JAI HIND COLLEGE

BASANTSING INSTITUTE OF SCIENCE &

J.T. LALVANI COLLEGE OF COMMERCE

A PROJECT ON

INTEREST RATE PARITY

IN THE SUBJECT OF ECONOMICS

SUBMITTED TO UNIVERSITY OF MUMBAI

For Semester 1 of M.Com Part 1

By

NAME: RUPEN CHALWA

ROLL NO.: 10 MCOM- PART-1

DECLERATION

I, Rupen Chawla, student of M.Com Part 1, Roll no. 10 hereby declare that the project for the Paper Economics titled Interest Rate Parity submitted by me for Semester- 2 during the academic year 2014-15, is based on actual work carried out by me. I further state that this work is original and not submitted anywhere else for any examination.

NAME: RUPEN CHALWA MCOM- PART-1 ROLL NO.: 10

DATE OF SUBMISSION: , 2014

Acknowledgement

I wish to thank Professor Vadehi for his

encouragement and support throughout the project it is due to his best effort and continued guidance that I was able to

prepare this project.

Rupen Chawla

JAI HIND COLLEGE ‘A’ ROAD, CHURCHGATE, MUMBAI- 400020

CERTIFICATE

This is to certify that Mr. Rupen Chawla of M.Com Accountancy and Finance Semester 2 (2014-15) has successfully completed the project Interest Rate Parity under the guidance of Professor Vadehi. __________ __________ Course coordinator Principal __________ ___________ Internal Examiner External Examiner

__________ College Seal

INDEX

1. Introduction 2. Assumptions 3. COVERED AND UNCOVERED INTEREST

RATE PARITY

4. COVERED INTEREST RATE PARITY {CIP}

5. UNCOVERED INTEREST RATE PARITY {UIP}

1) INRODUCTION

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.[1] The

fact that this condition does not always hold allows for potential

opportunities to earn riskless profits from covered interest

arbitrage. Two assumptions central to interest rate parity are capital

mobility and perfect substitutability of domestic and foreign assets.

Given foreign exchange market equilibrium, the interest rate parity

condition implies that the expected return on domestic assets will

equal the exchange rate-adjusted expected return on foreign

currency assets. Investors then cannot earn arbitrage profits by

borrowing in a country with a lower interest rate, exchanging for

foreign currency, and investing in a foreign country with a higher

interest rate, due to gains or losses from exchanging back to their

domestic currency at maturity.[2] Interest rate parity takes on two

distinctive forms: uncovered interest rate parity refers to the parity

condition in which exposure to foreign exchange risk (unanticipated

changes in exchange rates) is uninhibited, whereas covered interest

rate parity refers to the condition in which a forward contract has

been used to cover (eliminate exposure to) exchange rate risk. Each

form of the parity condition demonstrates a unique relationship with

implications for the forecasting of future exchange rates:

the forward exchange rate and the future spot exchange rate.[1]

Economists have found empirical evidence that covered interest

rate parity generally holds, though not with precision due to the

effects of various risks, costs, taxation, and ultimate differences in

liquidity. When both covered and uncovered interest rate parity

hold, they expose a relationship suggesting that the forward rate is

an unbiased predictor of the future spot rate. This relationship can

be employed to test whether uncovered interest rate parity holds,

for which economists have found mixed results. When uncovered

interest rate parity and purchasing power parity hold together, they

illuminate a relationship named real interest rate parity, which

suggests that expected real interest ratesrepresent expected

adjustments in the real exchange rate. This relationship generally

holds strongly over longer terms and among emerging

market countries.

EXAMPLES

For our illustration purpose consider investing € 1000 for 1 year.

We'll consider two investment cases viz:

Case I: Domestic Investment

In the U.S.A., consider the spot exchange rate of $1.2245/€ 1.

So we can exchange our € 1000 @ $1.2245 = $1224.50

Now we can invest $1224.50 @ 3.0% for 1 year which yields

$1261.79 at the end of the year.

Case II: Foreign Investment

Likewise we can invest € 1000 in a foreign European market, say at the rate of 5.0% for 1 year.

