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Economics 243

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					FIN 40500: International Finance
Interest Rate Parity

Spot market volume is small relative to total currency volume
Swaps 56%

Spot 33%

Forward contracts refer to contracts that define a currency transaction at some future date (usually 30,90,180, or 360 days)

Forward 11%

EUR/USD 1 month 3 months 6 months 12 months

1.2762 1.2786 1.2836 1.2905 1.3026

EUR/USD 1 month 3 months 6 months

1.2762 1.2786 1.2836 1.2905

Forward rates are often expressed as (annualized) percentage differences from the current spot rate – called the forward premium/discount

Forward Price

Spot Price

 F  e  360  1.2786  1.2762  360  FP      .0226   1.2762  e  n    30 
Days until expiration

The 30 Day EUR is selling at a premium of 2.26%
EUR/USD 1 month 3 months 6 months --2.26% 2.32% 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.

The bank acts as the middleman in a forward contract

Deutsche Bank

Porsche approaches Deutsche Bank with an offer to buy Euro 30 days forward

Deutsche Bank offers a price of 1.2786 Dollars per Euro

Mercedes approaches Deutsche Bank with an offer to sell Euro 30 days forward

On Settlement day, Porsche buys E 7.821M for $10M (Porsche gains by E 92,400)
1.3 1.295 1.29

e = 1.2939

EUR/USD

1.285 1.28 1.275 1.27 1.265 1.26 1.255 0 4 8 12 15 18 23 27

Days

On Settlement day, Mercedes buys $10M for E 7.821M (Mercedes loses E 92,400)

Futures are standardized, traded commodities (Chicago Mercantile Exchange)

EUR 125,000
Strike
SEP06 OCT06 NOV06

Opening, High, Low, and Closing Price
High
1.2804 1.2987 ------

Total Contracts bought/sold that day (000s)
Pt Chge
+170 -150 UNCH

Open
1.2700 1.2850 ------

Low
1.2698 1.2800 ------

Settle
1.2756 1.2799 -----

Volume
3500 3 -----

Interest
8993 34 -----

Settlement Date

Change From Prior Day (in Pips)

Contracts Outstanding (000s)

The exchange acts as the middleman in a futures contract

Chicago Mercantile Exchange

Porsche goes long on 7 Euro contracts

The CME simultaneously buys 7 contracts from Mercedes and sells 7 contracts to Porsche

Mercedes goes short on 7 Euro contracts

Why do we need a middleman?

Suppose that you observe the following information… Currency Markets EUR/USD 1 month 3 months 6 months 1.2762 1.2786 1.2836 1.2905

1.2786  1.2762  360  FP     .0226  1.2762   30 
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 % Money Markets (annualized Rates) EURO LIBOR (Euro Denominated) 1 months 2.82 % 3 months 3.00 % 6 months 3.09 %

i  i   5.08  2.82   2.26 %
*

Hmmm….the (annualized) difference between Dollar denominated loans and Euro denominated loans is also 2.26%

Is this just a crazy coincidence?

Now, try the 3 month yields Currency Markets EUR/USD 1 month 3 months 6 months 1.2762 1.2786 1.2836 1.2905

1.2836  1.2762  360  FP     .0232  1.2762   30 
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 % Money Markets (annualized Rates) EURO LIBOR (Euro Denominated) 1 months 2.82 % 3 months 3.00 % 6 months 3.09 %

i  i   5.21  3.00   2.21 %
*

Hmmm….the (annualized) difference between Dollar denominated loans and Euro denominated loans is 2.21%

Can we profit off this information??

Consider the following investment strategy:
Convert the $1 to Euros

1  E.7836 1.2762
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

i  1.30%

i  .75%
E.7836 1.0075   .7895

Convert the proceeds back to dollars and repay your loan

.7895 1.2836   (1.0130 )  .0003

Financial markets will adjust so that you can’t earn risk free profits – the condition that insures this is called covered interest parity

F *   1  i  (1  i ) e
Dollar return on foreign bonds





Dollar return on domestic bonds

A useful approximation can be written as follows

 F e *    i i  e 





Interest Differential Forward Premium/Discount Note: this only holds if the two assets have the same risk characteristics

Now, suppose that we tried a similar strategy, but without using forward contracts.

Convert to foreign currency at current spot rate

1 e

This strategy involves risk, and is, hence, called uncovered interest parity

$1
Borrow in the US

Invest Abroad

1 i 
*

e

1  i e'  1  i  ? 0  
*

1  i e'
*

e
Convert to dollars at some future spot rate

e

Financial markets will adjust so that you can’t EXPECT to earn risk free profits –this is called uncovered interest parity

 e'  (1  i ) E   *  e  1 i





Expected spot rate change A useful approximation can be written as follows

 e'e  * E   i i  e 





Expected appreciation/depreciation

Interest Differential

Note: this only holds if the two assets have the same risk characteristics

Dollar interest rates rise
2.80 2.70 2.60

Euro interest rates rise

Dollar interest rates rise
5.20 5.00 4.80

Euro LIBOR

2.50 2.40 2.30 2.20 2.10 2.00 1/3/2006 1/31/2006 Difference 2/28/2006 Euro Libor 3/28/2006 LIBOR

LIBOR

4.60 4.40 4.20 4.00 4/25/2006

Throughout January, LIBOR is 2% above Euro LIBOR – the dollar should depreciate by 2% (annualized) over the upcoming month
2.25 2.15 1.24

Interest Differential

2.05 1.95

1/31: Euro trades at $1.2158 2/28: Euro trades at $1.1925

1.23 1.22

EUR/USD

1.85 1.75 1.65 1.55 1.45 1.35 1.25 1/3/06 1/31/06 Interest Differential

1.21 1.20 1.19

A 23% (annualized) dollar appreciation???

