currency arbitrage... please, currency, somebody

hoangvu90

I just dont get it!!! can somebody please give me a dummy proof explanation....

thank you

CPATrader

Thank You

Suppose the GBP trades for CHF 2.20279 in Zurich and USD 1.62699 in London. The USD trades for CHF 1.2755 in Zurich. Is there an arbitrage opportunity available for a currency trader?

Analyze_This

okay here is what i do, first i write any rates no matter how they are given in the mathmaticly correct way. a/b, you might not see it now, but one day you will realise it makes things much easier

2.20279 CHF/GBP
1.62699 USD/GBP
1.2755 CHF/USD

now it is kind of hard to see it here because the "/" sign should be a flat line, but no such charachter exists in ASCII code lol...but if you look at the last two rater you can see that you can cancel out the USD from both and end up with CHF/GBP by simply multiplying them

just put them next to each other and see

so, 1.62699*1.2755=2.07522

which is clearly not = to 2.20279

so there is arbitrage

someone out there, as indicated by the exchange rates you gave me is willing to pay 2.20279 CHF for each GBP

but by jumping from currency to another, i can end up buying 1 GBO for 2.07522 and selling it to him for 2.20279, instant profit

to do that, i would start with 2.07522 CHF, i would convert them to 1.626 USD
then i would convert that to 1 GBP

and i would sell it to some fool for 2.20 CHF....

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to sum it up, if you are looking for some shorcut, there is not, or at least i am not the guy to teach it to you

but all this is, math and logic and arbitrage...

with practice, you WILL get it

just look at the rates and start thinking, how can I make instant money, it would get more complicated when you involve bids and asks, but the concept is the same, try to understand this, and when you do maybe we try one with bid and ask ....

mp3bu

ok thanks let me see what I can do

FinancialAnaly

i probably should have gave you the example from the perspective of a USD investor, thats just how CFAI mostly asks for it

should not affect your understanding much, i am here for another hour, let me know if i can help

jacksparrow

This is my first post on this forum. So far this forum was extremely helpful.
I hope someone finds my first attempt helpful as well.
This approach should be useful to find the profit on a triangular arbitrage opportunity starting with X amount of currency Y.

Let's assume problem states that you start with GBP.

We start with 3 quotes:
GBP:CHF 2.20279 (GBP 1.00 = CHF 2.20279)
USD:CHF 1.2755
GBP:USD 1.62699

First, you have to line up exchange rates in such a way that you start with GBP and finish with GBP:

GBP:CHF -> USD:CHF -> GBP:USD (GBP to CHF to USD to GBP)

Ending currency and beginning currency for adjacent exchange rates (linked by arrow ->) in the chain should match in order to cancel each other. To accomplish that you need to flip exchange rates (take the reciprocal of the original exchange rate).
In our example we need to flip last two exchange rates to get a chain like this:

GBP:CHF -> CHF:USD -> USD:GBP

2.20279 (1/1.2755) (1/1.62699)

Now take the product of these rates to find how much in GBP we will get starting with GBP 1 :

GBP 1 -> 2.20279*(1/1.2755)*(1/1.62699) = GBP 1.06147

We made GBP 0.06147 risk free starting with GBP 1.
If question asked how much you could make starting with let's say GBP 1MM,
then multiply 1,000,000 by 0.06147 to get GBP 61,470 profit.

If resulting product of exchange rates is less than 1 you need to reverse the chain and start with GBP:USD exchange rate instead.
If product equals to 1 then there is no arbitrage.

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For problems with spreads you need to remember the rule "up the bid and down the ask":

Let's modify our example to include spreads:

GBP:CHF 2.20274 - 2.20284
USD:CHF 1.2750 - 1.2760
GBP:USD 1.62694 - 1.62704

We start with chain of exchange rates as before:

GBP:CHF -> USD:CHF -> GBP:USD

We need to flip two last rates to cancel the intermediate currencies (the adjacent currencies in chain have to match).

The resulting product

(GBP:CHF) * 1/(USD:CHF) * 1/(GBP:USD)

gives you how much in GBP we will get staring with GBP 1 .

Think about this product as a fraction with GBP:CHF exchange rate in the numerator (up)
and USD:CHF and GBP:USD rates in the denominator (down).

The question is should we use bids or asks to calculate the product?

Now the rule "Up the Bid and Down the Ask" comes in handy.

If rate is in the numerator of the fraction you have to use bid price of the quote (up the bid) and if rate is in the denominator you have to use the ask (down the ask).

This rule makes a lot of sense, since every time you convert currency you get the worst price from FX dealer. If rate goes to numerator you should use smaller number, bid of the spread. If rate goes to denominator you should use larger number, ask, to get lower reciprocal.

Finally, calculate the product of exchange rates applying the rule to pick bid or ask:

2.20274(up the bid) * 1/1.2760(down the ask) * 1/1.62704(down the ask) = 1.060997

We made extra GBP 0.060997 starting with GBP 1 .

BTW, notice that in example with spreads we made slightly less than in
first example where we used midpoint quotes (FX dealers pocket the difference by making spread on exchange trades).

MiniMe7

good stuff

YAhmed

Im pretty sure you can start with any currency really, although the question will make it clear.

HOWEVER, make sure that you are first converting to the overvalued currency, and then to the undervalued currency. If you start with another currency, you need to see which of the other two is the overvalued compared to the other, and exchange into the overvalued currency first.

Im not sure if this makes sense, it does in my head haha

profil

You are welcome, JCM

beingthatguy,

My example is more specific version of triangular arbitrage problem where they ask to calculate the profit based on initial position in specific currency.

You are right. To verify if arbitrage possible you can start with any currency.
Btw, in problem without spreads you can stop as soon as the product of exchange rates is different from 1. More or less not important, the arbitrage is possible. If number is less than 1, the opposite direction will generate arbitrage.

In problem with spreads you have to be more careful, since combinations of exchange rates without arbitrage opportunity will result in product less than 1 no matter which way you rotate currencies (dealer keeps the difference between 1 and what you get). So you have to do it twice to confirm/reject presence of arbitrage opportunity if first time you get product less than 1.

Spanishesk,
I don't know how you do it, but I find it easy enough just plug numbers and see the result. You have 50% chance to get the direction right first time and calculation is fairly straightforward.