Exchange-Rate Determination and Forecasting

Introduction

Exchange rates connect national monetary systems. They affect export competitiveness, import costs, foreign-investment returns, debt service, inflation and the translated value of multinational operations. Yet an exchange rate is not determined by one variable. Goods-market conditions, interest rates, capital flows, expectations, risk premiums and policy interventions interact across different time horizons.

This chapter develops the principal theories used to explain exchange-rate movements and shows how they inform forecasting. Parity conditions provide disciplined benchmarks rather than infallible predictions. Balance-of-payments and asset-market approaches then broaden the analysis to incorporate international transactions, expectations and portfolio decisions. Finally, fundamental, technical and scenario-based methods are integrated into a practical forecasting process.

Learning Objectives

After studying this chapter, students should be able to:

1. Interpret direct exchange-rate quotations and identify appreciation or depreciation.
2. Apply absolute and relative purchasing power parity correctly.
3. Use covered and uncovered interest rate parity.
4. Explain the domestic and international Fisher effects.
5. Evaluate balance-of-payments, monetary and portfolio-balance explanations of exchange rates.
6. Assess major macroeconomic and institutional exchange-rate drivers.
7. Construct fundamental, technical and scenario-based forecasts.
8. Evaluate forecast accuracy and apply forecasts to international business decisions.

Exchange-Rate Conventions

Let S_t denote the spot exchange rate at time t, quoted as units of domestic currency per unit of foreign currency. If the United States is domestic and the euro area is foreign, S_t = 1.10 USD/EUR means that one euro costs USD 1.10.

Under this convention:

• An increase in S_t means that foreign currency appreciates and domestic currency depreciates.
• A decrease in S_t means that foreign currency depreciates and domestic currency appreciates.

The percentage change is:

For example, if the rate rises from 1.10 to 1.155 USD/EUR, the euro appreciates by 5% against the dollar. The reciprocal quotation does not generally change by exactly −5%; it changes from 0.9091 to 0.8658 EUR/USD, a decline of approximately 4.76%.

For continuously compounded analysis, analysts often use s_t = ln(S_t/S_ref), where S_ref is a fixed reference rate with the same quotation units. Changes satisfy Δs_t = ln(S_t/S_t-1), which is dimensionless and approximately equals the percentage change for small movements.

Purchasing Power Parity

Purchasing power parity (PPP) connects exchange rates to national price levels. It originates from the law of one price: in frictionless and competitive markets, an identical tradable good should have the same price in different countries after currency conversion.

Absolute PPP and Dimensional Consistency

Let:

• P_d = domestic-currency price of a specified comparable basket, measured in domestic currency per basket;
• P_f = foreign-currency price of the same basket, measured in foreign currency per basket;
• S = domestic currency per unit of foreign currency.

Absolute PPP requires:

Therefore:

The units are consistent: domestic currency per basket divided by foreign currency per basket gives domestic currency per foreign currency.

A corresponding real exchange rate is:

Here q is dimensionless because both numerator and denominator are measured in domestic currency per basket. Absolute PPP implies q = 1. A value above one means the foreign basket is relatively expensive after conversion; a value below one means the domestic basket is relatively expensive.

This interpretation requires currency-denominated prices for genuinely comparable baskets. Arbitrarily rebased consumer price indexes are dimensionless and cannot, by themselves, be inserted into S = P_d/P_f to obtain an exchange rate with currency units. Price indexes may be used for relative PPP or for real-exchange-rate indexes only when base-period normalizations are made consistently. For example, a dimensionless real-exchange-rate index can be constructed as:

where I_d and I_f are consistently defined price indexes. By construction, Q₀ = 1.

Absolute PPP rarely holds exactly because of transport costs, tariffs, taxes, nontradable services, differentiated products and imperfect competition.

