Currency Exchange Rates
READING 5
CURRENCY EXCHANGE RATES: UNDERSTANDING EQUILIBRIUM VALUE
EXAM FOCUS
There is no fluff here; all material is required. Read carefully and build a solid understanding of quotes, currency cross rates, triangular arbitrage, all parity conditions, and how these ideas interrelate. Forecasting exchange rates has important applications for valuation. Be prepared to recognise the signs of an impending currency crisis.
MODULE 5.1: FOREX QUOTES, SPREADS, AND TRIANGULAR ARBITRAGE
LOS 5.a
Calculate and interpret the bid-offer spread on a spot or forward currency quotation and describe the factors that affect the bid-offer spread.
Video covering this content is available online.
PROFESSOR'S NOTE
The term bid-offer spread is also commonly called the bid-ask spread. The words "ask" and "offer" are interchangeable; this material uses them interchangeably.
EXCHANGE RATES - DEFINITIONS AND QUOTE STRUCTURE
An exchange rate is the price of one currency expressed in terms of another currency. For example, the quote 1.4126 USD/EUR means that each euro costs USD 1.4126. In that quote, the base currency is the euro (EUR) and the price currency (also called the terms or quote currency) is the US dollar (USD). A quote shows the price of one unit of the base currency in the price currency.
A spot exchange rate is the exchange rate for immediate delivery; for most major currency pairs "immediate" means settlement two business days after the trade. A forward exchange rate is an exchange rate for delivery at a future date and is quoted for various maturities (e.g., 30, 60, 90 days, 1 year). A forward contract is an agreement to exchange a specific amount of one currency for another at a specified future date and rate.
Dealers typically quote both the bid and offer (ask) prices. For example: EUR could be quoted as $1.4124 - 1.4128. The bid ($1.4124) is the price at which the dealer will buy euros; the offer/ask ($1.4128) is the price at which the dealer will sell euros. The dealer's profit on such a quote is the spread between the offer and bid.
FOREIGN EXCHANGE SPREAD
The spread is the difference between the dealer's offer (ask) price and the bid price. Spreads are often stated as pips. When a spot quote is given with four decimal places, one pip is 0.0001 (1/10,000). In the example $1.4124 - 1.4128, the spread is $0.0004 (4 pips), representing the dealer's gross profit margin.
Dealers manage inventory and risk by transacting in the interbank market (a wholesale market for currency). Spreads tend to be narrower in the interbank market than in client quotes. The dealer-quoted spread depends on the following factors:
- Spread in the interbank market: Dealer spreads move directly with interbank spreads for the same currency pair.
- Size of transaction: Large or liquidity-demanding transactions generally receive wider spreads.
- Dealer-client relationship: Preferred clients may receive more favourable quotes based on ongoing business relationships.
The interbank spread itself is affected by:
- Currencies involved: High-volume pairs (e.g., USD/EUR, USD/JPY, USD/GBP) command narrower spreads; less liquid pairs (e.g., AUD/CAD) have wider spreads.
- Time of day: Spreads are narrower when major markets overlap (e.g., New York-London overlap).
- Market volatility: Higher volatility increases spreads because market makers require compensation for increased inventory risk.
In forward markets, spreads typically widen with maturity because longer-dated contracts are less liquid, carry greater counterpart credit risk, and expose dealers to greater interest-rate risk over longer horizons.
WARM-UP: WORKING WITH FOREIGN EXCHANGE QUOTES
A dealer sells a currency at the ask price and buys it at the bid price. To be precise:
- Given a USD/AUD bid-ask quote of 1.0508 - 1.0510, an investor can buy AUD (the base currency) from the dealer at the ask USD 1.0510. Conversely, an investor can sell AUD to the dealer at the bid USD 1.0508. In short: buy base at ask; sell base at bid.
- For transactions denominated in the price currency, the rule is reversed: buy price currency at bid; sell price currency at ask.
- A useful operational mnemonic is: up-the-bid-and-multiply, down-the-ask-and-divide. If you move from the top currency to the bottom currency in a quote (e.g., from USD to AUD in USD/AUD), you go "down the quote" and use the ask (divide). If you move from bottom to top you go "up the quote" and use the bid (multiply).
EXAMPLE: Converting currencies using spot rates
A dealer quotes AUD/GBP spot rate as 1.5060 - 1.5067. How would we:
- Compute the proceeds of converting 1 million GBP.
- Compute the proceeds of converting 1 million AUD.
Answer:
To convert 1 million GBP into AUD we go "up the quote" (from GBP in the denominator to AUD in the numerator) and therefore use the bid price of 1.5060 and multiply.
1,000,000 GBP × 1.5060 = 1,506,000 AUD
To convert 1 million AUD into GBP we go "down the quote" (from AUD in the numerator to GBP in the denominator) and therefore use the ask price of 1.5067 and divide.
1,000,000 AUD / 1.5067 = 663,702.13 GBP
LOS 5.b
Identify a triangular arbitrage opportunity and calculate its profit, given the bid-offer quotations for three currencies.
CROSS RATE
The cross rate is the exchange rate between two currencies implied by their exchange rates with a common third currency. When there is no active market for a currency pair, the cross rate is computed using each currency's rate against a major currency (commonly USD or EUR). The algebraic key is to make the common currency cancel out.
Example: Given USD/AUD = 0.60 and MXN/USD = 10.70, compute MXN/AUD. The common currency USD cancels and we have:
MXN/AUD = MXN/USD × USD/AUD = 10.70 × 0.60 = 6.42 MXN per AUD
CROSS RATES WITH BID-ASK SPREADS
When bid-ask spreads exist, computing cross rates requires care. Suppose three currencies A, B and C are involved leading to three pairs A/B, A/C and B/C. To compute A/C given A/B and B/C you must compute the bid and ask for A/C using the bid and ask of the constituent pairs and applying correct multiplication/division rules to preserve the dealer conventions (up-the-bid, down-the-ask). If quotes are given with reversed common-currency orientation (for example, C/B instead of B/C), the C/B quote must first be inverted to obtain B/C bid and ask, using the proper inversion formulas for bid and ask: if a quote is x (bid) - y (ask), the inverted quote is 1/ask - 1/bid (with appropriate rounding). Always ensure the common currency cancels in the algebraic operation.
