T7-T7-11

Arbitrage - The purchase of a commodity, including foreign exchange, in one market at one price while simultaneously selling that same currency in another market at a more advantageous price, in order to obtain a risk-free profit on the price differential.

The Arbitrageur is the person who performs the arbitrage.

INTERNATIONAL ARBITRAGEINTERNATIONAL ARBITRAGE

T7-T7-22

TYPES OF ARBITRAGETYPES OF ARBITRAGE

• Locational Arbitrage

• Triangular Arbitrage

• Covered Interest Arbitrage

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LOCATIONAL ARBITRAGELOCATIONAL ARBITRAGE

Locational arbitrage involves taking advantage of differential pricing between locations.

Buy at .67, sell at .68Buy at .67, sell at .68Buy at .67, sell at .68...

A B

B .65 B .68 A .67 A .69

T7-T7-44TRIANGULAR ARBITRAGETRIANGULAR ARBITRAGE

Triangular Arbitrage (aka “three-point” arbitrage) - involves taking advantage of unequal cross rates between two currencies, which is derived from their exchange rates with a third currency.

T7-T7-55 TRIANGULAR ARBITRAGE TRIANGULAR ARBITRAGE EXAMPLEEXAMPLE

London: $/£ = $2.00New York: $/DM = $.40£/DM should be: .40/2.00 = .2 Frankfurt: £/DM = .2 Assume that in London, $/£ is actually = $1.90 (out of line)

• Start with $ and buy £1mil for $1.9mil in London• Buy DM at £/DM = .2 in Frankfurt (£1mil =

DM5mil)• Use the DM5mil to buy $ in New York at $/DM =

$.40 (DM5mil * .40 = $2mil) • Your profit would be $2mil - $1.9mil = $100,000

T7-T7-66 COVERED INTEREST ARBITRAGECOVERED INTEREST ARBITRAGE

• Covered Interest Arbitrage will take place when... • the interest rate differential between two countries... • differs from the corresponding forward premium or

discount on the exchange rate between their currencies

Covered Interest Arbitrage - involves buying or selling assets internationally (i.e., in more than one country), and using the forward market to eliminate exchange rate risk, in order to take advantage of return differentials between the two countries

T7-T7-77 COVERED INTEREST ARBITRAGE COVERED INTEREST ARBITRAGE EXAMPLEEXAMPLE

• Borrow £1mil at 10% (£1.1mil due in 1 year)• Immediately convert the £ to $ and invest the $ at 25% (grows

to $1.25mil)• Simultaneously enter into a forward contract that guarantees

conversion of £ to $ at £/$ = $1.10 • At year end, deliver $1.25mil, and receive £1,136,364

($1.25mil/$1.10)• Pay off the £1.1mil and keep the difference (£36,364 * $1.10 =

$40,000 Profit)

spot £ = $1.001-year forward = $1.10 (i.e., forward premium is 10%)U.S. interest rate = 25%British interest rate = 10% note: the difference in interest rates is 15%, which is > the forward premium

T7-T7-88 INTEREST RATE PARITY (INTEREST RATE PARITY (IRPIRP))

Interest Rate Parity - the theory states: The difference in the national interest rates for securities of similar risk and maturity should be equal to, but opposite in sign to, the forward rate discount or premium for the foreign currency, except for transaction costs.

T7-T7-99 IRP EQUATIONS (1)IRP EQUATIONS (1)

(1) An = (Ah/Sj)*(1+ij)Fj

In words:

End Amt Hm Cur = (Beg Amt Hm Cur/Beg Spot Rate) *(1+Foreign int rate)*(Forward Rate)

An = Ending amount of the home currencyAh = Beginning amount of the home currencySj = The spot rate when the foreign currency was purchasedij = The foreign interest rateFj = The forward rate on the foreign currency

T7-T7-1010 IRP EQUATIONS (2)IRP EQUATIONS (2)

• Since Fj = Sj(1+p), we can restate eq(1) as:

An = (Ah/Sj)*(1+ij)*[Sj(1+p)]

• Simplifying the above we have eq(2):

(2) An = Ah(1+ij)*(1+p)

• In words:

End Amt of home currency = (Beg Amt home currency)*(1 + Foreign int rate) * (1 + forward premium or discount)

T7-T7-1111 IRP EQUATIONS (3)IRP EQUATIONS (3)

The rate of return on an investment is: what you end up with, minus what you started with, divided by what you started with.

rj = (An - Ah)/Ah

Substituting for An in terms of Ah and then simplifying, we have eq(3), which is the return from covered interest arbitrage.

