CFA Level II Exam · Currency Exchange Rates: Understanding Equilibrium Value

Parity Conditions: PPP and Interest Rate Parity

Updated 7 October 2026 · Fact-checked

Parity conditions link exchange rates to inflation and interest rates. Covered interest rate parity fixes the forward rate by no-arbitrage. Uncovered parity, relative PPP and the international Fisher relation predict the expected spot rate. To solve questions, use the price-currency quote, then apply the right formula and compare the result to the vignette data.

Understand Parity Conditions: PPP and Interest Rate Parity

A parity condition says that exchange rates should adjust so that no one earns an easy gain by moving money or goods across borders. There are two families: those tied to interest rates and those tied to prices.

Covered interest rate parity (CIRP) is a no-arbitrage condition. You can invest in a domestic bond, or convert to foreign currency, invest abroad and lock in the return with a forward contract. Both must earn the same. If they do not, arbitrageurs trade until the forward rate fixes it. CIRP holds well in practice, apart from small frictions and stress periods. It uses the forward rate, so it is about a locked-in outcome.

Uncovered interest rate parity (UIRP) drops the forward hedge. It says the expected change in the spot rate offsets the interest differential, so the expected return on foreign and domestic bonds is equal. It is a theory about expectations and risk-neutral investors. It often fails over short horizons, which is why carry trades can earn money for long periods.

Purchasing power parity (PPP) is about prices. Absolute PPP says the price of an identical basket is the same in both countries once converted: S = P(d) ÷ P(f), with S in domestic per foreign. It is the law of one price applied to baskets. It fails because of transport costs, trade barriers and non-traded goods. Relative PPP says the percentage change in the spot rate equals the inflation difference. It needs only changes in price levels, so it is more useful and is what the exam tests most.

The Fisher effect says nominal rate ≈ real rate + expected inflation. The international Fisher relation says that if real rates are equal across countries, the nominal interest differential equals the expected inflation differential. Combine it with relative PPP and you get UIRP: the currency with the higher interest rate is expected to depreciate. Always keep the quote convention in mind. Rates are quoted price/base, so the base currency is the one you hold one unit of.

Key formulas to remember

Covered interest rate parity (forward rate): F(d/f) = S(d/f) × (1 + i(d)) ÷ (1 + i(f)); Quote is domestic per 1 foreign (price/base, base = foreign). Use the same time period for the rates and the forward, scaled for the tenor.
Forward premium or discount: F − S = S × (i(d) − i(f)) ÷ (1 + i(f)); If i(d) > i(f), the base (foreign) currency trades at a forward premium. The higher-rate currency trades at a forward discount.
Uncovered interest rate parity: E(S1) = S0 × (1 + i(d)) ÷ (1 + i(f)); Same form as CIRP but with the expected spot rate. Holds only if investors are risk neutral and have no risk premium.
Approximate UIRP: %ΔE(S) ≈ i(d) − i(f); Use only for small differences. Exact form is better when the exam gives precise numbers.
Absolute PPP: S(d/f) = P(d) ÷ P(f); Basket prices in each currency. Based on the law of one price and rarely holds exactly.
Relative PPP (exact): E(S1) = S0 × (1 + π(d)) ÷ (1 + π(f)); π is inflation over the period. The currency of the higher-inflation country is expected to depreciate.
Relative PPP (approximate): %ΔS ≈ π(d) − π(f); Quote in domestic per foreign: a positive result means the foreign currency appreciates.
Fisher effect: i = r + E(π); Nominal rate equals real rate plus expected inflation (approximate form).
International Fisher relation: i(d) − i(f) ≈ E(π(d)) − E(π(f)); Holds if real rates are equal across countries. It implies equal expected real returns.
Ex-ante version of PPP: E(S1) = S0 × (1 + E(π(d))) ÷ (1 + E(π(f))); Uses expected inflation. Combine with the Fisher relation to link to UIRP.

How to solve Parity Conditions: PPP and Interest Rate Parity questions

Use the same routine for every parity question. The most common loss of marks is a flipped quote or a wrongly matched period.

