Exchange-Rate Determination: Theories and Models

Introduction

The exchange rate is the price of one currency expressed in units of another. It affects international trade, capital flows, inflation, corporate profitability, sovereign debt servicing and the competitiveness of multinational enterprises. Yet exchange rates are not determined by one universal mechanism. Their behaviour reflects the interaction of goods-market prices, interest rates, expectations, monetary policy, risk preferences, asset supplies and institutional credibility.

This chapter examines the principal theories and models of exchange-rate determination. Purchasing power parity explains exchange rates through relative price levels; interest-rate parity links spot and forward exchange rates to interest differentials; the Fisher effect connects nominal interest rates with expected inflation; monetary models emphasize money supplies, incomes and prices; portfolio-balance models incorporate imperfect substitutability among financial assets; and overshooting models explain why exchange rates may move more than their long-run equilibrium following monetary disturbances. The chapter also considers real exchange rates, expectations and behavioural approaches.

No model should be treated as a complete forecasting law. Each is conditional on assumptions that may be reasonable over some horizons and unrealistic over others. Professional analysis therefore combines models with market information, institutional knowledge and careful attention to structural change.

Learning objectives

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

1. Explain and critically evaluate purchasing power parity and its absolute and relative forms.
2. Apply covered and uncovered interest-rate parity while distinguishing arbitrage conditions from empirical forecasts.
3. Relate nominal interest rates, expected inflation and real interest rates through the Fisher effect.
4. Analyse monetary, portfolio-balance and overshooting models of exchange-rate determination.
5. Calculate and interpret nominal and real exchange rates.
6. Assess the role of expectations, risk premia, market imperfections and behavioural bias.
7. Use exchange-rate models in international business decisions without confusing equilibrium conditions with reliable short-term forecasts.

1. Exchange-rate concepts and conventions

Let S denote the spot exchange rate quoted as domestic currency units per unit of foreign currency. An increase in S is a domestic-currency depreciation: more domestic currency is required to buy one unit of foreign currency. A decrease is an appreciation. Quotation conventions must always be stated because the same movement can be described oppositely under the reciprocal quotation.

The forward exchange rate, F, is the contracted exchange rate for delivery at a future date. The domestic interest rate is i_d, the foreign interest rate is i_f, and the horizon is T years. Rates should refer to comparable instruments, maturities, compounding conventions and risk characteristics.

The exchange rate is an asset price. It responds not only to current trade flows but also to anticipated future monetary policy, inflation, productivity, fiscal policy, political risk and international portfolio allocation. This is why financial-market exchange rates can change substantially before trade data or consumer prices change.

2. Purchasing power parity

Absolute purchasing power parity

Absolute purchasing power parity (PPP) states that, under ideal conditions, identical tradable goods should have the same price when expressed in a common currency. If P_d is the domestic price of a representative basket and P_f is the foreign price, then:

This formulation assumes frictionless trade, identical baskets, no transport costs, no tariffs or taxes, competitive markets and price flexibility. These assumptions are rarely fully satisfied. Non-traded services, product differentiation and distribution costs create persistent deviations.

The law of one price applies to an individual identical tradable good. PPP applies the logic to a broad basket. A price index is not a neutral object: different countries assign different weights to housing, food, energy, services and manufactured goods. Consequently, an observed deviation from PPP may reflect measurement as well as market disequilibrium.

Relative PPP

Relative PPP is more useful empirically. It predicts that the rate of currency depreciation approximately equals the inflation differential:

Here, π_d and π_f are domestic and foreign inflation rates, and ΔS is the change in the domestic-currency price of foreign currency. The approximation is appropriate for moderate changes. A more exact expression is:

For example, if domestic inflation is 8% and foreign inflation is 3%, relative PPP predicts a depreciation of approximately 5%. The exact one-year factor is 1.08 ÷ 1.03 = 1.0485, implying a 4.85% depreciation.

PPP tends to perform better over long horizons and for countries experiencing very high inflation than over short horizons in low-inflation economies. Short-run deviations arise from sticky prices, interest-rate changes, capital flows, speculative positioning, terms-of-trade shocks and risk premia. The empirical tendency of high-interest-rate currencies sometimes to appreciate rather than depreciate also contradicts a simple mechanical use of relative PPP.

