# Arbitrage between markets

I'm trying to understand how arbitrage works, but I'm having some difficulties based on some restrictions:

• I have markets A, B and C.
• The currencies that are traded are X <-> Y, and X <-> Z.
• The only thing that can be transferred between markets A, B and C is currency X.
• The time it takes to transfer the funds (in currency X) between any market is about 2-10 minutes.
• The opportunity for arbitrage last for about 1 hour.

The exchange rates on market A

• 1 X exchanges for 3.22 Y
• 1 X exchanges for 5.11 Z

The exchange rates on market B

• 1 X exchanges for 3.25 Y
• 1 X exchanges for 5.07 Z

The exchange rate on market C

• Does not exchange X <-> Y
• 1 X exchanges for 4.98 Z

Suppose that exchange A is the exchange with the highest volume and presumably the most accurate exchange rate. How can one take advantage of the arbitrage opportunities if the only thing that can be transferred between exchanges is currency X and it takes 2-10 minutes?

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Have you looked at Triangular Arbitrage? en.wikipedia.org/wiki/Triangular_arbitrage – Ram Ahluwalia Apr 25 '12 at 2:32
@QuantGuy yes, but that presumes that if that you can "easily" take your currency between adjacent markets in currency other than X. In the situation I'm exploring, it's only feasible to move currency X between the markets, which seems to defeat the purpose of arbitrage (or at least that's how I see it). – Lirik Apr 25 '12 at 2:40

This is actually a stylized example of the classic dual-listed companies "arbitrage", the most famous example of which is Royal Dutch Shell. It is not a pure arbitrage, but rather is a case of "statistical arbitrage", specifically pairs trading.

First, express the prices of Y and Z in terms of X, and let's rename X "\$" for convenience's sake. Then Y costs about \$0.311 in market A and \$0.308 in market B. Assuming no bid/ask spread, therefore you should buy Y in B and sell it in A. Z costs \$0.196, \$0.197, \$0.201 in A, B, and C, respectively, so buy Z in A and sell it in C. Since money (X) is transferable between markets, you can use one market as a funding source for another, so that all arbitrages can be set up to have zero cost at inception.

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That's a very helpful answer! However, if you buy Y for \$0.311, you're holding Y and you can't transfer it to A to sell it. Same thing with buying Z in A, you're holding Z and you can't transfer it to C to sell it. The only thing that can transfer between the exchanges is X. I think I like the idea of pairs trading better, it might be a better option to trade when the correlation weakens... – Lirik Apr 26 '12 at 19:53
The idea behind pairs trading is that you never actually exchange Y in one market for Y in another market, you just wait for the prices to cross. – Tal Fishman Apr 27 '12 at 15:09
Oh, so you're describing pairs trading, I thought your example involved transferring currency. Is it possible to do pairs trading on a market that doesn't allow shorting? – Lirik Apr 27 '12 at 19:45
@Lirik No, you need to be able to sell short in order to do practically any sort of arbitrage. – Tal Fishman Apr 27 '12 at 19:53
I guess the other option is to simply get a lot of funds and buy X in market A, transfer X to market B, sell X, then take the long trip around (could be a couple of days) to re-fund A. If the flow is consistent and the money is big enough, then it might be feasible. Thanks for all of your help! – Lirik Apr 27 '12 at 20:37