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ECON5007代写-ECON 5007
时间：2022-10-30
ECON 5007
主讲人：Vincent
Week 4
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,
• t and tUS = the consumer price indices in the country considered and the US
at time t.
• t = exchange rate at time t, defined as the price of one USD in terms of the
country’s currency.
-
• The real depreciation rate of the country’s currency against the U.S. dollar, denoted
̇, is the growth rate of t
Let ̇ =
−1
− 1 denote the nominal depreciation rate of the country’s currency
against the U.S. dollar, and =
−1
− 1 and
=
−1
− 1 denote inflation rates
in the country considered and in the United States. This yields
• Taking the natural logarithm and using the approximation that, for small values of
, (1 + ) ≈
• Relative PPP holds if the real exchange rate does not change over time, ̇ = 0:
• According to the relative version of PPP, the percentage change in the spot exchange
rate (%∆/) will be completely determined by the difference between inflation
rates in X and Y:
%∆/ ≈ −
• Whereas the relative version of PPP focuses on actual changes in exchange rates
being driven by actual differences in national inflation rates, the ex-ante version of
PPP asserts that the expected changes in the spot exchange rate are entirely driven
by expected differences in national inflation rates
• Ex-ante PPP tells us that countries that are expected to run persistently high
inflation rates should expect to see their currencies depreciate over time, while
countries that are expected to run relatively low inflation rates on a sustainable basis
should expect to see their currencies appreciate over time
-
%∆/
≈
−
• where %∆/
represents the expected percentage change in the spot exchange
rate, while
and
represent the expected inflation rates in X and Y over the
same period
10. International Fisher Effect
• The Fisher effect: one can break down the nominal interest rate in a given country
into two parts: (1) the real interest rate in that particular country and (2) the expected
inflation rate in that country:
= +
• To relate this concept to exchange rates, we can write the Fisher equation for both
the domestic country and a foreign country. If the Fisher effect holds, the nominal
interest rates in both countries will equal the sum of their respective real interest
rates and expected inflation rates:
= +
= +
− = ( − ) + (
−
)
• The real interest rate parity: real interest rates will converge to the same level across
different markets − = 0
• If real interest rates are equal across markets, then it also follows that the foreign-
domestic nominal yield spread is determined solely by the foreign-domestic
expected inflation differential, This is known as the International Fisher effect
− =
−
11. FX Carry Trade
• FX carry trade involves taking long positions in high-yield currencies and short
positions in low-yield currencies. The latter are often referred to as funding
currencies
• As a simplified example of the carry trade, assume a trader can borrow Canadian
-
dollars at 1% and earn 9% on an investment in Brazilian reals for one year. To
execute the trade to earn 8% from the interest rate differential, the trader will do the
following:
• 1. Borrow Canadian dollars at t = 0
• 2. Sell the dollars and buy Brazilian reals at the spot rate at t = 0
• 3. Invest in a real-denominated investment at t = 0
• 4. Liquidate the Brazilian investment at t = 1
• 5. Sell the reals and buy dollars at the spot rate at t = 1
• 6. Pay back the dollar loan
• If the real appreciates, the trader’s profits will be greater than 8% because the
stronger real will buy more dollars in one year.
• If the real depreciates, the trader’s profits will be less than 8% because the weaker
real will buy fewer dollars in the future.
• If the real falls in value by more than 8%, the trader will experience losses. The
carry trader’s return consists of the intermarket yield spread, the currency
appreciation/depreciation, and the foreign investment appreciation/depreciation.
Typically, a carry trade is executed using an investment in highly rated government
debt so as to mitigate credit risk.
