## **Learning Outcomes**

This article explains how exchange rate equilibrium is linked to purchasing power parity (PPP) and interest rate parity (IRP) and how these parity conditions underpin valuation in FX markets. It explains the mechanics of absolute and relative PPP, shows how inflation differentials drive expected currency depreciation, and connects these relationships to long‑run exchange rate anchors. It also details covered and uncovered IRP, distinguishing between no‑arbitrage forward pricing under CIRP and expected-spot relationships under UIRP, and sets out how spot, forward, and expected future rates should align when parity holds. The article demonstrates how to compute forward rates from interest differentials, quantify potential arbitrage profits when CIRP is violated, and calculate the expected profit and loss profile of FX carry trades given assumed paths for spot rates. It examines why PPP and UIRP frequently fail in practice, highlights the role of risk premia and market frictions, and assesses the implications of persistent deviations for currency forecasting, valuation, and the risk–return characteristics of carry trade strategies in exam-style scenarios.

## **CFA Level 2 Syllabus**

For the CFA Level 2 exam, you are expected to understand the core valuation relationships in currency exchange, with a focus on the following syllabus points:

- Explain international parity conditions, including covered and uncovered interest rate parity, forward parity, and purchasing power parity.
- Describe the components and interpretations of PPP and IRP in modern FX markets.
- Compare spot, forward, and expected future exchange rates under different parity conditions.
- Calculate and interpret the profit and risks of FX carry trades and discuss their links to IRP.
- Evaluate reasons for deviations from parity and implications for forecasting exchange rates.

## **Test Your Knowledge**

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision._

1. If USD interest rates are higher than EUR rates, what does covered interest rate parity predict about the USD/EUR forward rate?
2. A spot GBP/USD rate is 1.30. UK inflation is expected at 6%, US inflation at 3%. According to PPP, what is the expected GBP/USD spot rate after one year?
3. Does an FX carry trade profit if uncovered interest rate parity holds exactly? Why or why not?
4. Explain one reason why relative PPP may fail in the short term.

## **Introduction**

A clear understanding of currency exchange valuation is essential for comparing international investments. Exchange rates are influenced by differences in prices and interest rates between economies, and theorists have developed frameworks like purchasing power parity (PPP) and interest rate parity (IRP) to forecast and explain currency movements. These relationships form the basis for forward pricing, currency risk assessment, and strategies such as the carry trade, all of which are core to CFA exam analysis and investment practice.

> **Key Term: Purchasing Power Parity (PPP)**
> An economic theory stating that the exchange rate between two currencies adjusts so that identical goods cost the same in each country, accounting for inflation differences.
>
> **Key Term: Interest Rate Parity (IRP)**
> A condition stating that the difference in interest rates between two countries is equal to the difference between the forward and spot exchange rates.
>
> **Key Term: FX Carry Trade**
> A trading strategy involving borrowing in a currency with a low interest rate and investing in a currency with a higher interest rate, seeking to profit from the interest rate differential rather than changes in exchange rates.

## PURCHASING POWER PARITY (PPP)

PPP suggests that, over time, exchange rates adjust to offset inflation differentials between economies. This means that countries with higher inflation should see their currencies depreciate relative to those with lower inflation.

There are two common forms:

- **Absolute PPP:** Exchange rates adjust so that identical goods have the same price in two markets.
- **Relative PPP:** The percentage change in the exchange rate over time offset the difference in inflation rates between two countries.

Relative PPP equation:
$$
\%\Delta S*{(A/B)} \approx \text{Inflation}\_A - \text{Inflation}\_B
$$
Where $ S*{(A/B)} $ is the price of currency A in terms of B.

PPP serves as a long-run anchor for exchange rates, but is often violated in the short term due to trade frictions, capital flows, and policy interventions.

### **Worked Example 1.1**

Suppose the spot rate is USD/BRL = 5.00 (US dollars per Brazilian real). If Brazilian inflation is 8% and US inflation is 3%, what is the expected USD/BRL rate after one year according to relative PPP?

> **Answer:**
> Inflation differential = 8% (Brazil) - 3% (US) = 5%.
> Expected BRL depreciation: 5.00 × 1.05 = 5.25 USD/BRL.
> The BRL is expected to depreciate by 5% against the USD.

## INTEREST RATE PARITY (IRP)

Interest rate parity links interest rate differentials to forward and spot exchange rates. IRP ensures that arbitrage opportunities are eliminated between foreign and domestic risk-free deposits.

- **Covered IRP (CIRP):** Uses forward contracts to remove FX risk. Predicts that any forward premium/discount equals the interest rate differential.

CIRP formula:
$$
F = S \times \frac{1 + r*{\text{domestic}}}{1 + r*{\text{foreign}}}
$$
Where F = Forward rate, S = Spot rate.