3. Interest-rate parity

Interest-rate parity connects exchange rates with international borrowing and lending.

Covered interest-rate parity

Covered interest-rate parity (CIP) is an arbitrage condition. An investor can invest domestically or convert funds into foreign currency, invest abroad and use a forward contract to eliminate exchange-rate risk. Under the domestic-per-foreign quotation:

Thus:

For continuously compounded rates, the equivalent expression is F = S × e^{(i_d − i_f)T}. CIP assumes comparable risk-free instruments, no capital controls, negligible transaction costs, and the ability to borrow and lend at the stated rates. If these conditions hold, a persistent violation creates a covered arbitrage opportunity. In practice, balance-sheet costs, counterparty risk, funding constraints and regulation can produce a small cross-currency basis.

Uncovered interest-rate parity

Uncovered interest-rate parity (UIP) leaves the future exchange rate unhedged. It predicts:

where E_t denotes the expectation formed at time t. UIP is not a pure arbitrage condition because the investor bears exchange-rate risk. It is a behavioural or equilibrium relationship that depends on risk neutrality or on a risk premium being zero. A more general representation is:

where ρ_t is the expected foreign-currency risk premium, with its sign depending on the quotation and definition. Empirically, high-interest-rate currencies have often failed to depreciate as UIP predicts, generating the well-known carry-trade anomaly. This may reflect time-varying risk premia, peso problems, funding liquidity and changing expectations rather than a simple rejection of rational pricing.

Forward rates and expectations

CIP determines the forward rate from interest differentials, but the forward rate need not equal the expected future spot rate. The relationship can be written conceptually as:

The exact sign and form depend on quotation and measurement. The central point is that forward prices incorporate hedging demand and risk-bearing capacity, not merely unbiased forecasts.

4. The Fisher effect and international Fisher relationships

The Fisher equation links nominal interest rates, real interest rates and expected inflation:

where i is the nominal interest rate, r is the real interest rate and π^e is expected inflation. For moderate rates:

The exact equation is preferable when rates are large because the approximation omits the interaction term rπ^e. The Fisher effect predicts that a rise in expected inflation increases the nominal interest rate approximately one-for-one if the real rate is unchanged.

The international Fisher effect combines the Fisher relationship with UIP. If real interest rates are equal across countries and risk premia are absent, a country with higher nominal interest rates is expected to experience currency depreciation because its higher nominal rate reflects higher expected inflation. This is a long-run proposition, not a reliable short-run trading rule.

A central analytical distinction is between nominal and real shocks. A credible tightening of monetary policy may raise real interest rates temporarily and appreciate the currency, even if inflation is expected eventually to fall. Conversely, a fiscal or political shock can raise nominal yields because of higher risk rather than higher expected productivity.

5. Monetary models of exchange-rate determination

Monetary models treat the exchange rate as the relative price of two monies. A basic flexible-price monetary model begins with money-market equilibrium:

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

where lowercase letters represent logarithms, φ > 0 is the income elasticity of money demand and λ > 0 is the interest sensitivity.

Combining relative money-market equilibrium with PPP gives a monetary exchange-rate relationship in which the exchange rate rises when domestic money supply rises relative to foreign money supply, rises when domestic income falls relative to foreign income, and falls when the domestic interest rate rises relative to the foreign rate, holding other variables constant. In log form, a representative expression is:

The precise sign of the interest term depends on the quotation and the way interest rates are solved from money demand. The economic interpretation must therefore be checked against the stated convention rather than memorised mechanically.

The monetary model’s strengths are its explicit link between monetary policy, inflation and exchange rates, and its usefulness for long-run analysis. Its limitations include the assumption of stable money demand, flexible prices, PPP and often exogenous output. Financial innovation, unstable velocity, interest-rate rules and supply shocks weaken these assumptions.

Monetary approach to the balance of payments

A related monetary approach views balance-of-payments disequilibrium as a monetary phenomenon. Excess domestic money supply encourages spending on domestic and foreign goods and assets, generating reserve losses under a fixed exchange rate or currency depreciation under a floating rate. The approach is especially relevant when central-bank reserve changes strongly affect the monetary base. It is less persuasive where sterilisation, capital controls or endogenous money creation dominate.

