Exchange-Rate Determination and Forecasting

Introduction

The foreign-exchange rate is the relative price of one currency expressed in another. It affects international trade, inflation, capital flows, external debt, investment returns and the valuation of banks, corporations and sovereign assets. For an investment banker, forecasting exchange rates is therefore not an academic exercise alone: it informs transaction pricing, hedging, cross-border mergers, sovereign financing, project valuation and risk management.

No single model explains exchange-rate movements consistently across all horizons. Purchasing-power parity is useful for long-run valuation; interest-rate parity links currencies to forward prices and hedging costs; monetary and balance-of-payments models explain macroeconomic pressures; portfolio-balance models emphasize asset supplies and risk premia; and market-microstructure models explain short-run movements through order flow, liquidity and information. Professional forecasting combines these approaches with technical and statistical evidence while recognising uncertainty.

Learning objectives

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

1. Explain the principal theories of exchange-rate determination.
2. Derive and apply purchasing-power parity and interest-rate parity relationships.
3. Distinguish monetary, balance-of-payments, portfolio-balance and microstructure explanations.
4. Evaluate assumptions, empirical limitations and forecast horizons.
5. Combine macroeconomic, technical and statistical forecasts in an investment-banking setting.
6. Design a disciplined forecasting and governance process.

1. Exchange-rate conventions and core concepts

Let S_t denote the spot exchange rate at time t, quoted as domestic currency units per unit of foreign currency. An increase in S_t represents domestic-currency depreciation under this convention. For example, if the euro-dollar rate is quoted as dollars per euro, a rise from 1.08 to 1.12 means that the dollar has depreciated against the euro.

The percentage change in the exchange rate is approximately:

where Δs is the proportional change. The continuously compounded change is:

The logarithmic form is convenient in statistical models and is approximately equal to the percentage change for small movements. A quotation convention must remain unchanged throughout an analysis; reversing the quotation reverses the sign and changes the interpretation of appreciation and depreciation.

Important distinctions include:

• Spot rate: the exchange rate for near-immediate delivery.
• Forward rate: a contracted exchange rate for delivery on a future date.
• Nominal exchange rate: the market price of one currency in another.
• Real exchange rate: the nominal rate adjusted for relative price levels.
• Effective exchange rate: an index against a basket of trading-partner currencies.
• Bilateral rate: a rate between two currencies.
• Currency appreciation/depreciation: a market-driven rise/fall in currency value.
• Revaluation/devaluation: an official change in a fixed or managed regime.

With P_t representing the domestic price index and P*_t the foreign price index, a real exchange rate consistent with the quotation above is:

Here q_t is measured in comparable price-index units. If q_t rises, domestic goods become relatively more expensive or the domestic currency becomes more depreciated in real terms, depending on the analytical convention. Researchers must state the convention because alternative definitions use the reciprocal.

2. Purchasing-power parity

Absolute purchasing-power parity

The law of one price states that, after allowing for transport costs, taxes and trade barriers, an identical tradable good should have the same price when expressed in a common currency. Extending this idea to representative price baskets gives absolute purchasing-power parity (PPP):

Under the domestic-currency-per-foreign-currency convention, this equation says that the exchange rate equals the domestic price level divided by the foreign price level. Absolute PPP assumes identical baskets, frictionless trade, no tariffs, no taxes, no non-traded goods and competitive arbitrage. These conditions rarely hold exactly.

Relative PPP

Relative PPP focuses on rates of change rather than price-level equality. In approximate form:

where π_t is domestic inflation and π*_t is foreign inflation. Thus, if domestic inflation exceeds foreign inflation by 3 percentage points, the domestic currency is expected to depreciate by approximately 3% over the relevant long-run period.

The exact one-period relationship is:

This formula is dimensionless and assumes that the price indices represent comparable baskets. For small inflation rates, the approximation is normally adequate; for high inflation, the exact expression should be used.

Worked example: relative PPP

Suppose domestic inflation is 6% and foreign inflation is 2%. The exact predicted depreciation is:

If the current spot rate is 80 domestic currency units per foreign currency, the PPP-implied future rate is:

The result is a long-run benchmark, not a guaranteed one-year forecast. Capital flows, interest-rate changes, commodity prices and risk sentiment may dominate over shorter horizons.

Uses and limitations of PPP

PPP is valuable for identifying apparent long-run currency misalignment, constructing real effective exchange-rate indices and framing inflation scenarios. It is less reliable in the short run because services and other non-traded goods are included in consumer prices, arbitrage is costly, prices adjust slowly and productivity differs across countries. The Balassa–Samuelson effect predicts that faster productivity growth in a country’s tradable sector can raise wages and non-traded prices, producing a real appreciation without a corresponding loss of competitiveness.