Relative PPP

Relative PPP predicts that exchange-rate changes offset differences in inflation. If PPP holds in both periods, then:

where π_d and π_f are domestic and foreign inflation over the same period. Thus:

For moderate inflation rates:

This approximation is not exact and becomes less reliable when inflation is high.

Worked Example: Relative PPP

Suppose S₀ = 1.10 USD/EUR. Expected US inflation is 3%, while expected euro-area inflation is 6%.

The euro is forecast to depreciate by approximately 2.83%. The inflation-differential approximation gives −3%, which is close but not identical.

PPP tends to perform better over long horizons and in high-inflation economies than as a short-term forecasting rule. Short-run deviations may persist because goods prices adjust slowly while financial-market prices change immediately.

Interest Rate Parity

Interest rate parity links spot rates, forward rates and returns on comparable financial assets. Comparisons require matching maturities, currencies, credit risk, liquidity and tax treatment.

Covered Interest Rate Parity

Covered interest rate parity (CIP) follows from no-arbitrage when exchange-rate risk is eliminated with a forward contract.

Let:

• i_d = domestic interest rate for the investment period;
• i_f = comparable foreign interest rate;
• F_0,1 = forward exchange rate for period 1, domestic currency per foreign currency;
• S₀ = current spot rate in the same quotation.

One unit of domestic currency invested domestically becomes 1+i_d. Alternatively, it can be converted into 1/S₀ foreign-currency units, invested abroad and sold forward. The covered foreign payoff is (1+i_f)F_0,1/S₀. No-arbitrage requires:

Therefore:

The exact forward premium is:

For small rates, it is approximately i_d-i_f.

Worked Example: Covered Interest Parity

Suppose the spot rate is 1.10 USD/EUR, the matched-period US interest rate is 4%, and the euro interest rate is 2%.

A materially different market forward rate could create arbitrage before transaction costs, credit constraints and bid–ask spreads. Since the global financial crisis, deviations have occasionally persisted because balance-sheet costs, collateral rules and funding constraints prevent costless arbitrage.

Uncovered Interest Rate Parity

Uncovered interest rate parity (UIP) replaces the known forward rate with the expected future spot rate:

Approximately:

UIP requires investors to be risk-neutral or to require no currency risk premium, and expectations must be formed consistently. In practice, currencies with high interest rates have not always depreciated as UIP predicts. This empirical pattern supports carry trades, although carry returns can reverse sharply during crises.

A risk-adjusted interpretation allows expected exchange-rate changes to differ from the interest differential because investors require compensation for currency risk. Consequently, the forward rate is a useful market benchmark but is not necessarily an unbiased predictor of the future spot rate.

Fisher Effects

The Fisher effect separates a nominal interest rate into an expected real return and expected inflation. The exact relationship is:

where i is the nominal interest rate, r is the expected real interest rate and Eπ is expected inflation over the same period. Solving for the real rate gives:

The familiar approximation is i ≈ r + Eπ.

For example, with a nominal rate of 7% and expected inflation of 4%:

The international Fisher effect combines the Fisher relationship with an assumption that expected real interest rates are equal across countries. Under that restrictive condition, nominal interest differentials primarily reflect expected inflation differentials and are associated with expected currency depreciation under UIP. Differences in risk, taxation, capital controls and real returns weaken this result.

Balance-of-Payments Approach

The balance of payments records transactions between residents and nonresidents. Under the IMF BPM6 presentation, a simplified identity is:

where:

• CA = current-account balance;
• KA = capital-account balance;
• FA = financial account, defined as net acquisition of financial assets minus net incurrence of liabilities;
• E = net errors and omissions.

Thus, ignoring the usually small capital account and statistical discrepancy, a current-account surplus corresponds to net financial acquisition abroad. Alternative publications may use opposite signs for financial inflows, so analysts must verify the accounting convention.

The traditional flow approach argues that exchange rates adjust to balance demand and supply arising from trade and financial transactions. Strong export demand can increase demand for a currency, while large import payments can increase its supply. However, a current-account deficit does not mechanically imply immediate depreciation. It may be financed by strong foreign direct investment or portfolio inflows that support the currency.

