Triangular Arbitrage Question

M

max_w

Say we have these bid/ask rates
usd.cad 1.0613 1.06135
eur.cad 1.4418 1.442
eur.usd 1.3586 1.35865

For fast execution you would buy at the ask and sell at the bid.

You start with 100K
Buy CAD and end up with 106135
Sell CAD for EUR and end up with 73612.8450547926
Buy USD with the EUR and end up with 100014.091933694

That is a profit of $14.09. Ignore the rounding.

So profit = (((units*a1) / b2) * a3) - units
a1 = Ask for USD.CAD
b2 = Bid for EUR.CAD
a3 = Ask for EUR.USD

Something is wrong because I end up loosing money. Also the synthetic bid ask rates are not off by much.

USD.CAD 1.0612395113 1.0613476613
EUR.CAD 1.44188218 1.4420031775
EUR.USD 1.3585225667 1.3586470062

Someone please tell me what I'm doing wrong.
 
Quote from max_w:

Say we have these bid/ask rates
usd.cad 1.0613 1.06135
eur.cad 1.4418 1.442
eur.usd 1.3586 1.35865

For fast execution you would buy at the ask and sell at the bid.

You start with 100K
Buy CAD and end up with 106135
Sell CAD for EUR and end up with 73612.8450547926
Buy USD with the EUR and end up with 100014.091933694

That is a profit of $14.09. Ignore the rounding.
More...

If you are a price-taker then you cannot buy CAD at 1.06135. You must buy at 1.0613.

Sell USD/CAD at 1.0613 (selling 100,000 USD), receive 106,130 CAD

If you are a price-taker then you sell CAD (buy EUR) at 1.442

Buy EUR/CAD at 1.442 (selling 106,130 CAD), receive 73,599.16782 EUR

If you are a price-taker then you buy USD at 1.3586

Sell EUR/USD at 1.3586 (selling 73,599.16782 EUR), receive 99,991.829 USD
 
Quote from m22au:

If you are a price-taker then you cannot buy CAD at 1.06135. You must buy at 1.0613.

Sell USD/CAD at 1.0613 (selling 100,000 USD), receive 106,130 CAD

If you are a price-taker then you sell CAD (buy EUR) at 1.442

Buy EUR/CAD at 1.442 (selling 106,130 CAD), receive 73,599.16782 EUR

If you are a price-taker then you buy USD at 1.3586

Sell EUR/USD at 1.3586 (selling 73,599.16782 EUR), receive 99,991.829 USD
More...

I did the math and got the same answer as m22au.
 
Quote from m22au:

If you are a price-taker then you cannot buy CAD at 1.06135. You must buy at 1.0613.

Sell USD/CAD at 1.0613 (selling 100,000 USD), receive 106,130 CAD

If you are a price-taker then you sell CAD (buy EUR) at 1.442

Buy EUR/CAD at 1.442 (selling 106,130 CAD), receive 73,599.16782 EUR

If you are a price-taker then you buy USD at 1.3586

Sell EUR/USD at 1.3586 (selling 73,599.16782 EUR), receive 99,991.829 USD
More...
I believe you did not answer his question, but may have answered a question you thought he should ask.
 
Thanks m22au. Actually you can buy at 1.06135 (I did it), but the problem is that I was multiplying instead of dividing. I get the loss now.

Quote from m22au:

If you are a price-taker then you cannot buy CAD at 1.06135. You must buy at 1.0613.

Sell USD/CAD at 1.0613 (selling 100,000 USD), receive 106,130 CAD

If you are a price-taker then you sell CAD (buy EUR) at 1.442

Buy EUR/CAD at 1.442 (selling 106,130 CAD), receive 73,599.16782 EUR

If you are a price-taker then you buy USD at 1.3586

Sell EUR/USD at 1.3586 (selling 73,599.16782 EUR), receive 99,991.829 USD
More...
 
It's nice to understand the relationships, but a complete waste of time to calc a triangular arb on your dealer's platform. It's how they maintain their pricing. For example, all of the crosses on IB's platform are derived by pricing the synthetic (two of three crosses necessary). Does anyone think they're going to find an arb within a single dealer?
 
You are right. That would be the second step after getting the algorithm right.
Quote from drownpruf:

It's nice to understand the relationships, but a complete waste of time to calc a triangular arb on your dealer's platform. It's how they maintain their pricing. For example, all of the crosses on IB's platform are derived by pricing the synthetic (two of three crosses necessary). Does anyone think they're going to find an arb within a single dealer?
More...
 
Quote from max_w:

You are right. That would be the second step after getting the algorithm right.
More...

I am all for arb opportunities on dealer platforms and exploited Oanda's digitals and knockouts for a long time, but nobody is going to screw up the three-way.
 
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