But we buy forward 1 year to lock in the future exchange rate at

$1.20025/€ 1 since we need to convert our € 1000 back to the

domestic currency, i.e. the U.S. Dollar.

So € 1000 @ of 5.0% for 1 year = € 1051.27

Then we can convert € 1051.27 @ $1.20025 = $1261.79

Thus, in the absence of arbitrage, the Return on Investment (RoI) is

same regardless of our choice of investment method.

There are two types of IRP.

2) ASSUMPTIONS

Interest rate parity rests on certain assumptions, the first being

that capital is mobile - investors can readily exchange domestic

assets for foreign assets. The second assumption is that assets

have perfect substitutability, following from their similarities

in riskiness and liquidity. Given capital mobility and perfect

substitutability, investors would be expected to hold those assets

offering greater returns, be they domestic or foreign assets.

However, both domestic and foreign assets are held by investors.

Therefore, it must be true that no difference can exist between the

returns on domestic assets and the returns on foreign

assets.[2] That is not to say that domestic investors and foreign

investors will earn equivalent returns, but that a single investor on

any given side would expect to earn equivalent returns from either

investment decision.[3]

3)COVERED AND UNCOVERED INTEREST RATE PARITY

Key relationships

In international economics, key macroeconomic variables include

the following (symbols are in parentheses; * means a foreign variable):

Exchange rate (e) Prices (p, p*)

Interest rates (i, i*) Current account (CA)

Capital account (KA) GDP (y, y*)

How these variables are related is the central question of open

macroeconomics. In this lecture, interest parities, or the relationships between the exchange rate (e) and interest rates (i,

i*), are investigated. Please note that the arguments presented below are valid only among countries whose financial sectors are

sufficiently developed and externally open. If a country is financially closed or its financial sector lacks depth, liquidity and institutional

development (for example, without well-functioning spot and forward currency markets), interest parities do not hold.

There are two versions of interest parities: covered and uncovered. The covered version involves no exchange risks, while the

uncovered version entails such risks and elements of speculation. Both interest parities (especially the uncovered version) are key

building blocks of many open macroeconomic models. In the next lecture, purchasing power parity (PPP), namely the

relationship between the exchange rate (e) and prices (p, p*), will

be discussed. That is also a key input to open macroeconomic modeling. This lecture will also make references to it.

The law of one price (LOOP) and arbitrage

Interest parities (as well as PPP presented in the next lecture) are a

type of the law of one price in an integrated world. The law of one

price says that identical commodities (or anything) bought and sold in different markets should bear the same price. Otherwise, there

will be a profit opportunity in buying the commodity in one market and selling it in the other, and someone will surely do it (this

activity of pursuing gain by combined purchase and sale, without changing the physical characteristics of the commodity, is

called arbitrage). In an integrated and properly functioning market, arbitrage will surely continue until the law of one price is

established, eliminating any further opportunity for excess profit. Then the two markets are really one.

Some markets show LOOP, but others do not. Whether they do or do not depends on (i) the characteristics of the merchandise

(especially the transportation cost; heavy and bulky items are difficult to arbitrage); (ii) the characteristics of market competition

and strategies of traders; and (iii) policy intervention (e.g., capital

control, tax and tariff policies and other regulatory measures to artificially increase transaction costs or even entirely ban such

trade). If you are checking the prices of digital cameras or DVD players in

different outlets in the electronic town of Akihabara, Tokyo, you are also a potential arbitrager. You will soon realize that the same

models bear almost exactly the same price, namely LOOP holds quite firmly in Akihabara. A shuttle trader, or an individual who

carries merchandise, say, from China to Kyrgyzstan, is also

engaged in arbitrage. In this case, however, LOOP probably does

not hold exactly due to uncertainty and transportation cost. Sellers may overcharge without the buyer knowing it. Integrated global

financial markets also exhibits LOOP, and their arbitrage is extremely fast and tight.

In the case of interest parities, what are equalized are the rates of return across various interest-bearing financial instruments (bank

deposits, bonds, bills, etc). Under free capital mobility, LOOP holds firmly and trivially for covered interest parity, but the validity of

LOOP for uncovered interest parity is empirically very questionable. The difference is explained by the absence or presence of exchange

risk (see below).