12. The impact of Balance-of-Payments Accounts
• Current account represents the sum of all recorded transactions in traded goods,
services, income, and net transfer payments in a country’s overall balance of
payments
• Financial account (also known as the capital account) reflects financial flows
• Investment/financing decisions are usually the dominant factor in determining
exchange rate movements, at least in the short to intermediate term
• Current account trends influence the path of exchange rates over time through
several mechanisms:
• The flow supply/demand channel
• The portfolio balance channel
• The debt sustainability channe
• The flow supply/demand channel
• If a country was running a current account surplus, then the demand for its currency
should rise. Such shifts should exert upward pressure on the value of the surplus
nation’s currency and downward pressure on the value of the deficit nation’s
currency
-
• At some point, domestic currency weakness should contribute to improvement in
the trade competitiveness of the deficit nation. And vise visa. Thus, the exchange
rate responses to these surpluses and deficits should eventually help eliminate the
source of the initial imbalances
• The portfolio balance channel
• Countries with trade deficits will finance their trade with increased borrowing. This
behavior may lead to shifts in global asset preferences, which in turn could
influence the path of exchange rates
• Nations running account surpluses versus USA might find that they hold excessive
amount of USD-dominated assets. Once they reduced their dollar holdings, USD
might depreciate
• The debt sustainability channel
• If investors believe that the deficit country’s external debt is rising to unsustainable
levels, they are likely to reason that a major depreciation of the deficit country’s
currency will be required (capital outflow) at some point to ensure that the current
account deficit narrows significantly and that the external debt stabilizes at a level
deemed sustainable
• Financial account (Capital account)
• The increased freedom of capital to flow across national borders have increased the
importance of global financial flows in determining exchange rate
• Local currency would be appreciated by capital inflows attracted by the persistently
higher short-term interest rate
• Excessive surges in capital inflows to emerging markets have often planted the
seeds of an economic or currency crisis by contributing to:
• (1) an unwarranted appreciation of the emerging market currency
• (2) a huge buildup in external indebtedness
• (3) an asset bubble
• (4) a consumption binge that contributes to explosive growth in domestic
credit and/or the current account deficit, or
• (5) an overinvestment in risky projects and questionable activities
13. Mundell-Fleming Model
• The Mundell-Fleming model describes how changes in monetary and fiscal policy
affect the interest rates and economic activity within a country, which in turn leads
to changes in capital flows and trade and ultimately to changes in the exchange rate.
• Implicit assumption: The model focuses only on aggregate demand and assumes
-
there is sufficient slack in the economy to allow increases in output without price
level increases
• Flexible exchange rate regimes
• High capital mobility - Monetary policy
• Expansionary monetary policy: Downward pressure on domestic interest rates will
induce capital to flow to higher-yielding markets, putting downward pressure on
the domestic currency. The more responsive capital flows are to interest rate
differentials, the larger the depreciation of the currency
• A restrictive monetary policy: upward pressure on domestic interest rates will
induce capital to flow from lower-yielding markets, putting upward pressure on the
domestic currency
• Flexible exchange rate regimes
• High capital mobility - Fiscal policy
• An expansionary fiscal policy will exert upward pressure on domestic interest rates,
which in turn induce an inflow of capital from lower-yielding markets, putting
upward pressure on the domestic currency
• Expansionary fiscal policy will also increase economic activity (growth) and
inflation, leading to a deterioration of the current account and a decrease in demand
for the domestic currency
• A domestic currency will appreciate given a restrictive domestic monetary policy
and/or an expansionary domestic fiscal policy
• A domestic currency will depreciate given an expansionary monetary policy and/or
a restrictive fiscal policy
• Flexible exchange rate regimes
• Low capital mobility
• The impact of monetary and fiscal policy changes on domestic interest rates will
operate primarily through trade flows rather than capital flows
• Expansionary fiscal policy will increase imports and hence the trade deficit,
creating downward pressure on the currency. Layering on an expansive monetary
-
policy will further boost spending and imports, worsening the trade balance and
exacerbating the downward pressure on the currency
• The combination of restrictive monetary and fiscal policy will be bullish for a
currency. This policy mix will tend to reduce imports, leading to an improvement
in the trade balance
• Fixed exchange rate regimes
• High capital mobility - Monetary policy
• Expansionary Monetary Policy: To prevent the exchange rate from depreciating, the
monetary authority will have to buy its own currency in exchange for other
currencies in the FX market
• Doing so will tighten domestic credit conditions and offset the intended
expansionary monetary policy
• In the extreme case, expansionary monetary will be completely ineffective if the
central bank is forced to fully offset the initial expansion of the money supply and
allow the interest rate to rise back to its initial level
• Fixed exchange rate regimes
• High capital mobility - Fiscal policy
• Expansionary fiscal policy: To prevent the domestic currency from appreciating,
the central bank will have to sell its own currency in the FX market
• The expansion of the domestic money supply will reinforce the aggregate demand
impact of the expansionary fiscal policy
• Conclusion
High Capital Mobility Expansionary FP Restrictive FP
Expansionary MP Uncertain Appreciate
Restrictive MP Depreciate Uncertain
Low Capital Mobility Expansionary FP Restrictive FP
Expansionary MP Depreciate Uncertain
Restrictive MP Uncertain Appreciate
-
• The Trilemma
• From our comparison of fixed and floating exchange rates, we can see that it is not
possible to achieve all three of these goals.