6. Portfolio-balance models

Monetary models often assume that domestic and foreign assets are perfect substitutes or that asset markets adjust instantly. Portfolio-balance models relax this assumption. Investors allocate wealth among domestic money, domestic bonds and foreign bonds according to expected returns, liquidity, maturity, currency risk and perceived default risk.

A simplified balance-sheet identity is:

where W is domestic-currency wealth, M_d is domestic money, B_d is domestic bonds and B_f is foreign-currency bonds. The supply of assets matters because investors require compensation to hold a larger quantity of a risky or imperfectly substitutable asset.

Suppose the government increases the supply of domestic bonds without an equivalent increase in money. If domestic and foreign bonds are imperfect substitutes, investors may require a higher domestic yield or a depreciated currency to absorb the additional risk. The exchange-rate response depends on portfolio preferences, wealth effects and expectations. A central-bank purchase of domestic bonds can reduce yields and alter the currency through both interest-rate and portfolio-rebalancing channels.

Portfolio-balance models explain why sterilised intervention may influence exchange rates even when the monetary base is unchanged. Their limitation is empirical identification: risk preferences, expected returns and asset supplies are difficult to observe, and the model can become highly parameter-dependent.

7. Expectations, asset pricing and overshooting

Exchange rates are forward-looking. If markets expect a future policy change, the currency may move immediately, before the policy affects trade or prices. Expectations may be rational, adaptive, extrapolative or heterogeneous.

Under rational expectations, agents use available information efficiently in forming forecasts, although realized outcomes remain uncertain. Adaptive expectations revise forecasts using past errors. Behavioural participants may extrapolate recent trends, follow other investors or anchor on historical ranges. These mechanisms can coexist in markets.

Dornbusch overshooting

The overshooting model explains short-run exchange-rate volatility through differential adjustment speeds. Financial markets and exchange rates adjust rapidly, while goods prices are sticky. Consider an unexpected permanent increase in the domestic money supply. In the long run, the price level and exchange rate rise proportionately under PPP. In the short run, prices cannot adjust fully. Real money balances rise, domestic interest rates fall, and capital shifts toward foreign assets. The currency depreciates immediately—possibly beyond its long-run depreciation—before gradually appreciating toward its new long-run level as domestic prices increase.

The sequence is:

1. Money supply increases unexpectedly.
2. Goods prices remain temporarily sticky.
3. Real money balances rise.
4. Domestic interest rates fall.
5. The currency depreciates sharply.
6. Domestic prices gradually rise.
7. Real balances and interest rates return toward equilibrium.
8. The exchange rate moves back from its overshot value.

Overshooting is not a claim that every monetary expansion produces overshooting. It requires sticky prices, flexible financial markets, forward-looking expectations and an appropriate monetary shock. A credible interest-rate increase may instead appreciate the currency immediately if markets interpret it as disinflationary and sustainable.

8. Real exchange rates and competitiveness

The real exchange rate measures the relative price of foreign goods in terms of domestic goods. With S defined as domestic currency per foreign currency:

A rise in q represents a real depreciation under this convention: foreign goods become more expensive relative to domestic goods. A fall represents a real appreciation. Because alternative sources define the real exchange rate as the reciprocal, the quotation must always be reported.

The percentage change in the real exchange rate is approximately:

A nominal depreciation improves competitiveness only if it is not offset by higher domestic inflation. The real exchange rate is therefore more informative than the nominal rate for analysing exports, imports and trade-exposed investment. However, competitiveness also depends on productivity, quality, logistics, wages, taxes, energy prices, financing costs and supply-chain resilience.

A productivity increase in tradable industries can produce real appreciation through higher wages and prices in the broader economy—the Balassa–Samuelson mechanism—without necessarily indicating a loss of external efficiency. Real exchange-rate misalignment is therefore difficult to define independently of fundamentals.

