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Lecture Covered Interest Rate Parity

Learning Objectives

Examine how Covered Interest Rate Parity (CIRP) contributes to exchange rate determination

Be able to examine CIPR conditions empirically

without and with transaction costs

Illustrate how arbitrage opportunities

may exist and be exploited

Reading: Madura and Fox, Ch 7

A spot exchange rate, S

quoted for immediate delivery of the purchased currency, or

the currency is delivered “on the spot” (usually within two working days).

A forward exchange rate, F

The rate agreed today for delivery of the currency at a future date.

Typically the future date is 30, 90, 180 days and one year ahead.

A currency forward contract , is an agreement between two parties to exchange currencies at pre-specified price (ie, a forward exchange rate) that will be settled in a future date (i.e. to lock in an exchange rate for a period of time.)

Spot and Forward Exchange Rates

The Rationale of CIP

Say that the spot and forward, exchange rates between the euro and the

dollar are given by and respectively and that the one-month

interest rates on an annual basis are r€ (rh )and r$ respectively.

Suppose now that that you are a French investor and you have two

investment choices:

α) deposits in € and

b) deposits in $.

For the second option you can use the forward exchange rate for eliminating

exchange rate risk

The Rationale of CIP

Explain what your expectations, actions, and trades/exchanges will be today

and in one month from today

Note: We can use the following “time line” to keep track of the above.

Today (t=0)

+1 month (t=1)

The Rationale of CIP

1st choice: Deposit in €

Deposit € A Receive € (1+ r€ )A

Total flows: €(1+ r€ )A

2nd choice: Deposit in $

Convert € A into $ A/S€/$

Deposit $ A/S €/$ Receive $ (1+ r$ )A/S €/$

Agreement to sell Forward Receive €(1+ r$ )A/S €/$ * F €/$

in one month to convert $ back to € (with certainty in one month)

Total flows: €(1+ r$ )A/S €/$ * F €/$

Today (t=0)

+1 month (t=1)

The Rationale of CIP

The two investments must have the same future value (in other words, the investor will be indifferent between the two). That is

€(1+ r€ )A = € (1+ r$ )A /S €/$ * F €/$

Otherwise arbitrage exists.

After some manipulation the above gives

(1+ r€ )= (1+ r$ ) * F €/$ /S €/$

Re-arranging

F €/$ /S €/$ = (1+ r€ ) / (1+ r$ )

Covered Interest Rate Parity

Define F0,1 the forward exchange rate

-- contracted now and to be delivered in the next period (e.g., in 30 days);

Define S0 the currently prevailing spot exchange rate;

rh is the interest rate in the home country, and;

rf is the interest rate in the foreign country during the period

The following relationship (parity)

between the spot exchange rate, forward exchange rate, and the interest rates in the two countries must hold

to eliminate any arbitrage opportunities:

(1)

Covered Interest Rate Parity

We deduct 1 from both sides of Eq (1)

And obtain:

(2)

Covered Interest Rate Parity

Therefore, CIRP states

The forward premium equals

the difference between the two interest rates over the period 0 - 1.

CIRP is sometimes approximated as:

(3)

Covered Interest Rate Parity

If this does not hold then

There are opportunities for profit

Might represent diagrammatically

Graphic Illustration of CIP

rh – rf

Remain investing in home currency

Convert to foreign currency/enter into forward contract, invest in foreign currency, convert back with forward

No difference

f – s > rh – rf

Covered Interest Rate Parity Examples

Examine the following exchange rate and interest rate figures

Note: given a direct quotation, $ is the home currency

The $/€ spot rate	S0 = 1.1237
One year $/€ forward rate	F0,360 = 1.1128
US discount rate (home country)	2.50% pa
Euroland discount rate	3.75% pa

Covered Interest Rate Parity Examples

Questions

Part 1:

--- Do arbitrage opportunities exist?

Part 2:

--- If so, how would you invest to exploit the arbitrage

opportunities?

Covered Interest Rate Parity Examples

Answer to part 1:

The forward premium

The interest rate differential (exact) (rh - rf)/(1 + rf) = -0.01205

Conclusion:

As forward premium  interest rate differential, arbitrage opportunities exist

As forward premium > interest rate differential, it would be more profitable to invest in €.

Covered Interest Rate Parity Examples

Answer to part 2:

1. If you have $1,000,000, convert it to €:

$1,000,000 / $1.1237/€ = €889917.2;

2. Enter into a forward contract to sell €, size decided below (€923289.1)

3. Invest in € for one year: €889917.2 (1+0.0375)=€923289.1

4. Convert € to $ with forward: €923289.1$1.1128/€ = $1,027,436

Note that

If you invest in $ for one year: $1,000,000(1+0.025) = $1,025,000

The arbitrage profit is $1,027,436 - $1,025,000 = $2,436

- If you have €1,000,000, you remain investing in €

Exercise

Suppose the investor does not use his own funds and borrows $1,000,000 at the interest rate of 2.0% (r$ ), how does he exploit the arbitrage opportunities?

S0 = $1.1237/ €, F0,360 = $1.1128/ €, r€ = 3.75% pa

Hint:

Step1: Borrow $1,000,000, convert it to € at $1.1237/€

Step 2: Enter into a forward contract to sell € at F = $1.1128/ €,

Step 3: Invest in € for one year

Step 4: Convert € to $ with forward at $1.1128/ €

Step 5: Repay the lender (principle + interest):

Calculate the arbitrage profit

Covered Interest Rate Parity and Arbitrage

Can interest rate parity be restored as a result of the above

transactions? Yes

The dollar interest rate will rise, the euro interest rate will fall.

As funds are withdrawn from $ and placed in € accounts

The spot exchange rate (dollars per euro) will rise and the forward rate will fall. These adjustments will continue until interest rate parity is restored.

Covered Interest Rate Parity; Transaction Costs and Arbitrage

Covered interest arbitrage involves transaction costs

Transaction costs reduce arbitrage opportunities

or prevent arbitrage opportunities from materialising.

These transaction costs include:

Bid-ask spreads in exchange rates

In the case of using borrowed funds,

Different lending and borrowing rates

CIRP; Transaction Costs and Arbitrage

Example

In the previous case,

In the US

if the loan rate is 3.00% pa

and the deposit rate is 2.00% pa,

and a zero bid-ask spread is still assumed for exchange rates,

Is it possible to make arbitrage profit using borrowed funds?

The future value of your $ borrowing in one year

$1,000,000(1+0.03) = $1,030,000

This figure is > $1,027,436 obtained from your activity of investing in €

So, you will not profit following this procedure

Though, you will get a higher return from investing in € if you have $ funds of your own

Covered Interest Rate Parity in Practice

Does covered interest rate parity hold?

Prior to 2007, documented violations of interest rate parity were very rare

Frequency, size and duration of apparent arbitrage opportunities do increase with market volatility

Why Deviations from Interest Rate Parity May Seem to Exist

Too good to be true?

Default risks – risk that one of the counterparties may fail to honor its contract

Exchange controls

Limitations

Taxes

Political risk

A crisis in a country could cause its government to restrict any exchange of the local currency for other currencies.

Investors may also perceive a higher default risk on foreign investments.

Why is the € interest rate for your assignment that for Germany and not Greece?

Covered Interest Parity Deviations During the Financial Crisis

Have seen that we might expect returns to be the same

Irrespective of where funds are invested

We can examine this using Covered Interest Rate Parity

Using forward contracts

Should not be possible to make arbitrage profits

Have seen how deviations from CIRP

Result in a movement of funds

So that the markets move back towards balance

Next time

Uncovered interest rate parity

Conclusion

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