International Finance FINA 5331 Lecture 12: Covered interest rate parity reviewed Aaron Smallwood Ph.D.

Interest Rates and Exchange Rates Reviewed 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 : 4.00% (annualized interest rate in the US for an asset maturing in three months). i t *: 3.00% (annualized interest rate in Japan for a similar asset maturing in 3 months). S t : $ (dollar price of the yen on the spot market). F t : $ (assume asset matures in 90 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 domestic country. Let’s do it big! Let’s borrow $10,000,000. –We will have to repay: –$10,000,000*1.01= $10,100,000 Note, as a result of our actions, demand for loanable funds in US increases. US interest rates increase. Convert dollars to yen and lend in Japan. –$10,000,000/$0.01 = ¥1,000,000,000. –Lend at.75% yielding: –1,000,000,000*(1.0075) = ¥1,007,500,000. Note, two things happen here. On the spot market, demand for yen increases, driving up S t. Supply of loanable funds increases in the Japan, driving down i t *.

Last step… Finally, you use the pre-existing forward contract to sell the proceeds for euros. The result: ¥1,007,500,000* = $10,115, Profit: $10,115, $10,100,000 = $15, Note, in the final step, you sell forward yen. This likely causes, F t to fall.

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 fall. –2. The spot rate rises. –3. Domestic interest rates rise. –4. The forward rate falls.

No arbitrage Thus, we can expect smart traders will eliminate profitable arbitrage opportunities quickly when they exist. Thus, as a rule: Implications: Changes in interest rates are likely associated with changes in exchange rates. On July 31, 2013, the yen price of the dollar was 78.10

No arbitrage Since July of last year, two things have happened: According to CNBC, “The Bank of Japan stunned markets on April 4 by setting in motion an intense burst of monetary stimulus, promising to double its bond holdings and boost purchases of risky assets to meet its 2 percent inflation target in roughly two years.” According to an article published in Bloomberg on July 5, 2013, “Fed Chairman Ben S. Bernanke said last month policy makers may “moderate” their bond-buying program this year and may end it mid-2014 if growth meets forecasts.” Additional good news regarding the US economy has pushed down US interest rates. The article says: “US 10 year Treasury notes rose 22 basis points to 2.73%...It was the biggest one day increase since August 2011.

Covered interest rate parity Again, according to covered interest rate parity: What are the implications? US interest rates have been rising, while Japanese rates have been falling. On July 31, 2013, the yen price of the dollar was 78.10, meaning the dollar price of the yen was: 1/78.10=$ If the US is the domestic country, US interest rates rise, while foreign interest rates fall. Either the forward rate should increase, or even more likely, the spot dollar price of the yen should fall. In fact, the dollar spot price of the yen was $ on Friday, July 5. This implies: yen spot price of the dollar = The yen has depreciated sharply against the dollar since one year ago (29.5%)!