Exchange-Rate Theories and Forecasting

Introduction

Exchange-rate movements affect export prices, import costs, foreign-currency debt, investment returns and the reported earnings of multinational enterprises. Managers therefore need frameworks that explain why currencies move and methods that convert economic information into decision-relevant forecasts.

No single theory explains exchange rates at every horizon. Purchasing power parity emphasizes goods prices over long periods; parity conditions connect currencies with interest rates and inflation expectations; monetary and portfolio-balance models examine macroeconomic and asset-market equilibrium. Forecasting methods—including technical, fundamental, market-based and scenario approaches—translate these ideas into conditional estimates. Their usefulness depends on assumptions, data quality, horizon and purpose.

Throughout this chapter, the spot exchange rate S_t is quoted as units of domestic currency per unit of foreign currency. Thus, an increase in S_t represents domestic-currency depreciation, while a decrease represents domestic-currency appreciation.

Learning Objectives

After studying this chapter, students should be able to:

• apply absolute and relative purchasing power parity;
• distinguish covered and uncovered interest rate parity;
• explain the Fisher effect and international Fisher effect;
• derive the core logic of monetary and portfolio-balance models;
• construct technical, fundamental, market-based and scenario forecasts;
• evaluate forecasts using appropriate benchmarks and error measures;
• identify the managerial, ethical and governance implications of currency forecasting.

Exchange-Rate Measurement

The proportional change in the spot exchange rate is:

Here, S_t and S_t+1 are domestic-currency units per foreign-currency unit at dates t and t+1. A positive result means domestic depreciation under this quotation convention.

Analysts often use the continuously compounded exchange-rate change:

The lowercase variable s_t = ln(S_t) is the natural logarithm of the spot rate. For small changes, Δs closely approximates the proportional percentage change expressed as a decimal.

Purchasing Power Parity

The law of one price

The law of one price states that an identical tradable product should have the same price across countries after currency conversion when transportation costs, taxes, tariffs, market segmentation and other trading frictions are absent.

In this equation, P_d is the domestic-currency price of the good, P_f is its foreign-currency price, and S is domestic currency per unit of foreign currency. Both sides are measured in domestic currency.

If the converted foreign price is lower, arbitrageurs may buy abroad and sell domestically. In practice, transport costs, product differentiation, regulations and pricing-to-market create a band within which arbitrage is unprofitable.

Absolute purchasing power parity

Absolute purchasing power parity (PPP) extends the law of one price to comparable baskets of goods:

Here, P_d,t and P_f,t are compatible domestic and foreign price indices. The expression assumes that the baskets are comparable and that price indices can meaningfully represent national purchasing power. These conditions rarely hold exactly because consumption weights, product quality, taxes and nontradable services differ between countries.

Relative purchasing power parity

Relative PPP predicts that exchange-rate movements offset inflation differentials. Its exact discrete-time form is:

The variables π_d and π_f are domestic and foreign inflation rates over the same period, expressed as decimals. Consequently:

When inflation rates are moderate, the commonly used approximation is:

In the approximation, all terms must use the same units—for example, percentage points per year. Higher domestic inflation relative to foreign inflation predicts domestic-currency depreciation.

Worked example: relative PPP

Suppose the spot rate is 1.500 domestic currency units per foreign currency unit. Expected annual inflation is 6% domestically and 2% abroad. Relative PPP predicts:

The exact expected depreciation is:

The approximate inflation-differential estimate is 4%, which is close but not identical.

The real exchange rate

The real exchange rate measures the relative price of foreign goods in terms of domestic goods:

The variable q_t is dimensionless when the price indices are constructed on compatible bases. An increase in q_t is a real depreciation of the domestic currency. Under strict absolute PPP, q_t = 1, although empirical analysis usually focuses on whether the real rate is stable or mean-reverting rather than exactly equal to one.

PPP tends to perform better over long horizons and in high-inflation economies. Short-run deviations can persist because prices are sticky, services are nontradable, contracts adjust slowly and capital flows move faster than goods prices.

Interest Rate Parity

Covered interest rate parity

Covered interest rate parity (CIRP) is a no-arbitrage relationship between spot rates, forward rates and interest rates. Consider one unit of domestic currency invested for one period. A domestic deposit produces 1+i_d. Alternatively, the investor converts at the spot rate, invests abroad at i_f, and sells the future foreign proceeds at forward rate F_t. Equal risk-free domestic-currency payoffs require:

Rearranging gives:

Here, F_t is the forward rate for delivery at the investment horizon, and i_d and i_f are comparable default-free interest rates with the same maturity and day-count basis. Transaction costs, capital controls, counterparty risk and funding constraints must be negligible for strict arbitrage.

