Triangular Arbitrage

Overview

Triangular arbitrage is a forex trading strategy that exploits temporary price discrepancies among three currency pairs. A trader converts an initial currency into a second, switches the second into a third, and finally converts the third back into the original currency. If the cross‑rates are out of sync, this sequence can yield a risk‑free profit—after accounting for transaction costs and spreads.

How it works

• You identify three currencies (A, B, C) and their quoted pair rates (A/B, B/C, and A/C or C/A).
• Compute the implied cross rate from two quotes (for example, implied A/C = A/B × B/C).
• Compare the implied rate with the actual market rate for A/C. If they differ enough to overcome bid/ask spreads and fees, a triangular arbitrage opportunity exists.
• Execute the three trades simultaneously (or as close to simultaneous as possible) to lock in profit before the market corrects the discrepancy.

Currency pair basics (quick)

• A currency pair is quoted as Base/Quote (e.g., EUR/USD). Buying the pair = buying base and selling quote.
• Bid = price buyers will pay for the base. Ask = price sellers will accept for the base.
• When calculating profitability, use:
• the bid price when you are selling the base currency (you receive the bid),
• the ask price when you are buying the base currency (you pay the ask).
• Spreads and transaction fees must be subtracted from any theoretical profit.

Detecting an opportunity

1. Select three pairs connecting the currencies: A/B, B/C, and A/C (or C/A).
2. Calculate the implied A/C rate: implied A/C = A/B × B/C.
3. Compare implied A/C with the actual A/C market rate (adjusted for bid/ask directions).
4. If the implied and actual rates differ by more than spreads and fees, the arbitrage may be profitable.

Example

Assume quotes (interpreted as 1 unit of the first currency equals X units of the second):
– USD → EUR: 1 USD = 0.85 EUR
– EUR → GBP: 1 EUR = 0.70 GBP
– GBP → USD: 1 GBP = 2.00 USD

Implied USD→GBP = 0.85 × 0.70 = 0.595 GBP per USD
Actual USD→GBP (from GBP→USD = 2.00) = 1 / 2.00 = 0.50 GBP per USD

Because 0.595 (implied) > 0.50 (actual), an arbitrage exists.

Start with 100,000 USD:
– USD → EUR: 100,000 × 0.85 = 85,000 EUR
– EUR → GBP: 85,000 × 0.70 = 59,500 GBP
– GBP → USD: 59,500 × 2.00 = 119,000 USD

Profit (ignoring spreads/fees): 119,000 − 100,000 = 19,000 USD

Important: in real markets you must use the correct bid/ask for each leg and subtract all trading costs. These often eliminate apparent profit.

Role of automation

Triangular arbitrage opportunities are extremely short‑lived—often lasting only milliseconds—because markets self‑correct quickly. Successful execution typically requires:
– Automated, low‑latency trading systems to detect and execute the three legs almost simultaneously.
– High liquidity pairs to avoid price slippage and large spreads.
– Access to multiple market venues or quotes to capture mispricings.

Crypto triangular arbitrage

The same principle applies to cryptocurrencies: price discrepancies among three trading pairs can create arbitrage opportunities. Feasibility depends on liquidity, exchange fees, withdrawal/deposit times, and the ability to execute all legs quickly across exchanges.

Legality and ethics

Triangular arbitrage is a legal trading strategy. It becomes problematic only if it involves illegal practices (fraud, market manipulation, front‑running, or use of illicit funds). Using legitimate data sources and exchanges keeps the strategy within legal bounds.

Risks and limitations

• Transaction costs, bid/ask spreads, and slippage can erase theoretical profits.
• Execution risk: one or more legs may fail or fill at worse prices.
• Latency and competition: institutional traders and high‑frequency systems often capture opportunities first.
• Exchange risks for crypto: withdrawal limits, transfer delays, and counterparty risk.

Key takeaways

• Triangular arbitrage exploits temporary inconsistencies among three currency rates.
• Profits exist only if they exceed transaction costs and can be locked in quickly.
• Practically feasible for traders with automated, low‑latency systems and access to highly liquid markets.
• Applicable to both fiat currencies and cryptocurrencies, but operational and market frictions are decisive.