Interest rate parity is a no-arbitrage condition representing

an equilibrium state under which investors will be indifferent

to interest rates available on bank deposits in two countries.

A theory in which the interest rate differential between two

countries is equal to the differential between the forward

exchange rate and the spot exchange rate. Interest rate parity

plays an essential role in foreign exchange markets,

connecting interest rates, spot exchange rates and foreign

exchange rates.

Covered Interest Arbitrage

A strategy in which an investor uses a forward contract to hedge against

exchange rate risk. Covered interest rate arbitrage is the practice of using

favorable interest rate differentials to invest in a higher-yielding currency,

and hedging the exchange risk through a forward currency contract.

Covered interest arbitrage is only possible if the cost of hedging the

exchange risk is less than the additional return generated by investing in

a higher-yielding currency.

Such arbitrage opportunities are uncommon, since market

participants will rush in to exploit an arbitrage opportunity if

one exists, and the resultant demand will quickly redress the

imbalance.

An investor undertaking this strategy is making simultaneous

spot and forward market transactions, with an overall goal of

obtaining riskless profit through the combination of currency

pairs.

Covered interest arbitrage is not without its risks, which

include differing tax treatment in various jurisdictions, foreign

exchange or capital controls, transaction costs and bid-ask

spreads.

A savvy investor could therefore exploit this arbitrage

opportunity as follows -

Borrow 500,000 of currency X @ 2% per annum, which means that

the total loan repayment obligation after a year would be 510,000 X.

Convert the 500,000 X into Y (because it offers a higher one-year interest rate) at the spot rate of 1.00.

Lock in the 4% rate on the deposit amount of 500,000 Y, and simultaneously enter into a

forward contract that converts the full maturity amount of the deposit (which works out to

520,000 Y) into currency X at the one-year forward rate of X = 1.0125 Y.

After one year, settle the forward contract at the contracted rate of 1.0125, which would give the investor 513,580 X.

Repay the loan amount of 510,000 X and pocket the difference of 3,580 X.

As with the other forms of arbitrage, market forces resulting from

covered arbitrage will cause a market realignment. As many investors

capitalize on covered interest arbitrage, there is upward pressure on the

spot rate and downward pressure on the forward rate. Once the

forward rate has a discount from the spot rate that is about equal to the

interest rate advantage, covered interest arbitrage will no longer be

feasible.

Realignment due to Covered Interest Arbitrage

Once market forces cause interest rates and

exchange rates to adjust such that covered

interest arbitrage is no longer feasible, there

is an equilibrium state referred to as

Interest Rate Parity (IRP)

Graphical Analysis Of IRP

Zone of potential Covered

Interest Arbitrage by Home

Country Investors

Zone of potential Covered

Interest Arbitrage by Foreign

Investors

IRP Line

Interest Rate Differential

Forward Premium

Forward Discount

D

C

A

B

Y

Z

Purchasing Power Parity is a connection between

Inflation and Exchange Rates.

The PPP principle, which was popularized by

Gustav Cassell in the 1920s, is most easily

explained if we begin by considering the connection

between exchange rates and the local currency price

of an individual commodity in different countries.

This connection between exchange rates and

commodity prices is known as the Law of One

Price.

The law of One Price states that in the absence of friction such as

differential shipping costs and tariffs, the price of a product when

converted into a common currency such as US dollar, using the

spot exchange rate, is the same in every country.

The law of one price exists due to arbitrage opportunities. If the

price of a security, commodity or asset is different in two

different markets, then an arbitrageur will purchase the asset in

the cheaper market and sell it where prices are higher.

Law of One Price

Although it may seem as if PPPs and the law of one price are

the same, there is a difference, the law of one price applies to

individual commodities whereas PPP applies to the general

price level.

If the law of one price is true for all commodities then PPP is

also therefore true; however, when discussing the validity of

PPP, some argue that the law of one price does not need to be

true exactly for PPP to be valid.

If the law of one price is not true for a certain commodity, the

price levels will not differ enough from the level predicted by

PPP

The absolute form of PPP is based on a notion that without

international barriers, consumers shift their demand to

wherever prices are lower. It suggests that prices of the same

basket of products in two different countries should be equal

when measured in a common currency. If a discrepancy in

prices as measured by a common currency exists, the

demand should shift so that these prices converge.

Absolute PPP

However, it is difficult to test the validity of PPP in its

absolute form, because different baskets of goods are used

in different countries for computing prices indexes.

Different baskets are used because of taste and needs

differ between countries, affecting what people buy.

For example, people in cold, northern countries consume

more heating oil and less olive oil than people in more

temperate countries. This means that even if the law of

one price holds for each individual good, price indexes,

which depend on the weights attached to each good will

not conform to the law of one price.

For example, if heating oil prices increased more than olive oil

prices, the country with a bigger weight in tis price index for

heating oil would have a larger price index increase than the

olive oil consuming countries. Even though heating oil and

olive oil prices increased the same amount in both countries.

Partly for this reason an alternative form of PPP condition

which is stated in terms of rates of inflation can be useful. This

form is called the Relative form of PPP.

The relative form of PPP accounts for the possibility of

market imperfections such as transportation costs, tariffs,

and quotas.

This version acknowledges that because of these market

imperfections, prices of the same basket of products in

different countries will not necessarily be the same when

measured in a common currency.

It does state, however, that the rate of change in the prices in

the prices of the baskets should be somewhat similar when

measured in a common currency, as long as the

transportation costs and trade barriers are unchanged.

Relative PPP

For Example, Assume the US and UK trade extensively with

each other and initially have zero inflation. Now assume that

the US experiences a 9% inflation rate, while the UK

experiences a 5% inflation rate.

Under these conditions, PPP theory suggests that the British

pound should appreciate by approximately 4%, the differential

in inflation rates. Thus, the exchange rate should adjust to

offset the differential in the inflation rates of the two

countries.

If this occurs, the prices of the goods in the two countries

should appear similar to consumers. That is, the relative

purchasing power when buying products in one country is

similar to when buying products in the other country.

Derivation of PPP

Price Indexes at home country (h)

Inflation rate in home country Ih

Inflation rate in foreign country If

Price Indexes in foreign country (P)

Ph (1+Ih)

Due to inflation, the price index of goods in the consumer’s home

country becomes

The price index of foreign country will also change due to inflation in

that country

Pf (1+If)

The consumer’s purchasing power is greater on foreign

goods than on home goods. In this case PPP does not exist.

The Ex. Rate between the

currencies of the two countries

does not change

If Ih > If

The consumer’s purchasing power is

greater on home goods than on

foreign goods. In this case PPP does not

exist.

The Ex. Rate between the

currencies of the two countries

does not change

If Ih < If