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Yvonne0719 · 2024年07月15日

不太理解变动率公式的推导,是等式两边同时加1?

NO.PZ2023071902000093

问题如下:

Question Inflation rates rise by 1.4% in the US and by 4.6% in the Eurozone. If the nominal spot exchange rate for the USD/EUR falls by 3%, the precise shift in the real exchange rate is nearest to:

选项:

A.0%.

B.5%.

C.9%.

解释:

Solution

The adjustment in the real exchange rate can be formulated as:

(1-3%)*(1+4.6%)/(1+1.4%) -1 =0.000611≈0

The Foreign Exchange Market and Capital Flows

实际汇率的调整可表示为:

(1-3%)*(1+4.6%)/(1+1.4%) -1 =0.000611≈0

看不懂推导,麻烦解释一下

1 个答案

笛子_品职助教 · 2024年07月16日

嗨,爱思考的PZer你好:


在数学上,如果有:A = B * C / D

则有:(1+A的百分比变动率)= (1+B的百分比变动率)*(1+C的百分比变动率)/ (1+D的百分比变动率)

这一步的推导过程,涉及到微积分。CFA并不要求同学掌握微积分的计算过程,只需同学记住最终的结论。


有:(1+A的百分比变动率)= (1+B的百分比变动率)*(1+C的百分比变动率)/ (1+D的百分比变动率)

则:A的百分比变动率 = (1+B的百分比变动率)*(1+C的百分比变动率)/ (1+D的百分比变动率)-1


在汇率price currency / base currency这里,有两个公式,需同学记忆:

1)是本题的精确式:real exchange change = (1+ mominal exchange change)*(1+base currency infaltion) / (1+ price currency infaltion)-1

2) 书本例题的近似式:real exchange change = mominal exchange change + base currency infaltion - price currency infaltion

精确式和近似式都可以算出本题的答案。

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