FIN 40500: International Finance Interest Rate Parity

Spot market volume is small relative to total currency volume Forward contracts refer to contracts that define a currency transaction at some future date (usually 30,90,180, or 360 days) EUR/USD 1.2762 1 month 1.2786 3 months 1.2836 6 months 1.2905 12 months 1.3026

The 30 Day EUR is selling at a premium of 2.26% Forward rates are often expressed as (annualized) percentage differences from the current spot rate – called the forward premium/discount EUR/USD 1.2762 1 month 1.2786 3 months 1.2836 6 months 1.2905 Forward Price Spot Price The 30 Day EUR is selling at a premium of 2.26% Days until expiration EUR/USD --- 1 month 2.26% 3 months 2.32% 6 months 2.22%

Forwards/Futures can be used to eliminate the risk involved in international transactions Porsche expects $10M in US sales over the next month that that it would like to repatriate back to Germany Mercedes need to acquire $10M to meet its payroll for its Tuscaloosa, Alabama plant Porsche is worried that the dollar might depreciate over the next month Mercedes is worried that the dollar might appreciate over the next month Both of these companies could benefit from “locking in” their conversion rate.

Deutsche Bank Deutsche Bank offers a price of 1.2786 Dollars per Euro The bank acts as the middleman in a forward contract Deutsche Bank Deutsche Bank offers a price of 1.2786 Dollars per Euro Porsche approaches Deutsche Bank with an offer to buy Euro 30 days forward Mercedes approaches Deutsche Bank with an offer to sell Euro 30 days forward

On Settlement day, Porsche buys E 7 On Settlement day, Porsche buys E 7.821M for $10M (Porsche gains by E 92,400) e = 1.2939 EUR/USD Days On Settlement day, Mercedes buys $10M for E 7.821M (Mercedes loses E 92,400)

EUR 125,000 Total Contracts bought/sold that day (000s) Futures are standardized, traded commodities (Chicago Mercantile Exchange) Total Contracts bought/sold that day (000s) Opening, High, Low, and Closing Price EUR 125,000 Strike Open High Low Settle Pt Chge Volume Interest SEP06 1.2700 1.2804 1.2698 1.2756 +170 3500 8993 OCT06 1.2850 1.2987 1.2800 1.2799 -150 3 34 NOV06 ------ ----- UNCH Contracts Outstanding (000s) Settlement Date Change From Prior Day (in Pips)

Chicago Mercantile Exchange The exchange acts as the middleman in a futures contract Chicago Mercantile Exchange Mercedes goes short on 7 Euro contracts The CME simultaneously buys 7 contracts from Mercedes and sells 7 contracts to Porsche Porsche goes long on 7 Euro contracts Why do we need a middleman?

Suppose that you observe the following information… Currency Markets EUR/USD 1.2762 1 month 1.2786 3 months 1.2836 6 months 1.2905 The Euro 1 month forward is selling at a 2.26% (annualized) premium Money Markets (Annualized Rates) LIBOR (Dollar Denominated) 1 month 5.08 % 3 months 5.21 % 6 months 5.31 % Hmmm….the (annualized) difference between Dollar denominated loans and Euro denominated loans is also 2.26% Money Markets (annualized Rates) EURO LIBOR (Euro Denominated) 1 months 2.82 % 3 months 3.00 % 6 months 3.09 % Is this just a crazy coincidence?

Now, try the 3 month yields Currency Markets EUR/USD 1.2762 1 month 1.2786 3 months 1.2836 6 months 1.2905 The Euro 1 month forward is selling at a 2.32% (annualized) premium Money Markets (Annualized Rates) LIBOR (Dollar Denominated) 1 month 5.08 % 3 months 5.21 % 6 months 5.31 % Hmmm….the (annualized) difference between Dollar denominated loans and Euro denominated loans is 2.21% Money Markets (annualized Rates) EURO LIBOR (Euro Denominated) 1 months 2.82 % 3 months 3.00 % 6 months 3.09 % Can we profit off this information??

Consider the following investment strategy: Convert the $1 to Euros Borrow $1 in the US for 3 months This strategy yields a 3 month return of 3 basis points!!! RISK FREE!!! Invest the E .7836 for 3 months Convert the proceeds back to dollars and repay your loan

Financial markets will adjust so that you can’t earn risk free profits – the condition that insures this is called covered interest parity Dollar return on domestic bonds Dollar return on foreign bonds A useful approximation can be written as follows Interest Differential Forward Premium/Discount Note: this only holds if the two assets have the same risk characteristics

Convert to foreign currency at current spot rate Now, suppose that we tried a similar strategy, but without using forward contracts. This strategy involves risk, and is, hence, called uncovered interest parity Invest Abroad Borrow in the US ? Convert to dollars at some future spot rate

Financial markets will adjust so that you can’t EXPECT to earn risk free profits –this is called uncovered interest parity Expected spot rate change A useful approximation can be written as follows Interest Differential Expected appreciation/depreciation Note: this only holds if the two assets have the same risk characteristics

Euro LIBOR LIBOR Dollar interest rates rise Euro interest rates rise

Interest Differential Throughout January, LIBOR is 2% above Euro LIBOR – the dollar should depreciate by 2% (annualized) over the upcoming month 1/31: Euro trades at $1.2158 Interest Differential 2/28: Euro trades at $1.1925 EUR/USD A 23% (annualized) dollar appreciation???

