Interest Parity - Fall 2008

8/3/2019 Interest Parity - Fall 2008

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COVERED INTEREST PARITYAND

COVERED INTERESTARBITRAGE


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ASSUME (for now)

Perfect Capital Markets, which means:

1) no risk of default on loans

2) borrowing and lending rates are equal

(i.e., financial intermediaries fees are negligible)


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Assume there are:

1) Domestic bonds (rate of return = iUS)

2) Foreign bonds (rate of return = iFOR)

Given the assumption of perfect capital markets, there is zerodoubt that these bonds will pay their promised amount. Theclosest real-world assets that approach this risklesscharacteristic are government bonds (by governments that

issue their own currency).


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There are two ways to that individuals can invest $s thatwill earn a riskless return in $s:

1) Use $s to buy the (riskless) domestic bonds

or

2) Follow the following (riskless) three step process:

(i) Use $s to buy foreign currency, and then;

(ii) Use the foreign currency to buy (riskless)foreign bonds,while;

(iii) Selling the foreign currency forward that youwill earn on the foreign bond (i.e., buy $forward with the returns on the foreign bond)


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Assume one buys a 1-yr domestic bond for $X

After one year one receives: $X(1+iUS)

If: $X = $100

iUS = 10%

Then: $X(1+iUS) = $100(1.1) = $110


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OR,if buying the one-year foreign bond:

First, go to foreign exchange market where:

$X is exchanged for$X(e)

If: X = 100 and e = 0.5 (/$)

Then: $X(e) = $100*0.5 (/$) = 50


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Next, buy foreign (1 yr) bond with $X(e). At end

of year:

$X(e)(1+iFOR)

(whichis in the foreign currency)

If: X=100, e=.5(/$), and iFOR = 15%

Then: $X(e)(1+iFOR) = $100(.5)(1.15) = 57.50


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At the same moment of the purchase of the foreign bond, sellforeign currency forward. I.E., knowing that at the end of theyear one will receive

$X(e)(1+iFOR)

Sell that amount forward to receive

$X(e)(1+iFOR)(1/ef)

at the end of the year.

If X =100, e=0.5(/$),iFOR=15%, and ef= 0.53(/$)

then:$X(e)(1+iFOR)(1/ef) =

$100(0.5)(1.15)(1/.53) = $108.49


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NOTE:

If: e=0.5(/$), iFOR=15%, and ef= 0.53(/$)

Then: Devoting $100 to foreign bonds will provide $108.49 afterone year

i.e., $100(e)(1+iFOR)(1/ef) = $108.49

* The return on the foreign bonds IN TERMS OF $s is 8.49%

EVEN THOUGH the return is 15% IN TERMS OF the foreign currency.

Whats happening?


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Restating:

If: iUS=10%, e=0.5(/$), iFOR=15%, and ef= 0.53(/$)

Then: Devoting $100 to domestic bonds will provide $110 afterone year

i.e., $100(1+iUS) = $110

WhileDevoting $100 to foreign bonds will provide $108.49 afterone year

i.e., $100(e)(1+iFOR)(1/ef) = $108.49

* The return on the foreign bonds IN TERMS OF $s is 8.49%


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INTEREST PARITY exists when the returns on bonds (and

other debt instruments) are equal.

COVERED INTEREST PARITY exists when the returns on

bonds denominated in different currencies are equal whenit is assumed the forward markets are used to eliminate theERR associated with future currency exchanges (i.e.,whenthe bond matures).

In the pre

ced

ing example

,since t

he return

in t

heU

S (interms of $) of 10% does not equal the return on the foreign

bonds (in terms of $) of 8.49%, then COVERED INTERESTPARITY does NOT hold.


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Ifinterest parity does not exist, then (barring

sufficient transactions costs) there is anopportunity forInterest Arbitrage:

(1) Borrowwhere rate is lower

(2) Lend where rate is higher

Ofcourse, borrowing in lower rate market will

push up rates there,while lending in higherrate market will lower rates there until interestparity is established.


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Ifcovered interest parity does not exist, then

(barring sufficient transactions costs) there isan opportunity for

Covered Interest Arbitrage:


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Covered Interest Arbitrage consists ofconducting four transactions at same moment:

(1) Borrowin one currency(2) Exchange for othercurrency in spot market(3) Lend in the othercurrency(4) Sell future expected returns in othercurrency

forward (= buy currency of original loanforward)

Then,when future comes: Collect returns,honorforward contract, and payoff original loan


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SO, ifiUS = 10%, e=0.5,iFOR=15%, and ef= 0.53

then: 1+iUS = 1.10

(= return in US in terms of $ is 10%)

(e)(1+iFOR)(1/ef) =

(0.5)(1.15)(1/.53) = 1.0849

(= return in UKin terms of $ is 8.49%)

Since: 1+ iUS

> e(1+iFOR

)(1/ef)

Borrowin UK and Lend in US (and cover theinterest arbitrage using a forward contract).


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Given: iUS = 10%, e=0.5,iFOR=15%, and ef= 0.53

An example ofcovered interest arbitrage:

(1) Borrow 100 in UK (payback will be 115)(2) Go to spot market and exchange for $200(3) Lend $200 in US (to receive $220 in year)

(4) Sell $220 forward for 116.60

At end of year:

collect payment on loan ($220)

honor forward contract ($220116.60)payoff loan with 115 Gain = 1.60


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If everybody exploited this covered interest arbitrage opportunity:

Since: 1+ iUS > e(1+iFOR)(1/ef)

(1) Borrow s


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(2) Buy $ in spot market (with s)

e


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(3) Lend $ in US

iUS


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(4) Sell $ forward

ef


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The expression:

1+ iUS = e(1+iFOR)(1/ef)

is the Covered Interest Parity Condition (CIPC)

Interest Parity - Fall 2008

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