Foreign exchange market and the interest rate parity.

Exchange rates in the short run.

Dr hab. Gabriela GrotkowskaDr hab. Joanna Siwińska-Gorzelak

Agenda for today: interest rate parity condition

• Short introduction to the foreign exchange market

• A basic SHORT RUN model for explaining exchange rate fluctuations

• Foreign exchange market and money market

• Risk premium and foreign exchange rate

Foreign Exchange Markets

• The set of markets where currencies are exchanged

• Foreign currency includes foreign coins, banknotes, deposits at foreign banks and others foreign liquid, short-term financial instruments (what does short-term mean?)

• The primary purpose of this market is to permit transfer of purchasing power denominated in one currency to another. For example, a Japanese exporter sells automobiles to a U.S. dealer for dollars, and a U.S. manufacturer sells instruments to a Japanese Company for yen. The U.S. Company will like to receive payment in dollar, while the Japanese exporter will want yen.

• However, nowadays over 90% of the total volume of the transactions is represented by inter-bank transactions and the remaining 10% by transactions between banks and their non-bank customers

Exchange rate quotations

• Exchange rate quotations can be quoted in two ways

• Direct quotation is when the one unit of foreign currency is expressed in terms of domestic currency.

• Similarly, the indirect quotation is when one unit of domestic currency us expressed in terms of foreign currency.

• Appreciation versus depreciation of a currency

Exchange rate determination

• Where does foreign exchange come from?

• Role of exchange rate regime (fixed regime versus floating regime)

Exchange rate regimes• An exchange rate regime is the way a monetary authority of a

country or currency union manages the currency in relation to other currencies and the foreign exchange market.

• There are two major regime types:

– fixed (or pegged) exchange rate regimes, where the currency is tied to another currency, mostly reserve currencies such as the U.S. dollar or the euro or the British Pound Sterling or a basket of currencies, or

– floating (or flexible) exchange rate regimes, where the foreign exchange market determines changes of the exchange rate.

• There are also intermediate exchange rate regimes that combine elements of the other regimes.

• For the moment, let’s assume that we are analyzing an economy, where foreign exchange rate is determined by the market.

Participants of the Foreign Exchange Markets

The main participants (by type of institution):

1. Commercial banks and other depository institutions: transactions involve buying/selling of deposits in different currencies for investment purposes.

2. Non-bank financial institutions (mutual funds, hedge funds, securities firms, insurance companies, pension funds) may buy/sell foreign assets for investment.

3. Non-financial businesses conduct foreign currency transactions to buy/sell goods, services and assets.

4. Central banks: conduct official international reserves transactions.

Participants of the Foreign Exchange Markets: alternative approach

The main participants (by function):

1. Individual and corporate clients

2. Currency dealers

3. Currency brokers

4. Arbitrators (speculators)

5. Central banks and state treasures

Spot Rates and Forward Rates

• Spot rates are exchange rates for currency exchanges “on the spot,” or when trading is executed in the present (48-hour rule).

• Forward rates are exchange rates for currency exchanges that will occur at a future (“forward”) date.

– Forward dates are typically 30, 90, 180, or 360 days in the future.

– Rates are negotiated between two parties in the present, but the exchange occurs in the future.

– Forward versus futures transactions

– Options

A size of the Foreign Exchange Markets

The Demand of Currency Deposits

• The exchange rate is determined by the demand and supply of currency

• What influences the demand of (willingness to buy) deposits denominated in domestic or foreign currency?

• A very powerful determinant – the desire to make a profit. In general - factors that influence the return on assets determine the demand of those assets.

Nominal versus real rate of return

• Rate of return: the percentage change in value that an asset offers during a time period.

– The annual return for $100 savings deposit with an interest rate of 2% is $100 x 1.02 = $102, so that the rate of return = ($102 – $100)/$100 = 2%.

• Real rate of return: inflation-adjusted rate of return,

– which represents the additional amount of goods & services that can be purchased with earnings from the asset.

– The real rate of return for the above savings deposit when inflation is 1.5% is 2% – 1.5% = 0.5%. After accounting for the rise in the prices of goods and services, the asset can purchase 0.5% more goods and services after 1 year.

The Demand of Currency Deposits (cont.)

• If prices are fixed, the inflation rate is 0% and (nominal) rates of return = real rates of return.

• Because trading of deposits in different currencies occurs on a daily basis, we often assume that general prices do not change from day to day.

• Hence our assumption: prices are fixed - a reasonable assumption to make for the short run.

Rate of return: the role of currency

• Let’s consider a Polish investor• The rate of return on a PLN-denominated bond bearing 5%

p.a. (per annum) the rate of return was 5% • The rate of return on a painting purchased for 10 thousand

PLN, which a year later was resold for 12 thousand PLN (12 000-10 000)/10 000 = 0.2 the rate of return was 20%

• A painting bought in 2018 for EUR 300,000 at the exchange rate 3.96 PLN / EUR and sold a year later for 350.000 EUR at the exchange rate 3.55 PLN / EUR.

