Module 12

Locational and Triangular Arbitrage in FX Markets

This module focuses on exchange-rate inconsistencies across banks and across currency loops: locational arbitrage, triangular arbitrage, visual money-flow diagrams, interactive tools, and in-class exercises.

Theme
ArbitrageBid-askFX dealers

Locational arbitrage basics

Core idea

Locational arbitrage happens when the same currency is quoted at different prices by different dealers or banks. If one bank sells a currency cheaply and another bank buys that currency at a higher price, a round-trip arbitrage may exist.

Always remember:
Buy from the dealer at the ask price. Sell to the dealer at the bid price.

What to compare

  • Compare the lowest ask across dealers.
  • Compare the highest bid across dealers.
  • If highest bid > lowest ask, an arbitrage spread may exist.
  • If highest bid = lowest ask, there is no profit after the spread.
A currency can look cheaper at one bank and more expensive at another bank, but the bid-ask spread may eliminate the profit.
CalculatorLocational

Locational arbitrage calculator

Dealer comparison

Enter values and click compute.

Airport-booth picture

Profit per unit of foreign currency = highest bid − lowest ask
Read it left to right: start with dollars, buy the foreign currency at the cheaper booth's ask, then sell it back at the other booth's bid.
Start $1,610.00 Booth A Buy £ here ask = 1.6100 $/£ cheaper selling booth Pounds £1,000.00 Booth B Sell £ here bid = 1.6200 $/£ higher buying booth End = $1,620.00 | Profit = $10.00
If the selling bid is above the buying ask, buy the foreign currency where it is cheaper and sell it where it is more expensive.
ICELocational arbitrage

In-class exercises — Locational arbitrage

Exercise 1A

Bank 1 bid Bank 1 ask Bank 2 bid Bank 2 ask
£ in $ $1.60 $1.61 $1.62 $1.63
Buy pounds at Bank 1 ask and sell pounds at Bank 2 bid.
Profit per £ = 1.62 − 1.61 = $0.01
  1. Start with $1,610.
  2. Buy pounds: $1,610 / 1.61 = £1,000.
  3. Sell pounds: £1,000 × 1.62 = $1,620.
Profit = $10
Start $1,610 Booth 1 ask = $1.61/£ buy £ here £1,000 after step 1 Booth 2 bid = $1.62/£ sell £ here End = $1,620 | Profit = $10

Exercise 1B

Bank 1 bid Bank 1 ask Bank 2 bid Bank 2 ask
£ in $ $1.60 $1.61 $1.61 $1.62
Buy at Bank 1 ask and sell at Bank 2 bid, but now:
Profit per £ = 1.61 − 1.61 = $0
  1. Start with $1,610.
  2. Buy pounds: $1,610 / 1.61 = £1,000.
  3. Sell pounds: £1,000 × 1.61 = $1,610.
No arbitrage profit
Start $1,610 Booth 1 ask = $1.61/£ buy £ here £1,000 after step 1 Booth 2 bid = $1.61/£ sell £ here End = $1,610 | Profit = $0

Exercise 2

If you start with $10,000 and conduct one round transaction, how many dollars will you end up with?

Using 0.64 $/NZ$ to buy NZ dollars and 0.645 $/NZ$ to sell back:
NZ$ obtained = 10,000 / 0.64 = 15,625 NZ$
Final dollars = 15,625 × 0.645 = $10,078.125
Final answer ≈ $10,078.13
Start $10,000 Booth A ask = $0.640/NZ$ buy NZ$ here NZ$15,625 after step 1 Booth B bid = $0.645/NZ$ sell NZ$ here End = $10,078.13 | Profit = $78.13

Locational hint

Always buy from the dealer at the ask price and sell to the dealer at the bid price.
ArbitrageFX loopCross rates

Triangular arbitrage basics

🔺

Core idea

Triangular arbitrage tests whether three exchange rates are mutually consistent. You start with one currency, move around a three-currency loop, and return to the starting currency.

