CFA® Level II Economics - International Parity Conditions

Summary

This 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

00:00

📈 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.

05:00

🌐 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.

10:00

💵 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.

15:01

🔗 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.

Keywords

💡Forward Rates

Forward rates are the agreed-upon exchange rates for converting one currency into another at a future date. They are used to hedge against foreign exchange risk or to speculate on future exchange rate movements. In the video, forward rates are compared to spot rates to determine if there is a forward premium or discount, which indicates the expected direction of currency value changes.

💡Forward Premium

A forward premium exists when the forward rate is higher than the spot rate for a currency. This implies that the currency is expected to appreciate in the future. The video uses the example of the Euro having a forward premium against the Australian Dollar (AUD), suggesting that the Euro is expected to strengthen against the AUD.

💡Forward Discount

Conversely, a forward discount occurs when the forward rate is lower than the spot rate, indicating that the currency is expected to depreciate. The video explains this concept by stating that if one Euro buys less AUD in the future, the Euro is expected to depreciate against the AUD.

💡Arbitrage

Arbitrage is the practice of taking advantage of price differences in different markets to make risk-free profits. The video describes how arbitrageurs can exploit differences between spot and forward rates, as well as interest rates in different countries, to earn riskless profit without any initial investment.

💡Covered Interest Rate Parity

Covered interest rate parity is a condition in foreign exchange markets where the forward exchange rate premium or discount is equal to the interest rate differential between two countries. The video explains that this parity is maintained by arbitrage activity, ensuring that the forward rate is set at an equilibrium level where no arbitrage opportunities exist.

💡Uncovered Interest Rate Parity

Uncovered interest rate parity is a theory that suggests the forward exchange rate will adjust to offset differences in interest rates between two countries. The video illustrates this by explaining how an investor's preference for higher-yielding currencies can affect exchange rates, assuming investors are risk-neutral.

💡Risk Neutrality

Risk neutrality refers to the behavior of investors who are indifferent to risk, meaning they will not demand additional returns for taking on more risk. The video uses this concept to explain how investors might be indifferent to investing in currencies with different interest rates if they expect the exchange rate to change in a way that offsets the interest rate differential.

💡Purchasing Power Parity (PPP)

Purchasing power parity is an economic theory that suggests exchange rates between countries will adjust to equalize the purchasing power of different currencies. The video explains absolute and relative versions of PPP, which relate exchange rate changes to differences in price levels or inflation rates between countries.

💡Fisher Effect

The Fisher effect is the theory that nominal interest rates are the sum of real interest rates and expected inflation rates. The video discusses how the Fisher effect, in conjunction with real interest rate parity, leads to the international Fisher effect, which posits that nominal interest rate differentials should reflect expected inflation rate differentials between countries.

💡Real Interest Rate Parity

Real interest rate parity is the idea that real interest rates tend to be equalized across countries due to capital flows. The video suggests that if real interest rates converge, the differences in nominal interest rates between countries should be explained by differences in expected inflation rates.

💡International Fisher Effect

The international Fisher effect combines the Fisher effect with real interest rate parity to suggest that differences in nominal interest rates between countries should equal the differences in their expected inflation rates. The video uses this concept to explain how expected inflation rates can be inferred from interest rate differentials.

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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