TRIANGULAR ARBITRAGE
Dealers in real markets ensure their quoted bid/ask rates are internally consistent such that customers do not easily earn arbitrage profits. If quotes are inconsistent, customers can earn riskless profits through triangular arbitrage. Triangular arbitrage uses three currency pairs to form a closed triangle and tests whether moving around the triangle produces more of the starting currency than begun with. Use the rules: up-the-bid-and-multiply, down-the-ask-and-divide. Check both clockwise and counter-clockwise directions; only one direction (at most) will produce a profit.
EXAMPLE: Triangular arbitrage
Quotes from the interbank market:
- USD/AUD 0.6000 - 0.6015
- USD/MXN 0.0933 - 0.0935
- Dealer quotes MXN/AUD = 6.3000 - 6.3025
Questions:
- Compute the implied MXN/AUD cross rate.
- If your dealer quotes MXN/AUD = 6.3000 - 6.3025, is a triangular arbitrage profit possible? If so, compute the arbitrage profit in USD if you start with USD 1 million.
Answer:
1. Compute implied cross rates.
We are given USD/MXN quoted as 0.0933 - 0.0935 (USD per MXN). To obtain MXN/USD we invert the USD/MXN quotes using inversion rules for bid and ask:
MXN/USD (bid) = 1 / (USD/MXN ask) = 1 / 0.0935 = 10.695187... → 10.6952 (rounded)
MXN/USD (ask) = 1 / (USD/MXN bid) = 1 / 0.0933 = 10.717764... → 10.7178 (rounded)
Thus MXN/USD = 10.6952 - 10.7178.
Now compute MXN/AUD implied cross using MXN/USD × USD/AUD. For cross rates, apply the correct pairing for bid and ask:
MXN/AUD (bid) = MXN/USD (bid) × USD/AUD (bid) = 10.6952 × 0.6000 = 6.41712 → 6.4171
MXN/AUD (ask) = MXN/USD (ask) × USD/AUD (ask) = 10.7178 × 0.6015 = 6.4507 → 6.4507
So the implied MXN/AUD cross rate is approximately 6.4171 - 6.4507.
2. Check if dealer quote MXN/AUD = 6.3000 - 6.3025 allows arbitrage.
Because the dealer quote lies outside the implied cross-range, an arbitrage opportunity may exist. We must test by actually moving around the triangle.
Following the advice in the passage, label arrows using the "up-the-bid, down-the-ask" rule and use dealer quotes when transacting with the dealer.
Go clockwise starting with USD 1,000,000.
Convert USD → MXN using USD/MXN quote = 0.0933 - 0.0935. We are converting USD into MXN (down the quote with respect to USD/MXN), so use the offer (ask) 0.0935 and divide.
1,000,000 USD / 0.0935 = 10,695,187 MXN
Convert MXN → AUD using dealer MXN/AUD = 6.3000 - 6.3025. We are converting MXN into AUD (down the MXN/AUD quote), so use the ask 6.3025 and divide.
10,695,187 MXN / 6.3025 = 1,696,975 AUD
Convert AUD → USD using USD/AUD = 0.6000 - 0.6015. We are converting AUD into USD (up the quote), so use the bid 0.6000 and multiply.
1,696,975 AUD × 0.6000 = 1,018,185 USD
Result: USD 1,018,185 - USD 1,000,000 = USD 18,185 profit.
Check counter-clockwise direction (for completeness):
Convert USD → AUD using USD/AUD = 0.6000 - 0.6015. Converting USD to AUD is down the USD/AUD quote, so use the ask 0.6015 and divide.
1,000,000 USD / 0.6015 = 1,662,510 AUD
Convert AUD → MXN using dealer MXN/AUD = 6.3000 - 6.3025. Converting AUD to MXN is up the quote, so use the bid 6.3000 and multiply.
1,662,510 AUD × 6.3000 = 10,473,814 MXN
Convert MXN → USD using USD/MXN = 0.0933 - 0.0935. Converting MXN to USD is up the quote, so use the bid 0.0933 and multiply.
10,473,814 MXN × 0.0933 = 977,207 USD
Result: 977,207 USD - a loss of 22,793 USD. (Thus arbitrage profit exists only in the clockwise path above.)
LOS 5.c
Explain spot and forward rates and calculate the forward premium/discount for a given currency.
A currency is said to trade at a forward premium relative to another currency if the forward price (in units of the price currency) is greater than the spot price. Conversely, it trades at a forward discount if the forward price is less than the spot price. The premium or discount is expressed with respect to the base currency (the currency quoted first or at the bottom of an A/B structure depending on notation).
Example: If spot is 1.20 $/€ and the forward price is 1.25 $/€, the euro is trading at a forward premium versus the dollar.
A convenient measure of the forward premium (or discount) for the base currency (B) relative to the price currency (A) is:
Forward premium (approx) = (Forward price - Spot price) / Spot price
EXAMPLE: Spot and forward quotes
Given the following quotes for AUD/CAD, compute the bid and offer rates for a 30-day forward contract. (The example inputs show forward points that are added/subtracted to the spot.)
Answer:
Because the forward points are positive, the CAD (the base currency in the quote) is trading at a forward premium. Compute the all-in forward by adding forward points (converted to decimal form) to the spot bid and ask:
30-day bid = 1.0511 + 3.9/10,000 = 1.05149
30-day offer = 1.0519 + 4.1/10,000 = 1.05231
Thus the 30-day all-in forward quote for AUD/CAD is 1.05149/1.05231.
PROFESSOR'S NOTE: For an investor wishing to convert AUD into CAD in the forward market, the relevant quote is the ask (the "down-the-ask" rule) - here 1.05231. This is the all-in forward rate after applying the forward premium/discount to the spot.
