Exchange-Rate Determination and Parity Conditions

Introduction and context

The exchange rate is the price of one currency expressed in another. It affects the domestic-currency cost of imports, the foreign-currency price of exports, international investment returns, inflation, corporate competitiveness and sovereign debt servicing. For a finance professional, understanding exchange rates requires more than identifying whether a currency has appreciated or depreciated. It requires analysing the economic forces that generate currency values, the conditions under which parity relationships should hold, and the reasons actual markets can deviate from theoretical predictions.

This chapter develops the principal approaches to exchange-rate determination: purchasing power parity, interest-rate parity, the Fisher effect, expectations-based models, monetary models and portfolio-balance models. It also evaluates macroeconomic, political and behavioural influences and explains why exchange-rate forecasting remains difficult.

Learning objectives

By the end of this chapter, the reader should be able to:

1. Explain exchange-rate quotations and distinguish appreciation from depreciation.
2. Apply absolute and relative purchasing power parity.
3. Calculate and interpret covered and uncovered interest-rate parity.
4. Explain the Fisher effect and the international Fisher effect.
5. Analyse monetary, portfolio-balance and expectations-based exchange-rate models.
6. Evaluate macroeconomic, political and behavioural drivers of exchange rates.
7. Recognise the assumptions, empirical limitations and professional uses of parity conditions.
8. Use exchange-rate analysis to support hedging, investment and corporate-finance decisions.

1. Exchange-rate conventions and market meaning

Let S denote the spot exchange rate. In this chapter, the direct quotation is defined as the number of units of domestic currency required to purchase one unit of foreign currency:

For example, if a euro-area firm observes S = ₹90/€, one euro costs ₹90. An increase from ₹90/€ to ₹94/€ is an appreciation of the euro and a depreciation of the rupee. The reciprocal quotation is the foreign-currency value of one unit of domestic currency:

The asterisk here denotes the reciprocal quotation, not necessarily a foreign-market variable. A currency’s appreciation makes foreign goods cheaper in domestic-currency terms, holding other conditions constant, while making domestic goods more expensive to foreign buyers.

The exchange rate is determined in a market where demand and supply reflect trade payments, capital flows, central-bank operations, expectations and portfolio adjustments. The current spot rate is therefore both an outcome of current fundamentals and a price incorporating information about expected future conditions.

2. Purchasing power parity

2.1 Absolute purchasing power parity

Purchasing power parity (PPP) proposes that identical goods should cost the same in two countries once expressed in a common currency, assuming no transport costs, tariffs, taxes, market segmentation or other frictions. Let P_D be the domestic price level and P_F the foreign price level. With the direct quotation used above, absolute PPP is:

The units are domestic currency per foreign currency because the numerator is a domestic-currency price index and the denominator is a foreign-currency price index. The relationship is an equilibrium benchmark rather than a mechanical short-run law.

For a single tradable good, the law of one price states:

If a standard product costs ₹900 in India and €10 in the euro area, the implied PPP exchange rate is ₹90/€. Actual prices may differ because of shipping costs, local taxes, product differentiation and non-traded inputs.

2.2 Relative PPP

Relative PPP focuses on changes rather than price-level equality. It predicts that the percentage change in the exchange rate approximately equals the inflation differential:

where ΔS/S is the proportional change in the direct exchange rate, π_D is domestic inflation and π_F is foreign inflation. If domestic inflation exceeds foreign inflation, the domestic currency is expected to depreciate, meaning S rises under the direct quotation.

A more exact discrete form is:

This assumes that PPP holds initially and that inflation rates represent comparable price baskets. For small inflation rates, the approximate differential is usually sufficiently accurate.

Worked example: relative PPP

Suppose the current rate is ₹90/€, expected domestic inflation is 6% and euro-area inflation is 2%. The predicted future rate is:

The approximate method gives:

and therefore S_1 ≈ ₹93.60/€. The small difference results from the approximation. The implication is a predicted rupee depreciation of approximately 4% against the euro.

2.3 Uses and limitations of PPP

PPP is useful for assessing long-run currency valuation, comparing international purchasing power and constructing real exchange-rate measures. It is commonly used in strategic planning, sovereign analysis and long-horizon economic research.