• (1) + (2) imply interest rates must be equal—contradicting (3)
• (2) + (3) imply an expected change in the exchange rate—contradicting (1)
• (3) + (1) imply a difference between domestic and foreign returns contradicting
(2)
• These choices represent a trilemma. One of the three goals must be sacrificed to
achieve the other two.
14. Exchange Rate Management
• Capital flow surges can be both a blessing and a curse
• Capital inflows can be a blessing when they increase domestic investment
and therefore increase economic growth and asset values
• They can be a curse, if they fuel boom-like conditions, asset price bubbles,
and overvaluation of a country’s currency
• Objective of central bank: the key issue for policymakers is whether intervention
and capital controls will actually work in terms of
• Preventing currencies from appreciating too strongly
• Reducing the aggregate volume of capital inflows
• Enabling monetary authorities to pursue independent monetary policies
without having to worry about whether changes in policy rates might attract
too much capital from overseas
-
• Effectiveness
• Most industrial countries hold insufficient reserves to significantly affect the supply
of and demand for their currency, hence the effect of intervention in developed
market economies is limited.
• Emerging market policymakers might have greater success in controlling exchange
rates than their industrial country counterparts because the ratio of EM central bank
FX reserve holdings to average daily FX turnover in their domestic currencies is
actually quite sizable. Emerging market central banks appear to be in a stronger
position than their developed market counterparts to influence the level and path of
their exchange rates
15. Warning Signs of Currency Crisis
• Prior to a currency crisis, the capital markets have been liberalized to allow the free
flow of capital.
• There are large inflows of foreign capital (relative to GDP) in the period leading up
to a crisis, with short-term funding denominated in a foreign currency being
particularly problematic.
• Currency crises are often preceded by (and often coincide with) banking crisis.
• Countries with fixed or partially fixed exchange rates are more susceptible to
currency crisis than countries with floating exchange rates.
• Foreign exchange reserves tend to decline precipitously as a crisis approaches
• In the period leading up to a crisis, the currency has risen substantially relative to
its historical mean
• The ratio of exports to imports (known as “the terms of trade”) often deteriorates
before a crisis
• Broad money growth and the ratio of M2 (a measure of money supply) to bank
reserves tend to rise prior to a crisis
• Inflation tends to be significantly higher in pre-crisis periods compared with
tranquil periods
主讲人：Vincent
Week 4
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
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• 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,
• t and tUS = the consumer price indices in the country considered and the US
at time t.
• t = exchange rate at time t, defined as the price of one USD in terms of the
country’s currency.
-
• The real depreciation rate of the country’s currency against the U.S. dollar, denoted
̇, is the growth rate of t
Let ̇ =
−1
− 1 denote the nominal depreciation rate of the country’s currency
against the U.S. dollar, and =
−1
− 1 and
=
−1
− 1 denote inflation rates
in the country considered and in the United States. This yields
• Taking the natural logarithm and using the approximation that, for small values of
, (1 + ) ≈
• Relative PPP holds if the real exchange rate does not change over time, ̇ = 0:
• According to the relative version of PPP, the percentage change in the spot exchange
rate (%∆/) will be completely determined by the difference between inflation
rates in X and Y:
%∆/ ≈ −
• Whereas the relative version of PPP focuses on actual changes in exchange rates
being driven by actual differences in national inflation rates, the ex-ante version of
PPP asserts that the expected changes in the spot exchange rate are entirely driven
by expected differences in national inflation rates
• Ex-ante PPP tells us that countries that are expected to run persistently high
inflation rates should expect to see their currencies depreciate over time, while
countries that are expected to run relatively low inflation rates on a sustainable basis
should expect to see their currencies appreciate over time
-
%∆/
≈
−
• where %∆/
represents the expected percentage change in the spot exchange
rate, while
and
represent the expected inflation rates in X and Y over the
same period
10. International Fisher Effect
• The Fisher effect: one can break down the nominal interest rate in a given country
into two parts: (1) the real interest rate in that particular country and (2) the expected
inflation rate in that country:
= +
• To relate this concept to exchange rates, we can write the Fisher equation for both
the domestic country and a foreign country. If the Fisher effect holds, the nominal
interest rates in both countries will equal the sum of their respective real interest
rates and expected inflation rates:
= +
= +
− = ( − ) + (
−
)
• The real interest rate parity: real interest rates will converge to the same level across
different markets − = 0
• If real interest rates are equal across markets, then it also follows that the foreign-
domestic nominal yield spread is determined solely by the foreign-domestic
expected inflation differential, This is known as the International Fisher effect
− =
−
11. FX Carry Trade
• FX carry trade involves taking long positions in high-yield currencies and short
positions in low-yield currencies. The latter are often referred to as funding
currencies
• As a simplified example of the carry trade, assume a trader can borrow Canadian
-
dollars at 1% and earn 9% on an investment in Brazilian reals for one year. To
execute the trade to earn 8% from the interest rate differential, the trader will do the
following:
• 1. Borrow Canadian dollars at t = 0
• 2. Sell the dollars and buy Brazilian reals at the spot rate at t = 0
• 3. Invest in a real-denominated investment at t = 0
• 4. Liquidate the Brazilian investment at t = 1
• 5. Sell the reals and buy dollars at the spot rate at t = 1
• 6. Pay back the dollar loan
• If the real appreciates, the trader’s profits will be greater than 8% because the
stronger real will buy more dollars in one year.
