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ECON 5007
Overview
• Exchange Rate
• Bid-Offer Spread
• Cross Rate and Triangular Arbitrage
• Forward Discount or Premium
• The International Parity Relationships
• FX Carry Trade
• The impact of Balance-of-Payments Accounts
• Exchange Rate Determination: Mundell-Fleming Model
• Exchange Rate Management
• Warning Signs of A Currency Crisis
1. Exchange Rate
• Exchange rate (P/B) is the price of base currency (B) expressed in terms of the price
currency (P).
• Alternatively, exchange rates are quoted as foreign currency per unit of domestic
currency or domestic currency per unit of foreign currency (d/f)
• 0.7515 USD exchanges for 1 AUD
• 0.7515 USD = 1 AUD
• 0.7515 USD/AUD
• USD/AUD = 0.7515
• The price of AUD in terms of USD is 0.7515
• USD to AUD exchange rate is 0.7515
• AUD/USD?
• Example:
• The dollar-Swiss franc rate increase from USD: CHF = 1.7799 to 1.8100. Which
currency has appreciated?
-
• Nominal exchange rate: the price that we observe in the marketplace for foreign
exchange
• Real exchange rate: what the currencies actually purchase in terms of real goods
and services
(/) = (/) ∗
2. Bid-Offer(Ask) Spread
• The bid price is the price, defined in terms of the price currency, at which the
counterparty is willing to buy one unit of the base currency
• The offer (ask) price is the price, in terms of the price currency, at which that
counterparty is willing to sell one unit of the base currency
• The offer price is always higher than bid price
• Bid-offer spread = offer price – bid price
• If the quote in the interbank USD/EUR spot market is 1.1648/1.1652 (four pips
wide, 1.1652-1.1648=0.0004)
• One pip is 1/10000
• The interbank spread depends on the currency pair involved, the time of day, market
volatility, etc
3. Cross Rate and Triangular Arbitrage
• If a particular currency pair is not explicitly quoted, it can be inferred from the
quotes for each currency in terms of the exchange rate with a third nation’s currency
• Triangular arbitrage means converting from currency A to currency B, then from
currency B to currency C, then from currency C back to A. If we end up with more
of currency A at the end than we started with, we've earned an arbitrage profit
• Example:
/ 1.1649/1.1651
/ 9.6300/9.6302
• What is the bid–offer on the SEK/EUR cross rate implied by the interbank market?
-
• Triangular Arbitrage Example:
• 1GBP = 1.5AUD
• 150Yen = 1GBP
• 1AUD = 120Yen
Motivation Asset Liability
Borrow 1GBP sell for
1.5AUD
1.5AUD 1GBP
Buy 180Yen 180Yen – 1.5AUD
Buy back 1GBP for
150Yen
-150Yen -1GBP
Total 30Yen 0
• 1AUD = 100Yen to remove arbitrage
4. Forward Discount or Premium
• Spot exchange rate is used for settlement on the second business day after the trade
date (T+2 settlement)
• Forward exchange rate is used for transaction that has a settlement date longer than
T+2
• Currency forward contracts are agreements to exchange one currency for another
on a future date at an exchange rate agreed upon today
• Forward discount or premium: There is a premium (discount) on the quoted
currency when the forward exchange rate is higher (lower) than the spot rate.
• Forward premium: forward rate > spot rate.
• Forward discount: forward rate < spot rate.
• Forward points = forward rate – spot rate
• Assume that the bid-ask for the spot and forward points for the USD/EUR exchange
rate are as shown in the table below
• What are three-month forward bid rate?
-
5. The International Parity Relationships
• A Long-term Framework for Exchange Rates
• International parity conditions describe the inter-relationships that jointly
determine long-run movements in exchange rates, interest rates, and
inflation
• Interest Rate Parity (fx rate & interest rate)
• Covered Interest Rate Parity
• Uncovered Interest Rate Parity
• Forward Rate Parity
• Purchasing Power Parity (fx rate & inflation)
• Absolute PPP
• Relative PPP
• International Fisher Effect (interest rate & inflation)
6. Covered Interest Rate Parity
• Example:
• Sinan wants to invest $1 for 1 year. The spot rate is /) and forward rate is /)
• She considers the following two options:
• Option 1: Deposit it in a domestic bank (CommBank), and the interest rate
• Option 2: Deposit it in a foreign bank (Bank of China), and the interest rate
is
• For option 2, Sinan needs to exchange her $1 to Chinese yuan at the spot rate (t=0).
