Limited Time Offer: Save 10% on all 2021 and 2022 Premium Study Packages with promo code: BLOG10    Select your Premium Package »

Calculate and Interpret a Forward Discount or Premium

Calculate and Interpret a Forward Discount or Premium

Forward Discount

A forward discount is when the domestic current spot exchange rate is traded at a higher level than the current domestic future spot rates. The analysis of the expectations from the market depends mostly on discounts and premiums. Also, they enable one to know the currencies that should appreciate and those that will depreciate in the near future.

Forward Premium

A forward premium is a situation when the forward exchange rate is higher than the spot exchange rate. Conversely, a forward discount is when the forward exchange rate is lower than the spot exchange rate.

Irrespective of the quoting convention, the currency with the higher (lower) interest rate will always trade at a discount (premium) in the forward market.

Calculation

Interest parity states that both the spot and forward exchange rates between two currencies must be at equilibrium with the two nation’s interest rates. The formula includes four variables:

$$F_{f/d} = S_{f/d} (\frac{1 + i_f}{1 + i_d})$$

Where

\(S_{f/d}\) = current spot exchange rate

\(F_{f/d}\) = current forward exchange rate

\(i_d\) = domestic interest rate

\(i_f\) = foreign interest rate

We can rewrite the above equation to show the forward rate as a percentage of the spot rate:

$$\frac{F_{f/d}}{S_{f/d}} = \frac{1 + i_f}{1 + i_d}$$

It is easy to see that, given the foreign/domestic convention (f/d), the forward rate will be at a premium to the spot rate if the foreign interest rates are higher than the domestic interest rate.

Let’s say the current Kenyan Shilling to Ugandan Shilling exchange rate is Sh 100. The domestic interest rate in Kenya is 5%, and the foreign interest rate is 4.75%, causing the resulting equation to be:

$$F = \text{Ksh} 100 (\frac{1.0475}{1.05}) = \text 99.7619$$

The forward rate relates to the spot rate by a premium or discount, which is proved in the following relationship:

$$F = S (1 + x)$$

Where F is the current premium or discount.

Spot exchange rates differ from the forward currency exchange rates. When the forward currency exchange rate happens to be higher than the spot rate, then the currency is said to be at a premium. Conversely, discounts occur when the spot rates are higher than the forward exchange rates. Hence, a negative premium is equal to a discount.

A simpler way to look at it is when \(F/S – 1 > 0\), the denominator is at a discount. When \(F/S – 1 < 0\), the denominator is at a premium, and the numerator is at a discount. For instance, if we want to ascertain the premium of a forward trading rate, we can also do that using the formula below:

$$F_{f/d}=S_{f/d} (\frac{1 + i_f τ}{1+i_d τ})$$

Where (1 + i_f τ) is the interest earned in the foreign market and (1 + i_d τ) is the interest earned in the domestic market. Where τ is the fraction of the investment horizon at which the interest rates are quoted.

Example: Forward Discount or Premium

If we want to know the 31-day forward exchange rate from a 31-day domestic risk-free interest rate of 2.5% per year, given that the foreign 31-day risk-free interest rate is 3.5% with a spot exchange rate, \(S_{f/d}\), of 1.5630, then we simply have to substitute these values into the forward rate equation:

$$F_{f/d}=S_{f/d} (\frac{1 + i_f τ}{1+i_d τ})$$

$$F_{f/d}=1.5630 (\frac{1+0.035×\frac{31}{360}}{1+0.025×\frac{31}{360}})=1.5643$$

Hence, the forward trading premium is:

$$F_{f/d} – S_{f/d} = 1.5643 – 1.5630 = 0.0013$$

Since forward premiums or discounts are usually quoted in pips or points (1/100 of 1%), multiplying the result by 10,000 will give us \(0.0013 \times 10,000 = 13\) pips, which is the forward trading premium quoted in pips or points.

Question

When is a foreign currency most likely trading at a forward premium?

A. When the forward rate expressed in the domestic currency is below the spot rate.

B. When the forward rate expressed in the domestic currency is above the spot rate.

C. When the forward rate expressed in the foreign/domestic currency is at equilibrium.

Solution

The correct answer is B.

A foreign currency is at a forward premium if the forward rate expressed in domestic currency is above the spot rate.

Featured Study with Us
CFA® Exam and FRM® Exam Prep Platform offered by AnalystPrep

Study Platform

Learn with Us

    Subscribe to our newsletter and keep up with the latest and greatest tips for success
    Online Tutoring
    Our videos feature professional educators presenting in-depth explanations of all topics introduced in the curriculum.

    Video Lessons



    Sergio Torrico
    Sergio Torrico
    2021-07-23
    Excelente para el FRM 2 Escribo esta revisión en español para los hispanohablantes, soy de Bolivia, y utilicé AnalystPrep para dudas y consultas sobre mi preparación para el FRM nivel 2 (lo tomé una sola vez y aprobé muy bien), siempre tuve un soporte claro, directo y rápido, el material sale rápido cuando hay cambios en el temario de GARP, y los ejercicios y exámenes son muy útiles para practicar.
    diana
    diana
    2021-07-17
    So helpful. I have been using the videos to prepare for the CFA Level II exam. The videos signpost the reading contents, explain the concepts and provide additional context for specific concepts. The fun light-hearted analogies are also a welcome break to some very dry content. I usually watch the videos before going into more in-depth reading and they are a good way to avoid being overwhelmed by the sheer volume of content when you look at the readings.
    Kriti Dhawan
    Kriti Dhawan
    2021-07-16
    A great curriculum provider. James sir explains the concept so well that rather than memorising it, you tend to intuitively understand and absorb them. Thank you ! Grateful I saw this at the right time for my CFA prep.
    nikhil kumar
    nikhil kumar
    2021-06-28
    Very well explained and gives a great insight about topics in a very short time. Glad to have found Professor Forjan's lectures.
    Marwan
    Marwan
    2021-06-22
    Great support throughout the course by the team, did not feel neglected
    Benjamin anonymous
    Benjamin anonymous
    2021-05-10
    I loved using AnalystPrep for FRM. QBank is huge, videos are great. Would recommend to a friend
    Daniel Glyn
    Daniel Glyn
    2021-03-24
    I have finished my FRM1 thanks to AnalystPrep. And now using AnalystPrep for my FRM2 preparation. Professor Forjan is brilliant. He gives such good explanations and analogies. And more than anything makes learning fun. A big thank you to Analystprep and Professor Forjan. 5 stars all the way!
    michael walshe
    michael walshe
    2021-03-18
    Professor James' videos are excellent for understanding the underlying theories behind financial engineering / financial analysis. The AnalystPrep videos were better than any of the others that I searched through on YouTube for providing a clear explanation of some concepts, such as Portfolio theory, CAPM, and Arbitrage Pricing theory. Watching these cleared up many of the unclarities I had in my head. Highly recommended.