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SHAO · 2024年02月24日

老师，请问这道题

  1. CFA II
  2. Economics Analysis

NO.PZ2023041102000004

问题如下：

If a dealer's bid-side quote for the CAD/BRL is C$0.5250, Tremblay's profit on a US$1,000,000 initial investment in the triangular arbitrage opportunity is closest to:.

选项：

A.US$31,315.00 B.US$31,328.00 C.US$21,135.00

解释：

It is cheaper to buy Canadian dollars indirectly through Brazilian reals than directly with U.S. dollars. This creates a triangular arbitrage opportunity:

US$1,000,000 × 2.3844 = BRL2,384,400

2,384,400 × 0.5250 = C$1,251,810

C$1,251,810/1.2259 = US$1,021,135

US$1,021,135 – US$1,000,000 = US$21,135 profit.

老师，这道题给了CAD/BRL，但手里拿着的是1000000USD，请问这种情况怎么判断三角套利先换CAD（USD-CAD-BRL-USD）还是BRL（USD-BRL-CAD-USD）？

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SHAO · 2024年02月24日

题目中我们手里是1000000美元，而我们算出的交叉汇率是CAD/BRL，这只能看出来在哪个市场用BRL买CAD便宜，看不出来手里美元应该先换成哪个货币

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笛子_品职助教 · 2024年02月24日

嗨，从没放弃的小努力你好：


老师，这道题给了CAD/BRL，但手里拿着的是1000000USD，请问这种情况怎么判断三角套利先换CAD（USD-CAD-BRL-USD）还是BRL（USD-BRL-CAD-USD）？


Hello，亲爱的同学~

已经知道谁便宜，就可以直接确定交易方向了。


解题过程如下：


先计算出cross rate

CAD/USD = 1.2138-1.2259

BRL/USD = 2.3844 - 2.4082

那么CAD/BRL，我们是使用除法，根据相除对角的原则，计算过程为：

CAD/BRL = (CAD/USD) / (BRL/USD) = (1.2138/2.4082) ~ (1.2259/2.3844) = 0.5040 ~ 0.5141


再对比dealer报价：

If a dealer's bid-side quote for the CAD/BRL is C$0.5250


我们可以发现：dealer的bid价0.5250 > cross rate的ask价0.5141

由于BRL在CAD/BRL汇率里，属于base currency，以上汇率关系表明，在cross rate处买入BRL，更划算。

操作原理为：在cross rate处买入BRL，在dealer处卖出BRL。


如果我们一开始持有美元，也是这么操作：

1）在cross rate处，买入BRL

2）在dealer处，卖出BRL。


具体操作如下：

1）在cross rate处，买入BRL，即把手中的美元换成BRL：US$1,000,000 × 2.3844 = BRL2,384,400

2）在dealer处，卖出BRL，即把手里的BRL换成CAD：2,384,400 × 0.5250 = C$1,251,810

3）最后，在cross rate处，把CAD换成美元：C$1,251,810/1.2259 = US$1,021,135




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努力的时光都是限量版，加油！

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