R19 练习: Exchange Rate Calculations

R19 练习: 汇率计算

考纲范围

• calculate and interpret currency cross-rates.
• 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.

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Q1.

The table below shows the information about the spot exchange rate:

	Spot rate on July 1, 2017	Spot rate on July 1, 2018
CNY/USD	6.7790	6.6170
JPY/USD	112.2600	110.7300
JPY/GBP	146.0950	146.2190

The percentage change in the value of GBP (relative to CNY) is closest to:

A. 0.96%.

B. -0.96%.

C. 1%

查看答案与解析

答案：B

解析：需要计算CNY/GBP的交叉汇率变化。

计算过程：

2017年CNY/GBP交叉汇率： $CNY/GBP=\frac{CNY/USD}{JPY/USD}\times JPY/GBP=\frac{6.7790}{112.2600}\times 146.0950=8.8222$

2018年CNY/GBP交叉汇率： $CNY/GBP=\frac{6.6170}{110.7300}\times 146.2190=8.7374$

GBP相对CNY的变化： $\frac{8.7374-8.8222}{8.8222}=-0.96\%$

GBP相对CNY贬值了约0.96%。

选项	判断	解析
A	✗	符号错误，GBP相对CNY贬值（负值）
B	✓	GBP相对CNY贬值0.96%
C	✗	计算不准确

关联：R19: 汇率计算

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Q2.

A list of exchange rate quotes are stated as follows:

Pairs	Spot Rate
JPY/USD	105.46
USD/GBP	1.3244
GBP/CAD	0.5735

The spot JPY/GBP cross-rate is closest to:

A. 139.67.

B. 135.74.

C. 136.37.

查看答案与解析

答案：A

解析：

计算过程： $JPY/GBP=JPY/USD\times USD/GBP=105.46\times 1.3244=139.67$

直接将JPY/USD乘以USD/GBP即可得到JPY/GBP（USD在分子分母约掉）。

选项	判断	解析
A	✓	$105.46 \times 1.3244 = 139.67$
B	✗	可能错误使用了GBP/CAD
C	✗	计算错误

关联：R19: 汇率计算

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Q3.

ASML Holding N.V., a lithography machine manufacturer in the Netherlands, will receive 5 million USD payment from Samsung Electronics. The spot exchange rate of EUR/USD is 0.8398 and the 3-month forward rate quote is 25 points. Which of the following is closest to the 3-month forward rate of EUR/USD?

A. 0.8465

B. 0.8643

C. 0.8423

查看答案与解析

答案：C

解析：

计算过程： 远期汇率点数为25个点（points），需要转换为小数： $25 \text{ points} = 0.0025$$

3个月远期汇率： $F_{EUR/USD}=0.8398+0.0025=0.8423$

选项	判断	解析
A	✗	计算错误
B	✗	计算错误
C	✓	+ 0.0025 = 0.8423$

关联：R19: 汇率计算

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Q4.

The spot rate for USD in terms of CAD is 1.4211 and the 90-day forward rate is 1.2686. Relative to USD, the CAD is trading closest to a 90-day forward:

A. premium of 12.02%.

B. discount of 10.73%.

C. premium of 10.73%.

查看答案与解析

答案：A

解析：

计算过程： 即期汇率 CAD/USD = 1.4211，远期汇率 CAD/USD = 1.2686。

CAD/USD远期低于即期，意味着远期需要更少CAD买1USD→USD远期贬值→CAD远期升值（premium）。

CAD的远期升水百分比（年化）： $\frac{S-F}{F}\times \frac{360}{90}=\frac{1.4211-1.2686}{1.2686}\times 4=\frac{0.1525}{1.2686}\times 4=12.02\%\times 4=48.08\%$

但如果不年化： $\frac{1.4211-1.2686}{1.2686}=12.02\%$

CAD相对USD交易在90天远期升水（premium）12.02%。

选项	判断	解析
A	✓	CAD远期升水12.02%
B	✗	CAD是升水不是贴水，且比例不对
C	✗	比例10.73%不正确

关联：R19: 汇率计算

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Q5.

The annual interest rate for the US is 3% and for Canada is 6%. If the current spot rate is CAD/USD 1.4266, then the one-year forward rate in CAD/USD is closest to:

A. 1.3862.

B. 1.4682.

C. 1.4694.

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答案：B

解析：

计算过程： 利率平价公式： $F_{CAD/USD}=S_{CAD/USD}\times \frac{1+r_{CAD}}{1+r_{USD}}$

$F_{CAD/USD}=1.4266\times \frac{1+0.06}{1+0.03}=1.4266\times \frac{1.06}{1.03}=1.4266\times 1.02913=1.4682$

CAD利率高于USD利率，CAD远期贬值（CAD/USD远期高于即期）。

选项	判断	解析
A	✗	可能将分子分母搞反了
B	✓	$1.4266 \times 1.06/1.03 = 1.4682$
C	✗	计算不够精确

关联：R19: 汇率计算

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Q6.

According to interest rate parity, which of the following is most likely accurate about the forward discount?

A. The interest rate of price currency is lower than the base currency.

B. The interest rate of price currency is higher than the base currency.

C. The interest rate of price currency is equal to the base currency.

查看答案与解析

答案：A

解析：

根据利率平价，远期贴水（forward discount）意味着远期汇率低于即期汇率。

对于汇率 P/B（price currency / base currency）： $F_{P/B}=S_{P/B}\times \frac{1+r_P}{1+r_B}$

远期贴水（F < S）时：$\frac{1+r_P}{1+r_B}<1$，即 $r_P<r_B$。

计价货币（price currency）的利率低于基准货币（base currency）的利率。

选项	判断	解析
A	✓	远期贴水时计价货币利率低于基准货币利率
B	✗	计价货币利率高于基准货币利率会导致远期升水
C	✗	利率相等时远期等于即期，无升贴水

关联：R19: 汇率计算