CFA® Level II Economics - International Parity Conditions
Summary
TLDRThis video script explores international parity relationships, focusing on how forward exchange rates are determined by interest rate differentials and arbitrage. It explains the concepts of covered interest rate parity, uncovered interest rate parity, and purchasing power parity (PPP). The script also covers the Fisher effect and international Fisher effect, illustrating how inflation and interest rates influence currency values. These theories are used to predict future exchange rates and understand currency movements, though they hold more true in the long term.
Takeaways
- 📈 Forward rates are used to predict future exchange rates; a higher forward rate than the spot rate indicates a forward premium, while a lower rate indicates a forward discount.
- 💹 The forward premium or discount is determined by the arbitrage relationship between spot rates, forward rates, and interest rates in different countries.
- 🌐 Covered interest rate parity is the relationship between the interest rate differentials and the forward premium or discount, which is maintained by arbitrageurs to prevent arbitrage opportunities.
- 💼 Arbitrageurs can earn riskless profit by borrowing in a low-interest-rate currency, exchanging for a high-interest-rate currency, investing there, and using a forward contract to sell back at a future date.
- 📉 If the forward rate is at a discount, it is expected that the currency with the lower interest rate will appreciate against the higher interest rate currency.
- ⏳ The no-arbitrage relationship between forward rates, spot rates, and interest rates is adjusted for the number of days to maturity when calculating for periods less than a year.
- 🌐 Uncovered interest rate parity is based on investor preference and risk neutrality, assuming that investors will be indifferent to investing in different currencies if the expected change in exchange rates offsets the interest rate differential.
- 📊 Forward rate parity suggests that the forward exchange rate is an unbiased forecast of the future spot exchange rate, which is more evident in the long term than the short term.
- 💰 Purchasing power parity (PPP) is based on the law of one price, stating that identical goods should have the same price in all locations when adjusted for exchange rates.
- 📊 Relative PPP and ex-ante relative PPP relate exchange rate changes to inflation differentials, with the latter being a forward-looking version that uses expected inflation rates.
- 🔄 The international Fisher effect combines the Fisher relation and real interest rate parity, suggesting that nominal interest rate differentials should equal expected inflation rate differentials between two countries.
Q & A
What is a forward premium in the context of foreign exchange?
-A forward premium occurs when the forward rate is higher than the spot rate, indicating that one unit of a foreign currency can buy more of another currency in the future, suggesting an expectation that the first currency will appreciate against the second.
What is a forward discount and how does it relate to currency appreciation?
-A forward discount happens when the forward rate is lower than the spot rate. It implies that one unit of a foreign currency will buy less of another currency in the future, suggesting that the first currency is expected to depreciate against the second.
How does the arbitrage relationship between spot rate, forward rate, and interest rates work?
-The arbitrage relationship ensures that the forward rate is set at a level where no riskless profit can be earned. This is achieved by borrowing in a low-interest-rate currency, converting it to a high-interest-rate currency, investing it there, and simultaneously entering a forward contract to sell it back at the future date at the forward rate.
What is the covered interest rate parity and why is it significant?
-Covered interest rate parity is the relationship between the interest rate differentials of two countries and the forward premium or discount on their exchange rates. It's significant because it defines the equilibrium level for the forward exchange rate where no arbitrage opportunities exist.
How do you calculate the no arbitrage forward exchange rate?
-The no arbitrage forward exchange rate is calculated by adjusting the spot rate by the interest rate differential between two currencies, taking into account the time to maturity. This ensures that the forward rate reflects the cost of carry between the two currencies.
What is the difference between uncovered and covered interest rate parity?
-Covered interest rate parity is based on the arbitrage condition, whereas uncovered interest rate parity is based on investor expectations and risk neutrality. Covered interest rate parity involves hedging currency risk, while uncovered does not.
How does the expected change in exchange rates relate to interest rate differentials?
-According to uncovered interest rate parity, the expected change in the exchange rate is the difference between the interest rates of the foreign and domestic currencies. This reflects the idea that investors will move funds to the currency with the higher interest rate, adjusting the exchange rate accordingly.
What is the forward rate parity and how does it relate to future spot rates?