Exchange-rate depreciation may improve the trade balance only after delays. Existing contracts can initially make imports more expensive before quantities adjust, producing a J-curve pattern. Improvement is more likely when export and import demand respond sufficiently to relative-price changes, productive capacity is available and firms can switch markets.

Asset-Market Approaches

Modern foreign-exchange markets are dominated by transactions in financial assets. Exchange rates therefore respond rapidly to new information about future monetary policy, risk and expected returns.

Monetary Approach

The monetary approach combines money-market equilibrium with PPP. In a stylized flexible-price model, a relative expansion of domestic money supply tends to raise the domestic price level and depreciate the domestic currency. Higher domestic real income raises money demand and may appreciate the currency, other things equal.

A common log-linear representation is:

Here lower-case variables are logarithms of consistently normalized exchange-rate, money and real-income measures; c absorbs units and normalizations. The parameters α and β are positive under the model’s money-demand assumptions. The equation is a theoretical specification, not a universal empirical law.

Sticky Prices and Overshooting

Dornbusch’s overshooting model recognizes that financial markets adjust faster than goods prices. After an unexpected monetary expansion, domestic interest rates may fall. The currency can depreciate immediately by more than its eventual long-run depreciation so that investors expect a subsequent appreciation sufficient to restore return equilibrium. Overshooting helps explain why exchange rates are more volatile than consumer prices.

Portfolio-Balance Approach

Domestic and foreign assets may be imperfect substitutes because they differ in currency risk, sovereign risk and liquidity. Exchange rates must then adjust to make investors willing to hold the outstanding supplies of assets. Larger government debt, shifts in global risk tolerance or changes in reserve management may alter required risk premiums.

The portfolio-balance approach is particularly relevant when fiscal policy, safe-haven demand or central-bank asset purchases change the composition and perceived risk of global portfolios.

Figure: Exchange rates emerge from interacting goods-market, financial-market, policy and expectation channels.

Macroeconomic Drivers and Interpretation

No driver should be interpreted mechanically. Markets respond to surprises relative to prior expectations. A 5% policy rate can weaken a currency if investors expected 6%, while a lower-than-foreign rate may coexist with appreciation when the country is considered a safe haven.

Exchange-Rate Forecasting Methods

Forecasts should specify the quotation, horizon, information date, model assumptions and intended decision. A forecast suitable for a one-week trading decision may be inappropriate for a five-year investment appraisal.

Market-Based Benchmarks

The current spot rate is a difficult benchmark to outperform over short horizons because liquid markets incorporate public information rapidly. The forward rate is another benchmark, but it is principally a no-arbitrage price under CIP, not a guaranteed forecast.

Option prices provide information about market-implied volatility and risk-neutral distributions. These distributions include risk premiums and therefore need not equal investors’ actual probability beliefs.

Fundamental Forecasting

Fundamental forecasting estimates exchange rates from economic variables such as inflation, productivity, money supply, interest rates, commodity prices and external balances. A simplified statistical model might be:

where X_t represents additional explanatory variables and ε_t is an unexplained disturbance. Coefficient signs must be interpreted in light of the quotation convention and model structure; they should not be imposed without theory and evidence.

Good practice includes:

1. Avoiding regressions between unrelated trending level series.
2. Testing whether long-run relationships are stable.
3. Separating model estimation from out-of-sample evaluation.
4. Preventing the use of data that were unavailable at the forecast date.
5. Comparing performance with simple spot and forward benchmarks.

Fundamental models are useful for explaining scenarios and long-run valuation, but structural breaks and uncertain policy reactions limit precision.

Technical Forecasting

Technical analysis uses historical prices, returns, volume and market positioning. A k-period simple moving average is:

A rule may identify upward momentum when a short moving average crosses above a long moving average. Other tools include support and resistance levels, relative-strength measures and volatility bands.

