FRM Exam Part I · Foreign Exchange Markets

Uncovered Interest Parity and Purchasing Power Parity

Updated 11 October 2026 · Fact-checked

Uncovered interest parity (UIP) says the expected change in an exchange rate offsets the interest rate gap between two countries, so no expected profit remains. Purchasing power parity (PPP) says exchange rates move with relative price levels. To solve questions, set up the quote convention, apply the formula, and check the direction.

Understand Uncovered Interest Parity and Purchasing Power Parity

An exchange rate is the price of one currency in terms of another. Two big ideas try to explain how it is set. One links it to interest rates. The other links it to prices of goods.

Uncovered interest parity (UIP) says that if you borrow in a low-rate currency and invest in a high-rate currency, the high-rate currency is expected to lose value by about the interest gap. Your expected gain from the higher interest is wiped out by the expected currency loss. Nothing is hedged, so the word "uncovered" means you carry the exchange rate risk. Compare this with covered interest parity (CIP), where the forward contract locks in the rate. CIP is a no-arbitrage condition that holds closely. UIP is a statement about expectations and often fails in the data.

When UIP fails, the carry trade can earn money on average: you borrow low-rate currencies and lend high-rate ones. This is the forward premium puzzle. If CIP holds, the forward rate reflects the interest gap. If UIP held, the forward rate would be an unbiased predictor of the future spot rate. Empirically, high-rate currencies have often not depreciated as much as UIP predicts, and sometimes have appreciated. Carry trades carry crash risk, as returns can reverse sharply in a crisis.

Purchasing power parity (PPP) comes from the law of one price: the same good should cost the same everywhere once converted to one currency. Absolute PPP says S = P(domestic) ÷ P(foreign), where S is the domestic price of one unit of foreign currency. Relative PPP works with changes: the currency of the country with higher inflation is expected to depreciate by about the inflation gap. PPP is a long-run idea. Over short horizons, trade costs, sticky prices and non-traded goods break it.

The real exchange rate measures the relative price of foreign goods in domestic terms: q = S × P(foreign) ÷ P(domestic). If q is constant, PPP holds. If q rises, foreign goods have become more expensive for domestic buyers, which is a real depreciation of the domestic currency.

Key formulas to remember

Covered interest parity (direct quote, simple rates): F ÷ S = (1 + r_d × T) ÷ (1 + r_f × T); S and F are domestic currency per one unit of foreign currency. r_d is the domestic rate, r_f the foreign rate. With continuous compounding, F = S × e^((r_d − r_f)T).
Uncovered interest parity (exact): E[S_T] ÷ S = (1 + r_d × T) ÷ (1 + r_f × T); Same quote convention as CIP. It uses the expected future spot rate, not the forward rate, and is not hedged.
Uncovered interest parity (approximation): Expected % change in S ≈ r_d − r_f; S is domestic per foreign. If r_d > r_f, the domestic currency is expected to depreciate, so S rises by about r_d − r_f and the foreign currency appreciates.
Absolute PPP: S = P_d ÷ P_f; P_d and P_f are price levels of the same basket in each country. S is domestic per foreign.
Relative PPP (approximation): Expected % change in S ≈ π_d − π_f; π is the inflation rate. The foreign currency appreciates if domestic inflation is higher.
Relative PPP (exact): S_T = S × (1 + π_d)^T ÷ (1 + π_f)^T; Use for multi-year horizons with annual inflation rates.
Real exchange rate: q = S × P_f ÷ P_d; Constant q means PPP holds. A rise in q is a real depreciation of the domestic currency.
Carry trade excess return: Return ≈ (r_high − r_low) − % depreciation of the high-rate currency; The trade profits when the high-rate currency depreciates by less than the rate gap.

How to solve Uncovered Interest Parity and Purchasing Power Parity questions

Most questions on this topic are a short calculation plus a direction check. Use the same routine each time.

1Write down the quote convention first. Identify which currency is the domestic currency and whether S is domestic per foreign or foreign per domestic.
2Identify the theory: forward rate given (covered parity), expected spot rate (UIP), or inflation figures (PPP).
3Match each rate to its currency. Domestic rate goes with domestic currency, foreign rate with foreign currency, over the same time period.
4Apply the formula. Use the exact form when the question gives a long horizon or asks for precise numbers. Use the approximation only when options are far apart.
5Compute the result and state its direction: which currency appreciates or depreciates.
6Sanity check: the higher-rate or higher-inflation currency should be the one expected to depreciate.
7For carry trade questions, compute the interest gain and subtract the currency move, converting everything to the investor's base currency.

Quickest way: Direction-first shortcut

When to use it: Use it when answer options differ clearly and you need to save time on multiple-choice questions.

Decide the direction using the rule that the higher interest rate or higher inflation currency depreciates.
Use the approximation: % change ≈ rate gap or inflation gap.
Eliminate options with the wrong sign or the wrong size.
Run the exact formula only if two options remain close.
For PPP over several years, compute the ratio (1 + π_d) ÷ (1 + π_f) and raise it to the power of the years.

