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Weike · 2024年02月05日

exchange rate calculation

  1. CFA I
  2. Economics Analysis

NO.PZ2023071902000011

问题如下：

Question

A forex expert notices the following rates:

A riskless arbitrage profit exists that is closest to:

选项：

A.0.49%.

B.1.04%.

C.0.46%.

解释：

Solution
  1. The expert can secure a riskless arbitrage gain of 0.49%, determined as:

Return on the hedged foreign investment: Sf/d(1 + if)[1/Ff/d]-1 = 1.68(1.055)[1/1.72]-1 = 1.0246 -1= 3.05%.

Riskless arbitrage profit = Domestic risk-free rate – Return on the hedged foreign investment: 3.54% – 3.05% = 0.49%.

Exchange Rate Calculations

• explain the arbitrage relationship between spot and forward exchange rates and interest rates, calculate a forward rate using points or in percentage terms, and interpret a forward discount or premium

不太理解，可以一步一步转化的讲么

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2 个答案

笛子_品职助教 · 2024年02月07日

嗨，从没放弃的小努力你好：


为什么除1.72之后还要再减1

Hello，亲爱的同学~

场景二：把D货币换成F货币，存F国银行一年，赚F国利率，再把F货币换成D货币，看有多少收益。

这里为了计算方便，假设初始本金1元。

一开始，有1个D，换成1.68个F

将1.68个F，存F国银行，拿5.5%利率

随后再用1.72的汇率，把F换成D。


因此有：

Sf/d(1 + if)[1/Ff/d]-1 = 1.68*(1+5.5%)*[1/1.72]-1 = 1.0305 -1= 3.05%.

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

笛子_品职助教 · 2024年02月06日

嗨，努力学习的PZer你好：


不太理解，可以一步一步转化的讲么

Hello，亲爱的同学~

可以的。同学跟着老师的思路一步一步来。


就本题来说，这里比较两个场景。

场景一：持有D货币，存D国银行一年，看有多少收益。

场景二：把D货币换成F货币，存F国银行一年，赚F国利率，再把F货币换成D货币，看有多少收益。

两个收益之间的差距，就是套利利润。


具体来说：


1）先看直接持有D一年的收益，即3.54%

2）计算出hedge收益，即把D按照1.68换成F，持有F一年赚取F的利率，再以1.72的汇率换成D的收益。

计算方式为Sf/d(1 + if)[1/Ff/d]-1 = 1.68*(1+5.5%)*[1/1.72]-1 = 1.0246 -1= 3.05%.、

3）两者的差值为3.54%-3.05%，即套利利润。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

Weike · 2024年02月06日

为什么除1.72之后还要再减1

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NO.PZ2023071902000011 问题如下 QuestionA forex expert notices the following rates: A riskless arbitrage profit exists this closest to: A.0.49%. B.1.04%. C.0.46%. Solution The expert csecure a riskless arbitrage gain of 0.49%, termineas:Return on the heeforeign investment: Sf/1 + if)[1/Ff/-1 = 1.68(1.055)[1/1.72]-1 = 1.0246 -1= 3.05%. Riskless arbitrage profit = mestic risk-free rate – Return on the heeforeign investment: 3.54% – 3.05% = 0.49%.Exchange Rate Calculations• explain the arbitrage relationship between spot anforwarexchange rates aninterest rates, calculate a forwarrate using points or in percentage terms, aninterpret a forwarscount or premium专家可以获得0.49%的无风险套利收益，过程如下:套期保值的境外投资回报率:Sf/1 + if)[1/Ff/-1 = 1.68(1.055)[1/1.72]-1 = 1.0246 -1= 3.05%。无风险套利利润=境内无风险利率-套期境外投资回报率:3.54% - 3.05% = 0.49%。 老师上课讲可以用f/s（1+f外）-（1+f本）=1.72/1.68*（1+5.50%)-(1+3.54%)=0.044719。请问是哪里出错了

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NO.PZ2023071902000011问题如下 QuestionA forex expert notices the following rates: A riskless arbitrage profit exists this closest to: A.0.49%.B.1.04%.C.0.46%. Solution The expert csecure a riskless arbitrage gain of 0.49%, termineas:Return on the heeforeign investment: Sf/1 + if)[1/Ff/-1 = 1.68(1.055)[1/1.72]-1 = 1.0246 -1= 3.05%. Riskless arbitrage profit = mestic risk-free rate – Return on the heeforeign investment: 3.54% – 3.05% = 0.49%.Exchange Rate Calculations• explain the arbitrage relationship between spot anforwarexchange rates aninterest rates, calculate a forwarrate using points or in percentage terms, aninterpret a forwarscount or premium专家可以获得0.49%的无风险套利收益，过程如下:套期保值的境外投资回报率:Sf/1 + if)[1/Ff/-1 = 1.68(1.055)[1/1.72]-1 = 1.0246 -1= 3.05%。无风险套利利润=境内无风险利率-套期境外投资回报率:3.54% - 3.05% = 0.49%。 答案解析和助教老师的方法太过于复杂，我认为可以用何老师上课讲的方法计算，计算结果四舍入五也能做对题，毕竟这样算会快很多。

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