MODULE QUIZ 5.1
1. All of the following factors are likely to contribute to an increase in USD/EUR dealer spread except:
A. increase in the volatility of EUR/USD spot rate.
B. increase in the EUR/USD spread in the interbank market.
C. smaller order size.
2. The bid-ask quotes for the USD, GBP, and EUR are:
EUR/USD: 0.7000 - 0.7010
USD/GBP: 1.7000 - 1.7010
EUR/GBP: 1.2000 - 1.2010
The potential arbitrage profit from a triangular arbitrage based on an initial position of 1 million USD is closest to:
A. USD0.
B. USD7,212.
C. USD6,372.
MODULE 5.2: MARK-TO-MARKET VALUE, AND PARITY CONDITIONS
LOS 5.d
Calculate the mark-to-market value of a forward contract.
Video covering this content is available online.
If the forward contract price is consistent with covered interest rate parity, the contract has zero value at initiation to both parties. As forward quotes change after initiation, the contract acquires a non-zero mark-to-market value. The mark-to-market value of a forward contract prior to expiration equals the difference between the contract forward rate and the current market forward rate for the remaining maturity, multiplied by the size of the contract and then discounted to present value for the time remaining until settlement.
EXAMPLE: Valuing a forward contract prior to maturity
Yew Mun Yip entered into a 90-day forward contract long CAD 1,000,000 against AUD at a forward rate of 1.05358 AUD/CAD. Thirty days after initiation (t = 30), market quote information and AUD deposit rates are available:
- 30-day AUD rate: 1.12% (annualised, days/360 convention)
- 60-day AUD rate: 1.16%
- 90-day AUD rate: 1.20%
What is the mark-to-market value in AUD of Yip's forward contract at t = 30?
Answer - step-by-step valuation:
Yip is long CAD (that is, she agreed to buy CAD for AUD in 90 days). To unwind the position 30 days after initiation, she can enter an offsetting forward contract that sells CAD for AUD with the remaining maturity of 60 days (T - t = 60 days). The correct rate to use for the offsetting sale of CAD is the bid rate for the 60-day forward contract.
Forward bid price for a new 60-day contract = 1.0612 + 8.6/10,000 = 1.06206 AUD/CAD
Unwinding value before discount = (Offsetting bid rate - original forward rate) × contract size
Unwinding value before discount = (1.06206 - 1.05358) AUD/CAD × 1,000,000 CAD
Unwinding value before discount = 0.00848 × 1,000,000 AUD = 8,480 AUD
Discount the 60-day payoff back to present value using the 60-day AUD deposit rate of 1.16% (days/360 convention). The discount factor is 1 / (1 + r × days/360) = 1 / (1 + 0.0116 × 60/360) = 1 / (1 + 0.00193333) = 0.9980677.
Mark-to-market value = 8,480 AUD × 0.9980677 = 8,463.64 AUD
Therefore, thirty days into the contract, Yip's forward position has a positive value of AUD 8,463.64. (Note: use the AUD deposit rate for discounting because AUD is the price currency in the quote.)
PROFESSOR'S NOTE
Interest rates shown are bank deposit rates using the appropriate market reference rate and the days/360 convention. Use the price-currency deposit rate for discounting.
LOS 5.e
Explain international parity conditions: covered and uncovered interest rate parity, forward rate parity, purchasing power parity, and the international Fisher effect.
COVERED INTEREST RATE PARITY (CIRP)
The term covered denotes that the relation is enforced by arbitrage when forward contracts are available. CIRP states that the forward premium or discount offsets interest-rate differentials so that an investor will be indifferent between investing in either currency once exchange-rate risk is covered via forward contracts.
Given a quote structure A/B where S is spot (price currency per base currency), F is forward, rA is the domestic (numerator) interest rate, and rB is the foreign (denominator) interest rate, the no-arbitrage relationship is:
F = S × (1 + rA) / (1 + rB)
This is the discrete-time version consistent with days/360 or annualised convention; equivalent continuous-time expressions exist for continuously compounded rates.
PROFESSOR'S NOTE
Follow the numerator-denominator rule for parity relations: if you are given a USD/EUR quote, put the USD interest rate in the numerator and the EUR interest rate in the denominator when using parity equations.
EXAMPLE: Covered interest arbitrage
Data: USD MRR (domestic) = 8%; euro MRR = 6%. Spot exchange rate = $1.30/€ (USD/EUR); 1-year forward = $1.35/€. Determine whether arbitrage exists.
Compute the forward implied by CIRP:
F_implied = S × (1 + r_USD) / (1 + r_EUR) = 1.30 × (1.08 / 1.06) = 1.30 × 1.018867924 = 1.3245 USD/EUR
The market forward is $1.35/€ which is higher than the implied $1.3245/€. Because the market forward is too high, sell euros forward and buy euros in the spot market while investing euros - the arbitrage steps (explicit):
Borrow USD at 8% for 1 year.
Convert borrowed USD to euros at spot $1.30/€.
Invest euros at 6% for 1 year.
Enter forward contract to sell euros (maturity 1 year) at the market forward rate $1.35/€.
After 1 year, collect euro investment proceeds and deliver them under forward contract to receive USD at $1.35/€; repay USD loan plus interest. If the proceeds exceed the repayment, arbitrage profit exists.
Computationally:
Borrow $X today. Convert to euros: euros = X / 1.30.
Invest euros at 6%: euros_future = (X / 1.30) × 1.06.
Sell euros forward at 1.35 to get USD: USD_received = euros_future × 1.35 = (X / 1.30) × 1.06 × 1.35.
Repay USD loan at 8%: USD_repay = X × 1.08.
Arbitrage profitable if USD_received > USD_repay. Substituting values shows USD_received = X × (1.06 × 1.35 / 1.30) = X × (1.3245) < x="" ×="" 1.08?="" evaluating="" the="" algebra="" shows="" how="" prices="" violate="" parity;="" since="" market="" forward="" (1.35)=""> implied forward (1.3245), selling euros forward and buying spot euros is profitable.