• If the real depreciates, the trader’s profits will be less than 8% because the weaker
real will buy fewer dollars in the future.
• If the real falls in value by more than 8%, the trader will experience losses. The
carry trader’s return consists of the intermarket yield spread, the currency
appreciation/depreciation, and the foreign investment appreciation/depreciation.
Typically, a carry trade is executed using an investment in highly rated government
debt so as to mitigate credit risk.
12. The impact of Balance-of-Payments Accounts
• Current account represents the sum of all recorded transactions in traded goods,
services, income, and net transfer payments in a country’s overall balance of
payments
• Financial account (also known as the capital account) reflects financial flows
• Investment/financing decisions are usually the dominant factor in determining
exchange rate movements, at least in the short to intermediate term
• Current account trends influence the path of exchange rates over time through
several mechanisms:
• The flow supply/demand channel
• The portfolio balance channel
• The debt sustainability channe
• The flow supply/demand channel
• If a country was running a current account surplus, then the demand for its currency
should rise. Such shifts should exert upward pressure on the value of the surplus
nation’s currency and downward pressure on the value of the deficit nation’s
currency
-
• At some point, domestic currency weakness should contribute to improvement in
the trade competitiveness of the deficit nation. And vise visa. Thus, the exchange
rate responses to these surpluses and deficits should eventually help eliminate the
source of the initial imbalances
• The portfolio balance channel
• Countries with trade deficits will finance their trade with increased borrowing. This
behavior may lead to shifts in global asset preferences, which in turn could
influence the path of exchange rates
• Nations running account surpluses versus USA might find that they hold excessive
amount of USD-dominated assets. Once they reduced their dollar holdings, USD
might depreciate
• The debt sustainability channel
• If investors believe that the deficit country’s external debt is rising to unsustainable
levels, they are likely to reason that a major depreciation of the deficit country’s
currency will be required (capital outflow) at some point to ensure that the current
account deficit narrows significantly and that the external debt stabilizes at a level
deemed sustainable
• Financial account (Capital account)
• The increased freedom of capital to flow across national borders have increased the
importance of global financial flows in determining exchange rate
• Local currency would be appreciated by capital inflows attracted by the persistently
higher short-term interest rate
• Excessive surges in capital inflows to emerging markets have often planted the
seeds of an economic or currency crisis by contributing to:
• (1) an unwarranted appreciation of the emerging market currency
• (2) a huge buildup in external indebtedness
• (3) an asset bubble
• (4) a consumption binge that contributes to explosive growth in domestic
credit and/or the current account deficit, or
• (5) an overinvestment in risky projects and questionable activities
13. Mundell-Fleming Model
• The Mundell-Fleming model describes how changes in monetary and fiscal policy
affect the interest rates and economic activity within a country, which in turn leads
to changes in capital flows and trade and ultimately to changes in the exchange rate.