1Identify the quote. Write the rate as price/base, for example USD/EUR = 1.10 means 1 EUR costs 1.10 USD. Domestic is the price currency, foreign is the base.
2Decide which condition is asked: forward rate (CIRP), expected spot rate from rates (UIRP or international Fisher) or expected spot rate from inflation (relative PPP).
3Pull the data from the vignette. Match each rate or inflation figure to the right currency and to the correct time horizon.
4Scale rates to the horizon. For a six-month forward use the six-month rate, not the annual one. If only annual rates are given, scale them to the horizon, for example annual rate × days ÷ 360 for add-on rates, unless the question states otherwise.
5Apply the formula with domestic over foreign: (1 + domestic) ÷ (1 + foreign). The higher-rate or higher-inflation currency ends up weaker.
6Calculate the answer, then run a direction check: higher domestic rate or inflation means a higher price/base figure, so the base currency rises and the price currency depreciates.
7Compare with the data. For CIRP, compare the forward with the quoted forward to see arbitrage. For PPP or UIRP, compare the predicted rate with the actual to judge over- or undervaluation or the carry trade return.
8State the conclusion in words, for example forward premium or discount, or expected appreciation or depreciation.

Quickest way: Rate ratio and direction check

When to use it: Use when the options are numbers close together and you need an answer in under two minutes.

Compute the ratio (1 + domestic) ÷ (1 + foreign) once, using the right period.
Multiply the spot by that ratio. This gives the forward under CIRP or the expected spot under UIRP. Use the inflation ratio for relative PPP.
Check the direction: if the domestic rate or inflation is higher than the foreign one, the answer must be above the spot. Eliminate options on the wrong side.
If the approximation is enough, add the percentage difference to the spot and compare with the options, but use the exact form if two options are close.

Common mistakes in Parity Conditions: PPP and Interest Rate Parity

Flipping the quote and applying the ratio upside down.
Students think of the 'home' currency rather than reading price/base.
Fix: Write domestic = price currency, foreign = base currency before every calculation. The ratio is always (1 + price currency) ÷ (1 + base currency).
Using annual rates for a six-month or three-month forward.
The vignette gives annual rates and the student plugs them straight in.
Fix: Scale the rate to the horizon first, for example annual rate × days ÷ 360 for an add-on rate, unless the question states otherwise.
Treating UIRP as a no-arbitrage condition like CIRP.
The formulas look the same.
Fix: CIRP uses the forward rate and holds by arbitrage. UIRP uses the expected spot, depends on risk neutrality and often fails.
Confusing absolute and relative PPP.
Both mention prices and parity.
Fix: Absolute PPP is about price levels (S = P(d) ÷ P(f)). Relative PPP is about changes: the rate moves by the inflation difference.
Concluding that the higher-interest-rate currency will appreciate.
High rates seem attractive.
Fix: Under UIRP and the international Fisher relation the higher-rate currency is expected to depreciate by the differential. In practice, forward rate bias means it often does not, which is the carry trade.
Forgetting that the Fisher relation needs equal real rates.
Students memorise the formula without the condition.
Fix: State the assumption: nominal differential equals expected inflation differential only if real rates are the same across countries.

Worked examples

Example 1

Vignette: An analyst quotes USD/EUR spot at 1.1000 (USD per 1 EUR). The one-year USD interest rate is 4.0% and the one-year EUR rate is 2.0%. Q1: What is the one-year forward rate consistent with covered interest rate parity? Q2: Is the EUR at a forward premium or discount? Q3: The market forward is 1.1200. What is the arbitrage direction?

