FX forwards and covered interest parity · RiskAtoms Academy

By the end you will be able to

1Price an FX forward from the spot rate and the two currencies' interest rates.
2Explain why the higher-yielding currency trades at a forward discount, and why a forward is not a forecast.
3Apply money-market day counts and read forward points.
4Show how a mispriced forward creates a riskless arbitrage.

Why it matters

A German machine maker will be paid one million US dollars in a year. Its bank offers to fix, today, how many euros those dollars will buy. Where does that rate come from? Not from anyone's view of the dollar. It comes from two interest rates.

Core explanation

Two safe routes must meet

An FX forward is an agreement made today to swap two currencies on a later date, at a rate fixed today. Companies use forwards to remove the guesswork from future payments. Investors who buy foreign bonds use them to lock in the value of the coupons in their own currency.

A story with two routes. Suppose you have one euro today and want US dollars in a year, with no risk at all. You could:

Deposit, then convert. Put the euro in a euro deposit for a year, and agree today a forward rate to turn the proceeds into dollars.
Convert, then deposit. Swap the euro into dollars today at the spot rate, and put the dollars in a dollar deposit for a year.

Both routes start with one euro, end with dollars on the same date, and carry no risk. So they must end with the same number of dollars. If one route paid more, traders would borrow to use it, again and again, and their trades would move prices until the gap closed. A trade like that, with a sure profit and no money of your own, is called arbitrage.

The rule that results is covered interest parity (CIP). “Covered” means the currency risk is covered by the forward: nothing is left to chance.

The intuition in one line

The currency with the higher interest rate trades at a forward discount; the one with the lower rate trades at a forward premium. The forward takes back, in the exchange rate, the extra interest you would earn.

Think about why. With dollar rates above euro rates, route 2 earns more interest. For the routes to match, route 1 must make up for it with a better forward rate: more dollars per euro. So the forward EUR/USD sits above spot. The euro is at a forward premium and the dollar at a forward discount.

A forward is not a forecast. Nothing in the argument mentions where anyone expects the exchange rate to go. The forward is pinned down by spot and the two interest rates. Many people read a forward above spot as a prediction that the base currency will rise. It is not.

Forward points. Dealers usually quote the difference between forward and spot, in pips, rather than the full rate. These are forward points. A three-month EUR/USD quote of “+54.5 points” on a spot of 1.0850 means a forward of 1.0905.

FX swaps. Banks and investors often do a spot trade and an opposite forward together, for example sell dollars for euros today and buy them back in three months. This is an FX swap, a way to borrow one currency against another. FX swaps are the most traded FX instrument of all, and they are priced off the same forward points.

The formal version

We need four letters. $S$ is the spot rate and $F$ the forward rate, both written BASE/QUOTE. $r_B$ is the base currency's interest rate and $r_Q$ the quote currency's. $T$ is the time to delivery in years. The powers are the compound growth from L1.3.02.

The money-market version. For deliveries up to a year, dealers use simple interest and each currency's own day count (L1.3.06): ACT/360 for the US dollar and the euro, ACT/365 for sterling and the yen. Replace each growth factor with its simple-interest version:

F = S \times \frac{1 + r_Q \times \dfrac{\text{days}}{\text{basis}_Q}}{1 + r_B \times \dfrac{\text{days}}{\text{basis}_B}}

Forward points. Subtract spot and rescale. For small rates and short periods a rough guide follows, which shows that the points grow with the rate gap and with time:

F - S = S \times \frac{(r_Q - r_B)\,\tau}{1 + r_B\,\tau} \;\approx\; S \times (r_Q - r_B) \times \tau

Here $\tau$ is the year fraction, taken on one basis for both currencies to keep the approximation simple.

Try it

Start with EUR/USD at three months. Slide the euro rate up until it equals the dollar rate and watch the forward points vanish. Then switch to USD/JPY, where the base currency has the higher rate. Finally, type a dealer quote a few points away from parity and see the arbitrage.

Try itForward rate calculator

Currency pair

Spot EUR/USD

Days to delivery91 days

EUR rate (base, ACT/360)2.50%

USD rate (quote, ACT/360)4.50%

Forward EUR/USD

1.0905

Spot1.0850

Forward points+54.5

USD growth1.011375

EUR growth1.006319

EUR trades at a forward premium: its interest rate is lower.