Its short-run performance is limited because:

• Many services are non-traded and have country-specific prices.
• Transport costs, tariffs and quotas prevent complete arbitrage.
• Price indexes contain different goods and quality levels.
• Firms may price discriminate across markets.
• Productivity changes can alter relative prices.
• Capital flows can dominate trade flows over relevant investment horizons.

The Balassa–Samuelson effect is especially important. Faster productivity growth in a country’s tradable sector can raise wages economy-wide, increasing prices of non-traded services and causing the currency to appear overvalued relative to simple PPP, even when the economy is in a sustainable equilibrium.

3. Interest-rate parity

Interest-rate parity connects exchange rates with interest-rate differentials and arbitrage. It is particularly important for treasury operations, forward pricing and international investment.

3.1 Covered interest-rate parity

Covered interest-rate parity (CIP) states that an investor should obtain the same domestic-currency return from investing at home as from investing abroad while covering the exchange-rate risk with a forward contract. Let:

• S_0 = current spot rate in domestic currency per unit of foreign currency;
• F_0,T = forward rate for delivery at time T;
• i_D = domestic nominal interest rate for the period;
• i_F = foreign nominal interest rate for the period.

CIP is:

For continuously compounded annual rates over T years, the equivalent expression is:

where r_D and r_F are continuously compounded rates. The discrete formula assumes matching maturities, comparable credit risk, unrestricted borrowing and lending, no material transaction costs and enforceable forward contracts.

Worked example: covered interest parity

Assume S_0 = ₹90/€, the one-year rupee interest rate is 7% and the euro interest rate is 3%. CIP implies:

The euro trades at a forward premium in rupee terms because the rupee interest rate is higher. The premium is approximately 3.88%, equal to the ratio of the interest factors minus one.

If the observed forward rate were materially different after allowing for transaction costs and credit effects, an arbitrageur could borrow in one currency, convert at spot, invest in the other currency and use the forward market to eliminate exchange risk.

3.2 Uncovered interest-rate parity

Uncovered interest-rate parity (UIP) does not use a forward hedge. It states that the expected exchange-rate change offsets the interest differential:

Equivalently, for small rates:

E_t denotes the expectation formed at time t. Under the direct quotation, a higher domestic interest rate implies expected domestic-currency depreciation. Unlike CIP, UIP is not a pure arbitrage condition because investors bear exchange-rate risk. A risk premium may therefore cause systematic deviations.

3.3 Forward premium and discount

The forward premium on the foreign currency, expressed as an annualised proportion, is often calculated as:

where T is measured in years. With ₹90 spot and ₹93.50 one-year forward, the premium is approximately 3.89%. For a six-month contract, T = 0.5 and annualisation doubles the six-month proportional difference, subject to the market’s day-count convention.

3.4 CIP and UIP compared

4. The Fisher effect and international Fisher effect

The Fisher effect links nominal interest rates, real interest rates and expected inflation. The exact relationship is:

where i is the nominal interest rate, r is the real interest rate and π^e is expected inflation. Rearranging gives:

For modest rates, the approximation i ≈ r + π^e is often used. The exact formula should be preferred when rates or inflation are high.

The international Fisher effect combines the Fisher relationship with UIP. If real interest rates are equal across countries and capital markets are integrated, a country with higher expected inflation should have a higher nominal interest rate and an expected currency depreciation. In approximate form:

The result depends strongly on assumptions about equal real rates, rational or sufficiently informed expectations, capital mobility and comparable risk. In practice, nominal interest-rate differences also reflect sovereign risk, liquidity, taxation, regulation and central-bank credibility.

Worked example: real interest rate

If a one-year nominal interest rate is 8% and expected inflation is 5%, the exact expected real rate is:

The approximation gives 8% − 5% = 3%, which is close but not identical.

