International Finance FINA 5331 Lecture 14: Covered interest rate parity Read: Chapter 6 Aaron Smallwood Ph.D.

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.