• (350 000 – 300 000)/300 000 = 0.1667• (1 242 500- 1 188 000)/1 188 000 = 0.0459• The return on investment calculated in EUR was 16.7%,

while in PLN only 4.6%! EXCHANGE RATE MATTERS!

The Demand of Currency Deposits: Risk and liquidity

• Naturally, the rate of return is not the only factor that matters

• Risk of holding assets also influences decisions about whether to buy them.

• Liquidity of an asset, or ease of using the asset to buy goods and services, also influences the willingness to buy assets.

• We will assume that risk and liquidity of currency deposits in foreign exchange markets are essentially the same, regardless of their currency denomination.

– Risk and liquidity are only of secondary importance when deciding to buy or sell currency deposits.

– Importers and exporters may be concerned about risk and liquidity, but they make up a small fraction of the market.

The Demand of Currency Deposits

• We therefore say that investors are primarily concerned about the rates of return on currency deposits.

• Rates of return that investors expect to earn are determined by:

– interest rates that the assets will earn

– expectations about appreciation or depreciation

The Demand of Currency Deposits (cont.)

• The rate of return for a deposit in domestic currency is theannual interest rate that the deposit earns.

• To compare the rate of return on a deposit in domestic currency with one in foreign currency, consider– the interest rate for the foreign currency deposit

– the expected rate of appreciation or depreciation of the foreign currency relative to the domestic currency during that time.

The Demand of Currency Deposits (cont.)

• Suppose the interest rate on a dollar deposit is 2%.

• Suppose the interest rate on a euro deposit is 4%.

• Does a euro deposit yield a higher expected rate of return?

– Suppose today the exchange rate is $1/€1, and the expected rate one year in the future is $0.97/€1.

– $100 can be exchanged today for €100.

– These €100 will yield €104 after one year.

– These €104 are expected to be worth $0.97/€1 x €104 = $100.88 in one year.

The Demand of Currency Deposits (cont.)

• The rate of return in terms of dollars from investing in euro deposits is ($100.88 – $100)/$100 = 0.88%.

• Let’s compare this rate of return with the rate of return from a dollar deposit.– The rate of return is simply the interest rate.

– After 1 year the $100 is expected to yield $102: ($102 – $100)/$100 = 2%

• The euro deposit has a lower expected rate of return: thus, allinvestors should be willing to dollar deposits and none should be willing to hold euro deposits.

The Demand of Currency Deposits (cont.)

• Note that the expected rate of change of the value of euro was ($0.97 – $1)/$1 = –0.03 = –3% (depreciation of the euro)

• We simplify the analysis by saying that the dollar rate of return on euro deposits approximately equals

– the interest rate on euro deposits

– plus the expected rate of change of the value of euro deposits

– 4% + –3% = 1% ≈ 0.88%

– R€ + (Ee$/€ – E$/€)/E$/€

The rate of return – once again

Convert to foreign

currency,

exchange rate: E

Liquidate deposit and

convert back to Home

currency using Ee

Home strategyForeign

strategy

E

K

)1( iE

K

)1( iE

KE e

Initial

funds

)1( iK Funds after

1 year

K=100 $

The Demand of Currency Deposits

• Hence, we compare:

i$ and (i€ + (Ee$/€ – E$/€)/E$/€ ) where:

i$ i€ (Ee$/€ – E$/€)/E$/€

expected rate

of return =

interest rate

on dollar

(HOME)

deposits

interest rate

on euro

(FOREIGN)

deposits

expected rate of return on euro (FOREIGN)

deposits

expected

exchange rate

current

exchange rate

expected rate of

appreciation of the euro

Model of Foreign Exchange Markets

• We use the – demand of (rate of return on) home currency denominated deposits

– and the demand of (rate of return on) foreign currency denominated deposits

to construct a model of foreign exchange markets.

• This model is in equilibrium when deposits of all currencies offer the same expected rate of return: interest parity.– Interest parity implies that deposits in all currencies are equally

desirable assets.

– Interest parity implies that arbitrage in the foreign exchange market is not possible.

Uncovered interest rate parity (UIRP)

where

i – Home’s interest rate

i* – Foreign interest rate

– ratio of expected exchange rate to actual rate at the time of the decision

Alternatively:

i.e. i > i* when Ee >E or domestic interest rate is higher than foreign interest rate when domestic currency is expected to depreciate.

EEii e /)1()1( *

EEe /

E

E

i

i e

)1(

)1(*

UIRP: A simplification

Redefine

where

– expected rate of depreciation of the domestic currency.