Technical methods can capture momentum, liquidity effects and repeated trading behavior, but patterns are vulnerable to transaction costs, data mining and regime changes. A pattern discovered after testing many alternatives may reflect chance rather than genuine predictability.

Scenario-Based Forecasting

Scenario analysis is appropriate when outcomes depend on discrete policy or political events. A robust process includes:

1. Defining a base case, plausible upside and plausible downside.
2. Identifying internally consistent assumptions for growth, inflation, rates and risk.
3. Assigning probabilities only when defensible.
4. Translating each scenario into an exchange-rate range.
5. Testing the business decision under every scenario.

If scenarios have probabilities p_j and exchange rates S_j, the probability-weighted mean is:

The mean should not replace tail-risk analysis. A firm can fail because of an adverse scenario even when the expected rate appears acceptable.

Combining Forecasts

Forecast combinations can be more stable than reliance on one model:

Weights may be equal, based on historical out-of-sample performance or adjusted for changing regimes. Excessive optimization can overfit past data.

Evaluating Forecast Accuracy

Let e_t = S_t − Ŝ_t be the forecast error. Common measures include:

MAE is easy to interpret in the exchange rate’s quotation units. RMSE penalizes large errors more heavily. Directional accuracy measures the proportion of forecasts correctly predicting appreciation or depreciation. Economic evaluation should also consider whether forecasts improve hedging costs, cash-flow stability or risk-adjusted returns after transaction costs.

Models must be compared over identical currencies, horizons and information sets. A model selected and evaluated using the same sample will generally appear more accurate than it truly is.

Illustrative Case: Forecasting and Hedging a Euro Payable

Background

Northstar Medical Systems, a fictional US importer, must pay EUR 5 million in six months. The current spot rate is 1.10 USD/EUR. The firm budgets in dollars and is concerned that euro appreciation will increase the payment.

Problem

Management must establish a forecast range and choose whether to remain unhedged, lock in a forward rate or retain some favorable-currency potential through options.

Analysis

The matched six-month US and euro interest rates are 2.4% and 1.5%. CIP gives:

A full forward hedge would therefore lock in approximately:

Analysts then construct three internally consistent scenarios:

The probability-weighted rate is:

Although this is slightly below the forward rate, the strong-euro scenario would produce an unhedged cost of USD 6.10 million. The expected rate alone therefore understates the budget risk.

Approach and Outcome

Management chooses an illustrative layered hedge: 70% forward and 30% with a euro call option. Assume the call has a strike of 1.12 USD/EUR and a premium of USD 0.02 per euro. If the eventual spot rate is 1.19, the option is exercised. Ignoring the time value of the premium, total cost is:

The corresponding unhedged cost would have been USD 5,950,000. The hedge reduces the realized payment by USD 355,875, although it costs more than a full forward hedge would have cost. In exchange, the option-covered portion would have benefited if the euro had weakened sufficiently.

Learning Points

• Forward rates arise primarily from interest-rate parity, not certainty about future spot rates.
• Probability-weighted forecasts should be supplemented by stress scenarios.
• Hedging decisions depend on risk tolerance and cash-flow objectives, not merely the expected rate.
• Forecasting and hedging are related but distinct: a firm can hedge without claiming superior predictive ability.

Technology, Governance and Ethical Practice

Machine-learning systems can combine high-frequency prices, news sentiment and macroeconomic data. However, exchange-rate datasets contain few independent crisis episodes, changing regimes and substantial noise. Complex models can therefore overfit historical relationships.

Responsible practice requires documented data sources, version-controlled models, out-of-sample testing, human review and clear limits on automated execution. Firms should prevent confidential client order information from being misused in forecasting or trading. Analysts must disclose model uncertainty and avoid presenting a scenario mean as a guaranteed outcome.