5. Expectations and exchange-rate determination

Exchange rates are asset prices. Their current value depends not only on current fundamentals but also on expected future interest rates, inflation, fiscal policy, trade conditions and risk. A simplified asset-pricing representation is:

This expression is illustrative rather than a complete exchange-rate model. k represents an appropriate discount or risk-adjusted rate, and the equation assumes a simplified one-period valuation structure. In a multi-period setting, the current price reflects the discounted expected value of future currency payoffs and risk premia.

Expectations may be:

• Static: agents expect the current rate to persist.
• Adaptive: expectations adjust gradually in response to past forecast errors.
• Rational: expectations use available information and are correct on average, although individual outcomes remain uncertain.
• Heterogeneous: different participants hold different models, information and risk tolerances.

A credible announcement of future monetary tightening can cause immediate appreciation even before rates change, because the announcement changes expected future returns. Conversely, an interest-rate increase may fail to support a currency if markets interpret it as a response to severe economic weakness or political instability.

The overshooting model associated with Dornbusch explains why exchange rates can move beyond their long-run level after a monetary disturbance. Prices of goods adjust slowly, while financial markets adjust rapidly. A monetary expansion can initially cause a large currency depreciation and later partial reversal as domestic prices rise and real money balances return toward equilibrium.

6. Monetary models of exchange rates

6.1 Flexible-price monetary model

The monetary approach treats the exchange rate as the relative price of two monies. A simplified money-demand function is:

where M is nominal money supply, P is the price level, Y is real income, i is the nominal interest rate and L is real money demand. A common log-linear specification is:

with α > 0 and β > 0. Money demand rises with income and falls with the opportunity cost represented by the interest rate.

Under absolute PPP, S = P_D/P_F. Therefore, differences in money supplies, incomes and interest rates influence the exchange rate through their effects on relative price levels. The flexible-price monetary model predicts that, other things equal, higher domestic money supply increases domestic prices and depreciates the domestic currency. Higher domestic real income raises money demand and can appreciate the currency if the money supply does not adjust proportionally.

6.2 Sticky-price monetary model

The sticky-price model allows financial markets to respond faster than goods prices. A monetary expansion initially lowers domestic interest rates, encourages capital outflow and depreciates the currency. Because domestic prices are sticky, the initial depreciation may exceed the long-run depreciation. As prices adjust, the exchange rate can return toward its long-run monetary-equilibrium value.

These models are useful for understanding monetary shocks but are not complete forecasting machines. Their results depend on stable money-demand functions, credible policy transmission, meaningful PPP in the long run and an accurate treatment of expectations.

7. Portfolio-balance models

Monetary models often imply that domestic and foreign assets are perfect substitutes after risk and return are considered. Portfolio-balance models relax this assumption. Investors allocate wealth among domestic money, domestic bonds and foreign bonds. Because assets differ in currency denomination, liquidity, maturity, default risk and political exposure, investors require risk premia.

A simplified portfolio condition can be written conceptually as:

where w_j is the portfolio share of asset j, R_j^e is expected return, σ_j represents risk and covariances capture interactions among asset returns. This is not a universal estimation equation; it expresses the principle that portfolio shares depend jointly on expected returns and risk characteristics.

An increase in domestic government debt may require a higher expected return to induce investors to hold the additional supply. The required return can arise through a higher domestic interest rate, expected currency appreciation or depreciation, or both. Consequently, fiscal deficits and debt composition may affect exchange rates even when money supply is unchanged.

Portfolio-balance analysis is particularly relevant when:

• domestic and foreign bonds are imperfect substitutes;
• sovereign risk changes abruptly;
• central banks conduct quantitative easing or reserve accumulation;
• pension funds and insurers rebalance across currencies;
• capital controls restrict arbitrage.

8. Macroeconomic, political and behavioural drivers

Macroeconomic drivers

Important macroeconomic variables include inflation, interest rates, monetary policy, fiscal policy, economic growth, productivity, current-account balances, terms of trade, commodity prices and foreign-exchange reserves. Their effects are conditional rather than mechanical. For example, a current-account deficit may weaken a currency if it signals unsustainable external financing, but it may coexist with currency strength when it reflects productive investment financed by stable capital inflows.

