Covered Interest Arbitrage and Forward Rates

A bank that agrees today to sell you dollars in a year at a fixed rate has taken on a risk: if the dollar rises, the bank loses. It can remove that risk by buying dollars now, putting them on deposit to earn dollar interest until it must deliver them, and funding the purchase by borrowing naira.

What the bank earns and pays on those deposits and loans is what fixes the forward rate. The forward rate is the spot rate adjusted for the difference between the two interest rates. If a forward rate were quoted away from that level, anyone could borrow in one currency, lend in the other, lock in the rate for converting back, and make a profit with no risk.

That is covered interest arbitrage. It is also why forward rates cannot differ from interest rate parity for long. This topic explains how forward rates are derived and quoted (premiums and discounts and forward points), how to use them, the test for an arbitrage opportunity, a step-by-step covered interest arbitrage in both directions, why the profit is risk-free, and what limits it in practice, with worked examples. The next topic covers internal hedging of foreign exchange risk.

The covered interest parity test, the arbitrage profit and the reason why the profit is risk-free were parts of May Diet, 2026, Question 4 (20 marks). Read purchasing power parity, interest rate parity and four-way equivalence first.

Forward rates and forward contracts

Banks deal in foreign currency for immediate delivery at the spot rate and for future delivery at a forward rate. A forward exchange contract is an agreement made now between a customer and a bank to buy or sell a specified amount of a specified currency, on a specified date (or within a specified period), at a specified rate.

The customer chooses the amount and date; the bank sets the rate. Rates are commonly quoted for one, three and six months and a year, and contracts of more than a year are unusual except in the most heavily traded currencies.

The forward rate is calculated from the spot rate and the interest rates in the two currencies by the interest rate parity formula, because banks can borrow and lend in the money markets. With a spot rate of ₦1,345/$1, a naira rate of 20% and a dollar rate of 4.5%, the one-year forward rate is 1,345 × 1.20 ÷ 1.045 = ₦1,544.50.

It is higher than spot, so the dollar is at a forward premium and the naira at a forward discount: the currency with the higher interest rate is the one at a discount. A forward rate is not a forecast of the future spot rate; it is a price that follows from interest rates.

Premiums, discounts and forward points

Forward rates are usually quoted as an adjustment to spot, in points, with a premium (pm) when the foreign currency is stronger forward and a discount (dis) when it is weaker. How the adjustment is applied depends on the quote:

Example (direct quote): the spot rate is ₦1,340 – ₦1,350 per $1 and the three-month dollar is at a premium of 40 – 45 points. Forward rates: ₦1,380 – ₦1,395. A company that must buy $200,000 in three months pays the bank’s offer rate, 200,000 × 1,395 = ₦279,000,000; one that will sell $200,000 receives the bid rate, 200,000 × 1,380 = ₦276,000,000. Either fixes the naira amount today.

Example (indirect quote): a UK company will receive $90,000 in six months. Spot is $1.2950 – $1.3050 per £1 and the six-month dollar is at a premium of 150 – 140 points (0.0150 – 0.0140). With an indirect quote the premium is deducted: forward rates are 1.2950 − 0.0150 = 1.2800 and 1.3050 − 0.0140 = 1.2910. The company sells dollars to the bank, which uses the rate more favourable to itself, 1.2910 dollars per pound: £69,713.

(If you cannot tell which rate the bank will use, decide from the spot rates, as the bank always uses the rate that favours itself.) Points may be quoted in different units from the rate, such as cents against a rate in dollars, so check the decimal places.

Testing for an arbitrage opportunity

If the market’s forward rate equals the parity rate, there is no arbitrage. With a direct quote, parity requires 1 + i_d = (1 + i_f) × F ÷ S₀: investing at home for the period should give the same as converting, investing abroad and selling the proceeds forward. Compare the two sides:

• If 1 + i_d is less than (1 + i_f) × F ÷ S₀, borrowing at home is cheaper than the covered return abroad: borrow the domestic currency, invest abroad and cover.
• If 1 + i_d is greater, the covered foreign investment is worth less than the domestic one: borrow the foreign currency, invest at home and cover.

Take spot ₦1,345/$1, one-year forward ₦1,500, naira interest 20% and dollar interest 4.5%. The parity forward rate would be ₦1,544.50, but the market rate is only ₦1,500, so the dollar is too cheap forward. Test: 1 + i_d = 1.20; (1 + i_f) × F ÷ S₀ = 1.045 × 1,500 ÷ 1,345 = 1.1654. They differ, and 1.20 is greater, so the opportunity is to borrow the foreign currency.

