Prices and Policies
Second Edition ©2001
Richard M. Levich
5

McGraw Hill / Irwin

Overview

The Usefulness of the Parity Conditions in
International Financial markets: A Reprise

Interest Rate Parity: The Relationship between
Interest Rates, Spot Rates, and Forward Rates
 Interest Rate Parity in a Perfect Capital Market
 Relaxing the Perfect Capital Market Assumptions
 Empirical Evidence on Interest Rate Parity
5 - 2
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Overview

The Fisher Parities
 The Fisher Effect
 The International Fisher Effect
 Relaxing the Perfect Capital Market Assumptions
 Empirical Evidence on the International Fisher
Effect
5 - 3
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Overview

The Forward Rate Unbiased Condition
 Interpreting a Forward Rate Bias
 Empirical Evidence on the Forward Rate Unbiased
Condition
 Tests Using the Level of Spot and Forward
Exchange Rates
 Tests Using Forward Premiums and Exchange Rate
Changes
5 - 4
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Overview

Policy Matters - Private Enterprises
 Application 1: Interest Rate Parity and One-Way
Arbitrage
 Application 2: Credit Risk and Forward Contracts -
To Buy or to Make?
 Application 3: Interest Rate Parity and the Country
Risk Premium
 Application 4: Are Deviations from the
International Fisher Effect Predictable?
5 - 5
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Overview
 Application 5: Are Deviations from the
International Fisher Effect Excessive?
 Application 6: International Fisher Effect and
Diversification Possibilities
 Application 7: International Fisher Effect, Long-
Term Bonds, and Exchange Rate Predictions

Policy Matters - Public Policymakers
5 - 6
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The Usefulness of the Parity Conditions in
International Financial Markets: A Reprise
5 - 7

Compared to PPP, violations in the other parity conditions may present more immediate profit opportunities because the cost of entering into financial transactions is typically less than in goods markets.

If a parity financial condition is violated, an opportunity for profit may be present.

Note however that financial markets are often subject to controls and taxes.
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Interest Rate Parity: The Relationship between
5 - 8
Interest Rates, Spot Rates, and Forward Rates
The forward exchange rate premium equals
(approximately) the U.S. interest rate minus the foreign interest rate.

F

S

S
 i
$
 i
£
Driven by arbitrage between the spot and forward exchange rates, and money market interest rates.
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5 - 9
Interest Rate Parity

IRP draws on the principle that in equilibrium, two investments exposed to the same risks must have the same returns.

Suppose an investor puts $1 in a US$ security.
At the end of one period, wealth = $1

(1 + i
$
)

Alternatively, the investor can put the $1 in a
UK£ security and cover his or her exposure to
UK£ exchange rate changes. At the end of one period, wealth =
$ 1

1 .
0
S t


1
 i
£


F t , 1
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Interest Rate Parity

Driven by covered interest arbitrage , the two investments should produce identical ending wealth. So,
$ 1

1 .
0
S t


1
 i
£


F t , 1

$ 1


1
 i
$


F t , 1
S t

S t  i
$

1
 i i
£
£
5 - 10
% forward premium = % interest differential
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5 - 11
Interest Rate Parity

The term (F–S)/S is called the forward premium . When (F–S)/S < 0, the term forward discount is often used.

When the forward premium or discount is plotted against the interest rate differential, the
45° line represents the interest rate parity line .

The IRP line represents the dividing line between investments in the domestic security and investments in the foreign security that have been covered against exchange risk.
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The Interest Rate Parity Line
5 - 12
0.04
0.03
0.02
0.01
Capital Outflows
$ to Foreign Currency
A’
B’
B
0
A
- 0.01
B”
A”
- 0.02
- 0.03
Capital Inflows
Foreign Currency to $
- 0.04
- 0.04
- 0.03
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- 0.02
- 0.01
0 0.01
0.02
0.03
0.04
(i
$
– i foreign
) / (1 + i foreign
)
 2001 by The McGraw-Hill Companies, Inc. All rights reserved.

Perfect Capital Market Assumptions
5 - 13

Transaction costs has the effect of creating a
“neutral band” within which covered interest arbitrage transactions will not occur.
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Interest Differential
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Perfect Capital Market Assumptions
5 - 14

Differential capital gains and ordinary income tax rates can tilt the 45° slope of the IRP line.
 However, the actual impact depends on the exact tax rates, the number of people who are subject to those rates, and transactions costs which may dominate the role of taxes.