Central-bank communication is often as important as the current policy rate. Forward guidance changes expected short-term rates and risk premia. Quantitative easing can lower yields, alter global portfolio allocations and affect exchange rates through several channels.

Political and institutional drivers

Elections, government stability, sanctions, trade disputes, war, capital controls, debt restructuring and changes in tax or regulatory policy can affect currency values. Institutional quality matters because credible legal systems and independent monetary authorities reduce the risk premium demanded by investors.

Political events can generate non-linear effects. A small change in polling probabilities may have little impact until it crosses a threshold associated with policy reversal, capital controls or debt default. Scenario analysis is therefore often more useful than a single-point forecast.

Behavioural drivers

Exchange markets are influenced by momentum trading, carry trades, loss aversion, herding, anchoring and limits to arbitrage. A carry trade borrows in a low-interest-rate currency and invests in a high-interest-rate currency. It can produce gains for extended periods but may suffer large losses during risk-off episodes when investors unwind positions simultaneously.

Technical levels and order flow may matter in the short run because dealer inventories, stop-loss orders and liquidity conditions affect price formation. Behavioural explanations do not imply that fundamentals are irrelevant; rather, they explain why convergence toward fundamental values may be delayed or unstable.

9. Why exchange-rate forecasting is difficult

Exchange-rate forecasting faces several structural problems:

1. Model uncertainty: competing models identify different relevant variables.
2. Parameter instability: relationships change across regimes and crises.
3. Endogeneity: interest rates, inflation and exchange rates influence one another.
4. Unobservable expectations: risk premia and beliefs cannot be measured directly.
5. Rare events: wars, defaults and political surprises are difficult to estimate from historical frequencies.
6. Data limitations: revisions, measurement errors and differing price indexes distort tests.
7. Forecast comparison: a random walk can outperform sophisticated models at short horizons.

A professional forecast should therefore state its horizon, quotation convention, assumptions, probability distribution and key risks. A point estimate without a confidence range can create false precision. Forecasts should be evaluated out of sample using appropriate benchmarks, not merely by how well a model fits historical data.

A practical forecasting framework combines:

• long-run valuation using PPP and productivity analysis;
• cyclical analysis using monetary policy and economic activity;
• market pricing using forward rates, yield curves and options;
• positioning and sentiment indicators;
• political and scenario analysis;
• explicit risk-management limits.

The forward rate is not necessarily an unbiased forecast of the future spot rate. It is primarily an arbitrage-consistent price for a deliverable forward contract and may incorporate risk premia, funding effects and liquidity conditions.

10. Applied case: currency risk at Meridian Components

This is an illustrative case.

Background

Meridian Components, an Indian manufacturer, must pay €20 million to a German supplier in six months. Its functional currency is the rupee. The current spot rate is ₹90/€, and the six-month forward rate is ₹92/€. Management expects the rupee to weaken because domestic inflation is forecast to exceed euro-area inflation, but it also believes that a favourable trade announcement could strengthen the rupee.

Problem

The company must decide whether to hedge the full payable, hedge partially, or remain unhedged. The decision involves the contractual cost of a forward hedge, uncertainty about the future spot rate and the firm’s tolerance for cash-flow volatility.

Analysis

A six-month forward hedge fixes the rupee cost at:

If the spot rate in six months is ₹96/€, an unhedged payment would cost:

The forward hedge would save ₹80 million relative to that outcome. If the spot rate instead becomes ₹88/€, the unhedged payment would cost ₹1.76 billion, so the forward hedge would cost ₹80 million more than remaining unhedged. This is not a failure of the hedge: the forward contract exchanged uncertain currency cost for a known cost.

The treasury team should also examine the forward rate through CIP. If six-month domestic and foreign interest rates are 7% and 3% annualised, a simple half-year approximation gives:

The observed ₹92 forward rate is close, with the difference potentially explained by day-count conventions, bid–ask spreads, credit and liquidity costs.

Approach and solution

Meridian adopts a layered policy: hedge 70% of the confirmed payable with forwards and retain 30% flexibility. The firm also establishes a maximum unhedged exposure, monitors stress scenarios at ₹100/€ and ₹85/€, and requires board approval for speculative currency positions.

