Triangular arbitrage question

K

KSTHANE

New member
Joined
Jun 18, 2026
Messages
0
Reaction score
0
I just cannot seem to quite get triangular arbitrage. I just watched this youtube video that tried to explain it and I always seem to get hung up on the same place.
Here are the steps (I’m leaving off the numbers because they don’t matter to this question:
1. Start with $100.
2. Convert $ to Yen (Buy Yen with Dollars)
3. Convert Yen to Pounds (Buy Pounds with Yen)
4. Convert Pounds to Dollars (Sell pounds for dollars)
5. Once you convert you have an arbitrage profit.
My question is why do we all of the sudden sell pounds, or what is different in step 4 that tells us to sell instead of buy? I don’t see any difference between the previous transactions, why aren’t you buying Dollars with pounds? Or conversely, why aren’t we selling dollars for yen in step 2?
This section just haunts me.
 
I think what you’re trying to ask how do you know which to hop around the triangle. You don’t. You really have to try going both ways, and on each leg you take the most disadvantageous side of the transaction.
After you’ve practiced it a bunch of times, it’ll start to sink in
 
Hank Moody wrote:I think what you’re trying to ask how do you know which to hop around the triangle. You don’t. You really have to try going both ways, and on each leg you take the most disadvantageous side of the transaction.
After you’ve practiced it a bunch of times, it’ll start to sink in
Click to expand...

That’s not what he’s asking at all. To the OP you just buy all the way around it’s really simple just make sure to buy at the ask. That video is incorrect you don’t have to switch to selling.
 
Acutally based on a q i just did in q bank I may be wrong, and I have no idea why you would have to (Sell pounds for dollars)
 
First, to get the concept, solve a question without a bid-ask spread.
The general idea is that you can start with any of the three currencies, and then go around the triangle either way. If there is an arb opportunity, one way will generate a loss, the other way will generate a gain. No matter what currency you start with, it will be the same % gain or loss.
Think in terms of exchanging one currency for another, not necessarily buying or selling a currency. Without a bid ask, it’s easy to figure out what to exchange to.
With a bid-ask, always realize that you’re getting screwed by the bid-ask. You should choose the one that gives you less of the currency you are exchanging into. if the bid - ask for $1 into Euros is 1.2 euros - 1.25 euros, and you want to exchange, you’re going to get 1.2 EUR for your dollar. If you want to buy $1, it will cost you 1.25 EUR.
Just remember, a bid-ask is just a screw job. And triangular arbitrage is getting screwed three ways and still making some money.
 
Also, to answer the OP’s question - It doesn’t matter which way you think about it. When doing a pound to dollar exchange, selling pounds for dollars means the same thing as buying dollars for pounds.
You could think of the above example is terms of all buy decisions or all sell decisions as long as you are reading and using the FX quotes correctly.
 
ftwcfa wrote:Also, to answer the OP’s question - It doesn’t matter which way you think about it. When doing a pound to dollar exchange, selling pounds for dollars means the same thing as buying dollars for pounds.
You could think of the above example is terms of all buy decisions or all sell decisions as long as you are reading and using the FX quotes correctly.
Click to expand...
ftwcfa no selling pounds for dollars means the same thing as buying dollars for pounds, are not the same thing.
Could someone who actually knows what they are talking about chime in? I’ve got the schweser lecture on saturday to watch. Up the bid down the ask is the correct approach, I just can’t logically figure out WHY it is.
 
Well, guess I’ll just head back to the Level III forum…….
 
Hi everyone
With FX, you are always buying one currency and selling another. In the OP’s question, the last step is why do we sell pounds to buy dollars. This is the same as buying dollars for pounds. I think the confusion comes from whether to use the bid or ask rate, which will differ depending on the quotation.
In the video, the narrator sold pounds for dollars instead of buying dollars for pounds because of the way the currency pair was quoted in the question. We were given the quote in x dollars per 1 pound, or put another way, that we can sell one pound at the bid and buy one pound at the ask. So it was easier to say that we are selling our 64.75 pounds at the bid rate. If the quotation was given as x pounds per 1 dollar then it would have been easier, and identical, to buy USD but at the ASK rate.
In the video we were given the exchange rate as 1.5670-1.5675 dollars per pound. So we can sell one pound at the bid rate of 1.5670. This means we can sell 64.75 pounds for 64.75 x 1.5670 = 101.4633 dollars, as the narrator showed us.
If the quote was given in reverse, ie pounds per 1 dollar, we would buy dollars at the ask rate. To illustrate we can convert the rate to pounds per dollar. To do this, we would take the reciprocal of the ask as the bid and the reciprocal of the bid as the ask as outlined in the movie.
Ie Pounds per dollar bid = (1/ USD per GBP ask) = (1/1.5675) = 0.63796
Pounds per dollar ask = (1/ USD per GBP bid) = (1/1.5670) = 0.63816
This gives us a quote of 0.63796-0.63816 pounds per one dollar. If we BUY dollars for pounds now (the same outcome as selling pounds for dollars), we take the ask price because we are buying the dollars. Because of the reverse quote, we divide our pounds (as outlined in the movie too) by the dollar ask rate which gives 64.75/0.63816 = 101.4636. An identical (well, excluding rounding differences) result.
I hope that helps
Chris
 
You must log in or register to reply here.
Back
Top