CFA Level I: Currency Exchange Rates

Currency exchange rates are the backbone of global finance, directly determining the returns on international investments and the viability of cross-border business strategies. For a CFA candidate or an MBA professional, mastering this topic is not academic—it’s a practical necessity for risk management, valuation, and strategic decision-making. The progression from the mechanics of reading a quote to the fundamental economic theories that explain long-term currency movements provides the toolkit you need to analyze how forex fluctuations impact portfolio performance.

Exchange Rate Quotation and the Bid-Ask Spread

Every analysis begins with understanding how prices are quoted. A direct quotation expresses the domestic currency price of one unit of foreign currency (e.g., for a USD-based investor, EUR/USD = 1.10 means €1 costs $1.10).Conversely,an\ast \ast indirectquotation\ast \ast expressestheforeigncurrencypriceofoneunitofdomesticcurrency(e.g.,USD/EUR=0.9091means$1 costs €0.9091). These are reciprocals: Direct = 1 / Indirect.

You never trade at a single price. Dealers quote a bid-ask spread, representing their prices to buy (bid) and sell (ask) the base currency. For example, a dealer might quote EUR/USD as 1.1050/1.1055. This means they will buy euros (the base currency) from you at $1.1050pereuroand\ast sell\ast eurostoyouat$1.1055 per euro. The spread (1.1055 - 1.1050 = 0.0005) is the dealer’s compensation and a transaction cost for you. The ask is always greater than the bid. A key exam skill is inverting a quote: if EUR/USD = 1.1050/1.1055, then the USD/EUR quote is (1/1.1055)/(1/1.1050) = 0.9046/0.9050. Notice that the bid and ask swap positions after inversion.

Calculating Cross-Rates and Identifying Arbitrage

Often, you need the exchange rate between two currencies (A and B) that are not directly quoted against each other, but both are quoted against a common third currency, C (often the USD). This is a cross-rate calculation. The fundamental rule is to multiply the quotes such that the common currency cancels out.

If you have USD/EUR = 0.90 and USD/GBP = 0.75, what is EUR/GBP? You want euros per pound. The calculation is: (USD/GBP) ÷ (USD/EUR) = 0.75 / 0.90 = 0.8333. This gives you EUR/GBP = 0.8333. In essence, you are deriving the rate from two dollar-denominated pairs.

This leads directly to triangular arbitrage, a risk-free profit opportunity that arises when the quoted cross-rate does not align with the rate derived from two other pairs. The process is mechanical:

1. Identify a mispricing across three currencies (e.g., USD, EUR, GBP).
2. Start with a capital amount in one currency.
3. Execute three consecutive currency trades that return you to the starting currency.
4. If the ending amount exceeds the starting amount, arbitrage exists.

For instance, if the direct EUR/GBP quote is 0.8500, but our calculated cross-rate from the USD pairs is 0.8333, a discrepancy exists. An arbitrageur could start with $1,000,000, buy euros via USD/EUR, then use those euros to buy pounds at the inflated direct EUR/GBP rate, and finally convert pounds back to dollars. The profit is the difference net of transaction costs. In efficient markets, such opportunities are fleeting, but the concept is crucial for understanding market consistency.

Forward Markets: Premiums, Discounts, and Interest Rate Parity

While spot rates are for immediate delivery, forward exchange rates are contracts to exchange currency at a predetermined rate on a future date. The difference between the forward rate (F) and the spot rate (S) is the forward premium or discount. It is usually annualized and expressed as a percentage:

$$\text{Annualized Forward Premium/Discount}=\frac{F-S}{S}\times \frac{360}{\text{Days}}\times 100\%$$

If F > S, the base currency trades at a forward premium (it is expected to strengthen). If F < S, it trades at a forward discount.

