5. forecasting exchange rate

7/29/2019 5. Forecasting Exchange Rate

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International BankingProf. Alok Kumar


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WE shall be discussing

Interest Rate Parity

Purchasing Power Parity

The Fisher Effects

Forecasting Exchange Rates

Interest Rate Parity Covered Interest Arbitrage

IRP and Exchange Rate Determination

Reasons for Deviations from IRP


The Fisher Effects



Purchasing Power Parity PPP Deviations and the Real Exchange Rate

Evidence on Purchasing Power Parity

The Fisher Effects




The Fisher Effects Forecasting Exchange Rates




Efficient Market Approach

Fundamental Approach

Technical Approach Performance of the Forecasters





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Interest Rate Parity Defined

Covered Interest Arbitrage

Interest Rate Parity & Exchange RateDetermination

Reasons for Deviations from Interest Rate Parity


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IRP is an arbitrage condition.

If IRP did not hold, then it would be possible foran astute trader to make unlimited amounts ofmoney exploiting the arbitrage opportunity.

Since we dont typically observe persistent

arbitrage conditions, we can safely assume thatIRP holds.


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Interest Rate Parity Carefully Defined

Consider alternative one year investments for $100,000:1. Invest in the U.S. at i$. Future value = $100,000 (1

+ i$)

2. Trade your $ for at the spot rate, invest

$100,000/S$/ in Britain at i while eliminating anyexchange rate risk by selling the future value of theBritish investment forward.

S$/

F$/Future value = $100,000(1 + i)

S$/

F$/(1 + i) = (1 + i$)

Since these investments have the same risk, they must have the same future value(otherwise an arbitrage would exist)


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IRP

Invest thosepounds at i

$1,000

S$/

$1,000

Future Value =

Step 3: repatriatefuture value to the

U.S.A.

Since both of these investments have the same risk, they must have the same future

valueotherwise an arbitrage would exist

Alternative 1:invest $1,000 at i$

$1,000(1 + i$)

Alternative 2:Send your $on a round tripto Britain

Step 2:

$1,000

S$/

(1+ i) F$/

$1,000

S$/

(1+ i)

=

IRP


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The scale of the project is unimportant

(1 + i$)

F$/S$/

(1+ i)=

$1,000

(1 + i$)

$1,000

S$/ (1+ i

) F

$/=


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Interest Rate Parity DefinedFormally,

IRP is sometimes approximatedas

i$i S

F

S

1 + i$1 + i S$/

F$/=


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Forward Premium Its just the interest rate differential implied byforward premium or discount.

For example, suppose the is appreciating from

S($/) = 1.25 toF180($/) = 1.30 The forward premium is given by:

F180($/)S($/)

S($/)

360

180f180,v$ = =

$1.30 $1.25

$1.25 2 = 0.08


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IRP and Covered Interest Arbitrage

If IRP failed to hold, an arbitrage would exist. Itseasiest to see this in the form of an example.

Consider the following set of foreign and domesticinterest rates and spot and forward exchangerates.

Spot exchange rate S($/) = $1.25/

360-day forward rate F360($/) = $1.20/

U.S. discount rate i$ = 7.10%

British discount rate i = 11.56%


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IRP and Covered Interest ArbitrageA trader with $1,000 could invest in the U.S. at 7.1%, inone year his investment will be worth

$1,071 = $1,000 (1+ i$) = $1,000 (1,071)

Alternatively, this trader could1. Exchange $1,000 for 800 at the prevailing spot

rate,

2. Invest 800 for one year at i

= 11,56%; earn892,48.

3. Translate 892,48 back into dollars at the forwardrateF360($/) = $1,20/, the 892,48 will be

exactly $1,071.


