FIN 40500: International Finance Interest Rate Parity

FIN 40500: International Finance

Interest Rate Parity

Swaps56%

Forward11%

Spot33%

Spot market volume is small relative to total currency volume

EUR/USD 1.2762

1 month 1.2786

3 months 1.2836

6 months 1.2905

12 months 1.3026

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

The 30 Day EUR is selling at a premium of 2.26%

0226.30

360

2762.1

2762.12786.1360

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

EUR/USD1.2762 1 month 1.2786 3 months 1.2836 6 months 1.2905

Forward PriceSpot Price

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

Porsche is worried that the dollar might depreciate over the next month

Mercedes need to acquire $10M to meet its payroll for its Tuscaloosa, Alabama plant

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

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

1.255

1.26

1.265

1.27

1.275

1.28

1.285

1.29

1.295

1.3

0 4 8 12 15 18 23 27

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

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

Days

EU

R/U

SD

e = 1.2939

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 ----- -----

EUR 125,000

Settlement Date Change From Prior Day (in Pips)

Opening, High, Low, and Closing Price

Contracts Outstanding (000s)

Total Contracts bought/sold that day (000s)

Futures are standardized, traded commodities (Chicago Mercantile Exchange)

Chicago Mercantile Exchange

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

The exchange acts as the middleman in a futures contract

Porsche goes long on 7 Euro contracts

Mercedes goes short on 7 Euro contracts

Why do we need a middleman?

Suppose that you observe the following information…

EUR/USD 1.2762 1 month 1.2786 3 months 1.2836 6 months 1.2905

Currency Markets

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 %

Money Markets (annualized Rates)

0226.30

360

2762.1

2762.12786.1

FP

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The Euro 1 month forward is selling at a 2.26% (annualized) premium

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

EUR/USD 1.2762 1 month 1.2786 3 months 1.2836 6 months 1.2905

Currency Markets

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 %

Money Markets (annualized Rates)

0232.30

360

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The Euro 1 month forward is selling at a 2.32% (annualized) premium

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:

Borrow $1 in the US for 3 months

Convert the $1 to Euros

Invest the E .7836 for 3 months

Convert the proceeds back to dollars and repay your loan

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This strategy yields a 3 month return of 3 basis points!!! RISK FREE!!!

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

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F

Dollar return on foreign bonds

Dollar return on domestic bonds

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

A useful approximation can be written as follows

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eF

Forward Premium/Discount

Interest Differential

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

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e

1

e

i*1

e

ei '1 * 01

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ie

ei

Borrow in the US

Convert to foreign currency at current spot rate

Invest Abroad

Convert to dollars at some future spot rate

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

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

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i

i

e

eE

Expected spot rate change

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

A useful approximation can be written as follows

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eeE

Expected appreciation/depreciation

Interest Differential

2.00

2.10

2.20

2.30

2.40

2.50

2.60

2.70

2.80

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

4.00

4.20

4.40

4.60

4.80

5.00

5.20

Difference Euro Libor LIBOR

LIB

OR

Eu

ro L

IBO

R

Dollar interest rates rise

Euro interest rates rise

Dollar interest rates rise

1.25

1.35

1.45

1.55

1.65

1.75

1.85

1.95

2.05

2.15

2.25

1/3/06 1/31/06 2/28/06

1.16

1.17

1.18

1.19

1.20

1.21

1.22

1.23

1.24

Interest Differential EUR/USD

Inte

rest

Dif

fere

nti

al

EU

R/U

SD

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


A 23% (annualized) dollar appreciation???

1.25

1.35

1.45

1.55

1.65

1.75

1.85

1.95

2.05

2.15

2.25

2/1/06 3/1/06 3/29/06

1.16

1.17

1.18

1.19

1.20

1.21

1.22

1.23


Throughout February, LIBOR approaches 2% above Euro LIBOR – the dollar should depreciate by 2% (annualized) over the upcoming month



A 24% (annualized) dollar depreciation

1.25

1.35

1.45

1.55

1.65

1.75

1.85

1.95

2.05

2.15

2.25

3/1/06 3/29/06 4/26/06

1.14

1.16

1.18

1.20

1.22

1.24

1.26

1.28


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!!!

1.25

1.45

1.65

1.85

2.05

2.25

2.45

1/3/2006 1/31/2006 2/28/2006 3/28/2006 4/25/2006 5/23/2006

1.12

1.14

1.16

1.18

1.20

1.22

1.24

1.26

1.28

1.30


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)

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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

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We can test this hypothesis by running a linear regression of the following form

tt

ttt e

eFe

%

Percentage change in exchange rate

Previous Forward Premium/Discount

Error term 0tE

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!!

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Lets take a closer look at the international parity conditions…

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

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

1

2

3

Additionally, we need to recognize the Fischer effect

Expected Inflation

Nominal Interest Rate

Real Interest Rate

What happens if we combine these conditions?

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ir

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Lets take a closer look at the international parity conditions…

Purchasing Power Parity

Uncovered Interest Parity

** iiee A little manipulation…

ee ii **Fischer Effect

rr * Real Returns are equalized across countries

r

SI ,

r

TGI

S

Household savings (supply of funds)

Private capital investment plus government borrowing (demand for funds)

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)

Interest rates adjust to clear the domestic capital market

Real (inflation adjusted) interest rate

r

SI ,

r

TGI

S

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

Interest rates rise to clear the domestic capital market

The rise in government borrowing increases the demand for loans

r

SI ,

r

TGI

S

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

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**,SI

*r *** TGI

*S

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)

TGIS **** TGIS

r

SI ,

r

TGI

S

Now, allow the two countries to interact in international capital markets. Available savings from Japan flows to the US for a higher return

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**,SI

*r *** TGI

*S

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)

TGISNX ***** TGISNX

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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

Some countries run surpluses

Some countries run deficitsBut global trade is balanced!

r

SI ,

wr TGI

S

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

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ww SI ,

wr

www TGI

wS

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

TGISNX wwww TGIS

Back to our international parity conditions…

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*% e Purchasing Power Parity (zero arbitrage condition for trade in goods)

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

1

2

These conditions represent two fundamental principles…

1) Global capital markets are equating international real rates of return.

2) Nominal variables are being scaled consistently to account for inflation (PPP for exchange rates and the Fischer Effect for Interest rates)

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ri

ri

However, there are some more subtle reasons for the failure of uncovered interest parity

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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…

RERrr %*

Even with fully integrated capital markets, there should be a gap between international rates of return based on real exchange rate movements

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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

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E

Observable Un-observable forecast errors

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

***% rreE

E

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?

-10.00

-5.00

0.00

5.00

10.00

15.00

20.00

5/1/1953 5/1/1963 5/1/1973 5/1/1983 5/1/1993 5/1/2003

Nominal Return Inflation Real Return

US Interest Rates

Expectation Errors

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

Documents

FIN 40500: International Finance Interest Rate Parity