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Strategic Financial Management · Foreign Exchange Market

Forex Arbitrage Operations: Locational, Triangular and Covered Interest

Updated 11 October 2026 · Fact-checked

Forex arbitrage means earning a risk-free profit from price differences in currency quotes. Locational arbitrage uses different quotes in two centres. Triangular arbitrage uses an inconsistent cross rate among three currencies. Covered interest arbitrage uses a forward rate that differs from interest rate parity. Compute the fair rate, spot the gap, then trace the cash cycle.

Understand Forex Arbitrage Operations

Arbitrage is buying and selling at the same time to lock in a profit with no risk and no net investment of your own money. It works because one currency should have one price everywhere. When it does not, traders step in and push the prices back in line.

Locational (two-point) arbitrage: Two banks or two centres quote the same pair at different rates. You buy the currency where it is cheaper and sell it where it is dearer. Always buy at the quoting bank's selling (ask) rate and sell at the other bank's buying (bid) rate.

Triangular (three-point) arbitrage: You have three currencies and three quotes. If the cross rate implied by two quotes does not match the third quote actually on offer, a loop of three trades earns a profit. You start with one currency, move through the other two, and come back to the start with more than you began with.

Covered interest arbitrage: Interest rate parity says the forward rate should offset the interest differential between two countries. If the actual forward rate differs from the parity rate, you borrow in one currency, convert at spot, invest in the other, and cover the exchange risk with a forward contract. The profit is certain because the forward rate is fixed on day one.

Mispricing is the whole game. If the actual rate equals the fair rate (allowing for bid-ask spreads), there is no arbitrage and you must say so in your answer.

Key rules to remember

Cross rate
A/C = A/B × B/C
Use it to find the rate implied by two quotes and compare it with the third quote on offer. If they match, there is no triangular arbitrage.
Bid-ask rule for a customer using a bank's quote
You buy at the ask rate; you sell at the bid rate
Bid is the rate at which the bank buys the base currency. Ask is the rate at which the bank sells it.
Locational arbitrage gain
Gain per unit = Bid in the dearer centre − Ask in the cheaper centre
Positive only if the two spreads do not overlap. Multiply by the amount of currency traded.
Interest rate parity (simple interest)
Forward = Spot × (1 + i of quoted currency × n) ÷ (1 + i of base currency × n)
Here the rate is quoted as units of the quoted currency per one unit of the base currency. Use n in years, for example 0.5 for six months. Use the rates given for the period.
Covered interest arbitrage test
Actual forward vs parity forward
If actual forward is above parity, the base currency is dear forward; if below, it is cheap forward. Choose borrowing and investing currencies to match.
Arbitrage profit
Profit = Amount received at end − Amount owed at end (in the same currency)
Convert both to one currency using the forward rate before subtracting.

How to solve Forex Arbitrage Operations questions

Use this order for any forex arbitrage question. It keeps your cash flows clean and shows the examiner the reasoning.

  1. 1Identify the type: two centres (locational), three currencies (triangular), or spot, forward and interest rates (covered interest).
  2. 2Write each quote with its direction, for example ₹ per USD. Note bid and ask separately if given.
  3. 3Find the fair value: the cross rate for triangular, the parity forward for covered interest, or compare the spreads for locational.
  4. 4Compare fair value with the actual quote. If there is no gap, state that no arbitrage exists and stop.
  5. 5Start with a convenient amount, such as USD 1,00,000 or ₹1 crore, or the amount given. Trace each trade in order and use ask when you buy, bid when you sell.
  6. 6For covered interest, show four legs: borrow, convert at spot, invest, and settle the loan with a forward contract.
  7. 7Compute the closing amount and the opening obligation in the same currency and take the difference.
  8. 8State the profit and write a one-line conclusion naming the trades.

Quickest way: Round-trip check

When to use it: Use it when time is short, especially for triangular arbitrage with no bid-ask spread, to find the profit and the direction quickly.

  1. Start with one unit of your home currency, say ₹83 (or whatever sum is convenient).
  2. Run the loop one way through the three quotes, multiplying or dividing as the direction requires.
  3. If you end with more than you started, the loop is the arbitrage. If you end with less, run the loop in reverse.
  4. Example: USD/INR 83, EUR/USD 1.10, EUR/INR 92. The cross rate is 83 × 1.10 = 91.30, below 92. So ₹83 buys USD 1, which buys EUR 0.90909 (1 ÷ 1.10), which sells for ₹83.636 (0.90909 × 92). The gain is about ₹0.636 per ₹83.
  5. For covered interest, compute the parity forward once. Actual forward below parity means the base currency is cheap forward, so borrow the base currency and invest in the quoted currency. Actual forward above parity means the reverse.

Common mistakes in Forex Arbitrage Operations

  • Using the wrong side of the bid-ask quote

    Students forget the quote is from the bank's point of view.

    Fix: Remember: you buy at the ask and sell at the bid. Write 'buy at ask' or 'sell at bid' next to each leg.