Rewriting:

EEe /

e

ee

e EE

EE

E

EEEEE

11/

eE

)1)(1()1( * eEii ee EiEi **1

Unless the rate of currency depreciation is very high, the final term can be

ignored, so:

which is the approximate form of the uncovered interest rate parity

(UIRP) condition.

In equilibrium, domestic interest rate is higher (lower) than the foreign

interest rate by the expected rate of depreciation (appreciation) of the

domestic currency, so as to compensate holders of the currency for their

capital loss (gain) on the exchange rate.

E

EEii

e *

Uncovered interest rate parity

Impact of the current exchange rate on the expected rate of return

• Let's assume that the expected dollar exchange rate for the year is 3.10 PLN / USD

• The American annual interest rate is 3% and the domestic(Polish) interest rate 6%

• How will the expected rate of return on dollar deposits change depending on the current dollar exchange rate?

27

E i i* (Ee -E)/E i* + (E

e -E)/E

2.86 6% 3% 8.40% 11.40%

2.91 6% 3% 6.54% 9.54%

2.96 6% 3% 4.74% 7.74%

3.01 6% 3% 3.00% 6.00%

3.06 6% 3% 1.32% 4.32%

3.11 6% 3% -0.31% 2.69%

3.16 6% 3% -1.89% 1.11%

3.21 6% 3% -3.42% -0.42%

Determination of the Equilibrium Dollar/Euro Exchange Rate’

ii$

Effect of a Rise in the Dollar Interest Rate

i1 i2

Effect of a Rise in the Euro Interest Rate

i$

The Effect of an Expected Appreciation of the Euro

• If people expect the euro to appreciate in the future, then euro-denominated assets will pay in valuable euros, so that these future euros will be able to buy many dollars and many dollar-denominated goods.– The expected rate of return on euros therefore increases.

– An expected appreciation of a currency leads to an actual appreciation (a self-fulfilling prophecy).

– An expected depreciation of a currency leads to an actual depreciation (a self-fulfilling prophecy).

Where does interest rate come from?

Simultaneous Equilibrium in the

Money Market and the Foreign Exchange

Market

i$

Money Market/Exchange Rate Linkages

Effect on the Dollar/Euro Exchange Rate and Dollar

Interest Rate of an Increase in the U.S. Money Supply

ii2 i1

Changes in the Domestic Money Supply

• An increase in a country’s money supply causes interest rates to fall, rates of return on domestic currency deposits to fall, and the domestic currency to depreciate.

• A decrease in a country’s money supply causes interest rates to rise, rates of return on domestic currency deposits to rise, and the domestic currency to appreciate.

Changes in the Foreign Money Supply

• How would a change in the supply of euros affect the U.S. money market and foreign exchange markets?

• An increase in the supply of euros causes a fall in the euro interest rate and a depreciation of the euro (an appreciation of the dollar).

• A decrease in the supply of euros causes an appreciation of the euro (a depreciation of the dollar).

Effect of an Increase in the European Money Supply on the

Dollar/Euro Exchange Rate

i1

Covered interest rate parity

• Using the forward exchange rate F in place of expected future E and

• Defining f as the forward premium or discount

• The covered interest rate parity becomes

ef

fE

EF

)(

fii *

Forward premium (discount)

• Forward premium (discount) is the proportion by which a country’s forward value of the currency exceeds (falls below) the spot rate

• Assume that $ 1=PLN 4 (or 1 PLN=0,25 $) is the 12 month forward rate prevailing at the start of the year, when at the same time, the spot rate is $ 1=PLN 3.80 (1PLN=0,2631 $)

• It follows that a forward premium on $ is:

f= (4PLN-3.80PLN)/3.80 = 5,263%

It follows that a forward discount on PLN is:

f= (0,25$ -0,2631$)/0,2631$ = -5%

Risk premium and interest parity

• If domestic and foreign assets are not perfect substitutes, one might be considered more risky than the other

• The interest parity needs to be modified.

• Assume that investors perceive home’s assets to be more risky, then:

E

EEii

e

*

Risk premium and interest parity

• The risk premium compensates investors for increased risk

• Note that any change in perceived risk will change the equilibrium exchange rate

• Ceteris paribus, an increase in risk of the Home economy, will make current E go up (Home currency depreciates)

• Safe-haven currencies are currencies that tend to retain or increase in value during times of uncertainty and market instability (US Dollar(USD); Euro (EUR); Japanese Yen (JPY) Swiss Franc (CHF)

Interest parity in the short run- conclusions

• Shows how changes in the money market and the interest rate will affect exchange rate in the shortrun

• Shows the relationship between nominal interest rate differentials and expected changes in exchange rates

• Higher domestic nominal interest rate, compared to the foreign i* implies that domestic exchange rate is expected to depreciate (E<Ee)

• In case of a covered interest rate parity we may say, that i>i* implies a forward discount of domestic currency where a