Outcome and learning points

The policy aligns hedging with the certainty of the underlying exposure. It does not attempt to forecast the exchange rate perfectly. The case demonstrates that parity conditions support pricing and plausibility checks, while risk management determines the appropriate degree of coverage. A forecast that the rupee will weaken should not automatically lead to an unhedged position; the firm’s objective is stable cash flow, not directional speculation.

11. Professional practice, governance and technology

Treasury professionals should document the exposure, quotation convention, hedge ratio, maturity, counterparty, collateral terms and accounting treatment. Derivatives should be used to manage identifiable exposures rather than conceal losses or create unauthorised speculative positions. Segregation of duties, independent valuation, confirmation controls and counterparty limits are essential.

Technology improves monitoring through real-time market data, automated exposure aggregation, scenario analysis and algorithmic execution. Machine-learning systems may identify non-linear relationships, but they remain vulnerable to regime changes, data leakage, unstable correlations and extreme events. Explainability, human oversight, model validation and cybersecurity are therefore necessary. Artificial intelligence should complement, not replace, economic reasoning and governance.

Chapter Summary

Exchange rates are relative prices determined by trade, capital flows, expectations, risk and institutional conditions. Absolute PPP links the exchange rate to relative price levels, while relative PPP predicts that inflation differentials influence exchange-rate changes over longer horizons. Covered interest-rate parity is a no-arbitrage condition linking spot, forward and interest rates; uncovered parity links expected exchange-rate changes to interest differentials but is exposed to risk premia.

The Fisher effect separates nominal rates into real returns and expected inflation. Monetary models explain exchange rates through relative money supplies, incomes and interest rates, while sticky-price versions emphasise short-run overshooting. Portfolio-balance models add imperfect asset substitutability and risk premia. Political events, behavioural biases, order flow and regime changes explain many departures from simple models.

Parity conditions are valuable benchmarks for valuation, forward pricing, hedging and scenario analysis. They are not guaranteed short-run forecasting laws. Effective professional practice combines theory, market prices, macroeconomic analysis, political scenarios, statistical testing and disciplined risk governance.

Key Terms

Exchange rate: The price of one currency expressed in another currency.

Direct quotation: Domestic-currency units per unit of foreign currency.

Appreciation: An increase in a currency’s value relative to another currency.

Depreciation: A decrease in a currency’s value relative to another currency.

Purchasing power parity: The proposition that exchange rates reflect relative price levels.

Absolute PPP: PPP expressed as equality between the exchange rate and the ratio of price levels.

Relative PPP: The proposition that exchange-rate changes reflect inflation differentials.

Law of one price: The proposition that identical tradable goods have the same common-currency price.

Covered interest parity: A no-arbitrage relationship using a forward exchange contract.

Uncovered interest parity: The expected-return relationship between interest differentials and exchange-rate changes.

Forward premium: The percentage by which the forward rate exceeds the spot rate, usually annualised.

Fisher effect: The relationship among nominal interest, real interest and expected inflation.

International Fisher effect: The proposition that nominal interest differentials predict currency changes through inflation expectations.

Risk premium: Additional expected return required for bearing risk.

Monetary model: An exchange-rate model based on relative money supply, money demand and price levels.

Overshooting: A short-run exchange-rate movement beyond its longer-run equilibrium response.

Portfolio-balance model: A model in which asset supplies and imperfect substitutability affect exchange rates.

Carry trade: Borrowing in a low-interest-rate currency to invest in a higher-interest-rate currency.

Real exchange rate: A nominal exchange rate adjusted for relative price levels.

Exchange-rate risk: The possibility that currency movements will adversely affect value or cash flow.

Review Questions

5 Short Answer Questions

1. What is the difference between a direct and an indirect exchange-rate quotation?
2. State the absolute and relative forms of purchasing power parity.
3. Why is covered interest parity considered a no-arbitrage relationship?
4. What does the Fisher effect explain?
5. Identify two reasons why actual exchange rates may diverge from PPP.