3. Interest-rate parity and forward pricing

Covered interest parity

Covered interest parity (CIP) is an arbitrage condition linking the spot rate, forward rate and interest rates. Let F_t,T be the forward rate for maturity T, i_dom the domestic interest rate and i_for the foreign interest rate, all for the same maturity and compounding convention. Under the quotation used here:

For continuously compounded rates:

T is measured in years. CIP assumes the ability to borrow and lend in both currencies, negligible transaction costs, no capital controls, matching maturities and no counterparty or funding frictions. In modern markets, cross-currency basis, balance-sheet constraints and collateral conditions can produce persistent deviations.

Uncovered interest parity

Uncovered interest parity (UIP) compares expected future spot rates with interest differentials:

The domestic currency is expected to depreciate when domestic interest rates exceed foreign rates. Unlike CIP, UIP involves an uncertain future spot rate and is not an arbitrage identity. Empirically, UIP often performs poorly at short and medium horizons; high-interest-rate currencies have sometimes appreciated rather than depreciated, producing the well-known forward-premium puzzle.

Worked example: forward rate

Assume S_t = 1.1000 domestic currency units per foreign currency, a one-year domestic interest rate of 5%, and a foreign rate of 3%. Under simple annual compounding:

The forward premium is approximately 1.95%:

This is the no-arbitrage forward price under the stated assumptions. It is not necessarily the market’s unbiased expectation of the future spot rate.

4. Monetary models of exchange-rate determination

Monetary models explain exchange rates through money supply, money demand, income, interest rates and prices. A basic flexible-price monetary model assumes purchasing-power parity and stable money demand. A stylised money-demand function is:

where m_t is the logarithm of nominal money supply, p_t is the logarithm of the price level, y_t is real income, i_t is the nominal interest rate, and α, β > 0. Higher income raises money demand; higher interest rates increase the opportunity cost of holding money and reduce money demand.

Combining money-market equilibrium with PPP produces a relationship in which the exchange rate is influenced by relative money supplies, relative incomes and relative interest rates. The flexible-price version predicts that an increase in domestic money supply, holding other factors constant, causes domestic prices and the domestic-currency price of foreign currency to rise.

The overshooting model adds sticky prices and rational expectations. When the central bank unexpectedly expands money supply, interest rates may fall immediately. Because goods prices adjust slowly, the exchange rate can depreciate by more than its eventual long-run level and then appreciate as prices catch up. This explains why exchange rates may be highly volatile even when long-run monetary fundamentals move gradually.

Monetary models are useful for scenario analysis involving inflation, central-bank balance sheets and policy regimes. They are weakened by unstable money demand, financial innovation, endogenous credit creation, uncertain expectations and the difficulty of measuring the relevant monetary aggregate.

5. Balance-of-payments models

The balance of payments records transactions between residents and non-residents. In simplified form:

The current account includes trade in goods and services, primary income and secondary income. The financial account records investment flows, such as direct investment, portfolio investment, loans and reserve transactions.

A current-account deficit must be financed by net financial inflows, reserve reduction or some combination. Persistent deficits may place depreciation pressure on a currency if investors become unwilling to finance them. However, a deficit is not automatically a sign of impending depreciation. A country with strong institutions, attractive investment opportunities and reserve-currency status may sustain deficits for long periods.

The absorption approach distinguishes national income from domestic expenditure. A country can improve its trade balance through increased output, reduced absorption, exchange-rate depreciation or changes in relative prices. The elasticity approach focuses on how export and import volumes respond to relative prices. The Marshall–Lerner condition states, in simplified terms, that a depreciation improves the trade balance when the sum of the absolute price elasticities of exports and imports exceeds one, assuming an initially balanced trade position and other restrictive conditions.

The J-curve effect explains why a depreciation may initially worsen the trade balance: contracts and import prices adjust before quantities respond. Forecasts must therefore distinguish immediate valuation effects from later volume effects.

6. Portfolio-balance and asset-market models

Currencies are financial assets. Investors allocate wealth among domestic bonds, foreign bonds, equities, deposits and real assets. Portfolio-balance models reject the assumption that domestic and foreign assets are perfect substitutes. Exchange rates adjust to clear markets when the relative supplies and perceived risks of assets change.