• Implicit assumption: The model focuses only on aggregate demand and assumes
-
there is sufficient slack in the economy to allow increases in output without price
level increases
• Flexible exchange rate regimes
• High capital mobility - Monetary policy
• Expansionary monetary policy: Downward pressure on domestic interest rates will
induce capital to flow to higher-yielding markets, putting downward pressure on
the domestic currency. The more responsive capital flows are to interest rate
differentials, the larger the depreciation of the currency
• A restrictive monetary policy: upward pressure on domestic interest rates will
induce capital to flow from lower-yielding markets, putting upward pressure on the
domestic currency
• Flexible exchange rate regimes
• High capital mobility - Fiscal policy
• An expansionary fiscal policy will exert upward pressure on domestic interest rates,
which in turn induce an inflow of capital from lower-yielding markets, putting
upward pressure on the domestic currency
• Expansionary fiscal policy will also increase economic activity (growth) and
inflation, leading to a deterioration of the current account and a decrease in demand
for the domestic currency
• A domestic currency will appreciate given a restrictive domestic monetary policy
and/or an expansionary domestic fiscal policy
• A domestic currency will depreciate given an expansionary monetary policy and/or
a restrictive fiscal policy
• Flexible exchange rate regimes
• Low capital mobility
• The impact of monetary and fiscal policy changes on domestic interest rates will
operate primarily through trade flows rather than capital flows
• Expansionary fiscal policy will increase imports and hence the trade deficit,
creating downward pressure on the currency. Layering on an expansive monetary
-
policy will further boost spending and imports, worsening the trade balance and
exacerbating the downward pressure on the currency
• The combination of restrictive monetary and fiscal policy will be bullish for a
currency. This policy mix will tend to reduce imports, leading to an improvement
in the trade balance
• Fixed exchange rate regimes
• High capital mobility - Monetary policy
• Expansionary Monetary Policy: To prevent the exchange rate from depreciating, the
monetary authority will have to buy its own currency in exchange for other
currencies in the FX market
• Doing so will tighten domestic credit conditions and offset the intended
expansionary monetary policy
• In the extreme case, expansionary monetary will be completely ineffective if the
central bank is forced to fully offset the initial expansion of the money supply and
allow the interest rate to rise back to its initial level
• Fixed exchange rate regimes
• High capital mobility - Fiscal policy
• Expansionary fiscal policy: To prevent the domestic currency from appreciating,
the central bank will have to sell its own currency in the FX market
• The expansion of the domestic money supply will reinforce the aggregate demand
impact of the expansionary fiscal policy
• Conclusion
High Capital Mobility Expansionary FP Restrictive FP
Expansionary MP Uncertain Appreciate
Restrictive MP Depreciate Uncertain
Low Capital Mobility Expansionary FP Restrictive FP
Expansionary MP Depreciate Uncertain
Restrictive MP Uncertain Appreciate
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• The Trilemma
• From our comparison of fixed and floating exchange rates, we can see that it is not
possible to achieve all three of these goals.
• (1) + (2) imply interest rates must be equal—contradicting (3)
• (2) + (3) imply an expected change in the exchange rate—contradicting (1)
• (3) + (1) imply a difference between domestic and foreign returns contradicting
(2)
• These choices represent a trilemma. One of the three goals must be sacrificed to
achieve the other two.
14. Exchange Rate Management
• Capital flow surges can be both a blessing and a curse
• Capital inflows can be a blessing when they increase domestic investment
and therefore increase economic growth and asset values
• They can be a curse, if they fuel boom-like conditions, asset price bubbles,
and overvaluation of a country’s currency
• Objective of central bank: the key issue for policymakers is whether intervention
and capital controls will actually work in terms of
• Preventing currencies from appreciating too strongly
• Reducing the aggregate volume of capital inflows
• Enabling monetary authorities to pursue independent monetary policies
without having to worry about whether changes in policy rates might attract
too much capital from overseas
-
• Effectiveness
• Most industrial countries hold insufficient reserves to significantly affect the supply
of and demand for their currency, hence the effect of intervention in developed
market economies is limited.
• Emerging market policymakers might have greater success in controlling exchange
rates than their industrial country counterparts because the ratio of EM central bank
FX reserve holdings to average daily FX turnover in their domestic currencies is
actually quite sizable. Emerging market central banks appear to be in a stronger
position than their developed market counterparts to influence the level and path of
their exchange rates
15. Warning Signs of Currency Crisis
• Prior to a currency crisis, the capital markets have been liberalized to allow the free
flow of capital.
• There are large inflows of foreign capital (relative to GDP) in the period leading up
to a crisis, with short-term funding denominated in a foreign currency being
particularly problematic.
• Currency crises are often preceded by (and often coincide with) banking crisis.
• Countries with fixed or partially fixed exchange rates are more susceptible to
currency crisis than countries with floating exchange rates.
• Foreign exchange reserves tend to decline precipitously as a crisis approaches
• In the period leading up to a crisis, the currency has risen substantially relative to
its historical mean
• The ratio of exports to imports (known as “the terms of trade”) often deteriorates
before a crisis
• Broad money growth and the ratio of M2 (a measure of money supply) to bank
reserves tend to rise prior to a crisis
• Inflation tends to be significantly higher in pre-crisis periods compared with
tranquil periods