5 Long Answer Questions

1. Explain covered and uncovered interest-rate parity, including their assumptions and practical uses.
2. Discuss the monetary and portfolio-balance approaches to exchange-rate determination.
3. Explain how expectations and sticky prices can produce exchange-rate overshooting.
4. Evaluate the usefulness and limitations of PPP for corporate financial decisions.
5. Analyse the macroeconomic, political and behavioural factors that influence exchange rates.

3 Analytical / Application Questions

1. The spot rate is ₹90/€, domestic interest is 7% and foreign interest is 3% for one year. Calculate the CIP-implied forward rate and explain the direction of the forward premium.
2. Domestic inflation is expected to be 8% and foreign inflation 3%, with a current exchange rate of ₹90 per foreign currency unit. Use relative PPP to estimate the future exchange rate and state the assumptions involved.
3. A firm has a foreign-currency payable in six months. Compare full hedging, partial hedging and no hedging, and recommend a policy using exposure certainty, risk tolerance and scenario analysis.

Multiple Choice Questions with Answers

Question 1

Under the direct quotation used in this chapter, an increase in the exchange rate from ₹90/€ to ₹94/€ represents:

A. Rupee appreciation and euro depreciation

B. Rupee depreciation and euro appreciation

C. Depreciation of both currencies

D. No change in relative currency value

Correct Answer: B. Rupee depreciation and euro appreciation

Question 2

If domestic inflation is 6% and foreign inflation is 2%, relative PPP approximately predicts that the domestic currency will:

A. Appreciate by 4%

B. Depreciate by 4%

C. Appreciate by 8%

D. Remain unchanged

Correct Answer: B. Depreciate by 4%

Question 3

Which feature distinguishes covered interest parity from uncovered interest parity?

A. CIP uses a forward contract to hedge exchange risk

B. CIP assumes inflation is zero

C. UIP eliminates all exchange-rate risk

D. UIP is a pure arbitrage condition

Correct Answer: A. CIP uses a forward contract to hedge exchange risk

Question 4

If S₀ = ₹90/€, i_D = 7% and i_F = 3%, the one-year CIP-implied forward rate is closest to:

A. ₹86.64/€

B. ₹90.00/€

C. ₹93.50/€

D. ₹97.20/€

Correct Answer: C. ₹93.50/€

Question 5

The exact Fisher relationship is:

A. i = r − πᵉ

B. 1 + i = (1 + r)(1 + πᵉ)

C. r = i × πᵉ

D. 1 + r = i + πᵉ

Correct Answer: B. 1 + i = (1 + r)(1 + πᵉ)

Question 6

Under approximate uncovered interest parity, a higher domestic interest rate implies:

A. Expected domestic-currency appreciation equal to the interest differential

B. Expected domestic-currency depreciation equal to the interest differential

C. No expected exchange-rate movement

D. A guaranteed domestic-currency appreciation

Correct Answer: B. Expected domestic-currency depreciation equal to the interest differential

Question 7

The Balassa–Samuelson effect is associated with:

A. Higher tradable-sector productivity affecting domestic non-traded prices

B. A legal prohibition on forward contracts

C. Equal inflation in all countries

D. The elimination of sovereign risk

Correct Answer: A. Higher tradable-sector productivity affecting domestic non-traded prices

Question 8

A portfolio-balance model differs from a simple monetary model because it emphasises:

A. Perfect substitutability of all assets

B. Asset supplies, imperfect substitutability and risk premia

C. The irrelevance of capital flows

D. Only the quantity of exports

Correct Answer: B. Asset supplies, imperfect substitutability and risk premia

Question 9

If a six-month foreign-currency payable is €20 million and the six-month forward rate is ₹92/€, the hedged rupee cost is:

A. ₹920 million

B. ₹1.84 billion

C. ₹2.20 billion

D. ₹18.4 billion

Correct Answer: B. ₹1.84 billion

Question 10

Why can exchange-rate forecasting remain difficult even when economic models are sophisticated?

A. Exchange rates never respond to expectations

B. Parameters, regimes and risk premia can change over time

C. Interest rates are irrelevant to currencies

D. Political events are always predictable

Correct Answer: B. Parameters, regimes and risk premia can change over time