1. FIN 40500: International Finance
Interest Rate Parity

2. 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 month
3 months
6 months
12 months

3. 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 month
3 months
6 months
Forward Price
Spot Price
The 30 Day EUR is selling at a premium of 2.26%
Days until expiration
EUR/USD ---
1 month %
3 months %
6 months %

4. 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.

5. 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 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

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

7. 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)

8. 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?

9. Suppose that you observe the following information…
Currency Markets
EUR/USD
1 month
3 months
6 months
The Euro 1 month forward is selling at a 2.26% (annualized) premium
Money Markets (Annualized Rates)
LIBOR (Dollar Denominated)
1 month %
3 months %
6 months %
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 %
3 months %
6 months %
Is this just a crazy coincidence?

10. Now, try the 3 month yields
Currency Markets
EUR/USD
1 month
3 months
6 months
The Euro 1 month forward is selling at a 2.32% (annualized) premium
Money Markets (Annualized Rates)
LIBOR (Dollar Denominated)
1 month %
3 months %
6 months %
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 %
3 months %
6 months %
Can we profit off this information??

11. 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 for 3 months
Convert the proceeds back to dollars and repay your loan

12. 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

13. 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

14. 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

15. Euro LIBOR LIBOR Dollar interest rates rise Euro interest rates rise

16. 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???

17. 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

18. 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

19. 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)

20. 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

21. 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

22. 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!!

23. 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?

24. 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

25. 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

26. 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

27. 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)

28. 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)

29. 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!

30. 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

31. 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)

32. 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

33. 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

34. 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?

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