9. Behavioural and institutional explanations

Behavioural approaches challenge the assumption that all participants process information identically. Important mechanisms include:

• Overreaction and underreaction: investors may respond too strongly to news or adjust gradually because of ambiguity.
• Herding: managers imitate other investors, especially when reputational incentives discourage independent positions.
• Anchoring: forecasts remain tied to a previous exchange rate or round-number level.
• Loss aversion: participants may hold losing positions too long or close profitable positions prematurely.
• Limits to arbitrage: funding risk, margin requirements and uncertain timing prevent traders from eliminating mispricing.
• Order-flow effects: customer trades convey dispersed information and can move prices even without public macroeconomic news.

Institutional credibility is equally important. A central bank with a credible inflation target may cause a monetary tightening to appreciate the currency because expected inflation falls. The same rate increase in a fiscally fragile economy may trigger depreciation if investors interpret it as compensation for default or inflation risk. Political institutions, capital-account rules, reserve adequacy and external debt currency composition shape these responses.

10. Applying models in international business

Managers should use models diagnostically rather than mechanically. A practical workflow is:

1. State the quotation and horizon.
2. Identify whether the decision concerns a transaction rate, a budget rate, a long-run investment rate or a risk scenario.
3. Establish a baseline using PPP, interest differentials and macroeconomic fundamentals.
4. Add expected policy changes, risk premia, market positioning and institutional conditions.
5. Construct adverse and favourable scenarios rather than relying on one point forecast.
6. Match the exposure with hedging instruments, operational flexibility or financing choices.
7. Review the forecast and document the assumptions.

For example, a firm pricing a three-month import should prioritize the contracted forward rate and hedging cost. A firm deciding where to locate a factory should emphasize the real exchange rate, productivity, wages, infrastructure and long-run policy credibility. A treasury department should distinguish forecast error from hedge performance: a hedge can be successful even when the currency moves favourably, because its purpose is to reduce unwanted risk rather than maximize speculative profit.

11. Worked application: importing machinery

An Indian firm must pay USD 10 million in six months. The current quote is ₹83 per USD. The six-month Indian interest rate is 6% annualized and the US rate is 4% annualized, with simple proportional compounding for the half-year. Under CIP:

The rupee cost locked through a forward contract is approximately:

or approximately ₹83.81 crore. This calculation assumes the quoted rates are comparable, the forward is fairly priced, counterparty performance is reliable and transaction costs are excluded. It does not predict the future spot rate. If the firm remains unhedged, its eventual rupee cost will depend on the spot rate at maturity; if it hedges, it gives up favourable spot movements in exchange for certainty.

12. Illustrative case: a currency depreciation after monetary easing

Background. Consider an illustrative emerging economy, Arandia, whose central bank unexpectedly cuts its policy rate while inflation expectations are already rising. The government also announces a large fiscal programme financed partly through domestic borrowing.

Problem. The currency depreciates by 12% in three weeks, although the country’s trade deficit has changed little. Exporters welcome the initial movement, but firms with foreign-currency debt face sharply higher repayment costs.

Analysis. A simple PPP model cannot explain the speed of the movement because consumer prices are sticky. A monetary model predicts depreciation from easier monetary conditions and increased expected inflation. A portfolio-balance model adds that the larger supply of domestic bonds requires compensation through higher yields, a risk premium or currency depreciation. The overshooting model explains the immediate movement beyond the eventual long-run adjustment: asset markets react quickly while goods prices adjust slowly. Behavioural factors may amplify the change if investors herd after observing reserve losses and negative news.

Approach. Arandian firms construct scenarios. In the baseline, policy credibility is restored and the currency partially recovers. In the adverse scenario, inflation expectations become unanchored and foreign funding is withdrawn. Firms with dollar liabilities hedge a portion of their exposure, extend maturities and increase the share of local-currency revenues. The central bank improves communication, publishes intervention principles and coordinates fiscal and monetary signals without sacrificing operational independence.

Outcome. The currency stabilizes after real interest rates become positive and fiscal financing is clarified. It does not return immediately to its pre-shock nominal level, but the real exchange rate becomes less overvalued and external adjustment improves.

Learning points. Exchange-rate determination is a joint outcome of monetary conditions, expectations, asset supplies, credibility and risk. A model that explains one horizon may be unsuitable for another. Corporate responses should address both price risk and balance-sheet risk.

