International FinanceFINA 5331

Lecture 11:

Non-deliverable forward contracts reviewed. Covered interest rate

parityAaron Smallwood Ph.D.

Non-deliverable yuan forward contracts reviewed

• Money will be added or subtracted from the trader’s account depending on whether the RMB appreciates or depreciates.

• The trader will receive or pay:

• If trader sells dollars (buys RMB), they:

– Pay the bank if Forward rate exceeds settlement price

– Money is added to the traders account if F<S.

• If trader buys dollars, the reverse is true.

€

1−Forward

Settlement

⎛

⎝ ⎜

⎞

⎠ ⎟x(Amount invested)

€

Example: NDF yuan contract

• A US firm with operations in China wishes to convert RMB into dollars. In this case, the trader wants to buy $1,000,000

• The trader cares about $ proceeds and is concerned with a possible RMB depreciation.

• On July 8, the one year NDF forward rate was RMB 6.2968.

Example: NDF yuan contract

• In one year, suppose the yuan price of the dollar is 6.1895.

• Given that one year NDF forward rate was RMB 6.2968, money is subtracted from the trader’s account:

• The RMB has appreciated relative to the forward contract. The trader will have money subtracted from her account, but she will also benefit from RMB appreciation.

€

(1−6.2968

6.1895) *1,000,000 = $17,335.81€

Example: NDF yuan contract

• Trader will buy $1,000,000 at 6.1895 paying: RMB 6,189,500.

• The trader also has subtracted from her$17,335.81 bank account.

• $17,335.81 at the official settlement rate one year from today: $17,335.81*6.1895=107,300.00

• Total amount paid = 107,300+6,189,500=RMB 6,296,800.

• Exactly equal to $1,000,000*6.2968

€

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:

360~

,360

~ ** Mii

Mii tttt

Borrowing in the domestic currency; lending in the foreign

• If I borrow one unit of the domestic currency, in M days, I will repay:

• 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.

ti~

1

Lending

• Now I lend the proceeds in the foreign country…I have 1/St units of the foreign currency…I will receive:

• 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:

t

t Si

1~1 *

t

tt S

Fi *~

1

The result:

• Suppose• 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,

• I can still profit…Start by borrowing in the foreign currency.

t

ttt S

Fii *~

1~

1

*

*

~1)

~1(

~1)

~1(

tt

tt

t

ttt

iF

Si

S

Fii

Implications

• The no arbitrage condition implies:

• 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).

t

ttt S

Fii *~

1~

1

An arbitrage opportunity exists:

• First, interest rates are adjusted:• We have:

• As thus:

• PROFIT TIME!

004375.0360

300525.0

~

005.0360

3006.0

~

*

t

t

i

i

956288.36537.1

30.1)004375.1()

~1(

005.1~

1

*

t

tt

t

S

Fi

i

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:

• However, as a result of your actions:– 1. Foreign interest rates rise.– 2. The spot rate falls.– 3. Domestic interest rates fall.– 4. The forward rate rises.

*

*

~1)

~1(

~1)

~1(

tt

tt

t

ttt

iF

Si

S

Fii

No arbitrage

• Thus, we can expect astute traders will eliminate profitable arbitrage opportunities quickly when they exist. Thus, as a rule:

• 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.

t

ttt S

Fii *~

1)~

1(

Covered Interest Rate Parity

• The no arbitrage condition is frequently re-arranged in a more convenient way:

t

tttt

t

tt

t

tt

S

SFii

S

SF

i

ii

*

*

*

~~

or

~1

~~

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.