- **Uncovered IRP (UIRP):** Uses expected future exchange rates, not a forward contract. Predicts that currencies with higher interest rates are expected to depreciate.

$$
\mathbb{E}(\%\Delta S) \approx r*{\text{domestic}} - r*{\text{foreign}}
$$

### **Worked Example 1.2**

The one-year spot rate is GBP/USD = 1.32, UK rates = 2%, US rates = 4%. Calculate the one-year forward rate using CIRP.

> **Answer:**
> F = 1.32 × (1 + 0.04) / (1 + 0.02) = 1.32 × 1.04 / 1.02 ≈ 1.348.
> The one-year forward rate is 1.348 GBP/USD.

### **Exam Warning**

> For IRP calculations, always match the compounding frequency and interest calculation convention for both rates. Using annual rates with monthly terms, or ignoring day count conventions, leads to incorrect results.

## Relations Between PPP and IRP

If real interest rates are equalized abroad, and relative PPP holds, then uncovered IRP should also hold. This means expected exchange rate changes match interest rate differentials, creating no arbitrage. The _international Fisher effect_ makes this connection explicit.

> **Key Term: International Fisher Effect**
> The theory that currencies with higher nominal interest rates will depreciate because higher interest rates reflect higher expected inflation.

## Forward Rate as Forecast

Forward rates (from CIRP) may be used to forecast future spot rates. If UIRP holds, the forward rate should be an unbiased predictor of the future spot rate. However, in practice, these relationships often fail in the short term and can result in systematic forecast errors.

## The FX Carry Trade

A carry trade profits by exploiting differences between high- and low-yielding currencies. The investor borrows in a currency offering a low interest rate (the funding currency) and invests in a currency with a higher interest rate. If UIRP fails and the high-yielding currency does not depreciate as much as predicted, the carry trade generates positive returns.

Carry trade profits are calculated as:
$$
\text{Profit} = \text{Interest Differential} - \text{Currency Depreciation}
$$

Carry trades tend to be profitable during periods of low volatility, but are subject to "crash risk" when funding currencies appreciate rapidly. Returns are characterized by steady small profits punctuated by occasional large losses.

### **Worked Example 1.3**

Suppose the AUD 1-year rate is 4%, the JPY 1-year rate is 0.5%, and the spot AUD/JPY is 85.00. An investor borrows JPY and invests in AUD for one year, assuming no change in spot rate at the end of the period. What is the carry trade profit per 1 AUD invested?

> **Answer:**
> Interest differential = 4% - 0.5% = 3.5%.
> If AUD/JPY remains at 85.00, the investor earns the full 3.5%.
> If AUD depreciates by less than 3.5% against JPY, the trade is still profitable.
> If it depreciates by more than 3.5%, the trade loses money.

### **Exam Warning (Carry Trade)**

> Carry trades assume no large, sudden currency moves. In reality, large losses are possible when high-yielding currencies depreciate abruptly. Be careful not to ignore risk and skewness of returns.

## Limitations, Violations, and Forecasting

- PPP holds better over longer horizons and for broad baskets of goods, but can be distorted by price stickiness, trade barriers, taxes, and non-tradable goods.
- CIRP holds tightly for traded, liquid currencies due to arbitrage, but UIRP and PPP often fail in practice, especially in the short run, due to risk premia and investor behavior.
- Carry trade returns are not risk-free: they exhibit negative skew ("crash risk") and are subject to sudden unwinds in times of market stress.

## **Summary**

PPP and IRP provide theoretical frameworks linking exchange rates, inflation, and interest rates. Covered IRP holds well in liquid markets, aligning interest differentials and forward rates, but uncovered IRP and PPP are prone to short-term violations. Carry trades exploit persistent deviations, but do so at the expense of increased risk and the chance of severe losses in stressed markets. For the CFA exam, be prepared to apply these parity conditions for exchange rate forecasting, carry trade profit calculations, and critical analysis of model assumptions.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Differentiate between absolute and relative purchasing power parity (PPP) and their application in FX valuation.
- Explain and calculate covered and uncovered interest rate parity (CIRP and UIRP).
- Understand the international Fisher effect and its connection to these parity conditions.
- Calculate forward rates and use parity conditions for forecasting exchange rates.
- Recognize the mechanics, potential profit, and risks of FX carry trades.
- Identify limitations of PPP and IRP in real-world exchange rate determination.

## **Key Terms and Concepts**

- Purchasing Power Parity (PPP)
- Interest Rate Parity (IRP)
- FX Carry Trade
- International Fisher Effect

Currency exchange and valuation - PPP IRP and carry trade fundamentals