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. Covered interest arbitrage allows an investor to exploit interest rate differentials between currencies by investing in the higher yielding currency and hedging exchange risk through a forward contract. Once market forces eliminate arbitrage opportunities, interest rate parity is achieved where exchange rates align so that covered interest arbitrage is no longer feasible.

1. Interest rate parity is a relation between Interest Rate
differential and Forward Rate discount and premium

2. 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.

3. 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.

4. 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.

5. 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 intoY (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.

6. 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.

7. 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

8. 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)

9. Graphical Analysis Of IRP

10. 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

11. Purchasing Power Parity is a relation between
Inflation and Exchange Rates.

12. 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.

13. 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

14. 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

15. 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

16. 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.

17. 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.

18. 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

19. 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.

20. 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 (f)

21. 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)

22. 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

23. 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

24. The PPP theory suggests that the exchange rate will not remain
constant but will adjust to maintain the parity in purchasing power. If
inflation occurs and the exchange rate of the foreign currency
changes, the foreign price index from the home consumer’s
perspective becomes
ph (1+Ih ) (1+ef)
ef represents
the % change
in the value of
the foreign
currency

25. Pf(1+If)(1+ef) =Ph(1+Ih)
1+ef = Ph (1+Ih)
Pf (1+If)
ef = Ph (1+Ih) -1
Pf (1+If)
Since Ph equals Pf ( because prices indexes were initially
assumed equal in both countries), they cancel, leaving

26. ef = 1+Ih -1
1+If
If Ih > If
ef
Foreign
Currency
If Ih < If
-ef
Foreign
Currency

29. International Fisher Effect is a relation between Interest Rate
Differential and Expected Exchange Rate

30. International fisher effect uses Interest Rate rather than inflation rate
differentials to explain why exchange rates change over time but it is
closely related to PPP theory because interest rates are often highly
correlated with inflation rates. According to IFE, nominal risk-free
interest rates contain a real rate of return and anticipated inflation. If
investments of all countries require the same real return, interest rate
differential between countries may be the result of differentials in
expected inflation.

31. The International Fisher Effect (IFE) is an exchange-rate model
designed by the economist Irving Fisher in the 1930s. It is based on
present and future risk-free nominal interest rates rather than
pure inflation, and it is used to predict and understand present and
future spot currency price movements.

34. Anand Verma
Rohit Kumar
Mahesh Gupta
Madan Mavi
Sagar Parmar