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CFA Level I Exam · Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities

Currency Forwards and Covered Interest Rate Parity

Updated 7 October 2026 · Fact-checked

Covered interest rate parity says a currency forward price must make borrowing in one currency and lending in another earn no riskless profit. In price/base quotes: F = S × (1 + r_price) ÷ (1 + r_base), for matching maturities. Forward points are F − S. Value an existing forward by discounting the gap to the new forward price.

Understand Forwards on Currencies and Interest Rate Parity

A currency forward fixes an exchange rate today for exchange at a future date. Its price is not a forecast. It is set by no-arbitrage, using the spot rate and the interest rates in both currencies.

Think of two routes to hold the base currency at time T. Route one: buy it at spot now and invest it at the base rate. Route two: invest the price currency at the price rate and lock in a forward to buy base currency at T. If the two routes end with different amounts, you can arbitrage. So the forward rate must remove the gap. This is covered interest rate parity.

Quotes are price currency per 1 unit of base currency. For example, USD/EUR = 1.10 means 1 EUR costs USD 1.10. USD is the price currency and EUR the base. The currency with the higher interest rate trades at a forward discount relative to the other currency. The one with the lower rate trades at a forward premium relative to the other currency. So when r_price > r_base, the price currency is at a forward discount and the base currency is at a forward premium, and F is above S. Intuitively, the higher-rate currency has already paid you extra interest, so it is worth less in the forward, measured in terms of the other currency.

Forward points are the forward rate minus the spot rate, usually quoted in units of the fourth decimal place (pips) and scaled by 10,000. For yen pairs, scale by 100. A positive number means the base currency is at a forward premium.

Covered parity differs from uncovered interest rate parity. Covered parity uses a forward contract to lock in the exchange rate, so it is an arbitrage relation and holds closely. Uncovered parity says the expected future spot rate changes to offset the interest rate gap, with no hedge. It rests on expectations and risk neutrality, so it is a theory and often fails in practice.

After initiation, a forward has value. At time t, with the original contract rate F0 and the current forward rate Ft for the remaining term, the long base-currency position is worth the present value of (Ft − F0) × notional, discounted at the price-currency rate.

Key formulas to remember

Covered interest rate parity (annual periods)
F = S × (1 + r_price)^T ÷ (1 + r_base)^T
S and F are price/base. Rates must match the currency and the term. T is in years.
Short-term (simple interest) form
F = S × [1 + r_price × (days ÷ 360)] ÷ [1 + r_base × (days ÷ 360)]
Use the day-count given in the question (360 or 365). Money market quotes are usually simple interest.
Forward points
Forward points = (F − S) × 10,000
Use ×100 for yen quotes. Positive means base currency at forward premium.
Forward premium or discount
Base currency at premium if r_price > r_base; at discount if r_price < r_base
The currency with the higher interest rate trades at a forward discount relative to the other currency. When r_price > r_base, the price currency is at a discount and the base currency is at a premium.
Value of an FX forward at time t
V_t (long base) = [F_t − F_0] ÷ (1 + r_price)^(remaining T) × notional
Ft is the new forward rate for the remaining term. Result is in the price currency.
Uncovered interest rate parity
Expected % change in spot ≈ r_price − r_base
Based on expectations, no hedge. Not an arbitrage relation.

How to solve Forwards on Currencies and Interest Rate Parity questions

Use this order for any currency forward question. Most errors come from the quote direction, not the arithmetic.

  1. 1Identify the quote as price/base. Write down which currency is the base (the one you are buying or selling in the contract).
  2. 2Match each interest rate to its currency and to the term of the forward. Convert the term to a fraction of a year using the stated day count.
  3. 3Apply F = S × (1 + r_price) ÷ (1 + r_base), with the correct compounding for the term.
  4. 4If the quote is the inverse of what you were given, invert S first, or swap the roles of the two rates.
  5. 5For forward points, compute F − S and scale by 10,000 (100 for yen).
  6. 6For valuation after initiation, find the new forward rate for the remaining term, take the difference to F0, multiply by the notional, and discount at the price-currency rate.
  7. 7Sanity check: the currency with the higher interest rate must be at a forward discount relative to the other currency. So if r_price > r_base, the base currency is at a forward premium and F is above S. If not, you inverted something.

Quickest way: Rate-gap shortcut with an elimination check

When to use it: Use it when options are far apart and you only need to find the right one in about 90 seconds.

  1. Compare the two rates. Decide whether the forward should be above or below spot. Price rate above base rate means F above S.
  2. Cross out any option on the wrong side of spot. This often removes one or two options.
  3. Estimate F ≈ S × (1 + (r_price − r_base) × T). Pick the closest option.
  4. Calculator: enter S, press × , then (1 + r_price) ÷ (1 + r_base) using brackets, then =. Do not round the ratio early.

