CFA Level I Exam · Capital Flows and the FX Market

Parity Conditions and Exchange Rate Determinants Explained

Updated 7 October 2026 · Fact-checked

Parity conditions link exchange rates to interest rates and inflation. Covered interest rate parity fixes the forward rate: F/S = (1 + price-currency rate) ÷ (1 + base-currency rate). Uncovered parity, relative PPP and the international Fisher effect use expected changes instead. To solve, identify the quote, pick the condition, and apply the ratio with the price currency on top.

Understand Parity Conditions and Exchange Rate Determinants

An exchange rate is the price of one currency in terms of another. Parity conditions say that, in a world without frictions, that price should adjust so that no one earns a free profit from differences in interest rates or inflation. Each condition links the exchange rate to a different variable.

In a quote P/B, the base currency B is the one being priced, and the price currency P is the one you pay with. So USD/EUR = 1.10 means 1 EUR costs 1.10 USD. Every parity formula uses this layout. The price currency's rate goes on top and the base currency's rate goes on the bottom.

Covered interest rate parity (CIRP) is a no-arbitrage condition. You can lock in the forward rate today, so borrowing in one currency and investing in the other, fully hedged, must earn the same as staying in one currency. The forward rate is therefore set by the interest rate differential. CIRP holds closely in practice because arbitrageurs enforce it. The forward premium or discount comes from the rate gap, not from a forecast. The currency with the higher interest rate trades at a forward discount.

Uncovered interest rate parity (UIRP) drops the hedge. It says the expected change in the spot rate offsets the interest rate gap, so the expected return from investing abroad unhedged equals the domestic return. The higher-yielding currency is expected to depreciate. Empirically this often fails. High-yield currencies have tended not to depreciate as much as UIRP predicts, which is called forward rate bias. The carry trade exploits this by borrowing a low-yield currency and investing in a high-yield one. It earns the rate gap while the spot rate stays put, but it carries crash risk. Returns tend to be negatively skewed, with large losses when the high-yield currency falls sharply.

Purchasing power parity (PPP) links exchange rates to prices. Absolute PPP says the exchange rate equals the ratio of price levels, S = P(price currency) ÷ P(base currency), so a basket costs the same everywhere. It fails because of transport costs, trade barriers and non-traded goods. Relative PPP says the percentage change in the exchange rate offsets the inflation differential. The currency with higher inflation depreciates. It tends to hold better over long horizons than short ones. The international Fisher effect combines the Fisher relation (nominal rate = real rate + expected inflation) with relative PPP. If real rates are equal across countries, the nominal rate gap equals the expected inflation gap, and so the expected change in the exchange rate.

Beyond the parities, several approaches explain currency moves. The Mundell-Fleming model studies how monetary and fiscal policy affect exchange rates under floating rates, depending on capital mobility. With high capital mobility, expansionary monetary policy lowers rates, capital flows out, and the currency depreciates. Expansionary fiscal policy raises rates, capital flows in, and the currency appreciates. With low capital mobility, fiscal expansion widens the trade deficit through higher imports, and the currency depreciates. The monetary approach assumes PPP holds, so faster money growth means higher inflation and depreciation. Its sticky-price version, the Dornbusch overshooting model, says that after a monetary expansion the currency first depreciates by more than its long-run level, then partly reverses as prices adjust. The portfolio balance approach says persistent fiscal deficits can weaken a currency when investors demand a higher risk premium to hold the extra government debt.