Assumptions

In order for interest parities to hold, the following assumptions are

required. (1) Free capital mobility--there is no official hindrance to arbitrage

across countries. (2) No transaction cost--there is no natural (market) hindrance to

arbitrage across countries. Transaction is without charge or carries only a negligible charge.

(3) No default risk--financial investment is safe against business

defaults, country risks, etc. The above are necessary conditions for covered interest parity.

There are no exchange, default or other risks related to financial investment. We are assuming a perfectly safe, risk-free world.

In the case of uncovered interest parity, the following assumption is added.

(4) Risk neutrality--investors care only about the long-run average return and do not care about the outcome of each investment.

Here, exchange risk is present although all other risks of financial investment are still assumed away. Investors are assumed to be

neutral against this risk. That means they care only about the average results. Whether the variance (volatility) of the return of

each investment is large or small does not concern them. Covered and uncovered interest parities should not be confused

with each other. They refer to two completely different situations.

4)COVERED INTEREST RATE PARITY {CIP}

What is CIP?

Covered Interest Parity (CIP) is also called covered interest rate

parity. Under the assumption of free capital flow, it states that the

forward premium of a foreign currency should be equal to the

interest rate differential between a domestic asset and a substitutable foreign asset.

CIP implies the equality of returns on comparable financial assets denominated in different currencies. The underlying mechanism for

CIP is covered interest arbitrage. What is Covered Interest Arbitrage?

Covered interest arbitrage is the transfer of liquid funds from one

monetary center to another to take advantage of higher rates of return or interest, while covering the transaction with a forward

currency hedge. Suppose the 3-month T-bill rate in the U. S. is 12%, higher than

the 3-month T-bill rate of 8% in Canada. Attracted by the higher interest rate, investors would tend to change their Canadian dollar

into U.S. dollar and invest their funds in the U.S. Simultaneously,

they buy contracts to sell dollars in 3 months in the forward market. If the spot exchange rate is 1.00CAD/USD at present, and the 3-

month forward exchange rate is 0.99CAD/USD at present, then the investors' losses in exchange conversion will be 1%. From the

interest rate differential, they will earn 1% in 3 months (since annually they earn (12%-8%)=4% by investing in U.S. rather than

in Canada). This profit is just offset by the loss. However, if the interest rate in U.S. is higher, making the earning in interest rate

differential much larger in absolute value than the loss in foreign exchange, this arbitrage process will continue. Then, large amount

of funds flow from Canada into U.S., putting pressures for U.S. to lower its interest rate and for Canada to raise its interest rate. In

addition, the increasing demand of U.S. dollar in the current market tends to raise the spot rate for U.S. dollar. The increasing demand

of Canada dollar in the forward market tends to decrease the future

rate for U.S. dollar. The process continues until returns from investing in the two countries reach the same level. Then the CIP

conditions will be satisfied again.

When the no-arbitrage condition is satisfied with the use of a forward

contract to hedge against exposure to exchange rate risk, interest rate

parity is said to be covered. Investors will still be indifferent among the

available interest rates in two countries because the forward exchange rate

sustains equilibrium such that the dollar return on dollar deposits is equal

to the dollar return on foreign deposit, thereby eliminating the potential

for covered interest arbitrage profits. Furthermore, covered interest rate

parity helps explain the determination of the forward exchange rate. The

following equation represents covered interest rate parity.[1][4]

where

is the forward exchange rate at time t

The dollar return on dollar deposits, , is shown to be equal to the dollar

return on euro deposits, .

Empirical evidence[edit]

Covered interest rate parity (CIRP) is found to hold when there is open

capital mobility and limited capital controls, and this finding is confirmed

for all currencies freely traded in the present-day. One such example is

when the United Kingdom and Germany abolished capital controls

between 1979 and 1981. Maurice Obstfeld and Alan Taylor calculated

hypothetical profits as implied by the expression of a potential inequality

in the CIRP equation (meaning a difference in returns on domestic versus

foreign assets) during the 1960s and 1970s, which would have constituted

arbitrage opportunities if not for the prevalence of capital controls.