A simplified expected-return comparison is:

where ρ is a risk premium measured in domestic-currency return units. The expression assumes small returns and the domestic-currency-per-foreign-currency quotation. A higher perceived risk of foreign assets, represented by a larger ρ, reduces their attractiveness unless compensated by interest or expected currency appreciation.

A government issuing more domestic debt may need to offer a higher yield or accept currency depreciation to induce investors to hold the additional supply. Conversely, credible fiscal consolidation, reserve accumulation or stronger institutional quality can reduce the risk premium. Portfolio models are especially relevant when quantitative easing, sovereign-debt issuance, pension rebalancing or geopolitical risk changes the composition of global portfolios.

The principal challenge is measurement: expectations, risk aversion, asset substitutability and the effective supply of assets are not directly observable. Nevertheless, the framework explains why identical interest-rate differentials can produce different exchange-rate outcomes across countries and time.

7. Market microstructure and order flow

Macroeconomic models often treat prices as responding immediately to publicly available information. Market-microstructure models focus on how information is dispersed among dealers and how trades move prices. Order flow is the signed net pressure from buyer-initiated and seller-initiated transactions. A simple price-impact relationship is:

where OF_t is order flow, λ is the price impact per unit of order flow, α is a constant or predictable component and ε_t is an unexplained innovation. Units depend on the data: order flow may be measured in currency value, contracts or signed volume, while Δs may be a return or log exchange-rate change.

Order flow can reveal information about dispersed expectations, hedging demand, corporate transactions and liquidity conditions. Price impact tends to increase when market depth is low, uncertainty is high or dealers face balance-sheet constraints. Microstructure helps explain intraday volatility, bid–ask spreads, jumps around data releases and the temporary effects of large client orders.

It does not replace macroeconomic analysis. A transaction may move the exchange rate temporarily because liquidity is scarce, while persistent order flow may reflect genuine information about future fundamentals. Data confidentiality, fragmented markets and changing electronic-trading practices also complicate estimation.

8. Forecasting across horizons

A professional forecast begins by defining the horizon and decision. A one-day forecast for a trading desk, a three-month hedge recommendation and a five-year acquisition valuation require different information and loss functions.

Fundamental forecasting

Fundamental forecasts use inflation, interest rates, growth, fiscal policy, external balances, commodity prices, reserves, political risk and central-bank communication. Scenario analysis is generally superior to a single-point estimate. A useful structure is a baseline, an upside-appreciation scenario and a downside-depreciation scenario, each with explicit assumptions and probabilities.

Technical forecasting

Technical methods use market prices, returns, trends, momentum, support and resistance, volatility and positioning. A moving average is:

where n is the number of observations. Technical signals can describe market state and timing, but they are vulnerable to data snooping, transaction costs, regime changes and false discoveries. They should not be presented as structural laws.

Statistical forecasting

A benchmark autoregressive model for log exchange-rate changes is:

where r_t = Δln S_t, c is a constant, φ is the autoregressive coefficient and ε_t has conditional mean zero. Exchange-rate levels are often close to a random walk, so forecasting changes or excess returns may be more appropriate than forecasting levels. Volatility models such as GARCH can improve risk estimates even when they do not reliably improve the direction forecast.

Forecast evaluation must use a genuine out-of-sample period. Mean absolute error is:

where S_t is the realised value, Ŝ_t is the forecast and N is the number of observations. Root mean squared error is:

RMSE penalises large errors more heavily than MAE. Forecasts should also be evaluated economically through hedge effectiveness, transaction costs and the consequences of forecast errors.

Combining forecasts

Suppose three forecasts are produced: macroeconomic, technical and statistical. A weighted forecast is:

with w_M + w_T + w_S = 1. Weights may be based on historical out-of-sample performance, model uncertainty or a transparent expert process. Equal weighting is often a robust benchmark because estimated optimal weights can be unstable. Combining forecasts does not eliminate model risk; it diversifies it.

9. Integrated investment-banking application

Illustrative case: acquisition of a foreign target

Background. A domestic investment bank advises a corporation acquiring a target priced at EUR 500 million. The buyer’s reporting currency is domestic currency (DC). The current rate is DC 1.10 per euro, and completion is expected in six months.

Problem. The buyer must estimate the domestic-currency purchase price and decide how much foreign currency to hedge. The principal risk is a euro appreciation, which raises the acquisition cost.

Analysis. The advisory team constructs three scenarios:

The baseline reflects relative inflation, expected interest-rate differentials, euro-area growth and current forward pricing. The appreciation case reflects a risk-off episode, stronger euro-area policy credibility and heavy euro demand from investors. The depreciation case reflects weaker growth and easier monetary policy.