UNCOVERED INTEREST RATE PARITY (UIP)
Uncovered means not covered by forward contracts and therefore not enforced by arbitrage. Under UIP, expected changes in the spot rate should equal the interest-rate differential. If Country A's nominal rate is RA and Country B's is RB, then:
E[%ΔS(A/B)] ≈ RA - RB
where S(A/B) is the price of B in units of A (structure consistent with numerator-denominator rule). UIP predicts that higher nominal interest rates imply expected depreciation of the currency by approximately the interest differential, assuming risk neutrality (no currency risk premium).
EXAMPLE: Forecasting spot rates with UIP
Spot quote: ZAR/EUR = 8.385. One-year nominal rate in eurozone = 10%; one-year nominal rate in South Africa = 8%. Expected percentage change in exchange rate over the coming year according to UIP?
Answer:
RA - RB = ZAR interest - EUR interest = 8% - 10% = -2%.
Since the base currency is EUR in ZAR/EUR, a -2% implies the euro is expected to depreciate by 2% relative to the rand - the quoted ZAR/EUR is expected to move from 8.385 to 8.217 (approximately 8.385 × 0.98 = 8.217).
Comparison: CIRP gives the no-arbitrage forward rate; UIP gives the expected future spot rate when forward contracts are not used and investors are risk neutral. UIP need not hold in the short term.
FORWARD RATE PARITY
If the forward rate equals the expected future spot rate, the forward rate is an unbiased predictor of the future spot: F = E(S1). If UIP and market expectations align, forward rate parity holds.
(DOMESTIC) FISHER RELATION
Irving Fisher posited that the nominal interest rate is approximately the sum of the real interest rate and expected inflation:
Rnominal ≈ Rreal + E(inflation)
INTERNATIONAL FISHER RELATION
If real interest rates converge across markets (real interest rate parity), then taking the Fisher relation for two countries leads to the international Fisher effect:
Rnominal_A - Rnominal_B = E(inflation_A) - E(inflation_B)
Thus nominal interest-rate differentials should reflect expected inflation differentials. This result relies on free capital mobility and homogenous risk premia across countries.
EXAMPLE: Calculating the real interest rate
Given nominal South African rate = 9.0% and expected inflation = 3.5%. Compute real interest rate.
0.090 = real_rZAR + 0.035
real_rZAR = 0.090 - 0.035 = 0.055 = 5.5%
EXAMPLE: Using the international Fisher relation
Given eurozone expected inflation = 9.0%, South African expected inflation = 13.0%, and eurozone nominal interest rate = 10.09%. Compute South African nominal interest rate assuming real rates equal.
real_rate_EUR = 10.09% - 9% = 1.09%
nominal_rate_ZAR = expected_inflation_ZAR + real_rate_ZAR = 13% + 1.09% = 14.09%
PURCHASING POWER PARITY (PPP)
The law of one price holds that identical goods should cost the same in different locations once prices are expressed in a common currency (ignoring transaction costs and barriers). Extending the idea to a representative basket of goods gives absolute PPP, which states that:
S(A/B) = Price level A / Price level B (e.g., CPI_A / CPI_B)
Absolute PPP seldom holds exactly due to trade costs, non-tradables and different consumption baskets.
RELATIVE PURCHASING POWER PARITY
Relative PPP states that changes in exchange rates should approximately offset inflation differentials. If country A has inflation rate IA and country B has IB over a period, the expected change in the exchange rate is:
%ΔS(A/B) ≈ inflation_A - inflation_B
EX-ANTE VERSION OF PPP
The ex-ante version replaces actual inflation with expected inflation, so forecasts of future spot rates can use expected inflation differentials.
EXAMPLE: Ex-ante PPP
Current spot: USD/AUD = 1.00. Expected annualised Australian inflation = 5%, expected US inflation = 2%. According to ex-ante PPP, expected change in spot over one year:
Expected % change = inflation(USD) - inflation(AUD) = 2% - 5% = -3%
Expected USD/AUD in one year ≈ 1.00 × 0.97 = 0.97 USD/AUD
INTERRELATIONS AMONG PARITY CONDITIONS
It is useful to see how parity relations fit:
- CIRP is enforced by arbitrage and therefore holds in liquid, frictionless markets with forward contracts.
- If forward rate parity (F = E(S1)) holds, then UIP also holds, and vice versa, under the additional assumption of no risk premia.
- Interest-rate differentials should mirror inflation differentials under the international Fisher relation, linking PPP to interest parity.
- If both ex-ante PPP and the international Fisher relation hold, then UIP will also hold.
LOS 5.g and LOS 5.h
To forecast future spot rates, one may use ex-ante PPP, UIP or forward rates. None of these is bound by arbitrage (except where CIRP leads to the forward) and they often fail in the short run. Evidence suggests that PPP is more useful over long horizons. The real exchange rate typically fluctuates around a long-run mean; deviations may be exploited for mean-reversion style valuation in long-run currency fair-value analysis.
The international Fisher effect assumes zero differences in sovereign risk premia; in practice emerging-market risk premia mean nominal interest rates reflect more than expected inflation differences.
MODULE QUIZ 5.2
1. Suppose the spot exchange rate quote is 1.0120 Canadian dollars (C$) per U.S. dollar. The 1-year nominal interest rate in Canada is 3.0% and the 1-year nominal interest rate in the United States is 1.0%. The expected exchange rate at the end of the year using the uncovered interest rate parity is closest to:
A. C$1.0322.
B. C$0.9923.
C. C$0.9918.
2. The international parity relationships indicate that the expected return on risk-free securities should be the same in all countries and exchange rate risk is really just inflation risk. Which of the following is least likely to be considered a practical implication of this framework?
A. Investors will earn the same real rate of return on investments once their own currency impact is accounted for.
B. Interest rate differentials reflect currency expectations. As a result, covered interest arbitrage will provide a return in any foreign currency that is equal to the domestic return.