-Forward rate parity suggests that the forward exchange rate is an unbiased predictor of the future spot rate. If both covered and uncovered interest rate parity hold, the forward rate should reflect all available information about the future spot rate.
How does purchasing power parity (PPP) relate to exchange rates?
-Purchasing power parity (PPP) is based on the law of one price, which states that identical goods should have the same price in all locations after adjusting for exchange rates. PPP suggests that exchange rates will adjust to offset differences in price levels between countries.
What is the difference between absolute and relative PPP?
-Absolute PPP requires that the law of one price holds true for all goods and services, implying that exchange rates are determined by the ratio of national price levels. Relative PPP focuses on changes in exchange rates being equal to the difference in inflation rates between countries.
How does the Fisher effect connect nominal interest rates and expected inflation?
-The Fisher effect states that the nominal interest rate in a country is approximately the sum of the real interest rate and the expected inflation rate. This relationship suggests that differences in nominal interest rates between countries should reflect differences in their expected inflation rates.
Outlines
📈 Forward Rates and Arbitrage
This paragraph explains the concept of forward rates in currency exchange and how they relate to the spot rate. It introduces the terms 'forward premium' and 'forward discount' and uses the example of the Euro and Australian Dollar (AUD) to illustrate these concepts. The paragraph then delves into the arbitrage relationship between spot and forward rates and the interest rates of two countries. An example is given where an arbitrageur can profit risklessly by borrowing Euros, exchanging them for AUD, investing the AUD at a higher interest rate, and then selling the AUD forward at a predetermined rate. The concept of covered interest rate parity is introduced, which is the relationship between forward rates, spot rates, and interest rates. The paragraph concludes with a practical exercise for the viewer to calculate the no-arbitrage forward exchange rate for Japanese Yen per US dollar.
🌐 Covered and Uncovered Interest Rate Parity
The second paragraph discusses the concepts of covered and uncovered interest rate parity. Covered interest rate parity is explained as the relationship between interest rate differentials and forward premiums or discounts, which is bound by arbitrage. Uncovered interest rate parity, on the other hand, is based on investor preference and the assumption of risk neutrality. The paragraph uses an example to illustrate how an investor might prefer to invest in a currency with a higher interest rate, expecting the currency to depreciate, thus canceling out the interest rate differential. The paragraph also touches on forward rate parity, which suggests that the forward exchange rate is an unbiased forecast of the future spot rate, a condition that is more evident in the long term. The viewer is then prompted to calculate the expected future spot rate using uncovered interest rate parity.
💵 Purchasing Power Parity (PPP)
This paragraph explores the relationship between exchange rates and inflation rates through the lens of purchasing power parity (PPP). It starts by explaining the law of one price, which states that identical goods should have the same price in all locations when adjusted for exchange rates. The paragraph distinguishes between absolute and relative PPP, with absolute PPP applying to a basket of goods and services and relative PPP focusing on the change in price levels between two countries. The paragraph also introduces the ex-anti version of relative PPP, which forecasts future exchange rates based on expected inflation rates. An exercise is provided to calculate the expected future spot rate using ex-anti relative PPP.
🔗 International Fisher Effect and Parity Relationships
The final paragraph ties together the concepts of inflation rate differentials and interest rate differentials through the Fischer effect. It explains that the nominal interest rate in a country is the sum of the real interest rate and the expected inflation rate. The paragraph discusses the international Fisher effect, which posits that the difference in nominal interest rates between two countries should equal the difference in their expected inflation rates. Real interest rate parity is also mentioned, suggesting that real interest rates converge across different markets due to free capital flows. The paragraph concludes with an exercise to calculate expected inflation based on the international Fisher relation. The video script ends by summarizing the five international parity relationships that govern interest rates, inflation rates, and currency exchange rates between two countries.
Mindmap
Keywords
💡Forward Rates
💡Forward Premium
💡Forward Discount
💡Arbitrage
💡Covered Interest Rate Parity
💡Uncovered Interest Rate Parity
💡Risk Neutrality
💡Purchasing Power Parity (PPP)
💡Fisher Effect
💡Real Interest Rate Parity
💡International Fisher Effect
Highlights
Forward rates are higher than spot rates, indicating a forward premium and an expected appreciation of the Euro against AUD.
