如下题-有问必答-品职教育专注CFA ESG FRM CPA 考研等财经培训课程

如下题

* 问题详情，请查看题干

NO.PZ202106160100000103

问题如下：

Using the quotes from Dealer A and B, the triangular arbitrage profit on a transaction of MXN 27,000,000 would be closest to:

选项：

GBP 0.

GBP 5,400.

GBP 10,800.

解释：

A is correct.

Using quotes from Dealer A, she can find

$\frac{MXN}{GBP}=\frac{MXN}{USD}\times\frac{USD}{GBP}$

The bid from Dealer A for MXN/GBP is effectively

${(\frac{MXN}{GBP})}_{bid}={(\frac{MXN}{USD})}_{bid}\times{(\frac{USD}{GBP})}_{bid}$

The offer from Dealer A is

${(\frac{MXN}{GBP})}_{offer}={(\frac{MXN}{USD})}_{offer}\times{(\frac{USD}{GBP})}_{offer}$

To compare with Dealer B’s quote, she must take the inverse of MXN/GBP, so that she has an offer to sell MXN at a rate of 1/24.7742 = GBP 0.0404 and a bid to purchase MXN at a rate of 1/24.8069 = GBP 0.0403. Dealer A is effectively quoting. Although she can effectively buy pesos more cheaply from Dealer A (GBP 0.0404 from Dealer A, versus GBP 0.0406 from Dealer B), she cannot resell them to Dealer B for a higher price than GBP 0.0403. There is no profit from triangular arbitrage.

考点：Triangular arbitrage

能不能从三角套汇中获利的核心在于能不能实现低买高卖。

首先我们计算出Dealer A处MXN/GBP的报价

${(\frac{MXN}{GBP})}_{bid}={(\frac{MXN}{USD})}_{bid}\times{(\frac{USD}{GBP})}_{bid}$

${(\frac{MXN}{GBP})}_{offer}={(\frac{MXN}{USD})}_{offer}\times{(\frac{USD}{GBP})}_{offer}$

把上述形式转换一下可得 GBP/MXN的形式，

ASK: 1/24.7742 = 0.0404GBP/MXN

BID: 1/24.8069 = 0.0403GBP/MXN

注意到，MXN/GBP换成GBP/MXN后，因为标价货币和基础货币的地位对调了，所以取倒数后BID和ASK报价也要变化。现在我们可以拿Dealer A的报价与Dealer B的报价作比较了。

Dealer B关于GBP/MXN的报价是0.0403/0.0406。可以看到，Dealer A对于MXN报价便宜一些，那么投资者应该首先从Dealer A处以0.0404GBP/MXN的价格买进MXN，然后去Dealer B处卖掉MXN，但是在Dealer B卖掉MXN就要用Dealer B的买价，0.0403。可以直观看到投资者以0.0404价格买入，却以0.0403价格卖出，是没有利润可得的。所以投资者不会去做这笔三角套汇，那么三角套汇的利润自然为0。

请问老师为什么不用题目中更新的利率 Dealer A calls her back later with a revised USD/GBP bid–offer quote of 1.2299/1.2307？