International Finance
FINA 5331
Lecture 13:
Covered interest rate parity
Read: Chapter 6
Aaron Smallwood Ph.D.
Interest Rates and Exchange Rates
• One of the most important relationships in
international finance is the relationship between
interest rates and exchange rate.
• The setup:
• Suppose a trader has the ability to borrow or
lend in both the domestic market and a foreign
market.
– Denote the domestic annualized interest rate as it and
denote the foreign annualized interest rate as it*.
– Denote the spot and forward domestic currency price
of the dollar as St and Ft. Suppose the forward
contract matures in M days.
Interest Rate Adjustment
• The forward contract matures in M days.
• Interest rates are quoted in annualized
terms. We need to adjust interest rates to
facilitate a comparison:
M ~*
~
* M
it  it
, it  it
360
360
Borrowing in the domestic currency; lending
in the foreign
• If I borrow one unit of the domestic currency,
in M days, I will repay:
~
1  it
• To lend in the foreign currency, I must
convert domestic currency into foreign
currency. For each unit of domestic currency
I have, I receive, 1/St units of the foreign
currency.
Lending
• Now I lend the proceeds in the foreign country…I
have 1/St units of the foreign currency…I will
receive:
1
1  ~i  S
*
t
t
• Problem…these proceeds are in foreign currency units…I
want the proceeds in domestic currency. I could have
acquired a forward contract, to sell forward foreign currency
proceeds in M periods. The result:
1  ~i  SF
*
t
t
t
The result:
• Suppose


~
~* F
1  it  1  it t
St
• Then, to profit, I could borrow in the domestic
currency, convert the proceeds into foreign
currency, lend in the foreign market, and convert
proceeds back into domestic currency using a
forward contract.
• What if,


~
~* Ft
(1  i ) t  1  it
St

~ S
~*
 (1  i ) t t  1  it
Ft

• I can still profit…Start by borrowing in the foreign
currency.
Implications
• The no arbitrage condition implies:


~
~* Ft
1  it  1  it
St
• The equation, known as the no arbitrage condition, has important
implications.
• To illustrate suppose the equation didn’t hold.
• Example, suppose:
• it: 6.00% (annualized interest rate in the US for an asset maturing
in one month).
• it*: 5.25% (annualized interest rate in Germany for a similar asset
maturing in 1 month).
• St: $1.36537 (dollar price of the euro on the spot market).
• Ft: $1.30 (assume asset matures in 30 days time).
An arbitrage opportunity exists:
• First, interest rates are adjusted:
• We have:
30
~
it  0.06
 0.005
360
30
~*
it  0.0525
 0.004375
360
• As thus:
~
1  it  1.005
1.30
~* F
(1  it ) t  (1.004375)
 .956288
St
1.36537
• PROFIT TIME!
How do we profit
• Start by borrowing in the foreign country. Let’s
do it big! Let’s borrow €10,000,000.
– We will have to repay:
– €10,000,000*1.004375= €10,043,750
• Note, as a result of our actions, demand for loanable funds in Germany
increases. Foreign interest rates increase.
• Convert euros and lend in the US.
– €10,000,000*$1.36537 = $13,653,700.
– Lend at .5% yielding:
– 13,653,700*(1.005) = $13,721,968.50.
• Note, two things happen here. On the spot market, supply of
euros increases, driving down St.
• Supply of loanable funds increases in the US, driving down it.
Last step…
• Finally, you use the pre-existing forward
contract to sell the dollar proceeds for
euros. The result:
$13,721,968.50/1.30 = 10,555,360.38.
Profit: €10,555,360.38 - €10,043,750 =
€511,610.38.
Note, in the final step, you sell forward dollars.
You are buying forward euros. This likely
causes, Ft to rise.
No arbitrage opportunities?
• NOT ONCE YOU HAVE LEFT THE MARKET!
• Recall, our arbitrage opportunity existed because:


~
~* F
(1  it )  1  it t
St

~ S
~*
 (1  it ) t  1  it
Ft

• However, as a result of your actions:
–
–
–
–
1.
2.
3.
4.
Foreign interest rates rise.
The spot rate falls.
Domestic interest rates fall.
The forward rate rises.
No arbitrage
• Thus, we can expect astute traders will eliminate
profitable arbitrage opportunities quickly when they
exist. Thus, as a rule:


~
~* Ft
(1  it )  1  it
St
• Implications: Suppose domestic interest rates fall as a
result of, say, monetary policy.
• To ensure equilibrium:
– 1. Foreign interest rates must also fall…
– 2. and/or The forward rate must fall.
– 3. and/or…The spot rate must rise. An increase in the spot rate
implies a DOMESTIC CURRENCY DEPRECIATION.
Covered Interest Rate Parity
• The no arbitrage condition is frequently rearranged in a more convenient way:




~ ~*
it  it
Ft  S t
~* 
St
1  it
or
~ ~* Ft  S t
it  it 
St
Deviations from CIRP?
• Transactions Costs
– Without bid-ask spreads, it may have appeared that we
could borrow in the domestic country.
– The interest rate available to an arbitrageur for borrowing,
ib,may exceed the rate he can lend at, il.
– There may be bid-ask spreads to overcome, Fb/Sa < F/S
– Thus
(Fb/Sa)(1 + i¥l)  (1 + i¥ b)  0
• Capital Controls
– Governments sometimes restrict import and export of
money through taxes or outright bans.
• Taxation differences on capital gains.