4.5 Foreign Exchange, Capital Flows, and Arbitrage

FX Quotes, Capital Flows, Cross-Rates, and Forward Rates

Foreign exchange is quoted as one currency price for one unit of another currency. In a quote such as USD/EUR = 1.1000, one euro costs 1.1000 U.S. dollars if the convention is price currency per base currency. The base currency is the denominator currency. The price currency is the numerator currency.

A direct quote is domestic currency per unit of foreign currency. An indirect quote is foreign currency per unit of domestic currency. Direct and indirect depend on the investor's home currency, so always identify the perspective in the question. If EUR is domestic, USD/EUR is an indirect quote for a euro-based investor.

Currency appreciation means one currency buys more of another. If USD/EUR rises from 1.10 to 1.20, the euro has appreciated against the dollar because each euro buys more dollars or costs more dollars. The dollar has depreciated against the euro. Many exam errors come from naming the wrong currency.

Bid-ask spreads matter. The dealer bid is the price at which the dealer buys the base currency. The dealer ask is the price at which the dealer sells the base currency. Customers sell at the bid and buy at the ask. In cross-rate questions, using the wrong side can create a false arbitrage.

Cross-rates combine two exchange rates through a common currency. If USD/EUR = 1.20 and USD/GBP = 1.50, then EUR/GBP equals USD/GBP divided by USD/EUR, or 1.50 / 1.20 = 1.25 EUR per GBP. The algebra is easiest when currencies cancel like units.

Triangular arbitrage occurs when quoted cross-rates are inconsistent after considering bid-ask spreads and transaction costs. A trader converts through a cycle and ends with more of the starting currency. In competitive markets, arbitrage pressure pushes rates back into alignment quickly.

Forward exchange rates set a price today for currency exchange at a future date. Forward points are added to or subtracted from the spot rate, depending on quote convention. A currency at a forward premium has a forward rate that makes it more expensive in the price currency per base currency quote.

Covered interest rate parity links spot rates, forward rates, and interest rates. With quote price currency per base currency, F/S approximately equals (1 + price currency interest rate) divided by (1 + base currency interest rate). The currency with the higher interest rate usually trades at a forward discount under covered parity.

Forward premiums do not automatically mean the market expects appreciation. Under covered interest rate parity, the forward rate is a no-arbitrage price tied to interest differentials. Expected spot rates involve risk premiums, inflation expectations, policy credibility, and investor preferences.

Capital flows affect currencies and asset markets. Foreign direct investment is a lasting ownership interest, such as building a factory or buying a controlling stake. Portfolio investment is ownership of securities without control. Short-term flows can be sensitive to interest rates, risk appetite, liquidity, and policy credibility.

Exchange rate regimes shape adjustment. A floating currency moves with market forces. A fixed or pegged currency requires intervention and reserves. Capital controls limit flows. Pegs can support trade and credibility, but they are vulnerable if reserves are inadequate or domestic policy conflicts with the peg.

Structured Aid: FX Calculation Checklist

For exam speed, write rates as fractions and cancel currency labels. Then check intuition. The high-interest-rate currency should usually be at a forward discount under covered parity. If your answer says it trades at a forward premium, revisit the quote convention before selecting an option.