Covered interest arbitrage step by step

Covered interest arbitrage borrows in the currency with the lower covered cost, invests in the other, and fixes the exchange back with a forward contract. For the case above (borrow dollars), with $1,000,000:

1. Borrow $1,000,000 for one year at 4.5%: repayment due $1,045,000.
2. Convert.
   at the spot rate: 1,000,000 × 1,345 = ₦1,345,000,000.
3. Invest.
   the naira for a year at 20%: ₦1,345,000,000 × 1.20 = ₦1,614,000,000.
4. Sell the naira forward.
   (buy dollars forward) at ₦1,500: 1,614,000,000 ÷ 1,500 = $1,076,000.
5. Repay. the loan of $1,045,000.
   The profit is 1,076,000 − 1,045,000 = $31,000 (about ₦46.5 million at ₦1,500).

As a formula, profit = amount borrowed × [(1 + i_d) × S₀ ÷ F − (1 + i_f)] = 1,000,000 × (1.20 × 1,345 ÷ 1,500 − 1.045) = 1,000,000 × (1.076 − 1.045) = $31,000.

The opposite case: the forward rate is ₦1,600, above parity. Now (1 + i_f) × F ÷ S₀ = 1.045 × 1,600 ÷ 1,345 = 1.2431, which is greater than 1.20, so borrow naira. Borrow ₦1,345,000,000 and owe ₦1,614,000,000 after a year; convert at spot to $1,000,000; invest at 4.5% to $1,045,000; sell forward at ₦1,600 for ₦1,672,000,000; repay ₦1,614,000,000; profit ₦58,000,000.

Why the profit is risk-free, and what limits it

Every amount, interest rate and exchange rate in the transaction is fixed at the start: the loan rate, the deposit rate, the spot rate for converting, and the forward rate for converting back.

Nothing is left to chance (the spot rate used for the conversion is the one at which the deal is made), so the profit is known in advance and needs no capital of the arbitrageur, since the loan funds the deposit.

Because it is risk-free and costs nothing, everybody would want to do it:

• borrowing in the cheap currency pushes up its interest rate
• investing in the other pushes down its rate
• buying spot and selling forward moves the spot and forward rates towards parity

The profit disappears quickly, which is why markets are close to parity in practice.

In practice the opportunity is limited by transaction costs (bid-offer spreads on spot and forward, borrowing at a higher rate than lending), exchange controls and restrictions on borrowing or investing, tax, counterparty and settlement risk, and the fact that a bank must have the credit lines.

In Nigeria, forward-type contracts in naira are available only through authorised dealers, and rules on borrowing and conversion apply, so the arbitrage is not freely available to most firms.

The ideas in more depth

Why the forward rate equals the interest rate parity rate

Two ways of turning today’s naira into naira in a year with no risk must give the same result: deposit at the naira rate, or convert to dollars, deposit at the dollar rate and sell the dollars forward. If they did not, one would be strictly better and arbitrage would continue until they were equal.

This is why the forward rate depends on the spot rate and the two interest rates and not on anyone’s opinion about where the exchange rate will go.

Why a company can use the forward rate as a price but not a forecast

A forward contract fixes the naira cost of a future dollar payment, removing the uncertainty. But the forward rate already includes the cost of the interest difference, so it is typically worse than today’s spot rate for a currency at a premium.

A treasurer who hedges accepts that cost for certainty and cannot say that the contract has “saved” money unless the future spot rate turns out to be worse; hindsight comparisons are misleading.

Sources and references

• Interest rate parity (Keynes, 1923). The Central Bank of Nigeria regulates authorised dealers in foreign exchange and the products they may offer; the rates in the examples are illustrative.

These points are stated as at 5 November 2026.

Worked examples

1. Direct quote: add the premium.
   1,340 + 40 = 1,380
   1,350 + 45 = 1,395.
2. Forward rates. ₦1,380 – ₦1,395.

1. Compare.
   1.20 against 1.045 × 1,500 ÷ 1,345 = 1.1654.
2. Direction. 1.20 is greater, so borrow dollars.

1. Covered proceeds.
   1,000,000 × 1.20 × 1,345 ÷ 1,500 = $1,076,000.
2. Profit.
   1,076,000 − 1,045,000 = $31,000.

How to answer in the exam

• Do the test first, showing both sides and which is greater.
• State what to borrow and set out the steps in order with the amounts.
• Compute the profit in one currency and check it with the formula.
• Explain why it is risk-free and what limits it in practice.

Common mistakes in the exam

• Borrowing the wrong currency, so that the answer shows a loss.
• Using the forward rate for the first conversion or the spot rate for the last.
• Adding forward points to an indirect quote that should be deducted.
• Forgetting the interest on the loan.
• Mixing the currencies in the profit calculation.
• Saying the profit is risk-free without giving the reason.

Quick revision

• Forward rate = spot adjusted for the interest difference; higher-interest currency at a discount.
• Direct quote: add premium, deduct discount; indirect quote the reverse.
• Test: 1 + i_d against (1 + i_f) × F ÷ S₀; borrow the currency with the lower covered cost.
• Profit is known at the start; arbitrage drives rates to parity.

Practice questions

These are original questions written in the style of the Institute’s exams. Try each one before you open the answer. Section A is a recall check, because the paper itself is written.

Recall check: multiple choice

Section B style: written questions

A further written question

Model answers

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