However, given financial liberalization and resulting capital mobility,

arbitrage temporarily became possible until equilibrium was restored.

Since the abolition of capital controls in the United Kingdom and

Germany, potential arbitrage profits have been near zero. Factoring

in transaction costs arising from fees and other regulations, arbitrage

opportunities are fleeting or nonexistent when such costs exceed

deviations from parity.[1][5] While CIRP generally holds, it does not hold

with precision due to the presence of transaction costs, political

risks, tax implications for interest earnings versus gains from foreign

exchange, and differences in the liquidity of domestic versus foreign

assets.[5][6][7] Researchers found evidence that significant deviations from

CIRP during the onset of the global financial crisis in 2007 and 2008 were

driven by concerns over risk posed by counter parties to banks and

financial institutions in Europe and the US in the foreign exchange

swap market. The European Central Bank's efforts to provide US dollar

liquidity in the foreign exchange swap market, along with similar efforts

by theFederal Reserve, had a moderating impact on CIRP deviations

between the dollar and the euro. Such a scenario was found to be

reminiscent of deviations from CIRP during the 1990s driven by

struggling Japanese banks which looked toward foreign exchange swap

markets to try and acquire dollars to bolster their creditworthiness.[8]

When both covered and uncovered interest rate parity (UIRP) hold, such a

condition sheds light on a noteworthy relationship between the forward

and expected future spot exchange rates, as demonstrated below.

Dividing the equation for UIRP by the equation for CIRP yields the

following equation:

which can be rewritten as:

This equation represents the unbiasedness hypothesis, which states that

the forward exchange rate is an unbiased predictor of the future spot

exchange rate.[9][10] Given strong evidence that CIRP holds, the forward

rate unbiasedness hypothesis can serve as a test to determine whether

UIRP holds (in order for the forward rate and spot rate to be equal, both

CIRP and UIRP conditions must hold). Evidence for the validity and

accuracy of the unbiasedness hypothesis, particularly evidence

for cointegration between the forward rate and future spot rate, is mixed

as researchers have published numerous papers demonstrating both

empirical support and empirical failure of the hypothesis.[9]

UIRP is found to have some empirical support

in tests for correlation between expected rates of currency

depreciation and the forward premium or discount.[1] Evidence suggests

that whether UIRP holds depends on the currency examined, and

deviations from UIRP have been found to be less substantial when

examining longer time horizons.[11] Some studies of monetary policy have

offered explanations for why UIRP fails empirically. Researchers

demonstrated that if a central bank manages interest rate spreads in

strong response to the previous period's spreads, that interest rate

spreads had negative coefficients in regression tests of UIRP. Another

study which set up a model wherein the central bank's monetary policy

responds to exogenous shocks, that the central bank's smoothing of

interest rates can explain empirical failures of UIRP.[12] A study of central

bank interventions on the US dollar and Deutsche mark found only

limited evidence of any substantial effect on deviations from

UIRP.[13] UIRP has been found to hold over very small spans of time

(covering only a number of hours) with a high frequency of bilateral

exchange rate data.[14] Tests of UIRP for economies experiencing

institutional regime changes, using monthly exchange rate data for the

US dollar versus the Deutsche mark and the Spanish peseta versus

the British pound, have found some evidence that UIRP held when US

and German regime changes were volatile, and held between Spain and

the United Kingdom particularly after Spain joined the European Union in

1986 and began liberalizing capital mobility.[15]

Covered Interest Rate theory states that exchange rate forward

premiums (discounts) offset interest rate differentials between two sovereigns.

In another words, covered interest rate theory holds that interest rate differentials between two countries are offset by the

spot/forward currency premiums as otherwise investors could earn

a pure arbitrage profit.

Covered Interest Rate Examples

Assume Google Inc., the U.S. based multi-national company,

needs to pay it's European employees in Euro in a month's time. Google Inc. can achieve this in several ways viz:

Buy Euro forward 30 days to lock in the exchange rate. Then Google can invest in dollars for 30 days until it must convert

dollars to Euro in a month. This is called covering because now Google Inc. has no exchange rate fluctuation risk.

Convert dollars to Euro today at spot exchange rate. Invest Euro in a European bond (in Euro) for 30 days (equivalently loan

out Euro for 30 days) then pay it's obligation in Euro at the end of the month.

