Calculating Forward Premiums and Discounts

Overview and Economic Rationale

Sometimes, when I first encountered forward premiums and discounts, I caught myself thinking, “Um…why are we even doing this?” But it turns out that forward rates are a big deal in currency markets, especially if you’re hedging or speculating. In a nutshell, a forward premium or discount is all about interest rate differentials. If a currency has a higher interest rate, that currency often trades at a forward discount—meaning its forward price is relatively cheaper than its spot price (in direct-quote terms). Likewise, a currency with a lower interest rate generally trades at a forward premium.

In other words, if you can earn a higher yield by holding Currency A, you probably won’t also get an additional benefit of an expensive forward exchange rate for that same currency—otherwise, there’d be a free lunch (and we know free lunches are extremely rare in finance!). This notion is the cornerstone of interest rate parity (IRP), which basically ensures no-arbitrage conditions between two currencies.

Spot Rates, Forward Rates, and Interest Rate Differentials

To grasp the full picture:

• The spot rate is the current exchange rate at which you can buy or sell one currency for another.
• The forward rate is an agreed-upon rate today for an exchange of currencies at some future date (e.g., 30, 90, or 180 days from now).
• The difference between the spot rate and the forward rate ties closely to the difference in interest rates between the two currencies involved.

Picture it this way: If you borrow 1,000 home currency units, convert to foreign currency at today’s spot rate, invest the proceeds at the foreign interest rate, and then convert back in the future, you should end up with effectively the same return as if you had just invested at your home currency interest rate. Because if you gain more from one strategy than from the other, arbitrageurs would jump in, and that discrepancy would vanish pretty quickly.

Here’s a simple Mermaid diagram to visualize the logic behind it:

    graph LR
	    A["Home Currency at Interest Rate iₕ"] --> B["Convert at Spot Rate"]
	    B --> C["Foreign Currency at Interest Rate i𝒻"]
	    C --> D["Forward Conversion Back to Home Currency"]

In an efficient market, the left-hand path (hold home currency at rate iₕ) and the right-hand path (exchange to foreign currency, invest at i𝒻, then exchange back) should yield the same net result once you factor in forward rates.

Formulas for Forward Premiums and Discounts

Basic Annualized Formula

The most common formula for determining the forward premium or discount—annualized—is:

Some practitioners use 365 days (or actual day counts), but 360 is also quite standard in the FX world. You’ll want to be consistent with whichever convention is relevant to your scenario.

A forward premium indicates the forward rate is higher than the spot rate for the base currency (in direct terms). A forward discount indicates the forward rate is lower than the spot rate.

Non-Annualized vs. Annualized

If you’re only interested in a 30-day or 90-day horizon, you might simply calculate:

That measure would not be annualized. But exam questions often ask for the annualized figure, so be sure to watch the day count in the denominator. If an item set says “assume a 360-day year,” be consistent and do so.

Step-by-Step Calculation Examples

Example 1: 30-Day Forward Premium

• Spot rate (direct quote, USD/EUR): 1.2000
• 30-day forward rate (USD/EUR): 1.2020
• Days to maturity: 30
• Day count: 360

Step 1: Calculate the difference between forward and spot:
Forward – Spot = 1.2020 – 1.2000 = 0.0020

Step 2: Express it as a percentage of the spot:
(0.0020 / 1.2000) = 0.001667 (which is 0.1667%)

Step 3: Annualize that difference:
0.1667% × (360 / 30) = 0.1667% × 12 = 2.0004%

You might round that to 2.00%. So the forward premium is approximately 2% annualized.

Example 2: 90-Day Forward Discount

• Spot rate (direct quote, USD/GBP): 1.4000
• 90-day forward rate (USD/GBP): 1.3965
• Days to maturity: 90
• Day count: 360

Step 1: Forward – Spot = 1.3965 – 1.4000 = –0.0035 (it’s negative)
Step 2: (–0.0035 / 1.4000) = –0.0025 (–0.25%)
Step 3: –0.25% × (360 / 90) = –0.25% × 4 = –1.00%

So, this currency is trading at roughly a –1.00% annualized forward discount. Because the result is negative, the forward rate is below the spot rate in direct quote terms.

Example 3: 180-Day with Mixed Conventions

Maybe you’re dealing with a 365-day convention:

• Spot rate (CAD/USD): 1.2500 (note that this is an indirect quote for the USD if your home is Canada—but we’ll keep it as “direct,” just be consistent).
• 180-day forward rate: 1.2700
• Days to maturity: 180
• Day count: 365

Step 1: 1.2700 – 1.2500 = 0.0200
Step 2: (0.0200 / 1.2500) = 0.016 = 1.6% non-annualized
Step 3: Annualized: 1.6% × (365 / 180) ≈ 1.6% × 2.0278 ≈ 3.24%

Direct vs. Indirect Quotes

Things can get tricky: sometimes you see a currency pair quoted as EUR/USD, other times as USD/EUR. In direct quote form (home currency in the numerator), you interpret an “increase” as your home currency depreciating if the quote is “foreign currency per home currency.” Meanwhile, in indirect quotes, an “increase” can mean the opposite. So always confirm what the base currency is and what the quote currency is before plugging numbers into these formulas. If not, you can end up flipping answers upside down.