C. There are significant rewards for bearing foreign exchange risk.
3. For uncovered interest rate parity to hold, which condition is necessary?
A. Forward rate parity holds.
B. Covered interest rate parity holds and ex-ante relative PPP holds.
C. Real interest rate parity and ex-ante relative PPP holds.
CASE STUDY MATERIAL
Use the following information to answer Questions 4 through 9.
Sally Franklin, CFA, is a financial advisor to Jamie Curtess, a U.S. citizen interested in learning how international differences in exchange rates and interest rates will affect her investments. Franklin has gathered the following information based on Curtess's investment interests.
- The current spot exchange rate: $1 = €0.74.
- Franklin also gathers the following information (used in later questions).
4. According to the international Fisher relation, the 1-year nominal interest rate in the United States should be closest to:
A. 3.00%.
B. 4.34%.
C. 6.00%.
5. If the relative form of the PPP holds, the expected exchange rate in one year is closest to:
A. $1.3378 per €.
B. $0.7463 per €.
C. $1.3647 per €.
6. For this question only, assume that the U.S. interest rate is 3.5%. The 1-year forward rate should be closest to:
A. $1.3647 per €.
B. $0.7463 per €.
C. $1.3449 per €.
7. Curtess wonders how spot rates are expected to change in the future and asks: "What are the implications for the South African rand relative to the Swiss franc under uncovered interest rate parity, and the implications for the euro relative to the U.S. dollar under the relative form of purchasing power parity?" Franklin responds with two statements:
Statement 1: The South African rand is expected to depreciate relative to the Swiss franc.
Statement 2: The euro is expected to depreciate relative to the U.S. dollar.
Based on the parity relations cited, are Franklin's statements accurate?
A. No, both statements are inaccurate.
B. Yes, both statements are accurate.
C. One statement is accurate and one is inaccurate.
8. For this question only, assume the nominal interest rate in the United States is 3%. Real interest rates, using the Fisher relation, are most likely to be:
A. greater in the United States than in Europe.
B. lower in Europe than in South Africa.
C. equal among Europe, South Africa, Switzerland, and the United States.
9. A forecasted $/€ exchange rate in one year equal to the current 1-year forward rate is most likely to be based on the assumption that:
A. absolute PPP holds.
B. investors are risk neutral.
C. real interest rate parity holds.
LOS 5.d - MARK-TO-MARKET SUMMARY
The mark-to-market value of a forward contract is the profit (or loss) realised by offsetting the contract at current market forward prices, discounting for time remaining to settlement. Use the price-currency discount rate for discounting.
LOS 5.e - SUMMARY OF PARITY RELATIONS
Key parity relations and approximate forms:
- Covered Interest Rate Parity: F = S × (1 + r_dom)/(1 + r_for)
- Uncovered Interest Rate Parity: E(%ΔS)(A/B) ≈ RA - RB
- International Fisher Relation: Rnominal_A - Rnominal_B = E(inflation_A) - E(inflation_B)
- Relative PPP: %ΔS(A/B) ≈ inflation_A - inflation_B
- Forward Rate Parity (Unbiased Forward): F = E(S1)
MODULE 5.3: EXCHANGE RATE DETERMINANTS, CARRY TRADE, AND CENTRAL BANK INFLUENCE
LOS 5.i
Describe the carry trade and its relation to uncovered interest rate parity and calculate the profit from a carry trade.
Video covering this content is available online.
FX CARRY TRADE - DESCRIPTION
Uncovered interest rate parity implies that a currency with a higher nominal interest rate should depreciate relative to a lower-yielding currency by approximately the interest differential, so that investing yields the same expected return once exchange-rate changes are considered. The empirical fact is that UIP often fails over short to medium horizons. A carry trade borrows in a low-yielding funding currency and invests in a high-yielding currency; the strategy profits when the higher-yielding currency depreciates by less than the interest-rate differential (or appreciates).
EXAMPLE: Carry trade
Compute the profit to an investor borrowing in the United States and investing in the U.K. (The original example in the module illustrates that profit equals the interest differential minus the percentage change in the investment currency over the investment horizon.)
General profit formula for carry trade:
Profit ≈ interest differential - change in the spot rate of the investment currency
Carry trades typically perform well in low-volatility, risk-on environments. Herding into carry trades can itself push up the value of the high-yielding currency, increasing profitability if the appreciation occurs; however the strategy is leveraged and asymmetrically exposed to large negative returns ("crash risk") if many participants unwind simultaneously during a flight-to-safety.
RISKS OF THE CARRY TRADE
Principal risks:
- Exchange-rate risk: Funding currency appreciation or investment currency depreciation can wipe out interest gains.
- Crash risk: Return distributions of carry trades show negative skewness and excess kurtosis (fat tails), meaning large losses are more likely than under a normal distribution.
- Liquidity and funding risk: Leverage and margining can force abrupt unwinds.
LOS 5.j
Explain how flows in the balance of payments accounts affect currency exchange rates.
BALANCE OF PAYMENTS (BOP)
The balance of payments tracks all transactions between residents of a country and the rest of the world. The two principal components are:
- Current account: Trade in goods and services, investment income (interest, dividends), and unilateral transfers.
- Financial account (capital account): Cross-border flows for debt and equity investment, reserve assets and other financial instruments.
When a country runs a current account deficit, it must run a capital account surplus (net inflows) to finance the difference or else its currency will depreciate. In practice, capital flows often dominate goods flows in the short run because capital transactions are typically larger and more mobile.
INFLUENCE OF BOP ON EXCHANGE RATES
Current Account Influences
Current-account deficits tend to increase the supply of the domestic currency in FX markets (as importers sell foreign currency to obtain domestic currency), putting downward pressure on the domestic currency. Mechanisms and considerations include:
- Flow supply/demand mechanism: A current account deficit raises the supply of the domestic currency and tends to depreciate it; the magnitude of adjustment depends on the initial deficit, pass-through of exchange rate changes to import and export prices, and the price elasticity of demand for traded goods.
- Portfolio balance mechanism: Countries with persistent current-account surpluses may invest abroad, causing their residents' portfolios to accumulate foreign-currency assets; rebalancing by these investors can affect exchange rates of recipient countries.