Foreign-exchange markets are also subject to market-conduct rules concerning manipulation, collusion, benchmark integrity, sanctions and anti-money-laundering controls. Forecasting systems should operate within approved exposure limits and segregation-of-duties arrangements.

Contemporary Developments and Practical Guidance

Exchange-rate analysis increasingly must account for unconventional monetary policy, large public debt, geopolitical fragmentation, sanctions, digital trading and central-bank intervention. Commodity shocks can create sharply different effects for exporters and importers. Periods of global stress may also strengthen major funding or safe-haven currencies despite weak domestic fundamentals.

Professional forecasting practice should therefore:

• Maintain consistent quotation conventions and units.
• Distinguish identities, no-arbitrage conditions and behavioral theories.
• Use real-time information rather than revised historical data.
• Combine quantitative models with institutional analysis.
• Report ranges and scenarios rather than false precision.
• Benchmark forecasts against spot and forward rates.
• Link forecast evaluation to the underlying business decision.

Chapter Summary

Exchange-rate determination involves goods markets, financial markets, macroeconomic policy and expectations. Absolute PPP compares currency-denominated prices of the same basket, while relative PPP links exchange-rate changes to inflation differentials. Correct dimensional treatment is essential: arbitrarily rebased price indexes cannot directly produce a currency exchange rate.

Covered interest rate parity determines the no-arbitrage forward rate for comparable investments. Uncovered parity connects interest differentials to expected currency movements but may fail empirically because of risk premiums and expectation errors. The Fisher effect separates nominal returns into real returns and expected inflation.

The balance-of-payments approach emphasizes trade and financial flows, whereas monetary and portfolio-balance models treat the exchange rate as an asset price responsive to expected future conditions. No macroeconomic driver has a fixed effect independent of expectations, credibility and market regime.

Fundamental forecasting uses economic relationships; technical forecasting examines market patterns; and scenario analysis evaluates discrete, uncertain outcomes. Forecasts should be tested out of sample using statistical and economic criteria. In corporate practice, forecasts inform—but do not replace—disciplined exposure measurement and hedging.

Key Terms

Absolute purchasing power parity: The proposition that identical baskets have equal currency-converted prices.

Asset-market approach: An explanation of exchange rates based on expected returns and asset holdings.

Balance of payments: The statistical record of transactions between residents and nonresidents.

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

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

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

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

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

Forward exchange rate: An exchange rate agreed today for currency delivery on a future date.

Fundamental forecasting: Forecasting based on economic and financial explanatory variables.

International Fisher effect: The proposition connecting nominal interest differentials and expected exchange-rate changes under restrictive assumptions.

J-curve: A possible initial deterioration followed by improvement in the trade balance after depreciation.

Portfolio-balance approach: A model in which currencies adjust to equilibrate demands for imperfectly substitutable assets.

Real exchange rate: The relative price of comparable foreign and domestic baskets after currency conversion.

Relative purchasing power parity: The proposition that exchange-rate changes reflect inflation differentials.

Scenario analysis: Evaluation of outcomes under multiple internally consistent future states.

Technical forecasting: Forecasting based primarily on historical market data and trading patterns.

Uncovered interest rate parity: A relationship between interest differentials and expected exchange-rate changes without forward cover.

Review Questions

Short Answer Questions

1. Under a domestic-currency-per-foreign-currency quotation, what does an increase in the exchange rate mean?
2. Why cannot arbitrarily rebased consumer price indexes directly determine an absolute PPP exchange rate?
3. What economic condition underlies covered interest rate parity?
4. How does the Fisher effect distinguish nominal and real interest rates?
5. Why may a current-account deficit coexist with a strengthening currency?

Long Answer Questions

1. Compare absolute and relative PPP, including their assumptions, units and empirical limitations.
2. Derive covered interest rate parity and explain why deviations may persist in actual markets.
3. Compare balance-of-payments, monetary and portfolio-balance approaches to exchange-rate determination.
4. Evaluate the strengths and weaknesses of fundamental and technical exchange-rate forecasting.
5. Explain why expectations, risk premiums and policy credibility can change the effect of interest rates on currencies.