13. Limitations, governance and contemporary developments

Exchange-rate models face several persistent limitations. Parameters may change after financial liberalisation, crises or regime shifts. Inflation and interest-rate data are revised. Expectations cannot be observed directly. Structural breaks make historical relationships unreliable. Equilibrium concepts such as PPP may be useful benchmarks without being attainable targets.

Regulators and treasurers must also manage governance risks. Derivatives should be used under documented mandates, independent valuation, counterparty limits, collateral procedures and accounting controls. Firms should disclose material currency exposures and avoid presenting speculative positions as hedges. Public institutions must communicate intervention and reserve policies clearly to reduce disorderly market conditions without promising a specific exchange-rate level.

Technology has improved high-frequency data analysis, scenario generation and execution. Machine-learning systems can detect nonlinearities in order flow or volatility, but they do not eliminate model risk. Historical data may embed regime-specific relationships, and automated systems can amplify herding or liquidity shortages. AI outputs should therefore be tested for stability, monitored by human experts and governed through audit trails, explainability and access controls.

Best-practice synthesis

A robust exchange-rate assessment should:

• use clear quotation conventions;
• separate long-run equilibrium from short-run dynamics;
• distinguish arbitrage conditions from risky forecasts;
• compare nominal and real measures;
• include risk premia and imperfect substitutability;
• test sensitivity to inflation, interest rates, growth and credibility;
• use scenarios and probability ranges rather than false precision;
• integrate market evidence with institutional and balance-sheet analysis; and
• align forecasts with the actual decision horizon and exposure.

Chapter Summary

Exchange rates are determined through interacting goods-market, money-market and asset-market forces. Absolute PPP links the exchange rate to relative price levels, while relative PPP links currency depreciation to inflation differentials. Covered interest-rate parity is an arbitrage condition connecting spot, forward and interest rates; uncovered parity is an expectation-based relationship that may include a risk premium. The Fisher effect separates nominal interest rates into real rates and expected inflation.

Monetary models emphasize relative money supplies, incomes, interest rates and prices. Portfolio-balance models improve on them by recognizing that domestic and foreign assets are imperfect substitutes and that asset supplies affect required returns. Expectations make exchange rates forward-looking, and the overshooting model explains why a currency may move beyond its long-run equilibrium when financial markets adjust faster than goods prices. The real exchange rate is central to competitiveness, while behavioural and institutional factors explain deviations from purely rational, frictionless models.

For international business, these theories are best used as complementary diagnostic tools. Forecasts should be conditional, scenario-based and matched to the firm’s exposure, horizon, hedging policy and governance requirements.

Key Terms

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

Absolute PPP: PPP expressed as equality between a currency-adjusted domestic and foreign price basket.

Relative PPP: The proposition that currency depreciation approximately equals the inflation differential.

Covered interest-rate parity: The no-arbitrage relationship among spot rates, forward rates and interest rates.

Uncovered interest-rate parity: The expectation-based relationship between interest differentials and expected currency changes.

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

Risk premium: Compensation required for bearing currency, credit, liquidity or other risks.

Nominal exchange rate: The market price of one currency in another currency.

Real exchange rate: The relative price of foreign goods measured in domestic goods.

Monetary model: An exchange-rate model based on relative money supplies, prices, incomes and money demand.

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

Expectations: Beliefs about future economic variables that influence current decisions.

Rational expectations: Forecasts formed using available information without systematic errors in expectations.

Overshooting: A short-run exchange-rate movement beyond its eventual long-run adjustment.

Sticky prices: Prices that adjust slowly to economic disturbances.

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

Currency exposure: The sensitivity of a firm’s value or cash flows to exchange-rate changes.

Sterilised intervention: Foreign-exchange intervention offset by a central-bank operation that preserves the monetary base.

Balassa–Samuelson effect: Real appreciation associated with higher productivity in tradable goods.

Cross-currency basis: A deviation from covered interest parity observed in market funding prices.

Review Questions

Short Answer Questions

1. Distinguish absolute PPP from relative PPP.
2. Why is covered interest-rate parity considered an arbitrage condition?
3. State the Fisher equation and identify its components.
4. Define the real exchange rate using the domestic-currency-per-foreign-currency quotation.
5. Why can the forward exchange rate differ from the expected future spot rate?