Show the solution

Quote: USD is the price currency (domestic), EUR is the base (foreign).
Q1: F = 1.1000 × (1.04 ÷ 1.02) = 1.1000 × 1.019608 = 1.12157, about 1.1216.
Q2: F is above S, so the EUR trades at a forward premium. This matches the lower EUR interest rate.
Q3: The market forward 1.1200 is below the parity forward 1.1216. Test the route of borrowing USD and investing in EUR. 1 USD buys 1 ÷ 1.1000 = 0.90909 EUR. At 2.0% this grows to 0.92727 EUR. Selling that forward at 1.1200 gives 0.92727 × 1.12 = 1.03855 USD. This is less than the 1.04 USD you would earn by simply investing the USD at home, so that route loses money. Do the reverse: borrow EUR, convert to USD at spot, invest the USD at 4.0% and buy EUR forward at 1.1200. Check with 1 EUR borrowed: it converts to 1.1000 USD, grows to 1.1440 USD, and buys 1.1440 ÷ 1.12 = 1.02143 EUR forward. You owe 1.02 EUR, so you keep a risk-free profit of about 0.00143 EUR.

Answer: Q1: 1.1216. Q2: EUR at a forward premium. Q3: Reverse arbitrage: borrow EUR, convert to USD at spot, invest in USD and buy EUR forward at 1.1200.

Example 2

Vignette: GBP/CHF is quoted CHF per 1 GBP at 1.2000. Expected annual inflation is 1.5% in Switzerland and 3.5% in the United Kingdom. Q1: Using relative PPP, what is the expected spot rate in one year? Q2: What is the approximate expected change in GBP? Q3: If real rates are equal, what nominal interest differential (CHF − GBP) does the international Fisher relation imply?

Show the solution

Quote: CHF is the price currency (domestic), GBP is the base (foreign).
Q1: E(S1) = 1.2000 × (1.015 ÷ 1.035) = 1.2000 × 0.980676 = 1.17681, about 1.1768.
Q2: Approximate change = 1.5% − 3.5% = −2.0%. The exact change is 1.17681 ÷ 1.2000 − 1 = −1.93%. GBP is expected to depreciate against CHF.
Q3: The nominal differential equals the expected inflation differential: i(CHF) − i(GBP) ≈ 1.5% − 3.5% = −2.0%.

Answer: Q1: about 1.1768 CHF per GBP. Q2: GBP depreciates by about 2.0% (exactly about 1.93%). Q3: CHF rate about 2.0 percentage points below the GBP rate.

Exam tips

Write price/base next to every quote in the vignette before calculating. Most errors in this topic come from direction.
Know which condition is no-arbitrage (CIRP) and which are expectations-based (UIRP, relative PPP, international Fisher). Conceptual questions test this split.
Expect a question on what happens if a parity fails, such as the carry trade profiting when UIRP does not hold, or a real exchange rate that reverts toward PPP.
Check the horizon and compounding stated in the vignette before applying a rate. Use exact formulas when options are close.
With no penalty for wrong answers, always answer. Use the direction check to remove at least one option on a calculation question.

Parity Conditions: PPP 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.

Parity Conditions: PPP 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 in the exchange rate, so it holds by arbitrage. Uncovered parity uses the expected future spot rate and no hedge, so it relies on investors being risk neutral. Covered parity holds closely in practice; uncovered parity often does not.

What is the difference between absolute and relative PPP?

Absolute PPP says the exchange rate equals the ratio of price levels of the same basket. Relative PPP says the change in the exchange rate equals the inflation difference between the countries. Relative PPP is the version you apply to forecast an expected rate.

How do I calculate the expected exchange rate using relative PPP?

Multiply the spot rate by (1 + domestic inflation) ÷ (1 + foreign inflation), with the rate quoted as domestic per foreign. The country with higher inflation sees its currency weaken. Use the approximate form only when the numbers are small.

How does interest rate parity show a forward premium or discount?

If the domestic interest rate is higher than the foreign one, the forward rate in domestic per foreign is above spot. The foreign (base) currency is then at a forward premium and the higher-rate currency is at a discount. The size of the premium is about the interest rate differential.

What is the international Fisher relation?

It says that, if real interest rates are the same across countries, the nominal interest rate differential equals the expected inflation differential. Combined with relative PPP it gives uncovered interest rate parity. It rests on the Fisher effect, nominal rate = real rate + expected inflation.