The bank compares the forward rate with the client’s risk tolerance. A forward purchase of euros fixes the domestic cost but sacrifices any benefit from a later euro depreciation and creates a commitment if the transaction fails. A purchased call option on euros preserves upside from depreciation but requires a premium. A collar reduces the premium by selling a lower-strike put, while introducing an obligation under the put’s terms.

Approach and solution. The client hedges 70% of the expected consideration with forwards and retains 30% unhedged because the acquisition price and completion date remain uncertain. The hedge ratio is reviewed when regulatory approval and funding are confirmed. Stress tests include a 10% currency move, a delayed completion and a widening cross-currency basis.

Outcome. The structure materially limits the adverse cost in the appreciation scenario while avoiding an excessive hedge of an uncertain exposure. The result is not a prediction that the euro will rise; it is a risk-management decision based on the distribution of outcomes.

Learning points. Forecasting and hedging are distinct. A strong forecast may still justify hedging if the cost of being wrong is high. Forward rates are pricing relationships, not unbiased forecasts. Governance must document assumptions, model limitations, counterparty exposure, collateral requirements and hedge-accounting consequences.

10. Challenges, governance and contemporary developments

Exchange-rate forecasts face structural breaks, policy regime changes, geopolitical shocks, liquidity events and incomplete information. Historical relationships may fail when a central bank changes its reaction function or when capital controls are introduced. Correlations often rise during crises, reducing the benefits of diversification.

AI and machine learning can process news, text, order flow and high-frequency data, but predictive performance is vulnerable to non-stationarity, leakage, overfitting and unstable relationships. Models should use time-ordered validation, documented feature construction, explainability appropriate to the decision and independent monitoring. Human review remains necessary when data are sparse or the event is unprecedented.

Best practice includes:

• state the quotation, horizon, information set and decision objective;
• distinguish forecast, scenario and market-implied price;
• benchmark against a random walk and simple economic models;
• use out-of-sample testing and account for transaction costs;
• report confidence intervals or scenario ranges, not only point estimates;
• monitor forecast bias, model drift and structural breaks;
• separate research, trading and risk-control responsibilities;
• disclose conflicts of interest and avoid presenting speculative views as certainty.

For regulated institutions, controls should cover model validation, data lineage, valuation adjustments, suitability, market conduct, record retention and counterparty credit exposure. Forecasts used in client advice must be balanced, evidence-based and consistent with the institution’s risk disclosures.

Chapter Summary

Exchange rates are determined by interacting monetary, price, financial-market and microstructure forces. Absolute and relative PPP provide long-run benchmarks based on price levels and inflation differentials, while CIP links spot and forward prices through an arbitrage condition. UIP is an expectations hypothesis rather than a guaranteed arbitrage rule. Monetary models connect currencies to money, income, interest rates and price adjustment; balance-of-payments models emphasise external financing and trade responses; portfolio-balance models add asset supplies and risk premia; and microstructure models explain short-run price discovery through order flow and liquidity.

Forecasting should be horizon-specific and combine fundamental, technical and statistical evidence. Model comparison requires out-of-sample testing, economic evaluation and explicit treatment of uncertainty. In investment banking, the objective is often not to predict perfectly but to price transactions, design resilient hedges and communicate risks transparently. Governance, documentation and awareness of model limitations are as important as numerical sophistication.

Key Terms

Purchasing-power parity: The proposition that exchange rates adjust to equalise comparable price levels across countries.

Relative PPP: The relationship between exchange-rate changes and inflation differentials.

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

Uncovered interest parity: The hypothesis linking expected exchange-rate changes to interest-rate differentials.

Forward premium: The percentage by which a forward rate exceeds the spot rate under a stated quotation.

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

Monetary model: A model explaining currency value through money supply, money demand, income and interest rates.

Overshooting: Short-run exchange-rate movement beyond long-run equilibrium following a monetary shock.

Balance of payments: A systematic record of a country’s transactions with the rest of the world.

Current account: The balance of trade, income and current transfers.

Portfolio balance: The allocation of wealth among assets with differing supplies and risks.

Risk premium: Compensation required for bearing currency or asset risk.

Order flow: Net signed buying and selling pressure in a market.

Market microstructure: The study of trading mechanisms, liquidity, information and price formation.

Random walk: A process in which the best forecast of the next level is often the current level, subject to an innovation.

Out-of-sample testing: Evaluation using observations not used to estimate a model.

J-curve: The possibility that depreciation initially worsens and later improves the trade balance.

