为什么这么做,然后1+2+3算出来≠答案?


1. 欧元:25%*【1.05*1.02-1】=0.01775

2. 日元:25%*【0.97*1.04-1】=0.0088

3. 美元:0.5*【10%】=0.05


1 个答案

Hertz_品职助教 · 2022年02月23日

嗨,从没放弃的小努力你好:


同学你好

你1,2,3步骤加总其实是下面这个公式的求得的结果,是投资的总的return。并不是本题要求解的。

本题中求的是the contribution of foreign currency,它是包含了两部分的。

并且两种计算方法在解析中都做了详细的说明,同学可以仔细看一下哈~ 

----------------------------------------------
加油吧,让我们一起遇见更好的自己!

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