Interest Rate Parity: The Theoretical Anchor

Interest Rate Parity (IRP) is the backbone that keeps forward premiums and discounts from deviating too far. Given:

Where:
• \( F_{A/B} \) = forward exchange rate (A in terms of B)
• \( S_{A/B} \) = current spot exchange rate (A in terms of B)
• \( i_A \) = interest rate (annual) of currency A
• \( i_B \) = interest rate (annual) of currency B

If currency A has the higher interest rate, the forward rate \( F_{A/B} \) will typically be lower (relative to the spot) so that you don’t get a riskless profit by borrowing low, investing high, and converting back. Real markets might show small deviations (transaction costs, capital controls, or political risks), but the concept stands.

External Factors Influencing Premiums and Discounts

Central Bank Policy

If central banks raise interest rates, expect that currency to move into forward discount territory against a lower-rate currency. Overnight rate announcements can shift forward curves quickly.

Capital Controls

When a country imposes restrictions on moving money across borders, the forward market might not fully reflect the typical interest rate parity relationships. Investors can’t freely arbitrage away any discrepancy.

Expected Inflation

Higher expected inflation usually pushes up nominal interest rates in that currency. So you might see a forward discount if inflation is anticipated to be higher in the home currency.

Political Risk

Volatility in politics or policy can drive up risk premiums, requiring a higher forward discount (or lower forward premium) to compensate for extra risk. Sometimes forward markets price in potential black swan events.

Practical Applications

Let’s say you’re a U.S. investor who knows you’ll receive EUR 1,000,000 in 60 days. You can lock in a forward rate to convert those euros to dollars at a predetermined price. If the euro is trading at a forward discount, that means you’ll get fewer USD per EUR at the 60-day mark than if you used today’s spot rate (assuming the forward discount is consistent with IRP). But that might be okay if you want certainty and prefer to hedge your risk rather than gamble on the euro’s future spot rate.

In corporations, the treasury desk often quotes these forward premiums or discounts to estimate hedging costs or benefits. If a forward discount is large, a firm might consider alternative strategies—perhaps a currency swap or a money market hedge.

Item-Set Vignette Example

Imagine a short scenario:

“Vertex Brands, a European exporter, expects to receive USD 5 million in three months for a large shipment. The 90-day forward quote for USD/EUR stands at 0.8350, while the current spot rate is 0.8300 USD/EUR. The company sees 90-day European interest rates at 1.5% (annualized) and the U.S. interest rates at 2.0% (annualized). The CFO asks you to determine whether the euro is at a forward premium or discount relative to the USD and by how much. Then, evaluate whether interest rate parity appears roughly satisfied.”

You’d gather:
• Spot (S) = 0.8300 USD/EUR
• Forward (F) = 0.8350 USD/EUR
• Time = 90 days
• Day count = 360

Forward Premium or Discount:

1. F – S = 0.8350 – 0.8300 = 0.0050
2. (0.0050 / 0.8300) × 100% = 0.6024% (non-annualized)
3. Multiply by (360 / 90) = 0.6024% × 4 = 2.4096% annualized

So, the euro is trading at a forward premium of about 2.41% annualized. You then compare that with the interest rate differential:
• EUR interest rate = 1.5%
• USD interest rate = 2.0%
• The difference is 0.5%.

In theory, you might see the forward premium around that difference if everything matches IRP. The 2.41% is a bit higher than 0.5% difference—potentially due to supply-demand factors or short-term speculation. But for exam purposes, you’d talk about how such a difference might represent a quick arbitrage if the discrepancy is large enough to outpace transaction costs.

Glossary

• Forward Premium: When the forward exchange rate is higher than the spot rate (for the base currency in a direct quote).
• Forward Discount: When the forward exchange rate is lower than the spot rate (for the base currency in a direct quote).
• Interest Rate Parity (IRP): The no-arbitrage principle that links forward rates to the interest rate differentials across currencies.
• Annualized Forward Premium/Discount: Expressing a forward premium or discount as if it were measured over a 1-year horizon.
• Day Count Convention: The convention used (e.g., 360 or 365 days) to annualize figures.

References and Further Reading

• Obstfeld, M., & Rogoff, K. “International Finance.” Advanced treatment of the theories behind exchange rate determination.
• CFA Institute Level II Readings. The official companion for forward rate calculations and item-set practice.
• Bloomberg or Reuters. Check out real-time quotes for forward premium/discount data in multiple currency pairs.

Forward Premium & Discount Mastery: 10-Question Challenge