Exchange Rate Determination Models

TL;DR

Exchange rate models explain how different factors influence currency values. We'll look at purchasing power parity (PPP), interest rate parity (IRP), and the Fisher effect. Understanding these models helps predict future exchange rate movements and evaluate investment decisions.

1. The Mental Model

Think of exchange rates as prices reflecting the relative value of one country's goods, services, and financial assets compared to another's. These models try to capture what drives those relative values, whether it's inflation differences, interest rate differentials, or capital flows.

2. The Core Material

When we talk about exchange rate determination, we're looking at various economic theories that try to explain why one currency trades at a certain value against another. These models are crucial for understanding international finance and investment.

Purchasing Power Parity (PPP)

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PPP suggests that exchange rates adjust so that an identical good or service will cost the same in two different countries when expressed in a common currency. It comes in two forms:

• Absolute PPP: The exchange rate between two currencies is the ratio of their price levels. If a Big Mac costs \$5 in the US and £4 in the UK, absolute PPP suggests the exchange rate should be \$5/£4 = \$1.25/£. It rarely holds perfectly due to transaction costs, trade barriers, and differing consumption baskets.
• Relative PPP: This is a more practical version. It states that the change in the exchange rate between two currencies over a period is approximately equal to the difference in their inflation rates over that same period.
  • If US inflation is 3% and UK inflation is 1%, then the USD is expected to depreciate against the GBP by approximately 2%. This means it would take more USD to buy one GBP in the future.

Interest Rate Parity (IRP)

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IRP links interest rates and exchange rates. It states that the difference in interest rates between two countries should be equal to the difference between the forward exchange rate and the spot exchange rate. This prevents arbitrage opportunities.

• Covered Interest Rate Parity (CIRP): This is the no-arbitrage condition. An investor shouldn't be able to make a risk-free profit by borrowing in one currency, converting it, investing it at a higher rate in another currency, and then covering the exchange rate risk using a forward contract.
  • Formula: (1 + interest_rate_domestic) = (Spot_Rate * (1 + interest_rate_foreign) * Forward_Rate) / Spot_Rate
  • Rearranging: Forward_Rate / Spot_Rate = (1 + interest_rate_domestic) / (1 + interest_rate_foreign)
  • Approximately: (Forward - Spot) / Spot ≈ interest_rate_domestic - interest_rate_foreign
• Uncovered Interest Rate Parity (UIRP): Similar to CIRP, but it involves the expected future spot rate instead of a known forward rate. It implies that a higher interest rate in a country should be offset by an expected depreciation of its currency.

The Fisher Effect and International Fisher Effect

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• Fisher Effect: This theory states that the nominal interest rate in a country is approximately equal to the real interest rate plus the expected inflation rate.
  • Nominal Interest Rate ≈ Real Interest Rate + Expected Inflation
• International Fisher Effect (IFE): Combines the Fisher Effect with UIRP. It suggests that the difference in nominal interest rates between two countries is approximately equal to the expected change in the spot exchange rate.
  • If the US nominal interest rate is 5% and the UK nominal interest rate is 2%, the IFE suggests the USD is expected to depreciate by approximately 3% against the GBP. This means you'd expect to need more USD to buy one GBP in the future.

Here's how these models are interconnected:

graph TD
    A["Inflation Differentials"] --> B["Relative PPP"]
    B --> E["Expected Spot Rate Change"]
    C["Nominal Interest Rate Differentials"] --> D["Covered IRP (Forward Rate)"]
    C --> F["Uncovered IRP (Expected Spot Rate)"]
    G["Real Interest Rate Differentials"] --> H["Fisher Effect"]
    H --> C
    F --> E
    E --> I["Exchange Rate Impact"]
    D --> I

Other Models

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While PPP and IRP are core, other models exist:

• Balance of Payments (BoP) Model: Focuses on the flows of goods, services, and capital. A persistent current account deficit (more imports than exports) can lead to currency depreciation.
• Monetary Approach: Views exchange rates as determined by the relative supply and demand for national money stocks, influenced by money supply, income, and interest rates.
• Asset Market Approach: Treats exchange rates as determined by the demand and supply for financial assets. Capital flows, investor sentiment, and risk perceptions play a significant role.

3. Worked Example

Let's say you have the following information:
* Spot exchange rate: \$1.20/€ (meaning \$1.20 buys 1 Euro)
* US annual interest rate: 2.0%
* Eurozone annual interest rate: 4.0%
* One-year forward exchange rate: \$1.18/€

Question: Is there an arbitrage opportunity based on Covered Interest Rate Parity (CIRP)?

Solution:
First, let's calculate the theoretical forward rate implied by CIRP:

Theoretical Forward Rate / Spot Rate = (1 + interest_rate_domestic) / (1 + interest_rate_foreign)

Here, the domestic currency is USD and the foreign currency is EUR.
Theoretical Forward Rate / \$1.20/€ = (1 + 0.02) / (1 + 0.04)
Theoretical Forward Rate / \$1.20/€ = 1.02 / 1.04
Theoretical Forward Rate / \$1.20/€ ≈ 0.980769

Theoretical Forward Rate ≈ \$1.20/€ * 0.980769
Theoretical Forward Rate ≈ \$1.1769/€

Now, compare this to the actual one-year forward rate:
* Actual Forward Rate = \$1.18/€
* Theoretical Forward Rate = \$1.1769/€

Since the actual forward rate (\$1.18/€) is *higher* than the theoretical forward rate (\$1.1769/€), there is an arbitrage opportunity.

How to exploit it (briefly):
1. Borrow in the low-interest-rate currency (USD at 2%).
2. Convert USD to EUR at the spot rate (\$1.20/€).
3. Invest EUR at the higher interest rate (4% in Eurozone).
4. Simultaneously sell the future EUR principal + interest forward at the actual forward rate (\$1.18/€) to convert back to USD.
This will lock in a profit because you're selling EUR forward at a more favorable rate than what CIRP suggests.

4. Key Takeaways

• PPP explains exchange rate movements based on relative inflation rates and price levels.
• IRP links interest rate differentials to forward and expected spot exchange rates, preventing arbitrage.
• The Fisher Effect relates nominal interest rates to real interest rates and expected inflation.
• The International Fisher Effect extends this to exchange rates, suggesting interest rate differentials predict future spot rate changes.
• These models help predict currency trends but often don't hold perfectly due to real-world complexities like transaction costs, capital controls, and market inefficiencies.
• The BoP, Monetary, and Asset Market approaches offer broader perspectives on factors influencing exchange rates beyond just inflation and interest rates.

Common Mistakes to Avoid:
- Confusing absolute PPP with relative PPP; relative PPP is generally more empirically supported over the long term.
- Assuming CIRP implies a risk-free profit opportunity always exists; it's a no-arbitrage condition, meaning such opportunities are quickly eliminated.
- Ignoring the difference between nominal and real interest rates, especially when applying the Fisher Effect.
- Over-relying on any single model; real-world exchange rates are influenced by many factors simultaneously.

5. Now Try It

Assume the current spot rate is £0.80/\$ (meaning £0.80 buys 1 USD). US inflation is 3.5%, and UK inflation is 1.0%. Using the concept of Relative Purchasing Power Parity, calculate the expected spot rate in one year. What does this change imply for the value of the GBP relative to the USD? Success looks like calculating a specific expected future exchange rate and correctly interpreting whether the GBP has appreciated or depreciated.