Understanding Spot and Forward Exchange Rates

Introduction

Welcome to our next lesson. In the previous session, we focused entirely on spot rates—the exchange rates for immediate currency conversion. We learned how to read quotes and, importantly, how to calculate cross-rates when a direct quote isn't available.

Today, we expand our view from the present to the future. Businesses and investors often need to lock in an exchange rate for a transaction that will occur weeks or months from now to avoid the risk of unfavorable currency movements. This is where forward exchange rates come in.

This lesson will teach you to distinguish between spot and forward exchange rates. Crucially, you will learn the market conventions for quoting forward rates and how to calculate forward premiums and discounts, both from market quotes and from the underlying interest rates of the two currencies. This blend of market mechanics and economic theory is central to the CFA curriculum.

1. Spot vs. Forward Exchange Rates: Hedging Future Risk

As we've established, a spot exchange rate is the price for a currency to be delivered today (or within two business days, by market convention).

A forward exchange rate is different: it is a rate agreed upon today for the delivery of a currency at a specified future date. This agreement is called a forward contract. Its primary purpose is to hedge, or protect against, currency risk.

To understand the motivation behind using a forward contract, let's watch a brief segment from an AnalystPrep video.

Exchange Rate Calculations (2025 CFA® Level I Exam – Economics – Learning Module 8)

This video introduces the core concept of the forward market by explaining why someone would want to lock in a future exchange rate to avoid risk.

Watch from 11:21 to 14:43. Focus on the example of planning a trip to Canada in six months and the risk that the exchange rate might move against you. This illustrates the fundamental purpose of a forward contract.

As the video explains, by entering into a forward contract, you eliminate the uncertainty of what the spot rate will be in the future. You lock in a guaranteed rate today.

2. Quoting Forwards: Points, Premiums, and Discounts

A forward rate can be higher or lower than the current spot rate. This leads to two key terms:

Forward Premium: The forward rate is higher than the spot rate. We say the base currency is trading at a forward premium.
Forward Discount: The forward rate is lower than the spot rate. We say the base currency is trading at a forward discount.

In professional currency markets, dealers don't usually quote the full forward rate (known as the "outright" rate). Instead, they quote the difference between the forward rate and the spot rate in units called points or pips.

This is more efficient. For example, if the USD/EUR spot rate is 1.0850, and the three-month forward rate is 1.0875, a dealer wouldn't quote the full number. They would just quote the forward points, which is the difference.

The calculation is:
Forward Points = (Forward Rate - Spot Rate) * Scale Factor

The scale factor is typically 10,000 for currencies quoted to four decimal places, and 100 for currencies quoted to two decimal places (like the Japanese Yen).

In our example: (1.0875 - 1.0850) * 10,000 = 25 points.
Since the points are positive, the base currency (EUR) is trading at a premium.

To reconstruct the outright forward rate from points, you just reverse the formula:
Forward Rate = Spot Rate + (Forward Points / Scale Factor)

The following video provides a very clear, step-by-step guide on how to work with forward points.

Level 1 CFA Economics: Currency Exchange Rates-Lecture 4

This video from IFT clearly explains the market convention of using points (or pips) and walks through how to calculate the outright forward rate.

Watch from the beginning to 05:38. Pay close attention to the distinction between the scale factor for most currencies (10,000) and for yen-pairs (100).

Practice Calculation 1

Let's apply this. A dealer provides the following quotes for the Australian Dollar vs. the US Dollar (AUD/USD):

Spot Rate: 0.6610
6-month Forward Points: -35.5

What is the 6-month outright forward rate for AUD/USD? Is the base currency (USD) trading at a premium or a discount?

Click here for the solution

Identify the components:
- Spot Rate = 0.6610
- Forward Points = -35.5
- Scale Factor = 10,000 (since the spot rate has 4 decimal places)
Calculate the outright forward rate:
$Forward Rate = 0.6610 + \frac{- 35.5}{10 , 000} = 0.6610 - 0.00355 = 0.65745$
The 6-month outright forward rate is 0.65745.
Determine premium or discount:
- The forward rate (0.65745) is lower than the spot rate (0.6610).
- Therefore, the base currency (USD) is trading at a forward discount. The negative sign on the points is the direct indicator of this.

3. The "Why": Interest Rate Parity

Why is a currency's forward rate higher or lower than its spot rate? The answer lies in the interest rates of the two countries. This relationship, known as Interest Rate Parity (IRP), is a cornerstone of international finance and is based on a no-arbitrage condition.

The logic is as follows: An investor with domestic currency has two risk-free options for a one-year investment:

Invest at the domestic risk-free interest rate.
Convert the currency at the spot rate, invest at the foreign risk-free rate for a year, and simultaneously lock in a one-year forward rate to convert the funds back.

