Forward Exchange Rates and Forward Premiums

Why Forward Quotations Need a Currency Convention

A forward exchange rate is a rate agreed today for exchanging currencies on a specified future date. It can help a firm plan a future payment or receipt: for example, a business expecting to pay a foreign supplier may agree now on the exchange rate for that future payment. The forward rate is not the same thing as a prediction of the future spot rate. It is a contractual quotation for a specified maturity.

A quotation is meaningful only when its currency order is clear. If a rate is stated as domestic currency per unit of foreign currency, a rise in the number means that one unit of foreign currency costs more domestic currency. A forward rate above spot then indicates a forward premium for the foreign currency in this quotation convention. Reversing the currency order changes the interpretation and the premium calculation.

Forward Premiums and Discounts

The raw difference \(F-S\) measures the forward movement in the quoted exchange rate, but it is expressed in exchange-rate units. To compare movements across different spot-rate levels, divide by the spot rate. This gives the percentage change in the quoted rate over the contract period. To compare contracts with different maturities, that percentage change is often annualized.

For this tutorial, use a 360-day year unless a problem specifies another convention. If the contract matures in \(n\) days, the simple annualized forward premium (or discount) is:

The unannualized percentage movement over the contract period is \(\frac{F-S}{S}\times100\%\). A positive result is a premium in the stated quotation convention; a negative result is a discount. This is simple annualization: it scales the contract-period percentage by \(360/n\), rather than compounding it. If the contract uses a different day-count convention, use the number of days in that stated convention instead.

The formula’s denominator is the spot rate because the question is how large the forward rate’s change is relative to today’s quoted rate. For example, a difference of 0.02 is a larger proportional change from a spot rate of 1.00 than from a spot rate of 2.00. Dividing by spot captures that distinction. The annualization factor then expresses the contract-period proportional change on a common annual basis.

Reading Outright Rates and Forward Points

An outright forward rate is the full exchange-rate quotation for the specified maturity. Some quotations instead present forward points, the amount to add to or subtract from the spot rate to obtain the outright forward rate. Points are quoted in exchange-rate units, not as a percentage. Their scale must be supplied or understood from the quotation convention; do not assume a pip size without checking it.

For instance, if the quote is domestic currency per unit of foreign currency and the forward points are positive, adding them makes the foreign currency more expensive in domestic currency terms. The calculation of a premium or discount still uses the resulting outright forward rate, not the points alone:

The sign of the points describes the direction of the change in the quoted rate. The percentage premium or discount describes the size of that change relative to spot and adjusted for maturity. These are related but different pieces of information.

What Happens When the Quote Is Reversed?

A currency pair can be quoted in either order. Reversing the order means taking reciprocals of both rates. If the original quotation is domestic currency per foreign currency, the inverse quotation is foreign currency per domestic currency:

When \(F>S\), the reciprocal forward rate is below the reciprocal spot rate, so the sign of the premium or discount reverses. The percentage magnitude also changes because the inverse calculation uses the inverse spot rate as its denominator. Therefore, do not carry a premium percentage over unchanged when you reverse the currency order.

Worked Example: Converting Forward Points

A hypothetical exporter sees a spot rate of 0.9200 Swiss francs per euro. The three-month forward points are +18 pips, and the quotation convention defines one pip as 0.0001 Swiss francs per euro. Calculate the outright forward rate and its simple annualized premium using a 90-day maturity.

Method. Convert the points to exchange-rate units before adding them:

The outright forward rate is therefore \(F=0.9200+0.0018=0.9218\) Swiss francs per euro. The forward rate is above spot, consistent with a positive premium for the euro in this quotation. The contract-period percentage change is:

With a 90-day maturity, the annualization factor is \(360/90=4\). The annualized premium is \(0.195652\%\times4\approx0.782609\%\), or 0.783% to three decimal places. Check: adding 0.0018 to spot gives the stated outright rate, and its increase is positive. A common mistake is to treat “18 pips” as 18% or to annualize the points without first dividing the resulting rate change by spot.

Interpretation and Common Traps

A forward premium is a comparison between a forward quotation and today’s spot quotation for the same currency order. It is not, by itself, a statement that the future spot rate will rise by that amount. A forward contract specifies a rate for an exchange at a future date; the future spot rate is not known when the contract is made. Do not describe a forward premium as a guaranteed forecast or as a realized future appreciation.

Keep the following checks in mind when solving a quotation problem:

• Write the currency order. Label the units, such as CAD per USD. Then a higher quotation unambiguously means more CAD per USD.
• Use the same order for \(S\) and \(F\). If one rate is inverted, invert the other before comparing them.
• Use spot in the denominator. The proportional change is \((F-S)/S\), not \((F-S)/F\).
• Apply the stated maturity convention. A 90-day contract has factor \(360/90=4\) under a 360-day convention; it does not have a factor of 12 merely because it is three months.
• Distinguish points from percentages. Points are additions or subtractions in exchange-rate units. Convert them to an outright forward rate before finding the percentage.
• Label the result. State whether it is a contract-period percentage or an annualized percentage, and identify the currency convention.

The simple annualization in this tutorial is a standard way to compare quoted premiums or discounts across maturities. It is not a claim that the exchange-rate movement compounds at a constant rate over the year. If a question instead explicitly requests an effective annualized rate, it requires a compounding calculation and should not be answered by silently substituting that measure for simple annualization.