One year later, she needs to exchange the money back to Australian dollars at the
forward rate (at t=1)
• The covered interest rate parity condition describes the relationship among the spot
exchange rate, the forward exchange rate, and interest rates
• This parity condition describes a riskless arbitrage relationship in which an
investment in a foreign money market instrument that is completely hedged against
exchange rate risk should yield exactly the same return as an otherwise identical
domestic money market investment. (fully hedge)
/ = / ∗
1 +
1 +
-
• Assume that you own 1 EUR and you want to guarantee a return in EUR in 1 year.
You have two alternative investments:
• Invest in an EUR security with an interest rate ;
• Change 1 EUR now for 1/EUR/USD USD and invest in a USD security with
an interest rate ∗, while simultaneously buying forward exchange contracts
to convert each future USD into EUR/USD.
• Example: The fixed-income manager collects the following information and uses it,
along with the international parity conditions, to estimate investment returns and
future exchange rate movements
• If covered interest rate parity holds, what is the all-in one-year investment return to
a Japanese investor whose currency exposure to the GBP is fully hedged?
-
7. Uncovered Interest Rate Parity
• According to the uncovered interest rate parity condition, the expected return on an
uncovered (i.e., unhedged) foreign currency investment should equal the return on
a comparable domestic currency investment
• Uncovered interest rate parity states that the change in spot rate over the investment
horizon should, on average, equal the differential in interest rates between the two
countries. That is, the expected appreciation/depreciation of the exchange rate will
just offset the yield differential.
• Uncovered interest rate parity does not cover forex risks. Covered interest rate
parity covers forex risks by forward contracts
()/ = 0/ ∗
1 +
1 +
• Log Form
ln (()/) − ln (0/) = ln (
1 +
1 +
)
8. Forward Rate Parity
• Forward rate parity builds upon two other parity conditions, covered interest rate
parity and uncovered interest rate parity.
• Forward rate parity states that the forward exchange rate will be an unbiased
predictor of the future spot exchange rate. It does not state that the forward rate will
be a perfect forecast, just an unbiased one; the forward rate may overestimate or
underestimate the future spot rate from time to time, but on average, it will equal
the future spot rate.
• Covered IRP must hold because it is enforced by arbitrage. Uncovered IRP is often
violated. As a result, we can conclude that forward exchange rates are typically poor
predictors of future spot exchange rates in the short run. Over the longer term,
uncovered IRP and forward rate parity have more empirical support
-
9. Purchasing Power Parity (PPP)
• According to the law of one price, identical goods should trade at the same price
across countries when valued in terms of a common currency
• The Law of One Price (LOOP) holds when a good costs the same abroad and at
home. Formally, LOOP holds for a good if:
• Where:
• b = domestic-currency price of good b in the domestic country,
• b∗ = foreign-currency price of good b in the foreign country, and
• S = the nominal exchange rate (domestic-currency price of one unit of
foreign currency)
• Should the LOOP hold?
• In a frictionless world, yes. If a can of coke costs 1 dollar in the US and 2 dollars
in Australia, you could become infinitely rich buying cans of coke in the US and
selling them in Australia.
• Reasons why the LOOP may not hold: International transportation costs,
distribution costs (loading and unloading, domestic transportation, storage,
advertising, and retail services), taxes.
• Types of goods for which the LOOP holds fairly well: commodities (e.g., gold,
oil, soybeans, wheat), luxury consumer goods (e.g., Rolex watches, Hermes
neckties, and Montblanc fountain pens).
• Type of goods for which the LOOP doesn’t hold well: personal services (e.g.,
health care, education, restaurant meals, domestic services, and personal care, such
as haircuts), housing, transportation, and utilities.
• Purchasing power parity (PPP) is the generalization of the idea of the law of one
price for broad baskets of goods representative of households’ actual consumption,
as opposed to a single good
• The Absolute PPP asserts that the equilibrium exchange rate between two countries
is determined entirely by the ratio of their national price levels.
• Absolute PPP holds if the real exchange rate Q is equal to 1
-
• However, it is highly unlikely that this relationship actually holds in the real world.
• Trade costs
• Non-Tradables
• Differentiated Goods
• Hence, sizable and persistent departures from absolute PPP are likely
• Relative PPP
• Change in the exchange rate depends on the inflation rates in the two countries. In
its approximate form, the difference in inflation rates is equal to the expected
depreciation (appreciation) of the currency. The country with the higher inflation
should see its currency depreciate
• Most studies of purchasing power parity focus on changes in the real exchange rate,
rather than on its level
• Relative PPP holds if
• t = real exchange rate at time t ;
• t = nominal exchange rate at time t ;
• t and t∗ = domestic and foreign price indices at time t ;
• Δ = change over time.
• Let t be the real exchange rate of a given country with the United States in period
t. Then,
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