financial markets in the open economy - the interest rate...

Financial markets in the open economy - the interest rate parity.

Exchange rates in the short run.

Dr hab. Joanna Siwińska-Gorzelak

Foreign Exchange Markets

• The set of markets where foreign currencies and other assets are exchanged for domestic ones – Institutions buy and sell deposits of currencies or other

assets for investment purposes.

Foreign Exchange Markets (cont.)

The main participants:

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.

Spot Rates and Forward Rates

• Spot rates are exchange rates for currency exchanges “on the spot,” or when trading is executed in the present.

• 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.

The Demand of Currency Deposits

• The exchage 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?

• Factors that influence the return on assets determine the demand of those assets.

The Demand of Currency Deposits (cont.)

• 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.


• 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.


• 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.


• 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 rate of return for a deposit in domestic currency is the annual 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.


• 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 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, all investors should be willing to dollar deposits and none should be willing to hold euro deposits.


• 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 Demand of Currency Deposits

• The difference in the rate of return on dollar deposits and euro deposits is

i$ = (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) dollar 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.


• Interest parity says:

i$ = i€ + (Ee$/€ – E$/€)/E$/€

• Why should this condition hold? Suppose it didn’t. – Suppose i$ > i€ + (Ee

$/€ – E$/€)/E$/€

– Then no investor would want to hold euro deposits, driving down the demand and price of euros.

– Then all investors would want to hold dollar deposits, driving up the demand and price of dollars.

– The dollar would appreciate and the euro would depreciate, increasing the right side until equality was achieved:

i$ > i€ + (Ee$/€ – E$/€)/E$/€

Uncovered interest rate parity

• Free movement of capital

• UK-based investor chooses between deposit in UK (in £) or in USA (in $)

• Horizon 1-year

• Jan 1st (now), payoffs compared as of 31st December.

Uncovered interest parity

Convert to foreign

currency,

exchange rate: E

Liquidate deposit and

convert back to Home

currency using Ee

Home strategy Foreign

strategy

E

K

)1( iE

K

)1( iE

KE e

Initial

funds

)1( iK Funds after

1 year

K=100 £

If (expected) payoff from depositing in UK < (expected) payoff from

depositing in USA, then risk-neutral investors will rush to deposit in US,

and vice versa when (expected) payoff from depositing in UK >

(expected) payoff from depositing in USA.

This will change the current E

Conclusion (UIRP): if investors risk neutral, (expected) payoff from

depositing at Home and abroad must yield the same return

(denominated in the same currency)



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( *

EE e /

E

E

i

i e

)1(

)1(*

UIRP: A simplification

Redefine

where

– expected rate of depreciation of the domestic currency.

Rewriting:

EE e /

eee

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.

Interpretation: 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.

eEii *


Covered interest rate parity: Setting

Assumptions as for UIRP, but with addition:

• Forwards (or futures)

• Forward purchase (sale) of $ gives right to purchase (sell) $ with (for) £ on Dec 31st at rate specified on Jan 1st

• Forward purchase (sale) of $ = forward (purchase) sale of £

Covered interest rate parity

Using the forward exchange rate F in place of

Defining f as the forward premium)

and ignoring the final term (2nd order of smallness):

– the normal formulation of the CIRP hypothesis.

eS

SFii /)1()1( *

fSF 1/

fifii **1)1(

fii *

Note: UIRP vs. CIRP

• Both CIRP, UIRP are approximations – but will be close approximations unless interest rates (inflation rates) are very high.

• CIRP does not involve expectations or risk (forward contract eliminates uncertainty from payoff), so it applies whether investors are risk averse or risk neutral,

• whereas UIRP involves expectations (hence, risk of expectation error, so it only applies if investors are risk neutral. If they are risk averse, a risk premium will drive a wedge between the payoff to depositing at home or abroad.

The Relation between the Current HOME/FOREIGN Exchange Rate and the

Expected Return on FOREIGN Deposits (note: increase in E denotes a depreciation of Home

currency)

E - today’s

Home/Foreign

exchange rate

Expected return of foreign

deposits , holding i* and future E

constant

Determination of the Equilibrium Dollar/Euro Exchange Rate’

i i$


• The effects of changing interest rates:

– an increase in the interest rate paid on deposits denominated in a particular currency will increase the rate of return on those deposits.

– This leads to an appreciation of the currency.

– Higher interest rates on dollar-denominated assets cause the dollar to appreciate.

– Higher interest rates on euro-denominated assets cause the dollar to depreciate.

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).

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

i i2

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

Interest parity - conclusions

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

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

Purchasing power parity revisited

eri

which is the Fisher equation.

Note: r is observable, but πe is not, so r = i − π e is unobservable, though instead we often consider r = i − π, where π is the most recent inflation rate.

The approximation works well if inflation is expected to remain at its current level.

PPP and the interest parity

Fisher equation for the foreign country

Combine to get :

With risk neutrality, the nominal interest rate differential is equal to the expected rate of depreciation (UIRP), so:

e

ri ***

)()( ** eerrE

E

)()( *** eerrii

In the absence of barriers to cross border capital movements (recall the classical model):

Therefore:

This is the well known relative PPP!

*rr

eees *

PPP and the interest parity

UIRP, Fisher and PPP

• Any 2 parity relationships implies the 3rd:

Fisher + UIRP PPP

PPP + UIRP Fisher

• Reminder: this presupposes –risk neutral investors

–free movement of goods and capital

–no transaction costs.

Carry trade

• From Investopedia:

• „An investment strategy; the purpose is to make a profit over time from differences in interest rates between different currencies.

• To do this trade, one borrows currency with a low interest rate, converts it another currency, with a higher interest rate.

Carry trade

• Borrow 1 £ (short position); if the interest rate is 1% (so after 1 year, you need to give back 1,01 £

• Convert to USD – let’s say the exch rate is 2USD/1 £

• Create a USD deposit (long position)

• At the very beginning, the short and long positions offset each other

• After 1 year, you have 2 (1+R*) USD

• Convert it into pounds

• If you have more than 1,01 £ you have made a profit!

• Your short and long position may not match – a risk

Uncovered interest arbitrage with borrowing

UK strategy US strategy

12-month interest rate 5% 6%

Exchange rate, Jan 1st 0,5 £/USD

Position taken, Jan 1st Short: 1£ Short: 1£ Long: 2USD

31 December

Liquidate: 0,6 £/USD

2,12 USD Convert to £: 1,27£

Repay (close position) 1,05£ 1,05£

Profit 0

£ 0,22

Extensions to UIRP

• Should apply at all horizons

• Should apply to all assets, e.g. corporate debt, equities, mortgages, etc. – BUT:

• When assets are risky even in their own currencies (they all are!), there has to be a risk premium in addition to the currency risk premium.

financial markets in the open economy - the interest rate...

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