A forward discount occurs when the forward rate is lower than the spot rate, suggesting an expected depreciation of the Euro against AUD.
The forward premium or discount is determined by the arbitrage relationship between spot and forward rates and the interest rates in both countries.
An arbitrage example is given, showing how to earn riskless profit by borrowing Euros, buying AUD at the spot rate, investing in AUD at a higher interest rate, and selling AUD forward.
Covered interest rate parity is introduced as the relationship between the forward rate, spot rate, and interest rates, assuming no arbitrage opportunities.
The no arbitrage equilibrium level for the forward exchange rate is explained with an example where the forward rate is adjusted to eliminate arbitrage opportunities.
Interest rates should be annualized and adjusted for the number of days to maturity when calculating the forward rate.
A practical example calculates the no arbitrage 180-day forward exchange rate for JPY per USD using the covered interest rate parity.
Uncovered interest rate parity is discussed, which is based on investor preference and risk neutrality rather than arbitrage.
An example illustrates how a risk-neutral investor would be indifferent to changing Euros to AUD despite a higher return on AUD due to expected depreciation.
Uncovered interest rate parity and forward rate parity are conditions that govern interest rate differentials and future exchange rates.
Forward exchange rates are typically poor predictors of future spot exchange rates in the short run but have more empirical support in the long run.
Purchasing power parity (PPP) is introduced as the basis for the relationship between exchange rates and inflation differentials.
Absolute PPP suggests that the equilibrium exchange rate is determined by the ratio of national price levels.
Relative PPP, which considers the percentage change in exchange rates as the difference in inflation rates, is more practical in real-world scenarios.
An exercise calculates the expected spot JPY per CNY rate in one year using ex-anti relative PPP.
The international Fisher effect is explained, linking nominal interest rate differentials to expected inflation rate differentials.
An exercise calculates the expected inflation for China based on the international Fisher relation.
The five international parity relationships that govern interest rates, inflation rates, and currency exchange rates are summarized.
Transcripts
foreign
[Music]
we learned forward rates if the forward
rate is higher than the spot rate we say
there's a forward premium since one Euro
can buy more AUD in the future we expect
the euro to appreciate against AUD and
AUD to depreciate against the euro and
if the forward rate is lower we say
there's a forward discount since one
Euro buys less AUD in the future we
expect the euro to depreciate against
AUD and AUD to appreciate against the
euro now one important question that we
promise to address is what determines
the forward premiums or discounts
to answer this we need to understand the
Arbitrage relationship between the spot
rate forward rate and the interest rates
in the two countries
let's say the one-year interest rate for
risk-free government debt is five
percent in Australia and three percent
in the Eurozone
assuming that the spot and the one-year
forward rates are the same at 1.552 and
arbitration can earn riskless profit by
taking the following steps
first he borrows a thousand Euros for
one year at the risk-free rate of three
percent and uses it to purchase AUD at
the spot rate
he invests the AUD at the risk-free rate
of five percent for a year and at the
same time he enters into a currency
forward to sell AUD at a forward rate of
1.552
after one year he would have
1629.6 AUD including interest as he has
the forward contract he can sell the AUD
at 1.552 rate which means he exchanges
all the AUD for 1050 euros
he repays his loan with interest and he
Pockets 20 euros totally risk-free with
zero cash outlay
as we've learned in level 1 such
Arbitrage opportunities cannot persist
arbitrageurs will pursue this
opportunity which is to sell Euro to buy
AUD which decreases the AUD per Euro
spot rate and selling the AUD forward
which increases the forward exchange
rate
this continues until the forward rate is
at a no Arbitrage level against the spot
rate
so here we see that when the forward
rate is increased to 1.5821 the net cash
flow at the end of the year to the
arbitrager is zero this level where
there is no more Arbitrage opportunity
is the equilibrium level for the forward
exchange rate
the no Arbitrage relationship between
the forward rate spot rate and interest
rates is as such
as the interest rates are annualized you
should adjust the interest rates by the
number of days to maturity
this relationship between the forward
price spot price and interest rates is
known as the covered interest rate
parity
for now we assume that the covered
interest rate parity holds so if we plug
in all the figures into this
relationship the equation balances