Long Answer Questions

1. Critically evaluate the assumptions and empirical usefulness of purchasing power parity.
2. Compare monetary and portfolio-balance models of exchange-rate determination.
3. Explain the mechanism of Dornbusch overshooting following an unexpected monetary expansion.
4. Discuss how risk premia and imperfect asset substitutability affect uncovered interest-rate parity.
5. Evaluate the relevance of behavioural explanations for exchange-rate volatility.

Analytical / Application Questions

1. Domestic inflation is 9% and foreign inflation is 4%. Use relative PPP to estimate the approximate and exact one-year depreciation of the domestic currency.
2. A firm must pay USD 5 million in six months. The spot rate is ₹82 per USD, the domestic annual interest rate is 7%, and the foreign annual interest rate is 3%. Using simple six-month compounding and covered interest-rate parity, calculate the forward rate and the rupee cost of hedging.
3. A central bank unexpectedly increases the money supply while goods prices are sticky and capital markets are highly liquid. Use the monetary and overshooting models to predict the short-run and long-run exchange-rate effects, and identify two assumptions that could invalidate the prediction.

Multiple Choice Questions with Answers

Question 1

Under the domestic-currency-per-foreign-currency quotation, an increase in the spot exchange rate represents:

A. Domestic-currency appreciation

B. Domestic-currency depreciation

C. A fall in foreign inflation

D. A fall in the forward premium

Correct Answer: B. Domestic-currency depreciation

Question 2

Relative purchasing power parity primarily predicts that:

A. The forward rate always equals the future spot rate

B. Currency depreciation approximately equals the inflation differential

C. Real interest rates are identical in every country

D. Money demand is independent of income

Correct Answer: B. Currency depreciation approximately equals the inflation differential

Question 3

Covered interest-rate parity is best described as:

A. A condition involving unhedged foreign investment risk

B. A no-arbitrage relationship using a forward contract

C. A theory that prices never change

D. A rule that high-interest currencies always appreciate

Correct Answer: B. A no-arbitrage relationship using a forward contract

Question 4

If domestic expected inflation rises while the real interest rate remains unchanged, the Fisher effect predicts that the domestic nominal interest rate will:

A. Fall approximately one-for-one

B. Rise approximately one-for-one

C. Remain unchanged

D. Become zero

Correct Answer: B. Rise approximately one-for-one

Question 5

In the real exchange-rate formula q = S × P_f ÷ P_d, a rise in q under the stated quotation represents:

A. Real appreciation

B. Real depreciation

C. A fall in foreign prices only

D. A fall in the nominal exchange rate necessarily

Correct Answer: B. Real depreciation

Question 6

A key assumption behind exchange-rate overshooting is that:

A. Goods prices adjust faster than financial markets

B. Financial markets adjust faster than goods prices

C. Interest rates never change

D. Expectations are absent

Correct Answer: B. Financial markets adjust faster than goods prices

Question 7

Portfolio-balance models differ from simple monetary models because they emphasize:

A. Perfect substitutability of all assets

B. Asset supplies and imperfect substitutability

C. The irrelevance of wealth

D. Fixed consumer prices forever

Correct Answer: B. Asset supplies and imperfect substitutability

Question 8

If domestic inflation is 8% and foreign inflation is 3%, the approximate relative-PPP prediction is domestic-currency depreciation of:

A. 3%

B. 5%

C. 8%

D. 11%

Correct Answer: B. 5%

Question 9

A forward exchange rate need not equal the expected future spot rate because:

A. Forward contracts contain no prices

B. Risk premia and hedging demand may affect the forward rate

C. Interest rates cannot influence exchange rates

D. PPP requires all expectations to be correct

Correct Answer: B. Risk premia and hedging demand may affect the forward rate

Question 10

Which managerial practice is most consistent with sound exchange-rate governance?

A. Treating every derivative as a speculative position

B. Using one point forecast without assumptions

C. Matching hedges to documented exposures and decision horizons

D. Ignoring counterparty and collateral risk

Correct Answer: C. Matching hedges to documented exposures and decision horizons