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International Finance
FINA 5331
Lecture 11:
Covered interest rate parity, Hedging
currency risk in yuan, Uncovered interest
rate parity
Read: Chapter 5 (125-129)
Chapter 6 (134-142)
Aaron Smallwood Ph.D.
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.
No arbitrage
• Smart traders will eliminate profitable arbitrage
opportunities quickly when they exist. Thus, as a rule:


~
~* Ft
(1  it )  1  it
S t interest rates fall as a
• Implications: Suppose domestic
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
– 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.
Hedging with Yuan Non-deliverable Forward Contract
• Hedging is possible:
– Example: Nanyang Bank (among others) sell NDFs in yuan.
– Contracts settle in dollars. Forward rate is the rate you “lock in
at.” Settlement rate is the official closing RMB price of the dollar.
– Settlement amount: [1-(Forward Rate/Settlement Rate)]*Size
– If forward rate>settlement price:
• “Seller” of US dollars is paid by the buyer
• Example: Suppose you will receive $500,000 in one year. You may
be concerned that the RMB could appreciate significantly. The
current forward rate is RMB 6.3875.
• If you agree to sell dollars, and the future settlement price in one
year is RMB 6, you will receive a dollar amount that exactly offset
the costs of selling dollars at a rate below RMB 6.3875
FRUH and UIP
• Ft = E(St+1) if investors are risk neutral.
• Since investors are assumed to be rational,
E(St+1) = St+1 + εt+1 where εt+1 is a random
(unforecastable) forecast error.
• Then Ft = St+1 + εt+1 and the forward rate is
an unbiased predictor of the future spot rate.
• From CIP Ft – St
(it – i*t)
=
St
(1 + i*t)
FRUH and UIP
• Then it must be the case that
E(St+1) – St
St
*)
(i
–
i
t
= t
(1 + i*t)
• or approximately
This is the Uncovered Interest Parity
condition. E(st+1) – st=it-it*
It will only hold if investors are risk neutral or
equivalently they do not care about the currency
denomination of the assets they hold
FRUH and UIP
• If uncovered interest parity (UIP) holds
then FRUH is true and investors are risk
neutral.
• Risk neutrality implies that investors
have no currency preference in which
their investments are denominated.
• Assets with identical risk characteristics
but denominated in different currencies
will be viewed as perfect substitutes.