Key formulas to remember

Covered interest rate parity (forward rate): F(P/B) = S(P/B) × (1 + i_P × t) ÷ (1 + i_B × t); t is the fraction of a year, using the day-count convention given (usually days ÷ 360). For one year, t = 1. Price currency P on top, base currency B on the bottom.
Forward premium or discount rule: If i_P > i_B, then F > S: the base currency B trades at a forward premium and the higher-rate price currency P trades at a forward discount; The base currency has the lower interest rate and the forward rate is higher. The higher-rate currency, here P, is at a forward discount: its value in B terms falls.
Uncovered interest rate parity: E(S1) ÷ S0 = (1 + i_P) ÷ (1 + i_B); approx. expected % change in the P/B rate ≈ i_P − i_B; If i_P is higher, the P/B rate is expected to rise, so the base currency B appreciates and the higher-yield price currency P depreciates. Uses the expected spot rate. No hedge, so it is an equilibrium idea, not a risk-free arbitrage.
Absolute PPP: S(P/B) = Price level in P ÷ Price level in B; Applies to a common basket. Rarely holds exactly.
Relative PPP: E(S1) = S0 × (1 + π_P) ÷ (1 + π_B); approx. % change in the P/B rate ≈ π_P − π_B; The currency with higher inflation depreciates. If π_P is higher, the P/B rate rises and P depreciates against B. Ex-ante version uses expected inflation.
Fisher relation: i ≈ r + E(π); Nominal rate equals real rate plus expected inflation (approximation).
International Fisher effect: i_P − i_B ≈ E(π_P) − E(π_B), when real rates are equal; Combines Fisher with relative PPP. The nominal rate gap (i_P − i_B) approximately equals the expected percentage change in the P/B rate. If P has the higher nominal rate, the P/B rate is expected to rise, so P is expected to depreciate against B.
Mundell-Fleming summary (floating rates): Monetary expansion: currency depreciates. Fiscal expansion: appreciates if capital mobility is high, depreciates if low; For mixed policy combinations, check the effect of each policy separately and see whether they agree.

How to solve Parity Conditions and Exchange Rate Determinants questions

Use this routine for any parity question. It prevents the usual inversion errors.

1Write the quote as P/B and say which currency is the price currency and which is the base currency.
2Decide what the question asks for: a forward rate (CIRP), an expected future spot rate (UIRP, PPP or international Fisher), or a direction of currency movement.
3Pick the matching condition. Interest rates plus a hedge or forward means CIRP. Interest rates plus expectation means UIRP. Inflation means PPP. Real rates equal and nominal rates given means international Fisher.
4Put the price currency's rate or inflation on top and the base currency's on the bottom. Multiply by the spot rate.
5Adjust the rates for the horizon (days ÷ 360 for money market rates unless told otherwise) and compute the answer.
6Sanity check the direction. The higher-rate currency should be at a forward discount under CIRP, and the higher-inflation currency should depreciate under relative PPP.
7Pick the option that matches both your number and your direction, and eliminate the option that comes from inverting the ratio.

Quickest way: Rate ratio and direction check

When to use it: Use it for any numerical parity question when time is short. The two wrong options are usually the inverted ratio and the unadjusted spot rate.

Find the ratio (1 + price rate) ÷ (1 + base rate). If the price-currency rate is higher, the ratio is above 1 and the forward or expected rate is above spot.
Estimate with the approximation first: spot × (1 + rate gap). This usually leaves only one option near the answer.
If two options are close, compute the exact ratio. On the BA II Plus, which is a chain calculator, key 1.1 × 1.04 ÷ 1.02 =. On the HP 12C, which uses RPN, key 1.1 ENTER 1.04 × 1.02 ÷.
Eliminate the option equal to spot and the option that multiplies by the wrong currency's rate.
For conceptual questions, remember: higher rate means lower expected or forward value of that currency. Higher inflation means depreciation.

Common mistakes in Parity Conditions and Exchange Rate Determinants

Inverting the ratio, putting the base currency's rate on top.
Candidates forget which currency is priced in the quote and use home and foreign labels instead.
Fix: Always write P/B first. The price currency's rate goes on top. Check direction: the higher-rate currency must end at a forward discount.
Treating UIRP as a risk-free arbitrage like CIRP.
The two names and formulas look alike.
Fix: CIRP uses the forward contract and is enforced by arbitrage. UIRP uses an expected spot rate and carries exchange rate risk. It often fails empirically.
Claiming that high-yield currencies always depreciate.
Candidates read UIRP as a statement of fact rather than a theory.
Fix: UIRP predicts depreciation. The data show forward rate bias, so carry trades have often earned positive returns, with occasional large crashes.
Saying absolute PPP holds and relative PPP is the same thing.
Both are called PPP.
Fix: Absolute PPP compares price levels. Relative PPP compares changes (inflation rates). Relative PPP is the version used in calculations and holds better over the long run.
Using a full-year rate for a 90-day or 180-day forward.
The annual rate is quoted and the horizon is easy to overlook.
Fix: Multiply each annual rate by days ÷ 360 (or the stated convention) before forming the ratio.
Memorizing Mundell-Fleming results without the capital mobility condition.
The fiscal result flips depending on mobility.
Fix: Fiscal expansion raises rates. High mobility means inflows and appreciation. Low mobility means the trade effect dominates and the currency depreciates. Monetary expansion means depreciation in both cases.

