# Forward Premium and Discount

Forward premium is when the forward exchange rate is higher than the spot exchange rate. Forward discount is the opposite of forward premium, it when the forward exchange rate is lower than the spot exchange rate. Forward premium or discount is normally expressed as annualized percentage of the difference.

When the exchange rate is quoted as D/F, where D i.e. price currency is the domestic currency and F i.e. the base currency is the foreign currency and the forward exchange rate is higher than the spot rate, it means that the foreign currency is trading at a forward premium. It shows that the foreign currency has appreciated because it will take more units of the domestic currency to buy one unit of the foreign currency. An appreciation for foreign currency is the depreciation for domestic currency; hence, when the foreign currency trades at a forward premium, the domestic currency trades at a forward discount and vice versa.

Let’s say you are in Swiss market and the CHF/USD spot exchange rate is 0.9880 and 3-month forward exchange rate is 0.9895. It means that right now it takes 0.9880 Swiss Francs to buy 1 US Dollar and in 3 months it will take 0.9895 Swiss Francs to buy 1 dollar, i.e. 0.0015 Swiss Francs more per 1 US Dollar. It shows that the foreign currency i.e. the US Dollar is trading at a forward premium because it takes more Swiss Francs to buy US Dollar in future. The CHF is trading at forward discount because 1 Swiss Franc is worth less in future.

## Formula

We can use the following formula to work out the percentage forward premium or (discount) for the foreign currency, i.e. the currency in the denominator:

$$ Forward\ Premium =\frac{{\rm Forward}_\frac{D}{F}-{\rm Spot}_\frac{D}{F}}{{\rm Spot}_\frac{D}{F}} $$

When the result is positive, it is a forward premium and when its negative, it is the forward discount.

Using the example above, we can find out that the forward premium for USD is +0.15%:

$$ Forward\ Premium=\frac{0.9895-0.9880}{0.9880}=+0.15\% $$

Because we get a positive figure, the foreign currency (i.e. USD) trades at a forward premium.

Let’s convert the above quotes to USD/CHF i.e. foreign currency in numerator and domestic currency in numerator: the spot exchange rate works out to 1.0121 (=1/0.9880) and 1.0106 (=1/0.9895). By just looking at the figure we can conclude that US Dollar trades at a forward premium because it takes less USD (1.0106 is less than 1.0121) to buy CHF in 3 month.

When the indirect quote is used i.e. when the price is expressed in foreign currency terms, the formula for forward premium or discount is different:

$$ Forward\ Premium =\frac{\frac{1}{{\rm Spot}_\frac{D}{F}}-\frac{1}{{\rm Forward}_\frac{D}{F}}}{\frac{1}{{\rm Spot}_\frac{D}{F}}}\\=\frac{S_\frac{F}{D}-F_\frac{F}{D}}{F_\frac{F}{D}}=\frac{1.0106-1.0121}{1.0121}=-0.15\% $$