Estimated study time: 60 minutes
Content:
Currency exchange rate analysis at CFA Level 2 requires mastery of several parity conditions that link exchange rates to interest rates, inflation, and forward prices. The four key parity relationships are covered acid: Covered Interest Rate Parity (CIP), Uncovered Interest Rate Parity (UIP), Purchasing Power Parity (PPP), and the International Fisher Effect (IFE). These relationships are interlinked — they share assumptions about market efficiency and capital mobility, and violations of these parities create profit opportunities (or persistent puzzles in empirical finance). CFA Level 2 candidates must not only know the formulas but apply them to determine fair value of currencies, expected spot rates, and carry trade profitability.
Covered Interest Rate Parity (CIP) is an arbitrage-free relationship between spot exchange rates, forward exchange rates, and interest rate differentials. CIP states: F/S = (1 + r_d) / (1 + r_f), where F is the forward exchange rate (domestic currency per unit of foreign), S is the spot rate, r_d is the domestic interest rate, and r_f is the foreign interest rate. CIP must hold because it can be enforced by arbitrage through the foreign exchange forward market: if the forward rate diverges from CIP, arbitrageurs can lock in riskless profits. A common exam formulation uses the approximation: (F - S)/S = r_d - r_f, meaning the forward premium (or discount) equals the interest rate differential. A currency with higher interest rates trades at a forward discount; a currency with lower interest rates trades at a forward premium.
Uncovered Interest Rate Parity (UIP) extends CIP to the unhedged case. UIP asserts that the expected change in the spot rate equals the interest rate differential: E[%ΔS] = r_d - r_f. Unlike CIP, UIP cannot be enforced by arbitrage and is an expectations condition requiring rational markets and risk-neutral investors. Empirically, UIP fails — high-interest-rate currencies do not depreciate by the full interest differential, which is why carry trades (borrowing in low-rate currencies and investing in high-rate currencies) have historically generated positive returns. The gap between CIP and UIP is the basis of carry trade analysis at Level 2: carry trades profit as long as the currency does not depreciate by the amount predicted by UIP.
Purchasing Power Parity (PPP) connects exchange rate changes to inflation differentials. Absolute PPP states that exchange rates should equal the ratio of price levels across countries. Relative PPP (the more testable version) states: %ΔS = inflation_domestic - inflation_foreign. If domestic inflation exceeds foreign inflation by 3%, the domestic currency should depreciate by approximately 3% to maintain purchasing power parity. PPP holds poorly in the short run (currencies deviate significantly from PPP levels for extended periods) but has more empirical support over very long horizons. The International Fisher Effect combines PPP and the Fisher equation: nominal rate = real rate + inflation. IFE states that countries with higher nominal interest rates have higher inflation, and after adjusting for inflation, real interest rates equalize internationally. This implies: (1 + r_d) / (1 + r_f) = E[S_1] / S_0.
Exchange rate regime analysis and the carry trade are important applied topics at Level 2. Exchange rate regimes range from hard pegs (currency board, dollarization) to soft pegs (target bands, crawling pegs) to free floats. A currency peg's credibility depends on foreign exchange reserve adequacy, current account balance, and the central bank's ability to defend the peg with rate hikes. In a carry trade, an investor borrows a low-interest-rate currency (funding currency) and invests in a high-interest-rate currency (target currency). The carry trade profits when the target currency does not depreciate as much as UIP predicts. However, carry trades are subject to crash risk — when risk appetite falls, target currencies can depreciate sharply and rapidly as carry trades are unwound simultaneously. At Level 2, vignettes may describe cross-rate calculations, forward contract hedging, and carry trade return decomposition.
Key Terms:
Quiz Questions:
Q1. The USD/EUR spot rate is 1.1000 (USD per EUR). The one-year USD interest rate is 4.0% and the one-year EUR interest rate is 1.5%. According to Covered Interest Rate Parity, what is the one-year forward USD/EUR exchange rate?
A) 1.1000 * (1.04/1.015) = 1.1271 B) 1.1000 * (1.015/1.04) = 1.0736 C) 1.1000 + (0.04 - 0.015) = 1.125 D) 1.1000 / (1.04/1.015) = 1.0736
Answer: A — CIP states: F = S * (1 + r_d)/(1 + r_f). Here, the domestic currency is USD and the foreign currency is EUR. The quote is USD per EUR. F = 1.1000 * (1.04/1.015) = 1.1000 * 1.02463 = 1.1271. Because USD interest rates are higher than EUR rates, the EUR trades at a forward premium (more USD required to buy EUR forward). Equivalently, the USD trades at a forward discount.