Analytical / Application Questions

1. A currency is quoted at 0.80 domestic currency units per foreign unit. Domestic inflation is 8% and foreign inflation is 3%. Calculate the relative-PPP forecast and interpret the result.
2. Given a spot rate of 1.25 domestic currency units per foreign unit, a domestic period interest rate of 5% and a foreign period rate of 2%, calculate the CIP-consistent forward rate and design the arbitrage direction if the market forward is materially lower.
3. Design a three-scenario exchange-rate forecast for a multinational with a large foreign-currency payable. Explain how the forecast should influence, but not mechanically determine, its hedging decision.

Multiple Choice Questions with Answers

Question 1

An exchange rate quoted as domestic currency per unit of foreign currency rises from 1.20 to 1.26. What occurred?

A. The foreign currency appreciated by 5%

B. The domestic currency appreciated by 5%

C. The foreign currency depreciated by 4.76%

D. Neither currency changed value

Correct Answer: A. The foreign currency appreciated by 5%

Question 2

Why is q = SP_f/P_d dimensionless when used with currency-denominated basket prices?

A. Because the exchange rate has no units

B. Because SP_f and P_d are both measured in domestic currency per basket

C. Because all price indexes are naturally comparable

D. Because foreign prices are always normalized to one

Correct Answer: B. Because SP_f and P_d are both measured in domestic currency per basket

Question 3

The spot rate is 1.20 domestic currency units per foreign unit. Domestic inflation is 5% and foreign inflation is 2%. What is the relative-PPP forecast?

A. 1.1657

B. 1.2000

C. 1.2353

D. 1.2840

Correct Answer: C. 1.2353

Question 4

The spot rate is 1.10 domestic currency units per foreign unit. Matched-period domestic and foreign interest rates are 4% and 2%. What forward rate is implied by covered interest rate parity?

A. 1.0788

B. 1.1000

C. 1.1216

D. 1.1660

Correct Answer: C. 1.1216

Question 5

Which condition is central to the simplest uncovered interest rate parity interpretation?

A. Exchange risk is eliminated by a forward contract

B. Investors require no currency risk premium

C. All countries have identical inflation histories

D. Current accounts must be balanced

Correct Answer: B. Investors require no currency risk premium

Question 6

A nominal interest rate is 7% and expected inflation is 4%. Using the exact Fisher relationship, what is the expected real rate?

A. 2.89%

B. 3.00%

C. 4.00%

D. 11.28%

Correct Answer: A. 2.89%

Question 7

Under the IMF BPM6 convention used in the chapter, which simplified balance-of-payments identity is correct?

A. CA + KA - FA + E = 0

B. CA - KA - FA - E = 0

C. CA + FA = 1

D. CA = KA = FA

Correct Answer: A. CA + KA - FA + E = 0

Question 8

What does exchange-rate overshooting describe?

A. The trade balance immediately improving after every depreciation

B. A currency initially moving beyond its eventual long-run response because asset prices adjust faster than goods prices

C. A forward rate that always overpredicts the future spot rate

D. Inflation permanently remaining above money-supply growth

Correct Answer: B. A currency initially moving beyond its eventual long-run response because asset prices adjust faster than goods prices

Question 9

Which forecast-error measure penalizes large errors more heavily through squaring?

A. Directional accuracy

B. Mean absolute error

C. Root mean squared error

D. Median exchange-rate change

Correct Answer: C. Root mean squared error

Question 10

Three exchange-rate scenarios are 0.90, 1.10 and 1.30 with probabilities 0.20, 0.50 and 0.30. What is the probability-weighted exchange rate?

A. 1.06

B. 1.10

C. 1.12

D. 1.30

Correct Answer: C. 1.12