Exchange Rates and Foreign Exchange Market Essentials
Exchange Rate Essentials
An exchange rate (E) is the price of foreign currency in home currency (e.g., E_{\$/€} is U.S. dollars per euro).
Appreciation: Home currency buys more foreign currency; its value rises. If E_{\$/€} falls, the dollar appreciates.
Depreciation: Home currency buys less foreign currency; its value falls. If E_{\$/€} rises, the dollar depreciates.
Proportional Change: (\frac{\Delta E}{E}) \times 100\% measures appreciation/depreciation size.
E: The initial exchange rate.
\Delta E: The change in the exchange rate.
Multilateral / Effective Exchange Rate: A weighted average of bilateral exchange rates, with weights based on trade shares. Formula: \frac{\Delta E{effective}}{E{effective}} = \sum{i=1}^{N} (\frac{\Delta Ei}{Ei} \times \frac{Tradei}{Trade}).
E_{effective}: The effective exchange rate at a given time.
\Delta E_{effective}: The change in the effective exchange rate.
E_i: The bilateral exchange rate of the home country with country i.
\Delta E_i: The change in the bilateral exchange rate with country i.
Trade_i: The volume of trade (e.g., imports + exports) with country i.
Trade: The total volume of trade with all partner countries (\sum Trade_i).
N: The number of trading partners.
Impact on Prices: Depreciation makes home goods cheaper for foreigners and foreign goods more expensive for home residents.
Exchange Rate Regimes
Fixed (Pegged): Exchange rate fluctuates narrowly against a base currency, requiring government intervention.
Floating (Flexible): Exchange rate fluctuates widely, with no government attempt to fix it.
Other Regimes: - Band: Fixed rate with a small permissible variation.
Crawling Peg: Exchange rate adjusted gradually at a steady pace (depreciation/appreciation).
Dollarization: Unilateral adoption of another country's currency.
Currency Board: A highly rigid fixed regime with strict legal/procedural rules.
Exchange Rate Crisis: Sudden, large depreciation.
The Foreign Exchange (Forex) Market
An over-the-counter global market where exchange rates are set, with daily trading volumes in trillions of dollars.
Spot Contract: Immediate exchange of currencies at the spot exchange rate (E).
Transaction Costs (Spread): Difference between buy and sell prices, typically small for large transactions.
Derivatives: Forward contracts, swaps, futures, and options that derive their value from spot rates.- Forward Contract: Agreement today to exchange currencies at a specified future date and price (the forward exchange rate, F).
Key Actors: Commercial banks, corporations, central banks (often for intervention or fixed rates).
Capital Controls: Government policies restricting forex movement or cross-border financial transactions.
Arbitrage and Exchange Rates
Arbitrage: Risk-free profit from exploiting price differences.
Triangular Arbitrage: Ensures consistency across three currencies; the direct cross rate equals the indirect cross rate.
No-Arbitrage Condition (Cross Rate): For £/$, £/€, and €/$ rates, E{£/\$} = E{£/€} \times E_{€/\ Jefferson}. A vehicle currency (e.g., USD) may be used for intermediation.
E_{£/\ Jefferson}: The exchange rate of British Pounds per U.S. Dollar.
E_{£/€}: The exchange rate of British Pounds per Euro.
E_{€/\ Jefferson}: The exchange rate of Euros per U.S. Dollar.
Arbitrage and Interest Rates
Covered Interest Parity (CIP) (Riskless Arbitrage):- Condition: The dollar return on dollar deposits equals the dollar return on foreign (e.g., euro) deposits when exchange rate risk is "covered" using a forward contract.
Formula: 1 + i{\ Jefferson} = \frac{F{\$/€}}{E{\$/€}} (1 + i{€}).
i_{\$}: The interest rate on deposits in the home currency (e.g., U.S. dollar).
i_{€}: The interest rate on deposits in the foreign currency (e.g., Euro).
E_{\$/€}: The current spot exchange rate (U.S. dollars per Euro).
F_{\$/€}: The forward exchange rate (U.S. dollars per Euro) for a contract covering the same period as the interest rates.
Implication: The forward rate (F{\$/€}) is determined by the spot rate (E{\$/€}) and the interest rates (i{\$} and i{€}).
Uncovered Interest Parity (UIP) (Risky Arbitrage):- Condition: The dollar return on dollar deposits equals the expected dollar return on foreign deposits when exchange rate risk is not covered, and future spot rates are expected (E_{\$/€}^{e}).
Formula: 1 + i{\ Jefferson} = \frac{E{\$/€}^{e}}{E{\$/€}} (1 + i{€}).
i_{\$}: The interest rate on deposits in the home currency.
i_{€}: The interest rate on deposits in the foreign currency.
E_{\$/€}: The current spot exchange rate.
E_{\$/€}^{e}: The expected future spot exchange rate (U.S. dollars per Euro).
Implication: The current spot rate (E{\$/€}) is determined by the expected future spot rate and interest rates: E{\$/€} = \frac{E{\$/€}^{e} (1 + i{€})}{1 + i{\$}}.
Approximation: i{\ Jefferson} \approx i{€} + \frac{E{\$/€}^{e} - E{\$/€}}{E_{\$/€}} (home interest rate equals foreign interest rate plus expected depreciation of home currency).
This approximation states that the interest rate differential between two countries should be approximately equal to the expected rate of depreciation of the home currency.
Relationship between CIP and UIP: If both hold for risk-neutral investors, the forward rate must equal the expected future spot rate: F{\$/€} = E{\$/€}^{e}. Consequently, the forward premium (\frac{F{\$/€}}{E{\$/€}} - 1) equals the expected rate of depreciation (\frac{E{\$/€}^{e} - E{\$/€}}{E_{\$/€}}).
Forward Premium: \frac{F{\$/€}}{E{\$/€}} - 1 represents the percentage difference between the forward exchange rate and the spot exchange rate, indicating whether the foreign currency is expected to appreciate or depreciate in the forward market.
Expected Rate of Depreciation: \frac{E{\$/€}^{e} - E{\$/€}}{E_{\$/€}} represents the percentage change between the expected future spot rate and the current spot rate, indicating the expected depreciation or appreciation of the foreign currency.