Under this model Google Inc. is sure of the interest rate that it will

earn, so it may convert fewer dollars to Euro today as it's Euro will

grow via interest earned. This is also called covering because by converting dollars to Euro

at the spot, the risk of exchange rate fluctuation is eliminated.

When people and firms are permitted to buy and sell foreign

assets, they can hold various exchange "positions," which are net holding balances in foreign currency. The positions are classified

below.

Position Balance sheet situation

If home currency

depreciates

If home currency

appreciates

"Open"

"Long" Foreign assets > foreign liabilities Gain Loss

"Short" Foreign assets < foreign liabilities Loss Gain

"Square" Foreign assets = foreign liabilities No impact

For example, suppose you have foreign securities worth $500 but have also borrowed $700 from the bank.. This means that you

have the short position of $200. For simplicity, we assume all foreign assets and liabilities are denominated in USD. This allows

us to concentrate on the movement of the domestic currency against USD, without worrying about the fluctuations among major

currencies. Suppose you are a manufacturer of a certain product and also

engaged in foreign trade. As you conduct your daily transactions of buying foreign parts or exporting finished products to foreign

markets, the exchange position naturally fluctuates and does not remain "square." This means that you may incur gain or loss

depending on the exchange rate movement at any moment, which

is often hard to predict. Suppose also that your main business is manufacturing and you are not interested in foreign currency

speculation. Particularly, you want to avoid exchange losses. If your country has sufficiently developed and externally open

financial markets, there are two alternative ways to "cover" or "hedge"--i.e., make your exchange position square and avoid

exchange risk (see handout no.4). More concretely, assume that you are a Japanese exporter of an industrial product expecting a

receipt of $100 after 3 months. You want to fix this receipt in terms of yen (domestic currency) now. Suppose also that:

S (spot exchange rate) is currently $1=100 yen

F (3-month forward exchange rate) is--initially--$1=102 yen

i (Japanese interest rate) is 4%/year

i* (US interest rate) is 6%/year

The first method is forward cover. You go to a bank and make a forward contract today. That is to say, you agree to sell $100 to

the bank after 3 months and receive a specified amount of yen

(10,200 yen = $100 x 102) at that time. Then you wait for 3

months before executing this transaction. The exchange rate for selling USD in the future (forward rate, 102), offered by the bank,

is different from the exchange rate for today (spot rate, 100). The second method is borrow dollar and sell spot now. That is to

say, you go to a bank and borrow $98.52 today, immediately convert it to yen (9,852yen) in the spot market and deposit it at

the bank. After 3 months, you withdraw 9,951 yen (principal plus accrued interest) and simultaneously repay $100 (principal plus

accrued interest) to the bank with the export receipt. Either way, you fix the yen receipt as of today so there is no

exchange risk. But with the assumptions illustrated above, forward cover yields 10,200 yen and the borrowing method yields only

9,951 yen. Clearly, everyone prefers the first method. That means that the situation is not in equilibrium.

If everyone tries to sell USD forward while no one buys USD

forward, there will be an oversupply of forward dollar and its price will fall. It will fall until forward USD becomes precisely $1=99.51

yen; because at this rate, the first and second method will be equivalent. This is an example of financial arbitrage and LOOP. The

same "commodity" (export receipt after three months' wait) obtained through the forward exchange market and the bank loan

market now bears the same price. Needless to say, actual interest arbitrage occurs instantaneously, not sequentially and slowly.

The CIP condition can be written as follows: (F-S)/S = (i-i*)/(1+i*)

or approximately, (F-S)/S = i - i*

if i* is sufficiently small. This means that F>S if and only if i > i*

F<S if and only if i < i*

In words, if the domestic interest rate is higher than the foreign interest rate, the forward exchange rate (future dollar) must be

higher than the spot exchange rate (today's dollar), and vice versa. This relationship should always hold among high-quality,

low-risk financial instruments under capital mobility.

