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IFM LBSIM

COVERED INTEREST ARBITRAGES ---PROF DEEPAK TANDON

CIA is the movement of short term funds between countries to take advantage of

interest differentials with the exchange risk covered by the forward contracts .

When investors purchase the currency of a foreign country to take advantage of

the higher interest rates abroad , they must also consider any losses or gains .

Such gains or losses might occur due to fluctuations in the value of the foreign

currency prior to the maturity of their investment . Generally , the investors cover

against such partial losses by contracting for the future sale or purchase of a

foreign currency in the forward market . Their actions , aimed at profits from the

interest differentials between countries , lead , to an equilibrium , to a condition of

so called interest parity

IRP theory = Any exchange gains / losses incurred by simultaneous purchase / sale

in spot and forward markets are offset by interest rate differential on similarassets . Under these conditions , there is no incentive for capital to move in either

direction bcos the effective returns on foreign and domestic assets have been

equalized We ignore the Transaction costs for simplicity

Forward rate reflect the differential over spot rates ,=Difference of Intt rates in

Home & Foreign Country

Borrow at one - converting in another currency = proceeds deposited in 2nd

currency for certain period over during which forward rate differential is not

equivalent to interest rate differential .Deal is closed after arbitrage period, by

reconverting the foreign currency proceeds and earning the difference as profit

Net gain = Interest rate differential discount / premium on sale of foreign currency

in the forward market . (IRDiffential>Forward Discount }

LHS =(1+rh)

RHS =F/S *(1+rf) LHS is not = RHS ---- Arbitrage exists

If LHS

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If LHS > RHS ,one would borrow , foreign currency , convert receipts to

domestic currency at a prevailing rate ( Spot ), invest in domestic currency

denominated securities ( as domestic securities carry higher interest ) . At the

same time he would cover his principal and interest from this investment at

the forward rate . At maturity , he would convert the proceeds of the

domestic investment at the prefixed domestic forward rate and payoff theforeign liability . The difference between receipts and payments serve as

profit to customer .

EXAMPLE

Assume that currently , the spot rate is $1.50/Pd Stg and 3 MF is $1.52/Pd Stg . The

3 month Intt Rate is 8.00%p.a in US and 5.8% p.a in UK .Assumethat ewe

canborrow as much as $ 15,00,000 or Pd Stg 10,00,000. Rh=2.0% anfrf=1.45%

IRP

(1+rh)=F/sX(1+rf)

1.02($return ) is not equal to RHS (1.0145) ( 1.52/1.50) = 1.0280 PD Return

Since RHS >LHS We invest in Pound Stg

Arbitrage Process

STEP 1 : Borrow $15,00,000, Repayment will be 15,30,000 @2%

STEP 2 : Buy Pd Stg 10,00,000spot using $ 15,00,000

STEP 3 : Invest Pd Stg 10,00,000at pd interest rate maturity value Pd Stg

10,14,500 {1.45%}

STEP 4 : Sell Pd Stg 10,14,500 Forward for $ 15,42,040 {1PD Stg=$1.52}

Arbitrage profit will be

$ 15,42,040 -15,30,000=$ 12,040

Let us now examine that the Money Market and Forex Markets change post

arbitrage . Following arbitrage , Dollar rate will rise, ( as more $ are borrowed ) andthe Pound sterling rate will fall ( as there will be more inflows ), the spot rate will

rise ( as more pounds are bought in Spot market ) the forward exchange rate will

fall , because of more pounds being sold in the forward market . These adjustments

will continue until IRP is established

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ATTEMPT QUESTION

The annual interest rate in US is 5% and 8% in UK , The spot rate is Pd /$ =1.50 and

Forward exchange rate , with One year maturity is Pd /$ =1.48 . In view of the fact

that the arbitrager can borrow $ 1000000 at the current spot rate , what would be

the arbitrageur profit / Loss ?

HINT LHS not equal to RHS - arbitrage there

1.05 not equal 0.987X(1.08)=1.0656($return)

LHS Lower , borrowing in Dollars Converted in Pd Stg and invested

Borrowing = 1000000 at rate 5% in 12 M ==1.05x 1000000=1050000

$ 1000000 converted in Pd Stg at spot rate =Pd 666667

Deposit this at 12 m-------Pd Stg 720000 Convert this back in $ = $ 1065600

Our Net Arbitrage profit = $ 1065600 1050000=$15600 ANS

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