💵

What to check

  • Start with one currency amount.
  • Convert through the three quoted rates.
  • Compare the ending amount to the starting amount.
  • If the loop ends larger, an arbitrage opportunity may exist.
One triangular direction may be profitable while the reverse direction is not. Always test both paths.
VisualProfit / loss flow

Triangular arbitrage flow diagrams

Approach one works Start $1,600 → End $1,620 GBP £1,000 MYR MYR 8,100 Profit = $20 $1,620 − $1,600 $1,600 / 1.6 = £1,000 £1,000 × 8.1 = MYR 8,100 MYR 8,100 × 0.20 = $1,620
Approach two does not work Start $1,600 → End $1,580.25 MYR MYR 8,000 GBP £987.65 Loss ≈ $19.75 $1,580.25 − $1,600 $1,600 / 0.20 = MYR 8,000 MYR 8,000 / 8.1 = £987.65 £987.65 × 1.6 = $1,580.24
Positive loop Negative loop Currency conversion path
CalculatorTriangular

Triangular arbitrage calculator

USD → EUR → GBP → USD

Enter values and click compute.
Start with USD $100,000.00 EUR leg €85,000.00 GBP leg £63,750.00 End with USD $101,190.48 × USD→EUR × EUR→GBP ÷ USD→GBP Loop result Profit: $1,190.48 Return: 1.190% Interpretation Positive loop = possible triangular arbitrage
ICETriangular arbitrage

In-class exercises — Triangular arbitrage

Exercise 1

Given: £ is quoted at $1.50, MYR is quoted at $0.25, and the cross rate is £1 = MYR 6.1. How can you arbitrage?

Test both paths:
  1. $ → £ → MYR → $
  2. $ → MYR → £ → $
Profitable path:
  1. Start with $1,500.
  2. Buy pounds: $1,500 / 1.50 = £1,000.
  3. Convert pounds to MYR: £1,000 × 6.1 = MYR 6,100.
  4. Convert MYR to dollars: 6,100 × 0.25 = $1,525.
Profit = 1,525 − 1,500 = $25
USD $1,500 GBP £1,000 MYR MYR 6,100 $1,500 / 1.50 × 6.1 × 0.25 = $1,525 Profit = $25

Check the reverse direction

  1. Start with $1,500.
  2. Buy MYR: $1,500 / 0.25 = MYR 6,000.
  3. Convert MYR to pounds: 6,000 / 6.1 = £983.61.
  4. Convert pounds to dollars: 983.61 × 1.50 = $1,475.41.
Loss ≈ $24.59
USD $1,500 MYR MYR 6,000 GBP £983.61 $1,500 / 0.25 / 6.1 × 1.50 = $1,475.41 Loss ≈ $24.59
In triangular arbitrage, one direction may work while the reverse direction fails. That is why both loops should be checked.
HomeworkQuestion only

Module 12 homework

Show your work. No hints are provided below.

Homework 1 — Locational arbitrage
Bank 1 bid Bank 1 ask Bank 2 bid Bank 2 ask
£ in $ $1.60 $1.61 $1.62 $1.63

Assume you start with $1,610. Is locational arbitrage possible? If yes, explain the transaction and compute the ending dollar amount and profit.

Homework 2 — Locational arbitrage
Bank 1 bid Bank 1 ask Bank 2 bid Bank 2 ask
£ in $ $1.60 $1.61 $1.61 $1.62

Assume you start with $1,610. Is locational arbitrage possible? If yes, explain the transaction and compute the ending dollar amount and profit. If not, show why not.

Homework 3 — Locational arbitrage

You start with $10,000. One dealer will sell NZ dollars at $0.64/NZ$, and another dealer will buy NZ dollars at $0.645/NZ$.

Conduct one round-trip transaction. How many dollars will you have at the end? What is the profit, if any?

Homework 4 — Triangular arbitrage

The British pound is quoted at $1.60, the Malaysian ringgit is quoted at $0.20, and the cross rate is £1 = MYR 8.1.

Starting with $1,600, determine whether triangular arbitrage exists. If it does, show the profitable direction and compute the ending dollar amount and profit.

Homework 5 — Reverse direction check

Using the same rates as Homework 4, start with $1,600 and go the reverse way around the loop.

Compute the ending dollar amount and determine whether this direction yields a profit or a loss.

Homework 6 — USD, EUR, and GBP loop

Suppose the following quotes are observed:

  • 1 USD = 0.85 EUR
  • 1 EUR = 0.75 GBP
  • 1 USD = 0.63 GBP

Start with 1 USD and complete the loop USD → EUR → GBP → USD. Determine the ending dollar amount and the profit rate, if any.

Extra practiceHomework carryover

Extra practice

USD, EUR, and GBP loop

Suppose:

  • 1 USD = 0.85 EUR
  • 1 EUR = 0.75 GBP
  • 1 USD = 0.63 GBP
Starting with 1 USD:
1 USD → 0.85 EUR
0.85 EUR → 0.85 × 0.75 = 0.6375 GBP
0.6375 GBP → 0.6375 / 0.63 = 1.0119 USD
Profit per $1 = 0.0119 USD ≈ 1.19%