# Forward premium or discount - when is it "discount" vs "premium"?

I know this has been asked but i didn’t see a clear answer.

Say you have the dollar/eur at 1.10 spot and 1.25 1 year forward. so F/S - 1 is 13.636%, which is a positive number, yet the implication is that the dollar should depreciate since it will take more dollars in one year to make a euro. Intuitively I would say this means the dollar is at a forward DISCOUNT since it will depreciate, however I think I have seen some problems refer to it as a forward premium simply because the equation is positive, so in that case premium = depreciate…

What is the consensus here?

dollar is trading at a discount.

F/S-1 --> if positive - denominator is at premium (numerator at discount)

F/S - 1 --> if negative - denominator at discount (numerator at premium)

numerator / denominator is based on the Quote Dollar / Euro in this case - Dollar = numerator, Euro = Denominator.

US interest rate is 5%

China interest rate is 10%

The Yuan is trading at a forward discount.

Please see number 6.) A on page 149 of Book 4 CFAI 2011.

Dollar/Euro spot = 1.21

Dollar/Euro 1 year forward = 1.18

A.) Calculate the amount of the current forward exchange discount or premium -

Answer: The current discount rate is -2.48%

Yet the Dollar is strengthening relative to the EUR in one year.

that is explained by my explanation fine…

-2.48% is DISCOUNT of EURO WRT Dollar (Denominator of Dollar / Euro)

and 2.48% PREMIUM of Dollar WRT Euro.

F/S-1 –> if positive - denominator is at premium (numerator at discount)

F/S - 1 –> if negative - denominator at discount (numerator at premium)

Dollar is trading at a 2.48% discount to the euro. Therefore, the dollar should appreciate.

Spot = EUR 0.826/\$

Forward = EUR 0.847/\$

Dollar should strengthen.

.

This helped me out:

Note: Exchange rates can be quoted two ways:

e = ¥ / , or the **Foreign Currency per U.S **. When e gets bigger (100 to 120), dollar gets stronger, appreciates in value (and the Yen depreciates). \$1 will buy more foreign currency, or it takes more Yen to buy a \$1. When e gets smaller (100 to 80), dollar gets weaker, depreciates in value (and the Yen appreciates). \$1 will buy fewer Yen, or it takes fewer Yen to buy a \$1. Just like a price of \$2/gallon of gasoline, when the P gets bigger the value (price) of gas increases (it’s in the denominator), when P gets smaller the value (price) of gas decreases.

e = / £ (British pound), or the **U.S. equivalent** , or U.S. Dollars per national currency unit. When this e gets bigger, the £ get stronger (appreciates) and the dollar gets weaker (depreciates), because it takes more dollars to buy a £. When e gets smaller, the £ depreciates and the dollar gets stronger. It costs less for us, in U.S. \$, to buy a pound.

POINT:** 1. When e (exchange-rate) gets bigger, the currency in the DENOMINATOR gets stronger (appreciates).**2. When e (exchange-rate) gets smaller, the currency in the DENOMINATOR gets weaker (depreciates).

CPK, they don’t guide you by asking what the discount or premium is on the euro, they just ask what the discount or premium is in general. Since it is usually quoted in domestic/foreign, and they give you dollar/euro, I assume they are asking for the forward discount or premium on the dollar. In which case I would say (as verified by your equation) that the dollar is at a forward premium.

Even now we are all in disagreement. Mr-Z just said that the dollar is at a discount, meaning it will appreciate.

This notation is stupid. We can all easily agree that the dollar will appreciate, so when a currency is set to appreciate by the forward market, does that mean it is trading at a premium or discount? This stupid nuance is frustrating me. Lets forget about the numbers and just try to agree on this concept –

i think when currency is expected to appreciate it should trade at a premium and vice versa

I think the “premium” is not the premium of currency in spot market. The forward premium or discount just tell us if the currency forward is traded at a premium or discount relative to the spot exchange rate.

It’s does not tell what the currency exchange rate will be when the orward expires. In case of Q6, the dollar could depreciate or depreciate. The arbitrager won’t care, they will make \$ if IRP doesn’t hold – it doesn’t hold in Q6.

IMO, since Euro is in denominator, its a forward price of Euro. Now since Forward Euro is less than Spot Euro, it is selling at a discount (depreciating). Conversely, Dollar is selling at a premium (appreciating).

CPK’s equations are also holding good

F/S - 1 less than 0 - Numerator is at premium - Denominator is at discount

F/S - 1 greater than 0 - Numerator is at discount - Denominator is at premium

Suppose Spot is 1.4926 (SFr/) & forward is 1.5423 (SFr/)…so dollar forward is greater than spot, it is selling at a premium (appreciating - in forward one \$ is buying more SKr) & SFr is at a discount.

Also 1.5423 / 1.4926 - 1 = 0.03 > 0, so Numerator is at discount - Denominator is at premium