The approximate forward premium is:

#### Worked example

If S_t = 1.200, the domestic annual interest rate is 5%, and the foreign rate is 2%, the one-year parity forward rate is:

A materially different traded forward rate could create covered arbitrage, subject to actual transaction and funding costs.

Uncovered interest rate parity

Uncovered interest rate parity (UIRP) replaces the contracted forward rate with the expected future spot rate:

Approximately:

Unlike CIRP, UIRP is not a mechanical arbitrage condition because the future spot rate is uncertain. Its simple form assumes risk-neutral investors, rational expectations and no time-varying currency risk premium. More generally:

The variable ρ_t represents a currency risk premium under the stated sign convention. Empirically, high-interest currencies have sometimes appreciated rather than depreciated over shorter horizons, supporting carry-trade profits but exposing investors to occasional severe losses.

Fisher Effects and Exchange Rates

Domestic Fisher effect

The Fisher effect separates a nominal interest rate into a real interest rate and expected inflation:

Here, i is the nominal interest rate, r is the expected real interest rate and π^e is expected inflation for the same period. The exact equation implies:

For moderate rates:

A high nominal rate does not necessarily represent a high real return; it may primarily compensate for expected inflation.

International Fisher effect

The international Fisher effect (IFE) combines the Fisher relationship with uncovered interest parity. Its exact parity prediction is:

If expected real interest rates are equal internationally, nominal interest-rate differences principally reflect expected inflation differences. The approximate level-ratio relationship is then:

Equivalently, the percentage change—not the level ratio—is approximately:

Thus, a country with a higher nominal interest rate is expected, under the IFE assumptions, to experience currency depreciation. This is an equilibrium expectation, not a guaranteed trading outcome.

For example, if comparable nominal rates are 8% domestically and 3% abroad:

The exact predicted domestic depreciation is 4.85%; the simple interest-differential approximation is 5%.

Monetary Approaches to Exchange Rates

Monetary models treat the exchange rate as the relative price of national monies. A standard log-linear money-demand equation is:

The lowercase variables m, p and y are logarithms of nominal money supply, price level and real output. The nominal interest rate i is expressed consistently, while φ > 0 is the income elasticity of money demand and λ > 0 is its semi-elasticity with respect to the interest rate.

Solving for the domestic price level and subtracting the corresponding foreign equation gives:

Under flexible prices and purchasing power parity, s = p_d − p_f, so:

The model predicts that, other things equal:

• a larger domestic relative money supply raises s and depreciates the domestic currency;
• higher domestic relative output increases domestic money demand, lowers s and appreciates the currency;
• a higher domestic interest rate reduces money demand and raises s within this flexible-price model.

The interest-rate interpretation is model-specific. In this framework, a high nominal rate commonly signals high expected inflation rather than monetary tightness. In a sticky-price setting, an unexpected rate increase may instead attract capital and appreciate the currency initially.

Worked monetary-model change

Suppose the change in the relative money-supply term is +2.0%, relative domestic output rises by 0.5%, φ = 0.8, the domestic–foreign interest differential falls by 1 percentage point, and λ = 0.1 when interest rates are measured in percentage points. Then:

The output change offsets 0.4 percentage point of depreciation, while the lower interest differential offsets another 0.1 percentage point. It does not contribute to depreciation. The model predicts approximately 1.5% domestic depreciation.

Sticky prices and overshooting

In the Dornbusch overshooting model, asset markets adjust rapidly while goods prices adjust slowly. An unexpected monetary expansion lowers domestic interest rates. To make domestic assets attractive, the currency may depreciate immediately beyond its long-run equilibrium level and then appreciate gradually as prices rise. Overshooting helps explain why exchange rates can be more volatile than goods prices.

Monetary models are structurally informative but empirically unstable over short horizons. Money-demand parameters change, central-bank operating frameworks evolve, and market expectations may respond before published monetary data become available.

Portfolio-Balance Approach

The portfolio-balance approach allows domestic and foreign assets to be imperfect substitutes. Investors care about expected returns, risk, liquidity and currency exposure. Exchange rates and yields adjust so that investors willingly hold the outstanding supplies of assets.

A simplified domestic-currency wealth identity is:

Here, W is total wealth measured in domestic currency, M is domestic money, B_d is domestic bonds measured in domestic currency, and B_f is foreign bonds denominated in foreign currency. Because S is domestic currency per foreign currency, S B_f is the domestic-currency value of foreign bonds. The equation is therefore dimensionally consistent.

