COVERED INTEREST PARITY AND COVERED INTEREST ARBITRAGE.

COVERED INTEREST PARITYAND

COVERED INTEREST ARBITRAGE

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)

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 zero doubt that these bonds will pay their promised amount. The closest real-world assets that approach this riskless characteristic are government bonds (by governments that issue their own currency).

There are two ways to that individuals can invest $’s that will 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 you will earn on the foreign bond (i.e., buy $ forward with the returns on the foreign bond)

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

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

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

of year: $X(e)(1+iFOR)

(which is in the foreign currency)

If: X=100, e=.5(£/$), and iFOR = 15%

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

At the same moment of the purchase of the foreign bond, sell foreign currency forward. I.E., knowing that at the end of the year 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

NOTE:

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

Then: Devoting $100 to foreign bonds will provide $108.49 after one 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.

What’s happening?

Restating:

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

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

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

Devoting $100 to foreign bonds will provide $108.49 after one year

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

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

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 when it is assumed the forward markets are used to eliminate the ERR associated with future currency exchanges (i.e., when the bond matures).

In the preceding example, since the return in the US (in terms of $) of 10% does not equal the return on the foreign bonds (in terms of $) of 8.49%, then COVERED INTEREST PARITY does NOT hold.

If interest parity does not exist, then (barring sufficient transactions costs) there is an opportunity for “Interest Arbitrage”:

(1) Borrow where rate is lower(2) Lend where rate is higher

Of course, borrowing in lower rate market will push up rates there, while lending in higher rate market will lower rates there until interest parity is established.

If covered interest parity does not exist, then (barring sufficient transactions costs) there is an opportunity for

“Covered Interest Arbitrage”:

Covered Interest Arbitrage consists of conducting four transactions at same moment: (1) Borrow in one currency (2) Exchange for other currency in spot market (3) Lend in the other currency (4) Sell future expected returns in other currency forward (= buy currency of original loan

forward) Then, when future comes: Collect returns, honor forward contract, and payoff original loan

SO, if iUS = 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 UK in terms of $ is 8.49%)

Since: 1+ iUS > e(1+iFOR)(1/ef)Borrow in UK and Lend in US (and “cover” the interest arbitrage using a forward contract).

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

An example of covered 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 ($220→£116.60)payoff loan with £115 → Gain = £1.60

If everybody exploited this covered interest arbitrage opportunity:

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

(1) Borrow £’s

If everybody exploited this covered interest arbitrage opportunity:

Since: 1+ iUS > e(1+iFOR)(1/ef)(2) Buy $ in spot market (with £’s)

e↑

If everybody exploited this covered interest arbitrage opportunity:

Since: 1+ iUS > e(1+iFOR)(1/ef)(3) Lend $ in US

iUS↓

If everybody exploited this covered interest arbitrage opportunity:

Since: 1+ iUS > e(1+iFOR)(1/ef)(4) Sell $ forward

ef ↓

The expression:

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

is the “Covered Interest Parity Condition” (CIPC)