Forward rate by delivery dateDashed line: spot. The gap grows with time.

Is the dealer's forward fair?

Dealer quotes EUR/USD for 91 days

Within half a point of parity: no riskless profit. Change the quote to see what an arbitrageur would do.

Simple money-market interest, each rate on its own day count: USD and EUR ACT/360, GBP and JPY ACT/365. Rates are illustrative. Forward points are (forward − spot) in pips. The arbitrage check assumes you can borrow and lend at the same rates, with no spreads or fees.

Worked example

Pricing EUR/USD forwards

Spot EUR/USD is 1.0850. The US dollar rate is 4.50% and the euro rate is 2.50%. All rates are illustrative.

One year, annual compounding

Step 1 of 4

1
Which rate goes where?
EUR is the base, so $r_B = 2.5\%$ . USD is the quote, so $r_Q = 4.5\%$ . Quote on top, base underneath.

Three months (91 days), money-market convention

Step 1 of 4

1
Day count
Both currencies use ACT/360, so the year fraction is 91 ÷ 360 on each side.

Route for EUR 1,000,000 (3M)	Dollars at delivery
Deposit euros, sell forward at parity	1,097,342
Convert at spot, deposit dollars	1,097,342
Deposit euros, sell forward at the dealer's quote	1,098,901

The first two rows match: that is parity. The third beats them, which is why a dealer would not leave such a quote up for long.

Regulatory lens · looking ahead

FX forwards and swaps are over-the-counter derivatives. In many jurisdictions they must be reported to trade repositories (for example under EMIR in the EU), and banks hold capital against the risk that the other side fails before delivery. Module L1.7 Derivatives returns to forwards in general, and later levels cover counterparty credit risk.

Sparks

SparkThe textbook law that started to bend

For years before 2008, covered interest parity held almost exactly between major currencies. Since the global financial crisis, measurable gaps have persisted, especially around quarter-ends. Economists Wenxin Du, Alexander Tepper and Adrien Verdelhan documented them in 2018 and linked them to the cost of bank balance sheet space under the post-crisis rules. The gap has a name: the cross-currency basis.

SparkWhy a forecast would be a bad bet

If forwards were forecasts, the high-interest currency would be expected to fall. Studies have found that, over many periods, it has not fallen as much as the forward implies, or has even risen. This pattern, often called the forward premium puzzle, is the basis of the “carry trade”, which is not risk-free: carry trades can lose heavily when markets panic.

Key takeaways

An FX forward fixes today the rate for a future exchange of currencies.
Covered interest parity: $F = S \times (1+r_Q)^T / (1+r_B)^T$ , quote currency on top, base underneath.
The higher-yielding currency trades at a forward discount. A forward is not a forecast.
Up to a year, use simple interest with each currency's day count: ACT/360 for USD and EUR, ACT/365 for GBP and JPY.
Dealers quote forward points, F − S in pips. A forward away from parity offers a riskless arbitrage.

Reaction

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Glossary

FX forward: A contract agreed today to exchange two currencies on a later date at a rate fixed today, the forward rate.
Covered interest parity: The rule that a forward rate must equal spot scaled by the two currencies' interest growth, or a riskless profit would be possible.
Forward points: The forward rate minus the spot rate, written in pips. Dealers often quote these instead of the full rate.
Forward premium: A currency is at a forward premium when it buys more of the other currency forward than at spot.
Forward discount: A currency is at a forward discount when it buys less of the other currency forward than at spot.
Arbitrage: A set of trades that locks in a profit with no risk and no money of your own.
FX swap: A spot trade and an opposite forward trade done together: swap one currency for another now, and swap back later.

Deep Dives & Origins

Deep Dives

Hull, Options, Futures, and Other Derivatives, 11th edition (Pearson, 2021), the section on forward and futures contracts on currencies. Intermediate.
Du, Tepper and Verdelhan, “Deviations from Covered Interest Rate Parity”, Journal of Finance, 73(3), 2018. Advanced.

Origins

Hull, Options, Futures, and Other Derivatives, 11th edition (Pearson, 2021).
Borio, McCauley, McGuire and Sushko, “Covered interest parity lost: understanding the cross-currency basis”, BIS Quarterly Review, September 2016.
Bank for International Settlements, Triennial Central Bank Survey, 2022 and 2025 editions (FX swap turnover).

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