Throughout February, LIBOR approaches 2% above Euro LIBOR – the dollar should depreciate by 2% (annualized) over the upcoming month A 24% (annualized) dollar depreciation 3/29: Euro trades at $1.2139 3/1: Euro trades at $1.1899

Throughout March, LIBOR rises to over 2% above Euro LIBOR – the dollar should depreciate by 2% (annualized) over the upcoming month A 48% (annualized) dollar depreciation!!! 4/29: Euro trades at $1.2624 4/1: Euro trades at $1.2124

Here, the dollar is going in the wrong direction (according to UIP) Now we’re in the right direction, but by too much! (according to UIP)

Can futures markets actually predict the future? Covered Interest Parity Uncovered Interest Parity Combining our two conditions tells us that if both CIP and UIP hold, then the Forward/Futures market should provide an unbiased predictor of the future spot exchange rate

We can test this hypothesis by running a linear regression of the following form Previous Forward Premium/Discount Error term Percentage change in exchange rate The unbiased hypothesis would suggest that beta should equal one

It turns out that estimates of beta are routinely NEGATIVE It turns out that estimates of beta are routinely NEGATIVE!! This is known as the Forward Premium Puzzle These results suggests that you could systematically make money by exploiting interest rate differentials!!

1 2 3 Lets take a closer look at the international parity conditions… Purchasing Power Parity (zero arbitrage condition for trade in goods) 1 Uncovered Interest Parity (zero arbitrage condition for trade in assets) 2 Additionally, we need to recognize the Fischer effect Expected Inflation 3 Nominal Interest Rate Real Interest Rate What happens if we combine these conditions?

Lets take a closer look at the international parity conditions… Uncovered Interest Parity Purchasing Power Parity A little manipulation… Fischer Effect Real Returns are equalized across countries

We need to take a step back and recall where interest rates come from in the first place. For starters, assume a closed economy (i.e. no trade) Household savings (supply of funds) Real (inflation adjusted) interest rate Private capital investment plus government borrowing (demand for funds) Interest rates adjust to clear the domestic capital market

Suppose, for example, that the government increases its borrowing by $300B. The rise in government borrowing increases the demand for loans Interest rates rise to clear the domestic capital market

Now, lets consider the US as part of a larger global community In the absence of trade, US interest rates are high (due to excessive borrowing) while interest rates in Japan are low (due to excessive savings)

Now, allow the two countries to interact in international capital markets. Available savings from Japan flows to the US for a higher return With integrated capital markets, real return are equalized between the US and Japan. The US runs a trade deficit (net global borrower) while Japan runs a trade surplus (net global lender)

Actually, the US and Japan are only two of many countries in a global capital market. This global capital market aggregates savings and borrowing across the globe and determines a common global real interest rate $20 Some countries run surpluses Some countries run deficits But global trade is balanced!

With a globally integrated capital market, no country (even the US can have a significant impact on global returns. Hence, real interest rates are constant Suppose that savings in the US declines. Rather than raising interest rates, the US trade balance worsens

1 2 Back to our international parity conditions… Purchasing Power Parity (zero arbitrage condition for trade in goods) 1 Uncovered Interest Parity (zero arbitrage condition for trade in assets) 2 These conditions represent two fundamental principles… Global capital markets are equating international real rates of return. Nominal variables are being scaled consistently to account for inflation (PPP for exchange rates and the Fischer Effect for Interest rates)

However, there are some more subtle reasons for the failure of uncovered interest parity Suppose that PPP fails (for any one of the many reasons discussed earlier). Then changes in the nominal exchange rate have three components Some relative price effect Now, plug this into the UIP condition and use the Fischer relation as we did before… Even with fully integrated capital markets, there should be a gap between international rates of return based on real exchange rate movements

A second problem is that UIP involves (through the Fischer effect) EXPECTATIONS of inflation…we can’t really measure these Uncovered Interest Parity Fischer Relationship Suppose that individuals make forecast errors…then we can re-write the above expression Observable Un-observable forecast errors

Suppose that individuals make forecast errors…then we can re-write the above expression As long as people are not making systematic mistakes, then these error terms will be mean zero and will essentially disappear. However, if they are not mean zero… So, do individuals make systematic errors in their inflation forecasts?

Negative real returns in the 70’s suggest that individuals were making systematic mistakes for over ten years!! US Interest Rates Expectation Errors