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CFA一定过! · 2024年01月15日

exchange rate calculation

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

这题可以一步步详细解释一下吗?我是用( 1/1.68)x(1+3.5%)x1.72与1+3.54%轧差来算的,就是上课老师说的那个方法,不知道哪里错了。

2 个答案

笛子_品职助教 · 2024年01月17日

嗨,爱思考的PZer你好:


判断什么货币,要看具体是什么场景。

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,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。

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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01月16日

嗨,努力学习的PZer你好:


Hello,亲爱的同学~


这是一道covered 利率平价的题目。

我们看本题给的汇率是f/d形式。

因此同学用f/d形式来计算即可。


我们首先计算出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(1.055)[1/1.72]-1 = 1.0246 -1= 3.05%.、


再看直接持有D一年的收益,即3.54%

两者的差值为3.54%-3.05%,即套利利润。


再看同学哪里错了,同学列式:

( 1/1.68)x(1+3.5%)x1.72,与本题的列式1.68(1.055)[1/1.72]-1,完全相反了。

首先,正确的做法是1.68,而不是同学写的1/1.68。因为我们要把本币兑换成外币,1个本币,可以兑换1.68个外币。

其次,是持有外币一年,是赚外币利率,因此是5.5%利率,而不是同学写的本币3.5%利率(本币利率也是3.54%,不是3.5%)

最后,把持有的外币,用forward换会本币,此时,1个本币可以兑换1.72个外币,因此,外币换成本币,是/1.72,并不是同学写的*1.72。


同学主要是把换汇方向搞反了,理解上述套利过程即可纠正正确。





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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

CFA一定过! · 2024年01月16日

我们首先计算出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。———谢谢。老师,这里为什么要把D换成F?如果标价方式是USD/EUR这种,怎么判断要把什么币换成什么币? 就这种题我总是第一步就搞错,很晕。

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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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