Since both options are risk-free, they must have the same return. If they didn't, an arbitrageur could make risk-free profits, and their actions would quickly push the rates back into alignment. This no-arbitrage condition gives us the fundamental formula for the forward rate:

$F_{P / B} = S_{P / B} \times \frac{1 + i _{P}}{1 + i _{B}}$

Where:

$F_{P / B}$ is the forward rate (Price currency per Base currency).
$S_{P / B}$ is the spot rate.
$i_{P}$ is the interest rate of the price currency.
$i_{B}$ is the interest rate of the base currency.

The next video explains this no-arbitrage logic and derives this exact formula. It also presents a crucial rule of thumb for the exam.

Exchange Rate Calculations (2025 CFA® Level I Exam – Economics – Learning Module 8)

This AnalystPrep video explains the powerful no-arbitrage logic that connects spot rates, forward rates, and interest rates, leading to the Interest Rate Parity formula.

Watch from 19:07 to 26:53. Focus on understanding the two investment alternatives that must have equal returns. Most importantly, commit to memory the rule stated at the end: The currency with the higher interest rate will always trade at a discount in the forward market.

4. Adjusting the IRP Formula for Time

The formula above assumes a one-year time horizon. For any other period (e.g., 30, 90, or 180 days), you must adjust the interest rates to match the term of the forward contract. We do this by multiplying the annual interest rate by the fraction of the year.

The adjusted formula is:
$F_{P / B} = S_{P / B} \times \frac{1 + i _{P} \times ( \frac{days}{year} )}{1 + i _{B} \times ( \frac{days}{year} )}$
The day count convention is typically 360 days for money markets, but always follow what is specified in the exam question.

The next segment of the video shows a worked example of this calculation.

Exchange Rate Calculations (2025 CFA® Level I Exam – Economics – Learning Module 8)

Let's continue with the same video to see how to apply the Interest Rate Parity formula for periods other than one year.

Watch from 29:26 to 32:38. Observe how the annual interest rates are scaled by the time fraction (e.g., 31/360) before being used in the formula.

Practice Calculation 2

Let's tie this together with a problem. You are given the following information:

Spot Rate (CHF/GBP): 1.1250
180-day Swiss Interest Rate (i_CHF): 1.5% (annual)
180-day UK Interest Rate (i_GBP): 4.5% (annual)

Using a 360-day year, calculate the 180-day forward rate for CHF/GBP.

Click here for the solution

Identify the components:
- The quote is CHF/GBP. So, CHF is the price currency and GBP is the base currency.
- $S_{C H F / GB P} = 1.1250$
- $i_{P} = i_{C H F} = 1.5% = 0.015$
- $i_{B} = i_{GB P} = 4.5% = 0.045$
- Time fraction = $180/360 = 0.5$
Apply the IRP formula:
$F_{C H F / GB P} = S_{C H F / GB P} \times \frac{1 + i _{C H F} \times ( \frac{180}{360} )}{1 + i _{GB P} \times ( \frac{180}{360} )}$
Calculate:
$F_{C H F / GB P} = 1.1250 \times \frac{1 + 0.015 \times 0.5}{1 + 0.045 \times 0.5}$
$F_{C H F / GB P} = 1.1250 \times \frac{1 + 0.0075}{1 + 0.0225}$
$F_{C H F / GB P} = 1.1250 \times \frac{1.0075}{1.0225} \approx 1.1250 \times 0.98533$
$F_{C H F / GB P} \approx 1.1085$

The 180-day forward rate is approximately 1.1085.
Quick Sanity Check: The interest rate is higher in the UK (base currency) than in Switzerland (price currency). As per our rule, the currency with the higher interest rate (GBP) should trade at a forward discount. This means the forward rate should be lower than the spot rate. Our calculated rate of 1.1085 is indeed lower than the spot rate of 1.1250, so our answer makes sense.

For additional reading and more practice problems on these calculations, you can review the article "Spot vs. Forward Exchange Rates" on the AnalystPrep website. It covers all the formulas and concepts we've discussed today.

Conclusion

In this lesson, we made the crucial leap from spot rates to forward rates. You are now able to not only define these concepts but also perform the essential calculations required for the CFA exam.

Key Takeaways:

A spot rate is for immediate exchange, while a forward rate, secured via a forward contract, locks in a price for a future exchange to hedge risk.
If the forward rate is above the spot rate, the base currency is at a premium. If it's below, it's at a discount.
Forward premiums/discounts are quoted in points, which are converted to an outright rate using a scale factor (usually 10,000).
Interest Rate Parity (IRP) provides the no-arbitrage link between spot rates, forward rates, and interest rates.
The key rule to remember is: The currency with the higher interest rate will trade at a forward discount.

Preview of the Next Lesson:

So far, we have assumed that exchange rates are determined by market forces. However, governments and central banks can intervene in currency markets to influence their value. In our next lesson, we will explore the different exchange rate regimes, from freely floating rates to fixed pegs and managed systems.

Recommended resources

Introduction

1. Spot vs. Forward Exchange Rates: Hedging Future Risk

2. Quoting Forwards: Points, Premiums, and Discounts

Practice Calculation 1

3. The "Why": Interest Rate Parity

4. Adjusting the IRP Formula for Time

Practice Calculation 2

Conclusion