1. International Finance
Lecture 11:
Non-deliverable forward contracts reviewed. Covered interest rate parity
Aaron Smallwood Ph.D.

2. 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.

3. 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

4. Example: NDF yuan contract
In one year, suppose the yuan price of the dollar is
Given that one year NDF forward rate was RMB , 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.

5. Example: NDF yuan contract
Trader will buy $1,000,000 at paying: RMB 6,189,500.
The trader also has subtracted from her$17, bank account.
$17, 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

6. 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.

7. 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:

8. 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.

9. 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:

10. The result: Suppose What if,
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.

11. 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: $ (dollar price of the euro on the spot market).
Ft: $1.30 (assume asset matures in 30 days time).

12. An arbitrage opportunity exists:
First, interest rates are adjusted:
We have:
As thus:
PROFIT TIME!

13. 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* = €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*$ = $13,653,700.
Lend at .5% yielding:
13,653,700*(1.005) = $13,721,
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.

14. 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,
Profit: €10,555, €10,043,750 =
€511,
Note, in the final step, you sell forward dollars. You are buying forward euros. This likely causes, Ft to rise.

15. 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.

16. 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.

17. Covered Interest Rate Parity
The no arbitrage condition is frequently re-arranged in a more convenient way:

18. (Fb/Sa)(1 + i¥l)  (1 + i¥ b)  0
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.