this means there's no Arbitrage
opportunity and the forward rate is
priced correctly
let's have some practice
the spot Japanese Yen per US dollar rate
is
110.86 if the 180 day risk-free rate is
0.2 percent in Japan and 1.8 percent in
the U.S what is the no Arbitrage 180 day
forward exchange rate for JPY per USD
rate
pause the video now and work out your
answer
and we're back
first I hope you did not make this
mistake unless otherwise stated interest
rates are quoted in annualized figures
so to get the 180 day interest rate we
have to divide the annual rate by two
plug in the figures and we get a forward
rate of 109.98
as the forward rate is at a discount we
expect yen to appreciate and the US
dollar to depreciate
let us summarize what we've learned
about covered interest rate parity
for two countries with different
currencies
this defines the relationship between
the interest rate differentials between
the two countries and the forward
premium or discount of the exchange rate
between them
covered here means that the relationship
is bound by Arbitrage
another way of looking at it is to study
investor preference
in the CFA curriculum one convention is
to define the base currency as the
Investor's domestic currency and the
price currency as the foreign currency
so for a German investor the euro is his
domestic currency and the AUD is a
foreign currency so the AUD per euro is
his reference exchange rate
so let's say the AUD interest rate is 5
and Euro interest rate is three percent
the investor would prefer to buy AUD and
sell Euros if he does not expect any
change in the future exchange rate
this brings down the spot rate until
there is sufficient difference between
the spot rate and the expected change in
spot rate over the period that he would
be indifferent to investing in either
currency
mathematically this is the point where
the expected change in spot rate
is the difference between the interest
rates of the foreign and domestic
currencies
this is known as uncovered interest rate
parity
uncovered means that this relationship
is not bound by Arbitrage
rather this relationship is based on the
Assumption of risk neutrality of
investors
let's illustrate risk neutrality using
our example
when AUD interest rate is five percent
and Euro interest rate is three percent
the expected change in the AUD per euro
rate is an increase of two percent this
means that Euro will appreciate by two
percent against the AUD in one year
so even though AUD has a higher return
of five percent a risk neutral investor
will be indifferent to changing Euros to
AUD as he expects it to depreciate
canceling out the difference in the
yield
so as you can see uncovered interest
rate parity is also another condition
that governs interest rate differentials
between two countries and the future
exchange rate between their currencies
in this case it's the expectation of
change in exchange rate
in theory if both covered and uncovered
interest rate parity hold the forward
exchange rate will be an unbiased
forecast to the Future spot exchange
rate
this condition is often referred to as
forward rate parity
however note that this relationship is
only evident in the long term
as you would have known spot exchange
rates are highly volatile in the short
term as there are many other factors
that influence short-term exchange rate
movements 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 interest
rate parity and forward rate parity of
more empirical support
and let's pause for another exercise
the spot nzd per CHF rate is 1.6650
the one-year nominal interest rate is
1.1 percent in New Zealand and 2.5
percent in Switzerland
using uncovered interest rate parity
what is the expected spot nzd per CHF
rate in one year pause the video now and
work out your answer
and we're back
first we calculate the expected
percentage change in the spot rate which
is simply the difference between the
interest rates make sure that the order
is correct which is the interest rate
for the price currency minus that of the
base currency
plug in the figures and we get minus 1.4
percent
lower the spot rate by 1.4 percent and
we get an expected rate of 1.6417
so far we've looked at the relationship
between exchange rates and interest rate
differentials
now we turn to examining the
relationship between exchange rates and
inflation differentials
the basis for this relationship is known
as purchasing power parity or PPP in
short
the foundation of PPP is the law of One
Price which states that identical Goods
should have the same price in all
locations for instance a designer
handbag should in theory cost the same
in Australia as they do in Germany after
adjusting for the exchange rate
again the foundation of PPP is the
principle of no Arbitrage
if there is a significant price
difference between the two countries
arbitrages will buy from the cheaper
place to sell at the more expensive
place
until the price differential disappears
in practice you may have noticed that
PPP does not hold for many individual
goods or services however this may hold
true if you consider the aggregate of
