## What is a 'Forward Premium'

A forward premium occurs when dealing with foreign exchange (FX); it is a situation where the spot futures exchange rate, with respect to the domestic currency, is trading at a higher spot exchange rate then it is currently. A forward premium is frequently measured as the difference between the current spot rate and the forward rate, but any expected future exchange rate suffices.

It is a reasonable assumption to make that the future spot rate will be equal to the current futures rate. According to the forward expectation's theory of exchange rates, the current spot futures rate will be the future spot rate. This theory is routed in empirical studies and is a reasonable assumption to make over a long-term time horizon.

To calculate the forward premium on a currency, you first must understand covered interest parity and calculate the forward rate. Covered interest rate parity is a condition where the spot and forward exchange rates between two currencies are in equilibrium with the two countries' interest rates, preventing any arbitrage opportunities. The formula for covered interest rate parity includes four variables:

S = the current spot exchange rate

F = the current forward exchange rate

i(d) = the domestic interest rate

i(f) = the foreign interest rate

The formula is: (1 + i(d) = S / F x (1 + i(f)

This equation can then be rearranged to solve for the forward exchange rate, F. It appears as: F = S x (1 + i(f)) / (1 + i(d))

As an example, assume the current U.S. dollar to euro exchange rate is \$1.1365. The domestic interest rate, or the U.S. rate is 5%, and the foreign interest rate is 4.75%. Plugging the values into the equation results in: F = \$1.1365 x (1.05 / 1.0475) = \$1.1392

The forward rate relates to the spot rate by a premium or discount, which is shown in the following relationship: F = S x (1 + x), where z is the current premium or discount. Rearranging the formula, the forward premium, or discount if the result is negative, is calculated as: x = F / S - 1

However, since premiums are quoted as annualized percentages, the formula must take into account the number of days the contract stipulates. The formula is then adjusted to: x = (F / S - 1) x (360 / d), where d is the number of days.

Back to the example, assume the calculated forward rate is for a six-month forward for the euro versus the dollar, deliverable in 30 days. In this example, the forward premium is: x = (\$1.1392 / \$1.1365 - 1) x (360 / 30) = 2.851%

The result means the euro is trading at a 2.851% premium to the dollar for delivery in 30 days.