Cross-currency basis: A deviation from covered interest parity associated with funding and balance-sheet conditions.

Hedge ratio: The proportion of an exposure protected by a hedging instrument.

Model risk: The possibility that a model is incorrectly specified, estimated or applied.

Review Questions

Short Answer Questions

1. What does a rise in S_t mean when the exchange rate is quoted as domestic currency per unit of foreign currency?
2. State the approximate relative-PPP relationship.
3. Why is covered interest parity an arbitrage condition whereas uncovered interest parity is not?
4. What is order flow, and why can it affect short-run exchange rates?
5. Distinguish a forecast from a scenario analysis.

Long Answer Questions

1. Explain the assumptions, uses and limitations of absolute and relative purchasing-power parity.
2. Compare monetary, balance-of-payments and portfolio-balance models of exchange-rate determination.
3. Explain exchange-rate overshooting and the role of sticky prices.
4. Discuss how market microstructure complements macroeconomic exchange-rate models.
5. Design a governance framework for combining fundamental, technical and statistical forecasts.

Analytical / Application Questions

1. Domestic inflation is 7%, foreign inflation is 3%, and the current exchange rate is 50 domestic currency units per foreign currency. Calculate the exact one-period relative-PPP forecast and explain why it may not be reliable over a short horizon.
2. A six-month acquisition exposure has a 60% probability of costing DC 420 million and a 40% probability of costing DC 380 million without hedging. Explain how expected cost, downside risk and transaction uncertainty should influence the hedge ratio.
3. A statistical model performs well in-sample but loses money after transaction costs out-of-sample. Diagnose at least three possible causes and recommend a validation process.

Multiple Choice Questions with Answers

Question 1

Under the domestic-currency-per-foreign-currency quotation, a rise in the spot exchange rate represents:

A. Domestic-currency appreciation

B. Domestic-currency depreciation

C. Foreign-currency depreciation

D. No change in relative currency value

Correct Answer: B. Domestic-currency depreciation

Question 2

If domestic inflation is 6% and foreign inflation is 2%, the exact relative-PPP predicted depreciation is closest to:

A. 2.00%

B. 3.00%

C. 3.92%

D. 8.00%

Correct Answer: C. 3.92%

Question 3

Which relationship is a covered interest parity condition under simple annual compounding?

A. F = S × (1 + i_for) ÷ (1 + i_dom)

B. F = S × (1 + i_dom) ÷ (1 + i_for)

C. F = S + i_dom − i_for

D. F = S × i_dom × i_for

Correct Answer: B. F = S × (1 + i_dom) ÷ (1 + i_for)

Question 4

Why can the exchange rate overshoot after an unexpected monetary expansion?

A. Prices adjust instantly while interest rates are fixed

B. Goods prices are sticky while financial prices adjust quickly

C. Trade volumes immediately satisfy the Marshall–Lerner condition

D. Forward rates cease to exist

Correct Answer: B. Goods prices are sticky while financial prices adjust quickly

Question 5

Which item belongs primarily to the current account of the balance of payments?

A. Portfolio purchase of foreign bonds

B. Foreign direct investment inflow

C. Exports of services

D. Change in official foreign-exchange reserves

Correct Answer: C. Exports of services

Question 6

In a portfolio-balance model, a higher perceived risk of foreign assets generally:

A. Reduces the required return on those assets

B. Raises their attractiveness without compensation

C. Requires additional expected return to maintain demand

D. Eliminates the role of interest rates

Correct Answer: C. Requires additional expected return to maintain demand

Question 7

In the microstructure equation Δs_t = α + λ OF_t + ε_t, λ represents:

A. The inflation differential

B. The price impact of order flow

C. The foreign interest rate

D. The forecast horizon

Correct Answer: B. The price impact of order flow

Question 8

Which measure penalises large forecast errors more heavily than MAE?

A. Median error

B. Directional accuracy

C. RMSE

D. Forward premium

Correct Answer: C. RMSE

Question 9

A forward rate derived from covered interest parity should primarily be interpreted as:

A. A guaranteed future spot rate

B. A no-arbitrage pricing relationship under stated assumptions

C. A central-bank commitment

D. A measure of inflation only

Correct Answer: B. A no-arbitrage pricing relationship under stated assumptions

Question 10

Why is equal weighting sometimes used when combining exchange-rate forecasts?

A. It guarantees the best forecast

B. It eliminates model risk

C. Estimated optimal weights can be unstable

D. It makes all models structurally identical

Correct Answer: C. Estimated optimal weights can be unstable