Desired domestic-bond holdings may be represented as:

The portfolio share b is dimensionless and normally rises with the relative expected risk-adjusted return on domestic bonds. If the supply of domestic government debt increases without a corresponding increase in investor demand, domestic yields may need to rise, the currency may need to depreciate, or both, to induce investors to hold the additional debt.

Portfolio arithmetic example

Suppose investors initially hold domestic bonds worth 500 in a portfolio with domestic-currency wealth of 1,000. The domestic-bond share is:

Now wealth rises to 1,100, and investors still desire a 50% domestic-bond share. Desired holdings are:

If outstanding domestic bonds equal 600, there is an excess supply of domestic bonds of:

To restore equilibrium, domestic bond prices may fall and yields rise; the domestic currency may also depreciate enough to increase expected risk-adjusted returns. The precise adjustment depends on investor preferences and policy responses.

Compared with the monetary model, the portfolio approach emphasizes gross asset supplies, sovereign risk, home bias and changing risk premiums. Its main limitation is that desired portfolio shares and risk premiums are difficult to observe directly.

Comparing the Main Theories

The theories are complementary rather than mutually exclusive. Goods prices, monetary policy and portfolio rebalancing may dominate at different horizons.

Forecasting Exchange Rates

An exchange-rate forecast should state the currency quotation, horizon, information date, probability or uncertainty range, and intended managerial use. A point estimate without these elements can be misleading.

Figure: A disciplined forecast combines multiple information sources and continually evaluates performance.

Technical forecasting

Technical analysis uses past prices, returns, trading volume and market patterns. Methods include moving averages, momentum rules, support and resistance levels, and statistical time-series models.

An n-period simple moving average is:

A rule might interpret a short moving average crossing above a long moving average as upward momentum in S, meaning possible domestic depreciation under the chapter’s quotation convention.

Technical methods can identify trends and market positioning, but patterns may disappear after transaction costs or once widely exploited. Data mining, overfitting and look-ahead bias are serious risks.

Fundamental forecasting

Fundamental forecasts model exchange rates using variables such as inflation, interest rates, output growth, money supply, current-account balances, fiscal conditions, commodity prices and political risk. A generic forecasting regression is:

Here, h is the forecast horizon, X_t is a vector of information available at date t, β is a vector of estimated coefficients, and ε_t+h is the forecast error. Historical association does not establish causal stability. Coefficients may shift after crises, policy regime changes or structural reforms.

Market-based forecasting

Market-based forecasts extract information from traded prices:

• forward rates reveal the rate fixed today for future exchange but may include risk premiums;
• futures prices provide standardized market expectations and hedging prices;
• option-implied volatility summarizes the market price of uncertainty;
• risk reversals indicate asymmetric demand for protection against appreciation or depreciation;
• survey forecasts provide observable professional expectations.

A forward rate should not automatically be called an unbiased prediction of the future spot rate. Under a risk premium:

This additive representation is a simplified level-based decomposition, where RP_t has exchange-rate units and its sign depends on convention. Forward rates remain valuable because they are observable, tradable and relevant to hedging.

Scenario forecasting

Scenario analysis develops internally consistent alternative futures rather than pretending that one path is certain. A useful set might include:

• a base case based on expected monetary and fiscal policy;
• a domestic-inflation shock;
• a global risk-off episode;
• a commodity-price shock;
• a policy intervention or capital-control scenario.

Each scenario should specify assumptions, transmission channels, exchange-rate ranges, probabilities where defensible, and business consequences. Stress scenarios should be severe but plausible.

Combined forecasts

Forecast combinations often outperform a single model because model errors are imperfectly correlated. A weighted forecast is:

The variables Ŝ_k,t+h are forecasts from K models and w_k are predetermined or estimated weights. Simple equal weights may be more robust than repeatedly optimized weights when data samples are small.

Forecast Evaluation

Exchange-rate models should be assessed out of sample against a credible benchmark, often a random walk:

This benchmark predicts that tomorrow’s rate equals today’s rate. Beating it consistently is difficult, particularly at short horizons.

For T forecasts, the forecast error is e_t = S_t − Ŝ_t. Common measures include:

MAE and RMSE have the same currency-quotation units as S. RMSE penalizes large errors more heavily. Mean error measures bias, while directional accuracy records how often the forecast correctly predicts appreciation or depreciation. Economic evaluation should also examine whether a forecast improves hedging costs, cash-flow stability or risk-adjusted returns after fees.

Reliable evaluation requires a rolling or recursive real-time design. Analysts must not use revised data, future observations or model selections unavailable on the original forecast date. Statistical superiority does not necessarily imply commercially significant value.

