4.5 Foreign Exchange, Capital Flows, and Arbitrage

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

A foreign exchange quote states the price of one currency in units of another. The CFA convention writes price currency per base currency, with the base in the denominator of the label. In USD/EUR = 1.1000, the euro is the base currency and the U.S. dollar is the price currency, so one euro costs 1.1000 dollars. Misreading which currency is the base produces the most common FX error on the exam.

Direct vs. Indirect and Appreciation

A direct quote is domestic currency per unit of foreign currency; an indirect quote is foreign currency per unit of domestic currency. Direct versus indirect depends on the investor's home currency, so always fix the perspective. For a euro-based investor, USD/EUR (dollars per euro) is an indirect quote. Appreciation means a currency buys more of the other. If USD/EUR rises from 1.10 to 1.20, each euro now buys more dollars, so the euro has appreciated and the dollar has depreciated.

The percentage change in the base currency's value equals the percentage change in the quote; the price currency's change is found by inverting and is not simply the negative of that percentage.

Bid-Ask Spreads

The dealer bid is the price at which the dealer buys the base currency; the ask (offer) is the price at which the dealer sells it. Customers therefore sell the base at the bid and buy the base at the ask, and the spread is the dealer's compensation. Spreads widen with lower liquidity, higher volatility, larger trade size, and longer forward tenors. In cross-rate and arbitrage problems, using the wrong side of the spread can fabricate a false profit, so map each leg to bid or ask before computing.

Cross-Rates and Triangular Arbitrage

A cross-rate combines two quotes through a shared currency. Given USD/EUR = 1.20 and USD/GBP = 1.50, the dollars cancel: EUR/GBP = (USD/GBP) / (USD/EUR) = 1.50 / 1.20 = 1.25 euros per pound. Treat each rate as a fraction and cancel the matching currency labels to decide whether to multiply or divide. Triangular arbitrage exists when a quoted cross-rate is inconsistent with the implied no-arbitrage rate after spreads; a trader cycles through three currencies and ends with more of the starting currency. Competition closes such gaps within seconds.

Forward Rates and Covered Interest Rate Parity

A forward rate locks in a price today for exchange on a future date. Forward points are added to or subtracted from spot per the convention. Covered interest rate parity (CIRP) is enforced by arbitrage: with the price-per-base convention, F / S = (1 + i_price) / (1 + i_base), scaled by the day-count fraction for the tenor. The currency with the higher interest rate trades at a forward discount, because its higher yield must be offset by an expected currency loss for no-arbitrage to hold. Worked example: spot USD/EUR = 1.2000, one-year U.S.

rate 5%, euro-area rate 3%, so F = 1.2000 x (1.05 / 1.03) = 1.2233; the euro (base) trades at a forward premium because U.S. rates exceed euro rates. A frequent trap treats a forward premium as a forecast of appreciation; CIRP is a pricing relation, whereas uncovered interest rate parity links the expected future spot rate to risk premiums and expectations.

Capital Flows and Exchange-Rate Regimes

Foreign direct investment (FDI) is a lasting ownership stake, such as building a plant or buying a controlling interest; portfolio investment is holding securities without control and is more mobile, reacting quickly to rate differentials, risk appetite, and policy credibility. Exchange-rate regimes shape adjustment: a free float moves with market forces, a fixed or pegged rate requires intervention and reserves, and capital controls limit flows. Pegs can anchor trade and inflation expectations but are vulnerable when reserves are thin or when domestic policy conflicts with defending the peg.

Structured Aid: FX Calculation Checklist

Real Exchange Rates and the Mundell-Fleming View

The real exchange rate adjusts the nominal rate for relative price levels and determines actual purchasing power across borders; nominal appreciation with higher domestic inflation can leave the real rate unchanged. Over long horizons, relative purchasing power parity says the higher-inflation currency should depreciate. Over shorter horizons, the Mundell-Fleming model predicts that, with mobile capital, expansionary monetary policy weakens a currency by lowering rates, whereas expansionary fiscal policy can strengthen it by raising rates and attracting inflows.

The portfolio-balance and monetary approaches add longer-run links between money supplies, asset stocks, and the exchange rate.

Marshall-Lerner and the J-Curve

Whether a depreciation improves the trade balance depends on elasticities. The Marshall-Lerner condition holds that depreciation improves the current account only if the sum of export and import demand elasticities exceeds 1. In the short run, contracted quantities are sticky, so a depreciation can first widen the deficit before improving it, the J-curve effect. Exam items test whether candidates link a weaker currency mechanically to a smaller deficit; the correct answer conditions that on elasticities and time horizon.

For exam speed, write rates as fractions, cancel currency labels, then sanity-check intuition: the high-interest-rate currency should trade at a forward discount under CIRP. If your answer puts it at a premium, recheck the quote convention before locking in a choice.