This premium or discount is not a forecast, but a mechanical result of interest rate differentials, formalized by covered interest rate parity (CIRP). CIRP states that the forward rate must lock in the same return as investing domestically, eliminating arbitrage. The formula is:

$$F=S\times \frac{(1+i_d{)}^t}{(1+i_f{)}^t}$$

where $i_d$ is the domestic interest rate, $i_f$ is the foreign interest rate, and $t$ is the time in years. If U.S. interest rates ($i_d$) are 3% and eurozone rates ($i_f$) are 1%, the euro (the foreign currency in EUR/USD) should trade at a forward premium relative to the dollar. Why? The lower yield on euros must be compensated by an expected appreciation of the euro (locked in via the forward contract) to equalize returns.

Uncovered interest rate parity (UIRP), in contrast, is a theoretical and riskier proposition. It suggests that the expected future spot rate should differ from the current spot rate by an amount equal to the interest rate differential. Unlike CIRP, UIRP is not enforced by arbitrage as it relies on uncertain expectations, not a locked-in forward contract.

Purchasing Power Parity and Long-Term Currency Drivers

For long-term valuation, purchasing power parity (PPP) is a cornerstone theory. In its absolute form, it suggests that identical baskets of goods should cost the same in different countries when priced in a common currency (the "law of one price"). Its relative form is more practical, stating that currencies should adjust to offset differences in inflation rates.

The formula for relative PPP is:

$$\%\Delta S\approx {\pi }_d-{\pi }_f$$

where $\%\Delta S$ is the change in the spot exchange rate (domestic per foreign), ${\pi }_d$ is domestic inflation, and ${\pi }_f$ is foreign inflation. If U.S. inflation is 2% and U.K. inflation is 5%, the pound (the foreign currency in USD/GBP) should depreciate by approximately 3% against the dollar to maintain parity in purchasing power. While PPP is a poor predictor of short-term moves, it provides a fundamental anchor for assessing whether a currency is over- or under-valued over economic cycles, directly impacting long-term international investment returns.

Common Pitfalls

1. Misapplying Quote Conventions: Confusing direct and indirect quotes leads to calculation errors. Always identify the price currency and the base currency. In a quote A/B, B is the base, and the number is how many units of A you pay for one unit of B. On the CFA exam, carefully note the investor's home currency perspective.
2. Incorrect Cross-Rate Multiplication: A common mistake is multiplying the wrong quotes together or failing to invert a quote properly. Use the "cancel the common currency" rule methodically. Write the pairs as fractions and ensure the currency units cancel algebraically to leave your desired currency pair.
3. Confusing Covered and Uncovered Interest Rate Parity: Remember, CIRP uses the forward rate and is enforced by arbitrage (it always holds in the absence of capital controls). UIRP uses the expected future spot rate and is a non-arbitrageable economic theory that often fails in the short run. Do not substitute one for the other.
4. Misinterpreting Forward Premiums/Discounts: A forward premium does not necessarily mean the currency is "strong." It reflects the interest rate differential. A currency with high interest rates will typically trade at a forward discount relative to a low-interest-rate currency, as per CIRP. The premium/discount is a compensation mechanism, not a pure forecast.

Summary

• Exchange rates are quoted as bid-ask spreads. A direct quotation (domestic/foreign) and an indirect quotation (foreign/domestic) are reciprocals, and inverting a bid-ask quote requires swapping the bid and ask figures.
• Cross-rates are calculated from two currency pairs with a common currency, and misalignments can create triangular arbitrage opportunities, which involve three simultaneous transactions to capture a risk-free profit.
• The forward exchange rate is determined by covered interest rate parity (CIRP), which arbitrages away differences between interest rates and forward premiums/discounts. A forward premium implies the base currency is expected to be stronger in the forward market relative to the spot.
• Purchasing power parity (PPP), especially in its relative form, posits that currencies adjust over the long term to offset differences in national inflation rates, providing a fundamental benchmark for currency valuation.
• Together, these concepts provide the framework for analyzing how currency movements—driven by interest rates, inflation, and market inefficiencies—directly translate into the returns and risks of any global portfolio.