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Q2. Based on the interest rates in Q1, an investor borrows EUR 1,000,000 at 1.5% for one year and converts the proceeds to USD at the spot rate of 1.1000, investing in USD at 4.0%. The investor does NOT enter into a forward contract. According to Uncovered Interest Rate Parity, what is the expected outcome for the carry trade?
A) The carry trade is expected to profit because UIP guarantees USD appreciation. B) Under UIP, the USD is expected to depreciate by 2.5% (the interest differential), making the expected return on the carry trade approximately zero. C) Under UIP, the carry trade always generates positive returns equal to the interest rate differential. D) The carry trade return depends solely on changes in the EUR/USD spot rate, with no connection to interest rates.
Answer: B — UIP states that the expected change in the exchange rate equals the interest differential. With USD rates 2.5% above EUR rates, UIP predicts the USD will depreciate by approximately 2.5% against the EUR. The borrowing cost in EUR is 1.5%, the USD return is 4.0%, but the currency loss offsets the gain, leaving expected return approximately zero. In practice, UIP fails — the USD does not depreciate by the full amount — which is why the carry trade is empirically profitable on average (though with crash risk).
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Q3. Country A has an annual inflation rate of 6% and Country B has an annual inflation rate of 2%. The current spot rate is 10 units of A's currency per unit of B's currency. According to Relative Purchasing Power Parity, what is the expected spot rate in one year?
A) 10 * (1.02/1.06) = 9.62 units of A per unit of B. B) 10 * (1.06/1.02) = 10.39 units of A per unit of B. C) 10 + (0.06 - 0.02) = 10.4 units of A per unit of B. D) 10 * (0.06/0.02) = 30 units of A per unit of B.
Answer: B — Relative PPP states: F = S * (1 + inflation_A)/(1 + inflation_B). Since Country A has higher inflation, its currency should depreciate against B's currency — meaning more units of A are needed to buy one unit of B. F = 10 * (1.06/1.02) = 10 * 1.0392 = 10.39. The approximate form: expected depreciation of A = 6% - 2% = 4%, so expected rate = 10 * 1.04 = 10.40. Both the exact and approximate answers are very close.
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Q4. The JPY/USD spot rate is 150 (JPY per USD). A Japanese firm needs to purchase USD 5,000,000 in 90 days to pay a US supplier. The 90-day forward rate is 152 JPY/USD. The firm enters into a 90-day forward contract to buy USD at 152. In 90 days, the spot rate is 155 JPY/USD. What is the firm's effective cost per USD compared to the unhedged alternative?
A) The hedge costs 152 JPY/USD; the unhedged cost would have been 155 JPY/USD; hedging saved 3 JPY per USD. B) The hedge costs 155 JPY/USD; the forward contract settled at the spot rate. C) The hedge costs 150 JPY/USD because the firm locked in the original spot rate. D) Hedging always eliminates all currency risk regardless of contract terms.
Answer: A — By entering into the forward contract, the firm locked in a purchase price of 152 JPY/USD. In practice, the spot rate moved to 155, so without the hedge, the firm would pay 155 JPY/USD. The hedge saved 3 JPY per USD, or JPY 15,000,000 on the full USD 5,000,000 transaction. This illustrates the insurance value of forward contracts for transaction exposure hedging. The forward contract is not settled at the final spot rate (it was locked in at initiation).
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Q5. An analyst is evaluating whether a carry trade — borrowing Swiss Francs (CHF) at 0.25% and investing in New Zealand Dollars (NZD) at 5.5% — is attractive. The analyst notes that in the prior year, the NZD depreciated 4.5% against the CHF. Which of the following best describes the carry trade's historical outcome and its forward-looking risk?
A) The carry trade returned 5.25% because the NZD depreciation was offset by the full interest differential. B) The carry trade returned approximately 0.75% (5.5% - 0.25% - 4.5% currency loss), but the trade is subject to crash risk — sudden, large NZD depreciations during risk-off periods could produce severe losses. C) The carry trade returned 5.25% and has no downside risk as long as interest rates remain stable. D) The carry trade was unprofitable because UIP requires full offset of the interest differential.
Answer: B — The carry return = interest earned (5.5%) - funding cost (0.25%) - currency depreciation (4.5%) = approximately 0.75%. The trade was profitable but only modestly, because the NZD depreciated significantly (though not by the full UIP-predicted 5.25%). The key risk of carry trades is crash risk: during periods of financial stress or global risk aversion, carry trade unwinds lead to rapid, simultaneous depreciation of high-yield currencies, producing sudden large losses that more than offset accumulated interest gains.
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