- Debt sustainability mechanism: Financing current-account deficits by borrowing abroad increases sovereign and private external debt; when debt becomes unsustainable, investors may withdraw funding, causing sudden depreciation.
Capital Account Influences
Capital flows are a major determinant of exchange rates in the short term. Capital inflows increase demand for the domestic currency, leading to appreciation. Key considerations:
- Real rate differentials: Higher relative real returns attract capital.
- Emerging-market issues: Excessive inflows can cause real appreciation of the currency, asset price bubbles, increases in external debt, and credit-fuelled consumption.
- Authorities in emerging markets often respond to large inflows via capital controls or direct intervention to limit appreciation and dampen bubble risks.
LOS 5.k
Explain the potential effects of monetary and fiscal policy on exchange rates.
MUNDELL-FLEMING MODEL (SHORT-RUN ANALYSIS)
The Mundell-Fleming model analyses how monetary and fiscal policy affect interest rates and, consequently, exchange rates in an open economy. The model assumes sufficient slack (output gap) so inflation is not central to the short-term analysis. We examine two exchange-rate regimes (flexible vs fixed) and two degrees of capital mobility (high vs low).
Flexible Exchange Rate Regime
When the exchange rate floats and capital mobility is high:
- Expansionary monetary policy lowers domestic interest rates, reducing capital inflows and deteriorating the financial account; this decreases demand for the domestic currency and leads to currency depreciation.
- Restrictive monetary policy raises domestic interest rates, attracting capital, improving the financial account and causing currency appreciation.
- Expansionary fiscal policy (higher deficit) typically raises interest rates (crowding out), attracting capital inflows and creating currency appreciation.
Low Capital Mobility
When capital mobility is limited (typical for some emerging markets), trade flows (current account) have greater influence than financial flows. In such cases, both expansionary monetary and fiscal policy can lead to increased imports and a deterioration of the current account, leading to currency depreciation. Conversely, restrictive policies may appreciate the currency.
PROFESSOR'S NOTE: Students often find it counterintuitive that a higher interest rate can lead to appreciation under Mundell-Fleming, whereas UIP suggests a currency with a higher interest rate should depreciate. The difference arises because the Mundell-Fleming model does not assume equal real rates globally and does not model inflation; it focuses on short-run demand and capital flows.
Fixed Exchange Rate Regime
Under a fixed exchange-rate regime, domestic monetary expansion would normally depreciate the currency. Because authorities fix the rate, the central bank must intervene by buying domestic currency (selling foreign reserves) to maintain the peg, effectively reversing the monetary expansion. Consequently, with open capital markets, governments cannot simultaneously pursue an independent monetary policy, free capital mobility, and a fixed exchange rate (the "impossible trinity").
MONETARY APPROACHES TO EXCHANGE-RATE DETERMINATION
Monetary models emphasise the role of money supply and expectations in determining exchange rates. Two main variants:
- Pure monetary model: Assumes PPP holds at all times and output is fixed. A proportional change in money supply leads to proportional changes in price levels and proportional depreciation/appreciation of the currency. The model abstracts from expectations about future monetary policy.
- Dornbusch overshooting model: Recognises that prices are sticky in the short term. An unanticipated monetary expansion lowers interest rates and causes immediate capital outflows that lead the exchange rate to overshoot its long-run value implied by PPP; over time, prices adjust and the exchange rate moves back toward the PPP-implied long-run value.
PORTFOLIO BALANCE APPROACH
The portfolio balance approach focuses on fiscal policy and the supply of domestic versus foreign assets. Sustained fiscal deficits increase the supply of government debt; investors require appropriate compensation in yield and currency return. If deficits are perceived as unsustainable, yields or risk premia increase and the currency can depreciate. Combining short-run Mundell-Fleming intuition with long-run portfolio balance analysis implies:
- In the short run, expansionary fiscal policy with mobile capital → higher interest rates → currency appreciation.
- In the long run, persistent fiscal deficits may lead to higher sovereign risk and/or monetary financing (printing money), causing currency depreciation.
LOS 5.l
Explain objectives of central bank or government intervention and capital controls, and describe the effectiveness of intervention and capital controls.
OBJECTIVES
Policymakers may intervene or impose capital controls to:
- Prevent excessive appreciation of the domestic currency that would harm export competitiveness.
- Facilitate independent monetary policy without large exchange-rate side effects (especially relevant for emerging markets).
- Reduce excessive aggregate inflows that may create bubbles or macroeconomic instability.
EFFECTIVENESS
Effectiveness depends on relative market size and reserve sufficiency. For major developed-market currencies, average trading volume is very large relative to central-bank reserves, making intervention generally ineffective unless coordinated internationally or accompanied by credible policy changes. For some emerging markets, central banks with large reserves relative to trading volumes can have measurable short- to medium-term effects on the exchange rate via intervention or temporary capital controls.
LOS 5.m
Describe warning signs of a currency crisis.
Empirical warning signs commonly appearing before currency crises include:
- Deterioration in terms of trade (exports/imports ratio worsens).
- Fixed or partially fixed exchange-rate regimes (greater vulnerability).
- Sharp declines in official foreign-exchange reserves.
- Exchange rate appreciation above historical mean-reverting level (overvaluation).
- Rising inflation.
- Liberalised capital markets without adequate prudential controls.
- Rapid growth in money supply relative to bank reserves.
- Banking-sector problems or crises (often coincident with currency crises).
MODULE QUIZ 5.3
1. Vilasram Deshmukh is forecasting JPY/USD exchange rates based on balance-of-payments analysis. He notes the United States is running large current account deficits relative to Japan. Based on this information, he concludes that the JPY/USD rate should decrease. His conclusion is most likely supported by the:
A. flow mechanism of the current account influences.
B. portfolio composition mechanism of the current account influences.
C. capital account influences.
2. Stephen Hall consults forecasts of money supply growth. The chief economist expects U.S. money supply to grow much faster than U.K. or European money supplies. Hall states: "Under the pure monetary approach, an increase in the future growth rate of the money supply would lead to an immediate depreciation in the currency's value." Hall's statement is most likely:
A. correct.
B. incorrect, as the future growth rate in the money supply would not immediately affect currency values under the pure monetary approach model.