Common mistakes in Uncovered Interest Parity and Purchasing Power Parity

Using the forward rate in place of the expected spot rate for UIP.
Covered and uncovered parity look alike, and both use the same interest rate ratio.
Fix: CIP uses the forward rate F and is a no-arbitrage result. UIP uses the expected spot E[S_T] and is a hypothesis about expectations. Check which one the question names.
Flipping the quote convention, so the currency is predicted to move the wrong way.
Students apply S = domestic per foreign when the quote is foreign per domestic.
Fix: Write down what S means before calculating. If the quote is inverted, invert the ratio (swap domestic and foreign in the formula).
Thinking the high-interest-rate currency should appreciate.
High yields feel attractive, so the currency seems strong.
Fix: Under UIP and relative PPP, the higher-rate or higher-inflation currency is expected to depreciate by the gap. Carry trades work only because this often does not happen.
Treating UIP as a proven fact and the forward as an unbiased predictor.
Textbook equations are presented as equalities.
Fix: Remember the forward premium puzzle: empirically, high-rate currencies tend to depreciate less than UIP implies, so the forward is a biased predictor. Carry trades earn positive average returns but with crash risk.
Assuming PPP holds in the short run.
The formula looks exact.
Fix: PPP is a long-run tendency. Trade barriers, non-traded goods and sticky prices cause persistent deviations. A question that says "PPP holds" is giving you an assumption; otherwise treat it cautiously.
Mixing absolute and relative PPP, or confusing the real exchange rate direction.
Both involve price levels and look similar.
Fix: Absolute PPP is about levels, relative PPP is about changes. For the real rate q = S × P_f ÷ P_d, a rising q means foreign goods have become more expensive relative to domestic goods, which is a real depreciation of the domestic currency.

Worked examples

Example 1

The spot rate is USD 1.1000 per EUR 1. The one-year USD interest rate is 5% and the one-year EUR interest rate is 3%, both simple annual rates. Under UIP, what is the expected spot rate (USD per EUR) in one year?

Show the solution

Domestic currency is USD and S is USD per EUR, so S = 1.1000, r_d = 5%, r_f = 3%, T = 1.
UIP: E[S_T] = S × (1 + r_d × T) ÷ (1 + r_f × T).
E[S_T] = 1.1000 × 1.05 ÷ 1.03.
1.05 ÷ 1.03 = 1.019417.
E[S_T] = 1.1000 × 1.019417 = 1.12136.
Direction check: USD has the higher rate, so USD is expected to depreciate, meaning EUR appreciates from 1.1000 to about 1.1214 USD.

Answer: Expected spot rate ≈ USD 1.1214 per EUR.

Example 2

The current spot rate is INR 80.00 per USD. Expected inflation is 6% a year in India and 2% a year in the US. Using relative PPP, what is the expected spot rate (INR per USD) after 3 years?

Show the solution

Domestic currency is INR and S is INR per USD, so S = 80.00, π_d = 6%, π_f = 2%, T = 3.
Relative PPP: S_T = S × [(1 + π_d) ÷ (1 + π_f)]^T.
Ratio = 1.06 ÷ 1.02 = 1.039216.
Cube it: 1.039216² = 1.079971; 1.079971 × 1.039216 = 1.122328.
S_T = 80.00 × 1.122328 = 89.786.
Direction check: India has higher inflation, so INR depreciates and more rupees are needed per USD.

Answer: Expected spot rate ≈ INR 89.79 per USD.

Exam tips

Always write down the quote convention in the margin before touching a formula. Most lost marks come from inverted quotes.
Know the difference between covered and uncovered parity. A question may test which one is a no-arbitrage condition (CIP) and which depends on expectations (UIP).
Expect conceptual questions on the forward premium puzzle and carry trade risk: biased forward predictor, positive average carry returns, crash risk.
If options are far apart, use the approximations (rate gap or inflation gap) and move on. Keep the exact formulas for close options.
Remember that PPP is a long-run relation. Statements that say it holds exactly in the short run are usually wrong.

Practice questions from Foreign Exchange Markets

Uncovered Interest Parity and Purchasing Power Parity in other exams

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

Uncovered Interest Parity and Purchasing Power Parity: frequently asked questions

What is the difference between covered and uncovered interest parity?

Covered interest parity uses a forward contract to lock in the future exchange rate, so no exchange rate risk remains and arbitrage keeps it holding closely. Uncovered interest parity uses the expected future spot rate and leaves the risk open. It describes expectations and often fails in practice.

What is the forward premium puzzle?

If UIP held and CIP held, the forward rate would be an unbiased predictor of the future spot rate. In the data, currencies with high interest rates tend to depreciate less than predicted, or even appreciate. The forward rate is therefore a biased predictor, and this is why carry trades have earned positive average returns.

How does a carry trade work and what is its risk?

You borrow in a low-interest-rate currency and invest in a high-interest-rate currency. You profit if the high-rate currency does not fall by more than the rate gap. The main risk is a sudden reversal, often in a market crisis, which can cause large losses.

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 in two countries. Relative PPP says the change in the exchange rate equals the difference in inflation rates. Relative PPP is the version most often used in calculations.

Does PPP hold in practice?

PPP is a long-run tendency, not a short-run rule. Trade costs, non-traded goods, sticky prices and differences in baskets cause large and persistent deviations. The real exchange rate tracks these deviations.