many goods and services
the absolute version of PPP simply
extends the law of one price to the
basket of goods and services that are
consumed in different countries
absolute PPP requires only that the law
of One Price be correct on average that
is for similar baskets of goods in each
country
this implies that the equilibrium
exchange rate between two countries is
determined entirely by the ratio of
their National price levels
however it may also be unlikely that
this relationship holds in the real
world as transaction costs and trade
restrictions prevent Arbitrage from
taking place
but if we assume that the transaction
costs and trade restrictions remain
constant over time the change in
exchange rates can therefore be the
relative change in price levels of the
two countries
we call this relative PPP more
specifically the percentage change in
exchange rates is the difference in the
inflation rate between the foreign
country and the domestic country
the ax anti version of PPP is the same
as relative PPP except that it's
forward-looking
it exerts that the expected percentage
change in exchange rate is the
difference in expected inflation rates
between the two countries
because there's no true Arbitrage
available to force relative PPP to hold
violations of relative PPP in the short
run are common however because the
evidence suggests that the relative form
of PPP holds approximately in the long
run it remains a useful method for
estimating the relationship between
exchange rates and inflation rates
let's pause again for another exercise
the spot JPY per CNY rate is
15.4706 for the next year analysts
expect China's inflation to be 4.8
percent and Japan's inflation to be
minus 0.5 percent
using ex-anti relative PPP what is the
expected spot JPY per CNY rate in one
year
pause the video now and work out your
answer
and we're back
firstly according to the x-anti version
of relative PPP the expected percentage
change in spot exchange rate is the
expected inflation in the foreign
currency minus the expected inflation in
the domestic currency
plug the figures in and we get minus 5.3
percent
therefore we expect the exchange rate to
Fall by 5.3 percent to
14.6507 as China has relatively higher
inflation rate than Japan its currency
is expected to depreciate against the
Japanese Yen based on an xrt PPP
so far we've examined the relationship
between exchange rates and interest rate
differentials and between exchange rates
and inflation differentials
now we'll begin to bring these Concepts
together by examining the relationship
between inflation rate differentials and
interest rate differentials
according to what economists call the
Fischer effect the nominal interest rate
in a given country is approximately the
sum of the real interest rate and the
expected inflation rate
if this holds true for both the domestic
and foreign country
we would expect the difference between
nominal interest rates to be equal to
the difference between the real rates
minus the difference between the
expected inflation rates of the two
countries
under a condition known as real interest
rate parity real interest rates are
assumed to converge across different
markets this is based on the idea that
with free Capital flows funds will move
to the country with a higher real rate
until real rates between them are
equalized
taking the Fisher relation and real
interest rate parity together gives us
the international Fisher effect
where the difference in nominal interest
rates between two countries
should be equal to the difference
between their expected inflation rates
let's attempt one last exercise
for the next year Japanese economists
expect inflation in Japan to be minus
0.5 percent given that the interest rate
for JPY is 0.1 percent and 5.4 percent
for CNY what is the expected inflation
for China based on the international
Fisher relation
pause the video now and work out your
answer
and we're back
let's first bring out the international
Fisher effect equation
we have expected inflation in Japan at
minus 0.5 percent 5.4 interest rate in
China and 0.1 percent interest rate in
Japan
the expected inflation in China is
therefore 4.8 percent
in summary these are the five
International parity relationships that
govern the interest rates inflation
rates and currency exchange spot rates
and forward rates between two countries
we've learned that covered interest rate
parity holds by Arbitrage
if forward rate parity holds uncovered
interest rate parity should also hold
we've also learned that interest rate
differentials should mirror inflation
differentials if the international
Fisher relation holds
if that is true we can also use
inflation differentials to forecast
future exchange rates which is the
premise of the ex-anti version of PPP
and lastly if the xrt version of
relative PPP as well as the
international Fisher relation both hold
uncovered interest rate parity will also
hold
as noted earlier these relationships
usually do not hold over the short run
but in the long run such relationships
should hold
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