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 i t and denote the foreign annualized interest rate as i t *. –Denote the spot and forward domestic currency price of the dollar as S t and F t. 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:

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/S t units of the foreign currency.

Lending Now I lend the proceeds in the foreign country…I have 1/S t 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:

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.

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: i t : 6.00% (annualized interest rate in the US for an asset maturing in one month). i t *: 5.25% (annualized interest rate in Germany for a similar asset maturing in 1 month). S t : $ (dollar price of the euro on the spot market). F t : $1.30 (assume asset matures in 30 days time).

An arbitrage opportunity exists: First, interest rates are adjusted: We have: As thus: 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* = €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 S t. Supply of loanable funds increases in the US, driving down i t.

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, F t 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.

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.

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

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, i b,may exceed the rate he can lend at, i l. –There may be bid-ask spreads to overcome, F b /S a < F/S –Thus (F b /S a )(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.