Common mistakes in Forwards on Currencies and Interest Rate Parity

  • Putting the rates on the wrong currencies

    Candidates assume the domestic rate always goes on top, ignoring the quote direction.

    Fix: Price currency rate goes on top, base currency rate on the bottom. Label the quote before you touch the formula.

  • Using the same rate for the whole term when the question gives different terms

    Candidates grab the first rate they see.

    Fix: Use the rate that matches the forward's maturity and the currency. Ignore other maturities.

  • Treating forward points as the forward rate

    Points are quoted as small integers like +45.

    Fix: Divide points by 10,000 (100 for yen) and add to spot to get F.

  • Believing the forward is the expected future spot rate

    Mixing up covered and uncovered parity.

    Fix: The forward is set by arbitrage, not forecasts. Only uncovered parity involves expected spot rates.

  • Valuing the forward with the original contract rate in the wrong direction

    Candidates forget which side they hold, or forget to discount.

    Fix: Long base gains when Ft > F0. Discount the difference at the price-currency rate for the remaining term. Flip the sign for the short.

Worked examples

Example 1

The spot rate is USD/EUR 1.1000. The 180-day USD interest rate is 4.00% annualized and the 180-day EUR interest rate is 2.00% annualized, both using a 360-day year and simple interest. What is the 180-day forward rate? A) 1.0891 B) 1.1109 C) 1.1218

Show the solution
  1. USD is the price currency and EUR the base currency.
  2. Term fraction = 180 ÷ 360 = 0.5.
  3. USD growth factor = 1 + 0.04 × 0.5 = 1.02.
  4. EUR growth factor = 1 + 0.02 × 0.5 = 1.01.
  5. F = 1.1000 × 1.02 ÷ 1.01 = 1.1000 × 1.009901 = 1.11089, about 1.1109.
  6. Check: USD rate is higher, so F is above spot. This eliminates A. C is too large for a 2% rate gap over half a year.

Answer: B) 1.1109

Example 2

A trader entered a long position in a 1-year forward to buy EUR 1,000,000 at USD/EUR 1.1200. Six months later, the 6-month forward rate is 1.1500. The USD interest rate for the remaining 180 days is 3.00% annualized (simple interest, 360-day year). What is the value of the position in USD? A) 29,557 B) 30,000 C) 30,450

Show the solution
  1. The trader is long the base currency (EUR). A rise in the forward rate from 1.1200 to 1.1500 is a gain.
  2. Difference per EUR = 1.1500 − 1.1200 = 0.0300.
  3. Undiscounted gain = 0.0300 × 1,000,000 = USD 30,000.
  4. Discount at the USD rate for 180 days: 1 + 0.03 × 0.5 = 1.015.
  5. Value = 30,000 ÷ 1.015 = 29,556.65, about USD 29,557.
  6. Option B ignores discounting. Option C multiplies instead of dividing: 30,000 × 1.015 = 30,450.

Answer: A) USD 29,557

Exam tips

  • Write the quote as price/base before every question. Most wrong answers come from inverted quotes.
  • Use the direction test first: the higher-rate currency trades at a forward discount relative to the other currency. It often removes one or two options.
  • Read the day-count convention in the stem and use it. A 360 versus 365 difference can change the answer.
  • In valuation questions, check whether the answer needs discounting. One distractor is usually the undiscounted gain.
  • If a question mentions expected spot rates or no hedge, think uncovered parity. If it mentions a forward lock, think covered parity.

Practice questions from Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities

Forwards on Currencies and Interest Rate Parity in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Forwards on Currencies and Interest Rate Parity: frequently asked questions

What is the difference between covered and uncovered interest rate parity?

Covered parity uses a forward contract to lock the exchange rate, so any gap is an arbitrage and it holds closely. Uncovered parity has no hedge and relies on the expected future spot rate offsetting the interest rate gap. It is a theory based on expectations and often fails.

How do you calculate forward points?

Find the forward rate with covered parity, subtract spot, and multiply by 10,000. For yen pairs, multiply by 100. A positive result means the base currency is at a forward premium.

Which currency trades at a forward discount?

The currency with the higher interest rate trades at a forward discount relative to the currency with the lower rate. This follows from no-arbitrage. The extra interest earned is offset by a lower forward value. In a price/base quote, if r_price > r_base, the base currency is at a forward premium.

Do I need a calculator for covered interest parity?

Yes, usually. Compute the ratio of the two growth factors and multiply by spot. Keep full precision until the final step, then round to the option format.