(3) rj = (1+ij)*(1+p) - 1

In words:

return = (1 + foreign int rate)*(1 + forward premium or discount) minus 1

T7-T7-1212 IRP EQUATIONS (4)IRP EQUATIONS (4)

• If Interest Rate Parity exists then...

• The return from covered interest arbitrage...

• should be equal to the rate of return available from investing domestically

• In equation form we would say:

• rj = ih

• In words:

• The return from covered interest arbitrage is equal to the return on a purely domestic investment of equal risk

T7-T7-1313 IRP EQUATIONS (5)IRP EQUATIONS (5)

• rj = ih

• but from eq(3) we know that

rj = (1+ij)*(1+p) - 1

• therefore

(1+ij)*(1+p) - 1 = ih

(1+ij)*(1+p) = (1+ih)

(1+p) = (1+ih)/(1+ij)

T7-T7-1414 IRP EQUATIONS (6)IRP EQUATIONS (6)

(4) p = [(1+ih)/(1+ij)] - 1 (Covered Interest Parity)

In words:

The Forward premium or discount on the foreign currency is equal to (1 + domestic rate) divided by (1 + foreign rate) minus 1.

T7-T7-1515 IRP NUMERICAL EXAMPLE (1)IRP NUMERICAL EXAMPLE (1)

• Because the British rates are higher than the U.S. rates...

• The pound should be selling at a forward discount...

• In order to equalize the returns between the U.S. and Great Britain

• According to eq(4), that discount should be...

[(1+.052)/(1+.075)] - 1 = -2.14%

Spot Rate = 1.00

British Int. Rate = 7.5%

U.S. Int. Rate = 5.2%

T7-T7-1616 IRP NUMERICAL EXAMPLE (2)IRP NUMERICAL EXAMPLE (2)

• if the pound declines in value by 2.14%

• then this will offset the additional British returns

• and the returns to U.S. investors will be the same whether they invest in the U.S. or Great Britain

• Assuming that the spot rate is 1.00...

• Fj = Sj(1+p) = 1.00(1-.0214) = .9786

• 1.075 * .9786 = 1.052

T7-T7-1717 INTEREST RATE PARITYINTEREST RATE PARITY

• in other words, even if you had invested at the higher British rate

• by the time you converted your pounds back into dollars

• your return would have been exactly the same as if you had simply invested in the U.S. in the first place

T7-T7-1818 INTEREST RATE PARITYINTEREST RATE PARITY

(5) p = (Fj - Sj)/Sj ih - ij

A simplified form of the IRP equation:

In words:

The forward Premium or Discount (on the Foreign currency) is approximately equal to the difference between domestic and foreign interest rates.

T7-T7-1919 INTEREST RATE PARITYINTEREST RATE PARITY

Verifying...

-.0214 = (.9786 - 1.00)/1.00 .052 - .075

.052 - .075 = - .0230 -.0214

T7-T7-2020 INTEREST RATE PARITYINTEREST RATE PARITY

Foreign Rate > Domestic Rate Forward Currency Discount

Foreign Rate < Domestic Rate Forward Currency Premium

T7-T7-2121 INTEREST RATE PARITYINTEREST RATE PARITY

IRP Line

Forward

Premium %

ih - if (%)

Covered Arbitrage

possible for domestic

investors

Covered Arbitrage

possible for foreign

investors

Forward

Discount %

45 °

T7-T7-2222 TESTING IRPTESTING IRP

• Regress forward premium (or discount) on the interest rate differential

• p = a0 + a1(ih - if) + e

• Check to see if the slope coefficient, a1, is equal to 1.0 (which should be true if on 45 ° line.

• or if the error term, e, is insignificant (which should also be true if IRP holds.

T7-T7-2323 OTHER FACTORS IMPACTING IRPOTHER FACTORS IMPACTING IRP

• Taxes

• Transactions Costs

• Additional Risks

• Currency Restrictions

• Etc.