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Ykit · 2023年04月30日

No.PZ2023041102000005

NO.PZ2023041102000005

问题如下:

Anna Goldsworthy is the chief financial officer of a manufacturing firm headquartered in the United Kingdom.Goldsworthy must purchase MXN 27,000,000 to pay an invoice at the end of the quarter. In addition to the quotes from Dealer A, Underwood contacts Dealer B, who provides a bid/offer price of GBP/MXN 0.0366/0.0372.

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:

A.GBP 0. B.GBP 5,400 C.GBP 10,800.

解释:

The bid from Dealer A for MXN/GBP is effectively: 17.147 × 1.5762 = 27.0271The offer from Dealer A is: 17.330 × 1.5766 = 27.3225To 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 1/27.0271 = GBP 0.0370 and a bid to purchase MXN at a rate of 1/27.3225 = GBP 0.0366. Dealer A is effectively quoting MXN/GBP at 0.0366/0.0370. Although she can effectively buy pesos more cheaply from Dealer A (GBP 0.0370 from Dealer A, versus GBP 0.0372 from Dealer B), she cannot resell them to Dealer B for a higher price than GBP 0.0366. There is no profit from triangular arbitrage.

本题中,从DealerA购买比索更加便宜,不就是花更少的GBP,不就是有套利空间么?(节省了一部分GBP)为什么说没有套利呢

1 个答案

笛子_品职助教 · 2023年05月02日

嗨,努力学习的PZer你好:


从DealerA购买比索更加便宜,不就是花更少的GBP,不就是有套利空间么?(节省了一部分GBP)为什么说没有套利呢


关键是套利的定义是什么。


以苹果为例,水果店A,一个苹果卖2元,水果店B一个苹果卖2.5元。

此时套利有两个定义:

一是在水果店A买苹果,然后自己吃了,这就是套利。因为水果店A的苹果更便宜。

二是在水果店A买苹果,然后卖给水果店B,从而赚到了2.5-2=0.5元的差价,这是套利,因为通过低买高卖赚了0.5元。

但是如果我们以2元的价格买了苹果,然后想以2.5元的价格卖给水果店B,但是水果店B不要这个苹果,那么我们卖不掉,是无法套利的。


根据两种套利的定义,

如果我们使用第一个套利的定义,本题有套利机会。

如果我们采取第二个套利的定义,本题没有套利机会。

CFA采取了第二种。按照第二种套利的定义方式,本题没有套利机会。



dealerA的报价

GBP/MXN  = 0.0366 -0.0370 


dealerB的报价:

GBP/MXN =  0.0366/0.0372


因为我们需要以A的ask价0.0370买入,并以B的bid价0.0366卖出。这是做不到低买高卖的。


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