C. incorrect, as the future growth rate in money supply would actually increase the currency value under the pure monetary approach.
3. In Zambola (an emerging market with low capital mobility), the central bank is pursuing a restrictive monetary policy and the government is reducing budget deficits. Under the Mundell-Fleming model, the change in monetary and fiscal policy is most likely to cause the Zambolan currency to:
A. appreciate.
B. depreciate.
C. remain unchanged.
CASE STUDY MATERIAL - CFN CURRENCY OVERLAY
Use the following information to answer Questions 4 through 9.
Agnetha Poulsen (analyst) is concerned about unhedged currency exposure at CFN. She reviews spot and forward quotes and selected interest rates for certain currencies (Figures in the original dataset). She also reviews two open forward contracts as examples:
- Contract FX2001: 90-day forward initiated 60 days ago; purchase CHF 200 million at all-in rate USD 0.9832 (30 days to maturity).
- Contract FX2051: 90-day forward initiated 30 days ago; purchase EUR 100 million at all-in rate USD 1.2242 (60 days to maturity).
Poulsen is concerned about carry trades in emerging-market currencies and compiles a list of currency-crisis indicators. She notes Zambola (emerging market) is experiencing large capital inflows and a current account deficit; its currency (Zu) is trending well above its PPP-implied value.
4. The 30-day forward spread on USD/CHF is closest to:
A. 0.0005.
B. 0.0007.
C. 0.7000.
5. The current mark-to-market value of forward contract FX2001 in USD is closest to:
A. -USD460,000.
B. -USD451,924.
C. -USD357,940.
6. The current mark-to-market value of forward contract FX2051 in USD is closest to:
A. -USD215,900.
B. -USD107,900.
C. -USD216,000.
7. Poulsen's description of carry trade return distribution is best described as:
A. correct.
B. incorrect about skewness only.
C. incorrect about both skewness and kurtosis.
8. Which of the following indicators of impending currency crises should Poulsen exclude from her report?
A. Terms of trade improve.
B. Increase in money supply relative to bank reserves.
C. Increase in inflation.
9. If Zambolan government wanted to reduce inflow of foreign capital, it should:
A. pursue expansionary monetary policies.
B. pursue policies consistent with currency appreciation.
C. reduce inflation by increasing interest rates.
KEY CONCEPTS (CONCISE REFERENCE)
LOS 5.a - Bid-Ask Spread
Bid-ask spread (for base currency) = ask quote - bid quote
Dealer spreads depend on interbank spreads, transaction size, and dealer-client relationship. Interbank spreads depend on currency pair, time of day, and volatility. Forward spreads generally increase with maturity.
LOS 5.b - Triangular Arbitrage
To calculate triangular arbitrage profits, begin in the home currency and sequentially exchange around the currency triangle: home → first foreign currency → second foreign currency → home. If you end with more than you started, an arbitrage profit exists. Bid-ask spreads mean you buy at ask and sell at bid, thereby often eliminating simple arbitrage unless quotes are inconsistent.
LOS 5.c - Spot vs Forward; Premium/Discount
Spot exchange rate is for immediate delivery; forward exchange rate is for future delivery. For base currency B in quote A/B:
Premium (discount) for base currency = Forward price - Spot price (or expressed relative to spot: (F - S)/S)
LOS 5.d - Mark-to-Market of Forward Contracts
Mark-to-market value equals the profit from closing an existing forward by taking an equal and opposite forward position at current forward prices, discounted using the price-currency deposit rate for the remaining time to maturity.
LOS 5.e - Parity Summaries
Key relations:
- Covered interest parity: F = S × (1 + r_dom)/(1 + r_for)
- Uncovered interest parity: E(%ΔS)(A/B) ≈ RA - RB
- International Fisher relation: Rnominal_A - Rnominal_B = E(inflation_A) - E(inflation_B)
- Relative PPP: %ΔS(A/B) ≈ inflation_A - inflation_B
- Forward rate parity: F = E(S1)
LOS 5.f - Relations Among Parities
CIRP holds by arbitrage. If forward rate parity and UIP hold, then forward rates are unbiased predictors of future spot rates. Interest-rate differentials reflect expected inflation differentials under the international Fisher relation, linking PPP and interest parity.
LOS 5.i - FX Carry Trade
The carry trade profits when UIP fails: borrow in low-yielding currency and invest in a high-yielding currency. Profit approximates the interest differential minus the change in the investment currency's spot value. Carry trades have crash risk due to leverage and negative skewness/excess kurtosis in returns.
LOS 5.j - BOP and Exchange Rates
The BOP affects exchange rates through current-account flows (trade in goods/services) and capital-account flows (investment). Current-account deficits tend to increase supply of domestic currency and depress its value; capital inflows tend to appreciate the currency.
LOS 5.k - Monetary and Fiscal Policy Effects
Under the Mundell-Fleming model, the exchange-rate effects of monetary and fiscal policy depend on capital mobility and exchange-rate regime: with high capital mobility and floating rates, monetary easing depreciates the currency while fiscal expansion appreciates it in the short run; with low capital mobility, trade effects may dominate.
LOS 5.l - Central Bank Intervention and Capital Controls
Objectives: limit excessive appreciation, enable independent monetary policy, and reduce inflow volumes. Effectiveness depends on reserve adequacy and relative market turnover; more effective in some emerging markets than in deep developed markets.
LOS 5.m - Warning Signs of Currency Crisis
Warning signs include deterioration in terms of trade, sharp reserve declines, overvalued exchange rates, rising inflation, fixed exchange-rate regimes, increases in money supply relative to reserves, banking problems, and liberalised capital markets without adequate safeguards.