Applied Case: Meridian Appliances

Background

Meridian Appliances is an illustrative multinational manufacturer based in a country whose currency is quoted as domestic currency per euro. It must pay €20 million to a supplier in six months. The current spot rate is 1.100, so the payable currently represents 22 million domestic currency units.

Problem

The treasury team must prepare a budget rate and recommend a risk-management response. Domestic six-month interest is 4%, the euro interest rate is 2%, both stated for the six-month horizon. Domestic and euro-area inflation forecasts for the next year are 5% and 2%, respectively. Option markets indicate elevated volatility around an upcoming election.

Analysis

CIRP gives the six-month forward rate:

A full forward hedge would therefore fix the payable at approximately:

An annual PPP projection is:

This annual estimate cannot be mechanically treated as a six-month forecast. Under a simplifying assumption that inflation accrues evenly, a six-month PPP estimate would use consistent half-year inflation estimates, not the full-year rates.

The forward rate indicates the contractual cost of hedging, not certainty about the future spot rate. The technical model shows recent euro momentum, while the election scenario suggests a wide and asymmetric range. A severe risk-off scenario places the six-month rate at 1.180; a favorable policy scenario places it at 1.060.

Approach and solution

Meridian separates forecasting from risk appetite. Because the payable is committed and its operating margin is narrow, management decides to hedge 70% with a forward contract and 30% with a euro call option. The forward protects the core budget, while the option preserves some benefit if the euro weakens. The board approves a budget rate based on the hedged portfolio rather than relying solely on a point forecast.

Outcome

The decision reduces the cash-flow impact of an adverse euro appreciation while maintaining limited favorable participation. Forecast ranges are reported with assumptions and updated after monetary-policy and election events.

Learning points

• Different theories answer different questions: PPP concerns long-run purchasing power, while CIRP determines a no-arbitrage forward rate.
• A forecast should not substitute for hedging when an exposure threatens operating viability.
• Horizons and units must be matched before applying economic relationships.
• Scenario ranges can be more decision-relevant than a single point estimate.

Limitations, Governance and Contemporary Practice

Exchange rates react to expectations, so markets may move before economic data are released. Structural breaks, interventions, geopolitical shocks and liquidity crises weaken historically estimated relationships. Accurate macroeconomic forecasts do not guarantee accurate currency forecasts because the market may already have priced the information.

Machine-learning systems can process nonlinear interactions, news sentiment and high-frequency data. However, they remain vulnerable to overfitting, unstable relationships, opaque explanations and contaminated training data. They should be compared with simple benchmarks and tested on genuinely unseen periods.

Professional governance requires documented data sources, model versions, assumptions, overrides and performance. Forecast producers should disclose conflicts of interest and distinguish objective analysis from trading advocacy. Selectively presenting favorable back-tests or suppressing adverse scenarios can mislead decision-makers and investors. Firms must also respect market-conduct rules, confidentiality obligations, sanctions and restrictions on using material nonpublic information.

Best practice is to use multiple models, preserve independent challenge, report uncertainty, conduct stress tests and connect forecasts to explicit business decisions. Forecast failure should trigger diagnosis and model review, not retrospective alteration of the original record.

Chapter Summary

Exchange-rate theories describe equilibrium relationships operating through goods, money and asset markets. Relative PPP links depreciation to inflation differentials and is generally more useful over long horizons. Covered interest parity is a no-arbitrage relationship involving spot, forward and comparable interest rates, whereas uncovered parity and the international Fisher effect concern uncertain expected exchange-rate changes. The Fisher effect separates nominal rates into real returns and expected inflation.

Monetary models explain the exchange rate through relative money supplies, output and interest rates. Portfolio-balance models add imperfect asset substitution, asset supplies and risk premiums. Technical, fundamental, market-based and scenario methods provide complementary forecasting perspectives. Their forecasts should be evaluated out of sample against simple benchmarks using statistical and economic criteria. For managerial decisions, uncertainty ranges, governance and hedging implications are usually more important than false precision.

Key Terms

Absolute purchasing power parity: The proposition that comparable baskets have equal prices after currency conversion.

Carry trade: Borrowing in a low-interest currency to invest in a higher-interest currency while accepting exchange risk.

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

Currency risk premium: Compensation investors require for bearing uncertain exchange-rate risk.

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

Forecast combination: A weighted aggregation of forecasts from multiple models.

Forward premium: The proportional difference between the forward and spot exchange rates.

International Fisher effect: The prediction that nominal interest differentials are associated with expected currency changes.

Law of one price: The proposition that identical tradable goods should have equal converted prices without frictions.

Monetary model: An exchange-rate model based on relative money supply, output and interest rates.