Testing capital mobility

CIP can be used as a test for capital mobility. Sometimes the

government says capital movement is liberalized but actual transactions are secretly controlled. If CIP holds, we can say that

the country truly has an open capital market. The UK liberalized its capital market externally in 1979. Thereafter, CIP began to hold

(see p.122 of Batiz-Batiz). Japan revised its foreign exchange law in December 1980, and CIP began to hold after that. Since then,

CIP has always held between Japan and the US (handout no.4).

Since virtually all developed countries in North America, EU and

Japan have open capital markets, CIP holds trivially and as a matter of course among key currencies of dollar, euro and yen--it

would be surprising if the situation is otherwise (but not between Russia and China). You can check this with financial news reports

on any day. The following is the data for April 18, 2002 as published in Nihon Keizai Shimbun (Japan Economic Journal,

or Nikkei for short), the most influential Japanese economic newspaper:

CIP between Japan and the US (April 18, 2002) Source: Nikkei, the next day

Bilateral interest rate differential, (i - i*)

-1.7375%

Japanese interest rate, i (CD 3-month)

i = 0.0825%

American interest rate, i* (CD 3-month)

i* = 1.82%

Forward premium/discount on the dollar, (F-S)/S

-1.86%

Gap between (i - i*) and (F-S)/S 0.1225%

While there is a small gap between the interest rate differential and the forward discount, the magnitude is fairly small. Even if CIP

is holding, statistical discrepancy can arise from various reasons: (i) time difference between Tokyo and NY markets (data are not

taken exactly at the same moment); (ii) Japanese and US certificate of deposits (CDs) are not perfectly substitutable due to

different liquidity, tax rules, regulations, etc; and (iii) transaction costs.

There are a few additional remarks on CIP: (1) Don't try to perform CIP yourself. Arbitrage for CIP is

automatic and instantaneous. Leave it to banks and financial

companies. (2) While causality is often mutual in economics, we can say that,

for CIP, main causality runs from the interest rate gap to the forward exchange rate. In other words, F is determined by the

difference between i and i*. (3) Some exchange risks cannot be hedged (or covered).

Unhedgeable exchange risks include the following: (i) Protection against a high or low exchange rate level, in contrast

to protection against change from now to future. No banks will help you even if you complain about the current exchange rate

level.

(ii) Long-term exchange risks. Usually, forward markets beyond 1

year are either nonexistent or extremely thin. (iii) Business risks which are inseparable from exchange risk. If

you are a manufacturing firm, your business carries many risks other than the exchange risk. You don't know whether your

factories will operate smoothly without technical or labor troubles, whether the market will grow, and whether you can beat other

competitors. Because these business uncertainties always exist, you don't know what exchange positions you will have next month,

next year, or beyond. But if you don't know them, you can't go to the bank and hedge them! While fancy financial instruments like

futures, options and swaps are available, exchange risk cannot be eliminated but must be added to the existing business risks.

Technically speaking, this problem arises from the incompleteness of forward commodity contracts. Ronald McKinnon calls this

the Arrow-Debreu dilemma.

How can we explain deviations from CIP?

Academically, the empirical deviations from CIP are always explained as violations to the assumption of free capital flow and

the substitutability of assets from different countries. The possible

explanations include:

1. There may be transaction costs, which introduces a "transaction band" into the CIP equation. Recently, Cody (1990),

Moosa (1996) and Balke and Wohar (1998) studied about the relation between CIP and the transaction costs.

2. There may be possible capital controls, which actually adds costs to the investment in other countries and creates similar

effects of the transaction costs to the CIP equation. 3. There may be difference in tax rates on interest income and

foreign exchange losses/gains in different countries. This

difference contributes to the non-substitutability of investments in different countries and makes investment in a country more

preferable than the other.

5)UNCOVERED INTEREST RATE PARITY {UIP}

What is UIP?

UIP states that if funds flow freely across country boarders and investors are risk neutral, after the adjustment of expected

depreciation, the expected rates of return to substitutable assets denominated in different currencies should be equal. In equation,

it is expressed as the equality between the expected changes in spot exchange rate and the interest differentials of two countries.

Like that of CIP, the underlying mechanism of UIP is interest

arbitrage activities. For example, if domestic interest rate is lower than the expected rate of return on an identical foreign asset,

investors