Worked examples

Example 1

The spot rate is 1.1000 USD/EUR. The one-year USD interest rate is 4% and the one-year EUR interest rate is 2%. Under covered interest rate parity, the one-year forward rate (USD/EUR) is closest to: A) 1.0788, B) 1.1216, C) 1.1440.

Show the solution

The quote is USD/EUR, so USD is the price currency and EUR is the base currency.
CIRP: F = S × (1 + i_USD) ÷ (1 + i_EUR).
F = 1.1000 × 1.04 ÷ 1.02 = 1.1000 × 1.019608 = 1.1216.
Direction check: USD has the higher rate, so EUR trades at a forward premium (F above S). 1.1216 is above 1.1000.
Option A comes from inverting the ratio. Option C multiplies by only the USD rate and ignores the EUR rate.

Answer: B) 1.1216

Example 2

The spot rate is 150.00 JPY/USD. Expected inflation is 3% in the United States and 1% in Japan. Under relative PPP, the expected spot rate (JPY/USD) is closest to: A) 147.09, B) 150.00, C) 152.97.

Show the solution

The quote is JPY/USD, so JPY is the price currency and USD is the base currency.
Relative PPP: E(S1) = S0 × (1 + π_JPY) ÷ (1 + π_USD).
E(S1) = 150.00 × 1.01 ÷ 1.03 = 150.00 × 0.980583 = 147.09.
Direction check: the US has higher inflation, so the USD is expected to depreciate against the JPY. A lower JPY/USD rate matches that.
Option C inverts the ratio. Option B ignores the inflation gap.

Answer: A) 147.09

Exam tips

Most numerical items give three options spread widely. Decide direction first (is the answer above or below spot?) and you can often remove two options before calculating.
Watch whether the question asks for a forward rate (CIRP, hedged) or an expected spot rate (UIRP, PPP, international Fisher). The calculation can look the same, but the label tells you which theory applies.
Conceptual items often test whether you know which conditions hold well. CIRP holds closely, PPP tends to hold only over long horizons, and UIRP often fails in the short run.
For carry trade questions, link the strategy to UIRP failure: it profits when the high-yield currency does not depreciate as predicted, and it has negatively skewed, crash-prone returns.
For Mundell-Fleming, check the capital mobility wording first. Fiscal expansion is the case where the answer flips.

Practice questions from Capital Flows and the FX Market

Parity Conditions and Exchange Rate Determinants 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 and Exchange Rate Determinants: frequently asked questions

What is the covered interest rate parity formula for CFA Level I?

F(P/B) = S(P/B) × (1 + i_P × t) ÷ (1 + i_B × t), where P is the price currency and B is the base currency. For a one-year forward, t = 1. The currency with the higher interest rate trades at a forward discount.

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

Covered parity uses the forward rate, so the position is hedged and arbitrage enforces it. Uncovered parity uses the expected future spot rate, so there is exchange rate risk. CIRP holds closely, while UIRP often fails in the short run.

What is the difference between absolute and relative PPP?

Absolute PPP says the exchange rate equals the ratio of price levels, so the same basket costs the same everywhere. Relative PPP says the percentage change in the exchange rate offsets the inflation differential. Relative PPP is the one used for calculations.

What is the international Fisher effect?

It says that if real interest rates are equal across countries, the nominal interest rate gap equals the expected inflation gap. Combined with relative PPP, that gap also equals the expected change in the exchange rate. The currency with the higher nominal rate is expected to depreciate.

What is forward rate bias and why does it matter for carry trades?

Forward rate bias is the empirical finding that high-yield currencies do not depreciate as much as UIRP and the forward rate imply. This is why carry trades, which borrow low-yield currencies to invest in high-yield ones, have often been profitable. The risk is sudden large losses when the high-yield currency falls sharply.