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Calculate Triangular Arbitrage Lot Size

Have you ever wondered how to correctly size positions between the underlying pair and its synthetics to eliminate or hedge directional risk? This article describes  how to calculate triangular arbitrage lot size to fully hedge all exposure when initiating a triangular arbitrage trade. The arbitrage trade is at the heart of all good strategies that take advantage of inefficiency. In the forex market this means triangular arbitrage, so understanding how to correctly size positions to eliminate or minimize individual currency risk is very important.

Triangular Arbitrage Lot Size

Triangular Arbitrage Lot Size to capture 6 pip inefficiency synthetic pair
What triangular arbitrage lot size should be traded to capture this 6 pip inefficiency?
  1. February 2, 2013 at 12:55 pm

    Hi Patrick and thanks for a really interesting article.
    I have no doubt of the theoretical principle involved here as you have done a fine job explaining the detail. I am, however, curious to know whether such a strategy could be profitably employed by the minnows in the market – independent traders of limited capital (like me). With only a six pip premium to chase, would there be a risk that the market could simply wash away our profits with slippage, or that the arbitrage opportunity would close before all trades were placed, leaving only the likelihood of an overall loss?

    • February 2, 2013 at 11:26 pm

      Hi Ron,
      That’s a good point about the small size of the inefficiency. Six pips is likely insufficient to execute as a retail trader covering spread on three trades in addition to the substantial execution risk (one or more of the pairs could move unfavorably before execution). The pair that provides the bulk of the inefficiency will likely move before a fill can be made and thus you will find that the 6 pips has turned into 1-3 after execution, and in most cases will be less than the cost of executing three trades.

      One of the points that I think is important is that on a retail level, for the most part, chasing the risk free trade is a futile effort. There may be some limited arbs available but in order to not be qualified as toxic flow by a single broker, fills would need to be done on multiple brokers for the different legs of the trade so that you could fly under the radar. This starts to run into a technological issue at this point as simultaneously executing trades on multiple brokers (reliably) and then getting out of those trades is a significant technology accomplishment. This excludes all but the most tech savvy. And I don’t think this is the best way either.

      For retail traders I suggest being willing to accept some directional risk in return for not guaranteed rewards but rewards that may be within the grasp of retail traders, and trading that is not looked on as toxic flow by the broker. This way your broker lets you keep trading even while you are making money, because it isn’t coming out of their pockets. The key is to understand the triangular arbitrage trade, and then to develop a strategy to play with the concept of one or more pairs being out of balance, and taking mean reversion trades to capture this statistical inefficiency, or to make outright directional trades based on the inefficiency. For more information see the last two sections in this article: “Which pair is out of balance”, and “Triangular Arbitrage Strategy Summary” found here:

      Make sure to follow the link on that page to the Forex Factory thread. It is well worth reading all the OP’s posts (even on other threads). There are some interesting ideas there that can help in developing a strategy from the inefficiency. For further reading do a search on Forex Factory for the “Three Pairs Hedging” threads. The renko thread is shorter and easier to figure out if you trace back to the OP’s posts in the first thread. Essentially you are still doing three trades, but just placing them in different order, driven from a renko chart (for instance), allowing the closing of each pairs’ renko to be the timing for the trades. From my tests, there is some merit to that idea depending on how you define the actual strategy. I have done some preliminary testing but have not had time to develop a full strategy from this idea.


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