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Arbitrage I

Invest 800at i =11.56%$1,000

800

800 =$1,000 $1.25

1

In one year

800 will beworth

892.48 =

800 (1+ i

$1,071 = 892.48 1

F(360)

Step 3:repatriate to theU.S.A. at F360($/)

= $1.20/Alternative 1:invest

$1,000 at7.1%FV = $1,071

Alternative 2:buy pounds

Step 2:

892.48

$1,071


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Interest Rate Parity& Exchange Rate DeterminationAccording to IRP only one 360-day forward rate,F360($/), can exist. It must be the case that

F360($/) = $1.20/

Why?

IfF360($/) $1.20/, an astute trader couldmake money with one of the following strategies:


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Arbitrage Strategy I

IfF360($/) > $1.20/

i. Borrow $1,000 at t= 0 at i$ = 7.1%.

ii. Exchange $1,000 for 800 at the prevailing spot

rate, (note that 800 = $1,000$1.25/) invest800 at 11.56% (i) for one year to achieve892.48

iii. Translate 892.48 back into dollars, if

F360($/) > $1.20/, then 892.48 will be morethan enough to repay your debt of $1,071.


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Arbitrage I

Invest 800at i =11.56%$1,000

800

800 =$1,000 $1.25

1

In one year800 will be

worth892.48 =

800 (1+ i)

$1,071 < 892.48 1

F(360)

Step 4:repatriate to the

U.S.A.

If F(360) > $1.20/ , 892.48 will be more than enough to

repay your dollar obligation of $1,071. The excess is your

Step 1:borrow $1,000

Step 2:buypounds

Step 3:

Step 5: Repayyour dollarloan with$1,071.

892.48

Morethan $1,071


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Arbitrage Strategy IIIfF360($/) < $1.20/i. Borrow 800 at t= 0 at i= 11.56% .

ii. Exchange 800 for $1,000 at the prevailing spotrate, invest $1,000 at 7.1% for one year to achieve$1,071.

iii. Translate $1,071 back into pounds, if

F360($/) < $1.20/, then $1,071 will be morethan enough to repay your debt of 892.48.

St 2


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Arbitrage II

$1,000

800

$1,000 =

800 1

$1.25

In one year

$1,000 will beworth $1,071 > 892.48

1F(360)

Step 4:repatriate to

the U.K.

If F(360) < $1.20/ , $1,071 will be more than enough to

repay your dollar obligation of 892.48. Keep the rest as

Step 1:borrow 800

Step 2:buy dollars

Invest

$1,000 at i$

Step 3:Step 5: Repay

your poundloan with892.48 .

$1,071

Morethan

892.48


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IRP and Hedging Currency RiskYou are a U.S. importer of British woolens and have justordered nextyears inventory. Payment of 100M is due inone year.

IRP implies that there are two ways that you fix the cash outflow

to a certain U.S. dollar amount:a) Put yourself in a position that delivers 100M in one yeara

long forward contract on the pound.You will pay (100M)(1.2/) = $120M in one year.

b) Form a forward market hedge as shown below.

Spot exchange rate S($/) = $1.25/

360-day forward rate F360($/) = $1.20/U.S. discount rate i$ = 7.10%

British discount rate i = 11.56%


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IRP and a Forward Market Hedge

To form a forward market hedge:

Borrow $112.05 million in the U.S. (in one yearyou will owe $120 million).

Translate $112.05 million into pounds at the spotrateS($/) = $1.25/ to receive 89.64 million.

Invest 89.64 million in the UK at i = 11.56% forone year.

In one year your investment will be worth 100millionexactly enough to pay your supplier.


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Forward Market HedgeWhere do the numbers come from? We owe our

supplier 100 million in one yearso we know thatwe need to have an investment with a future value of100 million. Since i = 11.56% we need to invest

89.64 million at the start of the year.

How many dollars will it take to acquire 89.64 million at the start of the year ifS($/) = $1.25/?

89.64 =100

1.1156

$112.05 = 89.64 $1.00

1.25


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Reasons for Deviations from IRP Transactions Costs The interest rate available to an arbitrageur for

borrowing, ib,may exceed the rate he can lend at, il.

There may be bid-ask spreads to overcome,Fb/Sa

5. forecasting exchange rate

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