Triangular Arbitrage
Three currencies (dollar, euro, yen) and three exchange rates. If the third rate doesn't line up with the other two, going once around the triangle leaves you with extra money.
Risk warning: forex, CFDs, options, futures and crypto assets usually involve leverage or high volatility, and you can lose more than you put in. This lesson only teaches the concepts; all numbers are for illustration and are not investment advice.
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Text version · Arbitrage Strategies, lesson 4: “Triangular Arbitrage”
Three currencies (dollar, euro, yen) and three exchange rates. If the third rate doesn't line up with the other two, going once around the triangle leaves you with extra money.
The third rate is derived
If you know how many dollars a euro buys and how many yen a dollar buys, you can work out how many yen a euro should buy. That's the cross rate. Once the EUR/JPY the market quotes directly doesn't match it, there's a triangular arbitrage opportunity.
Small and fast
Every conversion costs a spread, and a full loop costs it three times. The gap has to beat those three costs to be profitable, and banks and high-frequency trading systems wipe it out in an instant.
Buy at the ask, sell at the bid
Every exchange rate has a Bid and an Ask, so the cross rate derived from two legs is a range too. Only when the market's bid is above the top of the implied range, or its ask below the bottom, is there a real opportunity. Looking only at mid prices makes you mistake the spread for profit.
Key takeaways
- Two exchange rates determine the third cross rate: EUR/JPY = EUR/USD × USD/JPY.
- When the market quote strays from the cross rate, going around the triangle back to your starting currency leaves you with extra money.
- You buy at the ask and sell at the bid, paying the spread on every conversion. The mispricing must beat all three costs combined, and it often lasts only an instant.
Try it yourself
You can do these exercises in this lesson's interactive simulation:
- Click "Example: 166 vs. 165" and watch a full loop: starting with $1,000,000, how much comes back? How much do you get at each stop?
- Drag the market EUR/JPY to 164: why does the route become $→¥→€→$?
- Go back to 166 and set the cost per conversion to 0.20%: is it still profitable? How big does the gap need to be to be worth doing?
- Click "Align the cross rate": once the three legs line up, does a loop still make money?
Quiz and explanations
- 1. EUR/USD = 1.10 and USD/JPY = 150. What's the implied EUR/JPY?
- Answer: 165.1.10 × 150 = 165.
- 2. The market quotes EUR/JPY at 166, above the implied 165. Starting from dollars, which way should you convert?
- Answer: USD → EUR → JPY → USD.The euro is more expensive in the yen market: buy euros with dollars, sell them for yen at 166, then convert back to dollars.
- 3. EUR/USD is 1.10, USD/JPY is 150, and the market quotes EUR/JPY at 166. Starting from $1,000,000 and ignoring costs, roughly what do you end up with after going $→€→¥→$?
- Answer: $1,006,061.$1,000,000 ÷ 1.10 = €909,091; × 166 = ¥150,909,091; ÷ 150 ≈ $1,006,061.
Terms in this lesson
- Ask: The price sellers are asking for. When you buy, you trade at the Ask.
- Bid: The price buyers are willing to pay. When you sell, you trade at the Bid.
- cross rate (Cross Rate): A third exchange rate worked out from two others, such as EUR/JPY = EUR/USD × USD/JPY.
- spread (Spread): The gap between the Ask and the Bid, a hidden cost on every trade.
- triangular arbitrage (Triangular Arbitrage): When quotes for three currencies don't line up, converting around the triangle back to your starting currency for a profit.