ANSWER KEY FOR MODULE QUIZZES
Module Quiz 5.1 - Answers and Explanations
1. C
Explanation: Dealer spreads tend to be larger for larger, liquidity-demanding orders; smaller orders usually have narrower spreads. Spreads increase with interbank spreads and with spot rate volatility. (LOS 5.a)
2. C
Explanation - triangle with bid-ask filled in and clockwise conversion steps:
Start with 1,000,000 USD. Convert USD → GBP at ask (since moving down USD/GBP): USD/GBP ask = 1.7010, so 1,000,000 / 1.7010 = GBP 588,478.54 (intermediate).
Sell GBP → EUR at bid (EUR/GBP bid = 1.2000): GBP 588,478.54 × 1.2000 = EUR 706,174.25.
Sell EUR → USD at ask (EUR/USD ask = 0.7010): EUR 706,174.25 × 0.7010 = USD 1,006,372 (approx).
Profit = USD 1,006,372 - 1,000,000 = USD 6,372. (LOS 5.b)
Module Quiz 5.2 - Answers and Explanations
1. A
Using UIP, USD (base) will appreciate by approximately 2% because US rate is lower than Canadian rate by 2%: 1.0120 × 1.02 = C$1.0322. (LOS 5.e)
2. C
Under parity implications, investors should earn the same real, risk-free return once currency effects are accounted for, and nominal high interest rates are offset by expected currency depreciation, so bearing foreign-exchange risk is not expected to produce consistent excess returns without risk. (LOS 5.f)
3. A
Covered interest parity holds by arbitrage; if the forward equals the expected future spot (forward rate parity), then UIP also holds. In this special case the forward rate is an unbiased predictor of future spot. (LOS 5.e)
4. A
Using the international Fisher relation and the example numbers: derive the US nominal rate as shown; result = 3%. (LOS 5.e)
5. A
Relative PPP predicts the euro will depreciate because European inflation is higher, thus the expected spot is $1.3378/€. (LOS 5.e)
6. C
Using covered interest parity the forward 1-year rate in $/€ is computed as shown in the module; the result is $1.3449/€. (LOS 5.e)
7. B
Both statements are correct given the data: higher South African inflation and higher nominal interest rates relative to Switzerland predict rand depreciation relative to the franc; similarly, higher eurozone inflation relative to the U.S. implies euro depreciation relative to USD under relative PPP and UIP. (LOS 5.e)
8. C
Using the Fisher relation and given data, real interest rates equalise at 2% in all specified countries in the example. (LOS 5.e)
9. B
A forecast equal to the forward rate assumes investors are risk neutral and that UIP/forward parity conditions align such that the forward equals expected future spot, which requires no currency risk premium. (LOS 5.e)
Module Quiz 5.3 - Answers and Explanations
1. A
Flow mechanism: current account deficits increase supply of the domestic currency in FX markets, leading to depreciation. The question's conclusion that JPY/USD should decrease (meaning USD depreciates vs JPY) is consistent with this explanation. (Module 5.3, LOS 5.j)
2. B
Under the pure monetary approach, future changes in money supply affect the trajectory of FX rates, but the model assumes PPP holds at every instant; future growth in money supply does not necessarily change the current exchange rate immediately. (Module 5.3, LOS 5.k)
3. A
In Zambola with low capital mobility, restrictive monetary policy and lower fiscal deficits improve trade balance and lead to currency appreciation under the Mundell-Fleming framework. (Module 5.3, LOS 5.k)
4. A
Computation (from the module data): (0.9821 - 0.00069) - (0.9817 - 0.00076) = 0.00047. (Module 5.1, LOS 5.c)
5. B
Contract FX2001: purchase CHF 200 million in 30 days. To compute the mark-to-market, use the all-in bid price for a 30-day USD/CHF forward to sell CHF (go up the quote). all-in bid = 0.9817 - 7.6/10,000 = 0.98094. Using the market steps yields -USD451,924 as the mark-to-market. (Module 5.2, LOS 5.d)
6. A
Contract FX2051: purchase EUR 100 million in 60 days. To compute mark-to-market, use the 60-day all-in bid for USD/EUR (going up the quote). all-in bid = 1.2235 - 14.56/10,000 = 1.22204. Computation yields -USD215,900. (Module 5.2, LOS 5.d)
7. C
Carry trade return distributions typically have negative skewness and excess kurtosis. Poulsen's statement is incorrect about both skewness and kurtosis if she described them otherwise. (Module 5.3, LOS 5.i)
8. A
An improvement (not deterioration) in terms of trade should be excluded from a list of currency-crisis indicators. Currency crises are associated with deterioration in terms of trade. (Module 5.3, LOS 5.m)
9. A
If the Zu is overvalued and Zambola runs a current account deficit, expansionary monetary policy would reduce interest rates and make yields less attractive to foreign investors, reducing inflows; therefore, to reduce inflows the government should pursue expansionary monetary policy (which reduces attractiveness of domestic yields). (Module 5.3, LOS 5.j)
FINAL KEY POINTS AND STUDY ADVICE
Study and practice the following thoroughly:
- Interpretation of bid-ask quotes and the practical rules: buy base at ask; sell base at bid and the mnemonic up-the-bid-and-multiply, down-the-ask-and-divide.
- Compute cross rates carefully, remembering to invert quotes correctly when necessary and to calculate bid and ask cross rates with the proper order of operations.
- Triangular arbitrage: always use dealer quotes, walk around the triangle both directions, and check which direction (if any) yields a profit.
- Mark-to-market forward valuation: determine the offsetting forward for the remaining maturity, compute the difference in forward rates, multiply by contract size, and discount using price-currency deposit rate.
- Memorise parity relations (CIRP, UIP, PPP, Fisher) and the conditions under which each holds; be able to derive implied forwards and expected spot changes from rates and inflation.
- Understand the mechanics and risks of the carry trade, and the macroeconomic determinants of exchange rates including BOP flows, monetary and fiscal policy impacts (Mundell-Fleming), monetary models, and portfolio balance implications.
- Learn common warning signs of currency crises and how capital flows and reserve adequacy influence central-bank policy effectiveness.
End of reading.
