Download INTEREST PARITY (COVERED AND UNCOVERED)

COVERED INTEREST PARITY
AND
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) = $110
While
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)