1.18 1.17 1.16 2/28/06

EUR/USD

Throughout February, LIBOR approaches 2% above Euro LIBOR – the dollar should depreciate by 2% (annualized) over the upcoming month
2.25 2.15 2.05 1.95 1.85 1.75 1.65 1.55 1.45 1.35 1.25 2/1/06 3/1/06 Interest Differential EUR/USD 3/29/06 1.19 1.21 1.20 1.23

A 24% (annualized) dollar depreciation

1.22

3/29: Euro trades at $1.2139 3/1: Euro trades at $1.1899

1.18 1.17 1.16

Throughout March, LIBOR rises to over 2% above Euro LIBOR – the dollar should depreciate by 2% (annualized) over the upcoming month
2.25 2.15 2.05 1.95 1.85 1.75 1.65 1.55 1.45 1.35 1.25 3/1/06 3/29/06 Interest Differential EUR/USD 4/26/06 1.28

A 48% (annualized) dollar depreciation!!!

1.26 1.24 1.22

4/29: Euro trades at $1.2624 4/1: Euro trades at $1.2124

1.20 1.18 1.16 1.14

Here, the dollar is going in the wrong direction (according to UIP)
2.45 2.25

Now we’re in the right direction, but by too much! (according to UIP)

1.30 1.28 1.26

2.05 1.85

1.24 1.22 1.20

1.65 1.45

1.18 1.16 1.14

1.25 1/3/2006 1/31/2006 2/28/2006 3/28/2006 4/25/2006

1.12 5/23/2006

Interest Differential

EUR/USD

Can futures markets actually predict the future?

Covered Interest Parity

Uncovered Interest Parity

F



(1  i ) e * 1 i



E e' 



(1  i ) e * 1 i



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

F  Ee'

We can test this hypothesis by running a linear regression of the following form Previous Forward Premium/Discount

 Ft  et %et       e  t
Percentage change in exchange rate

   t  
Error term

E  t   0

The unbiased hypothesis would suggest that beta should equal one

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!!

Lets take a closer look at the international parity conditions…

1

%e     *
E %e   i  i

Purchasing Power Parity (zero arbitrage condition for trade in goods) Uncovered Interest Parity (zero arbitrage condition for trade in assets)

2



*



Additionally, we need to recognize the Fischer effect

3

i  r 

e

Expected Inflation

Nominal Interest Rate

Real Interest Rate

What happens if we combine these conditions?

Lets take a closer look at the international parity conditions…

E %e   i  i *
Purchasing Power Parity





Uncovered Interest Parity

E %e     
e

e*

 e   e*  i  i*
Fischer Effect

A little manipulation…

r  i  e r *  i   e*

i*   e*  i   e
r r
*

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) Real (inflation adjusted) interest rate Household savings (supply of funds)

r

S

r

Private capital investment plus government borrowing (demand for funds)

I  G  T 

I, S
Interest rates adjust to clear the domestic capital market

Suppose, for example, that the government increases its borrowing by $300B.

r

S
The rise in government borrowing increases the demand for loans

r
I  G  T 

I, S
Interest rates rise to clear the domestic capital market

Now, lets consider the US as part of a larger global community

r
S

r

*

S*
I  G  T 

r

r*

I, S
S  I  G  T 

I *  G*  T * I *, S * S *  I *  G*  T *









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

r
S

r

*

S*
I  G  T 

r

r*

I, S
NX  S  I  G  T 

I *  G*  T * I *, S *



 

NX *  S *  I *  G*  T *



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
r

S

r

S

rw
D

rw
S, I
S

S

w

rw
D

r

S, I

rw
D $20

r

w

r

S

S, I
Some countries run surpluses

S  I  G T
w w w



Dw w S ,I
w

rw

D



S, I
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

r
S

r

*

Sw

rw

I  G  T 

rw
I w  Gw T w I w, S w S w  I w  Gw T w





I, S
NX  S  I  G  T 





Suppose that savings in the US declines. Rather than raising interest rates, the US trade balance worsens

Back to our international parity conditions…

1

%e     *
E %e   i  i

Purchasing Power Parity (zero arbitrage condition for trade in goods) Uncovered Interest Parity (zero arbitrage condition for trade in assets)

2



*



These conditions represent two fundamental principles… 1) 2) 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) e

i  r 

i *  r *   e*

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

%e  %RER     *
Some relative price effect

Now, plug this into the UIP condition and use the Fischer relation as we did before…

r  r  %RER
*

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

E %e   i  i *  r  r *  E    *
Uncovered Interest Parity Fischer Relationship



 

 



Suppose that individuals make forecast errors…then we can re-write the above expression

E      

E %e   r  r *     *     *
Observable



 

 



Un-observable forecast errors

Suppose that individuals make forecast errors…then we can re-write the above expression

E      
E %e   r  r *     *     *



 

 



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!!
20.00

US Interest Rates
15.00

10.00

5.00

0.00 5/1/1953 -5.00 5/1/1963 5/1/1973 5/1/1983 5/1/1993 5/1/2003

-10.00 Nominal Return Inflation

Expectation Errors
Real Return


				
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