Overshooting: An immediate exchange-rate movement beyond its long-run equilibrium following a shock.

Portfolio-balance model: A framework in which asset supplies, risk and investor preferences influence exchange rates.

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

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

Risk reversal: An options-market measure of asymmetric demand for protection against currency movements.

Scenario analysis: The construction of alternative, internally consistent future states and their consequences.

Technical analysis: Forecasting based mainly on historical market prices, volume and patterns.

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

Review Questions

Short Answer Questions

1. Under the quotation convention used in this chapter, what does an increase in the spot exchange rate mean?
2. Why is covered interest parity a stronger arbitrage condition than uncovered interest parity?
3. Distinguish the exact Fisher equation from its common approximation.
4. What does an increase in the real exchange rate represent?
5. Why should a forward rate not automatically be described as an unbiased spot-rate forecast?

Long Answer Questions

1. Explain absolute and relative purchasing power parity, including their assumptions and empirical limitations.
2. Derive covered interest rate parity by comparing domestic and covered foreign investment strategies.
3. Compare the monetary and portfolio-balance approaches to exchange-rate determination.
4. Critically evaluate technical, fundamental, market-based and scenario forecasting methods.
5. Explain how forecast governance can reduce model risk, ethical failures and misleading managerial decisions.

Analytical / Application Questions

1. The spot rate is 2.000 domestic currency units per foreign unit. Domestic inflation is expected to be 8% and foreign inflation 3%. Calculate the relative-PPP rate and interpret the result.
2. A firm must pay 5 million foreign currency units in one year. The spot rate is 0.900, domestic interest is 6% and foreign interest is 4%. Calculate the CIRP forward rate and the domestic-currency cost of a full forward hedge.
3. Design a forecasting and hedging process for an exporter exposed to uncertain foreign-currency receipts. Explain the models, scenarios, performance measures and governance controls you would use.

Multiple Choice Questions with Answers

Question 1

Under the chapter’s quotation convention, an increase in S_t indicates:

A. Domestic-currency appreciation

B. Domestic-currency depreciation

C. Foreign-currency depreciation against every currency

D. No change in purchasing power

Correct Answer: B. Domestic-currency depreciation

Question 2

If domestic inflation is 6%, foreign inflation is 2%, and the current spot rate is 1.500, relative PPP predicts a future rate closest to:

A. 1.4423

B. 1.5000

C. 1.5588

D. 1.6200

Correct Answer: C. 1.5588

Question 3

Which relationship is primarily a no-arbitrage condition involving a contracted future exchange rate?

A. Absolute purchasing power parity

B. Covered interest rate parity

C. International Fisher effect

D. Portfolio balance

Correct Answer: B. Covered interest rate parity

Question 4

If the spot rate is 1.200, domestic interest is 5%, and foreign interest is 2%, the CIRP forward rate is closest to:

A. 1.1640

B. 1.2000

C. 1.2353

D. 1.2840

Correct Answer: C. 1.2353

Question 5

With domestic and foreign nominal rates of 8% and 3%, respectively, the exact IFE parity prediction for domestic-currency depreciation is approximately:

A. 3.00%

B. 4.85%

C. 5.83%

D. 11.00%

Correct Answer: B. 4.85%

Question 6

In the flexible-price monetary model s=(m_d-m_f)-φ(y_d-y_f)+λ(i_d-i_f), a fall in the domestic–foreign interest differential, other things equal, causes:

A. A fall in s

B. A rise in s

C. No change in s

D. An increase in relative money supply

Correct Answer: A. A fall in s

Question 7

A portfolio contains domestic bonds worth 500 and total wealth of 1,000. What is the domestic-bond share?

A. 45%

B. 50%

C. 55%

D. 60%

Correct Answer: B. 50%

Question 8

In the wealth identity W=M+B_d+SB_f, why is B_f multiplied by S?

A. To convert foreign-currency bonds into domestic-currency value

B. To calculate the foreign interest rate

C. To remove exchange-rate risk

D. To convert domestic bonds into foreign-currency value

Correct Answer: A. To convert foreign-currency bonds into domestic-currency value

Question 9

Which forecast evaluation measure penalizes large errors more heavily because errors are squared?

A. Mean absolute error

B. Directional accuracy

C. Root mean squared error

D. Mean forecast

Correct Answer: C. Root mean squared error

Question 10

Which practice best prevents look-ahead bias in forecast evaluation?

A. Using revised data published after the forecast date

B. Selecting the best model after viewing the test-period results

C. Testing with only information available when each forecast was made

D. Removing all unusually large forecast errors

Correct Answer: C. Testing with only information available when each forecast was made