  • Inverting a cross rate the wrong way

    Mixing up which currency is the base currency, for example confusing EUR/USD with USD/EUR.

    Fix: Write the unit of each quote, such as ₹ per USD or USD per EUR, and cancel units like fractions. The units that remain must match the target quote.

  • Applying an annual interest rate to a six-month deal

    The rate is quoted per annum and students use it as it stands.

    Fix: Multiply each annual rate by n (for example 6/12) in both the parity formula and the investment leg, unless the question gives period rates.

  • Choosing the wrong borrowing currency in covered interest arbitrage

    Students memorise a direction instead of testing it.

    Fix: Compute the parity forward and compare. Then confirm the direction by tracing the cash flows. A positive closing balance means you chose correctly.

  • Measuring profit in two different currencies

    The loan is repaid in one currency and the investment matures in another.

    Fix: Convert the maturity proceeds into the loan currency at the forward rate (or the reverse) and subtract in one currency only.

  • Forcing an arbitrage when none exists

    Students expect every question to have a profit and ignore the spreads.

    Fix: After applying bid and ask, if the round trip returns less than the start, say there is no arbitrage.

Worked examples

Example 1

A bank in Mumbai quotes USD/INR at ₹83.20 – ₹83.30 (bid – ask). A bank in Singapore quotes USD/INR at ₹83.45 – ₹83.55. Is there an arbitrage opportunity? If yes, find the profit on USD 10,00,000, ignoring transaction costs.

Show the solution
  1. Direction 1: buy USD in Mumbai at the ask of ₹83.30 and sell USD in Singapore at the bid of ₹83.45.
  2. Gain per USD = 83.45 − 83.30 = ₹0.15.
  3. Direction 2 check: buy in Singapore at ₹83.55 and sell in Mumbai at ₹83.20. This loses 83.55 − 83.20 = ₹0.35 per USD, so it is not used.
  4. Profit on USD 10,00,000 = 10,00,000 × 0.15 = ₹1,50,000.

Answer: Arbitrage exists. Buy USD in Mumbai at ₹83.30 and sell in Singapore at ₹83.45. The profit is ₹1,50,000 on USD 10,00,000.

Example 2

Spot USD/INR is ₹83.00. The 6-month forward rate is ₹84.50. The 6-month interest rate is 8% p.a. in India and 4% p.a. in the USA (simple interest). Ignoring spreads, is there a covered interest arbitrage opportunity? Show the profit on a USD 1,00,000 loan.

Show the solution
  1. Six-month rates: India 8% × 6/12 = 4%; USA 4% × 6/12 = 2%.
  2. Parity forward = 83.00 × 1.04 ÷ 1.02 = ₹84.6275 (approx.).
  3. The actual forward of ₹84.50 is below parity, so USD is cheap forward. Borrow USD, invest in rupees, and buy USD forward.
  4. Today: borrow USD 1,00,000 at 2% for six months. The repayment due is USD 1,02,000.
  5. Convert at spot: USD 1,00,000 × 83.00 = ₹83,00,000 and invest in India at 4% for six months. Maturity = 83,00,000 × 1.04 = ₹86,32,000.
  6. Forward cover: buy USD 1,02,000 at ₹84.50 = ₹86,19,000 to repay the loan.
  7. Profit = 86,32,000 − 86,19,000 = ₹13,000.

Answer: Arbitrage exists. Borrow USD at 2% for six months, convert at spot, invest in India at 4%, and buy USD forward at ₹84.50. The risk-free profit is ₹13,000.

Exam tips

  • Write the quote units (₹ per USD) beside every rate. It prevents most inversion errors.
  • Read the question for the amount to trade. If none is given, pick a round figure and state it.
  • In covered interest problems, show the parity forward first. It earns method marks even if the later cash flows slip.
  • Always end with a statement of the arbitrage route and the profit, or a clear 'no arbitrage' conclusion. Examiners expect a recommendation.
  • Check whether interest rates are annual and the period is shorter than a year, and whether the question asks for profit in rupees or dollars.

Practice questions from Foreign Exchange Market

Forex Arbitrage Operations in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Forex Arbitrage Operations: frequently asked questions

How do I know which currency to borrow in covered interest arbitrage?

Compute the parity forward and compare it with the actual forward. If the actual forward makes the base currency cheap, borrow that currency, convert and invest in the other, and buy the base currency forward. Then trace the cash flows to confirm the profit is positive.

What is the difference between locational and triangular arbitrage?

Locational arbitrage uses one currency pair quoted differently in two places. Triangular arbitrage uses three currencies, where the cross rate implied by two quotes does not match the third quote. The first needs two trades, and the second needs three.

Do I need a starting capital for arbitrage problems?

In theory arbitrage needs no net investment of your own money, because you fund the trades by borrowing or by selling what you buy. In exam answers you still choose a convenient amount, such as USD 1,00,000, to show the working and profit.

Can arbitrage opportunities last in real markets?

Rarely for long. Traders act on any gap, and their trades move prices back into line. Costs and spreads also remove many small gaps. Exam questions are set with a clear gap so you can practise the method.