There are also uncertainty risks.
 Placing orders takes time and market prices may change.
 The foreign investment may present country risks.
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5 - 15

The Eurocurrency markets made it possible to examine two securities that differed only in terms of their currency of denomination.

The general result is that IRP holds in the shortterm Eurocurrency market after accounting for transaction costs.

For longer-term securities, a study found significant deviations from parity that represent profit opportunities even after adjusting for transaction costs.
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5 - 16
The Fisher Parities
For a single economy, the nominal interest rate equals the real interest rate plus the expected rate of inflation.
i
$
 r
$

E
Driven by desire to insulate the real interest against expected inflation, and arbitrage between real and nominal assets.
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5 - 17
The Fisher Effect

The Fisher effect represents arbitrage between real assets and nominal (or financial) assets within a single economy.

At the end of one period, a $1 commodity holding can be liquidated for $1[1+ E ( p
~
)], where
E ( p ) is the expected rate of inflation.

To be indifferent, an interest-bearing security will need an end-of-period value of
$1(1+ r )[1+ E ( p
~
)], or $1(1+ i ).
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The Fisher Effect

So, (1+ i ) = (1+ r )[1+ E ( p
~
)]
 i = r + E ( p
~
) + r E ( p
~
)

Where inflation and the real interest rate are low, the Fisher effect is usually approximated as: i = r + E ( p )
5 - 18
% nominal interest rate
=
% real interest rate
+
% expected inflation
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5 - 19
The Fisher Parities
or uncovered interest parity
For two economies, the U.S. interest rate minus the foreign interest rate equals the expected percentage change in the exchange rate.
i
$
 i
£

E


~
S pot

Driven by arbitrage in bonds denominated in two currencies.
McGraw Hill / Irwin  2001 by The McGraw-Hill Companies, Inc. All rights reserved.

The International Fisher Effect
5 - 20

Interest rates across countries must also be set with an eye toward expected exchange rate changes.

Suppose an investor puts $1 in a US$ security.
At the end of one period, wealth = $1

(1 + i
$
)

Alternatively, the investor can put the $1 in a
UK£ security. At the end of one period, wealth

$ 1

1 .
0
S t


1
 i
£


E
  t 1
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The International Fisher Effect
5 - 21

Under PCM assumptions, the ending wealth should be identical:
$ 1


1
 i
$


$ 1

1 .
0
S t


1
 i
£


E
  t 1

E
  t 1

S t
S t
 i
$
1

 i i
£
£
% expected exchange rate change = % interest differential
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The International Fisher Effect
5 - 22
 The market’s implied future spot rate :
E
  t 1



1
1

 i
$ i
£



S t

So, the market expects the US$ to appreciate when US$ interest rates are lower than foreign interest rates, and vice versa.

Note that the International Fisher Effect implicitly assumes that real interest rates are equal across countries.
McGraw Hill / Irwin  2001 by The McGraw-Hill Companies, Inc. All rights reserved.

Perfect Capital Market Assumptions
5 - 23

Transaction costs result in a neutral band around the parity line, while differential taxes can possibly tilt the parity line.

Since the ending value of the foreign investment depends on an uncertain future spot rate, an exchange-risk premium may be required.
McGraw Hill / Irwin  2001 by The McGraw-Hill Companies, Inc. All rights reserved.

the International Fisher Effect

Empirical tests indicate that the International
Fisher Effect condition performs poorly in individual periods.

However, over extended periods of time, it appears that currencies with high interest rates tend to depreciate, and vice versa, as predicted.
5 - 24
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The Forward Rate Unbiased Condition
5 - 25
Today’s forward premium (for delivery in n days) equals the expected percentage change in the spot rate
(over the next n days).

F t

S t

S t


E
  t n

S t

S t
Driving force: Market players monitor the difference between today’s forward rate (for delivery in n days) and their expectation of the future spot rate
( n days from today).
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The Forward Rate Unbiased Condition
5 - 26

From IRP and the International Fisher Effect:
E
  t
S
1 t

S t

F t , 1
S t

S t
% expected exchange rate change = % forward premium
 If the average deviation between today’s
F t ,1 and the actual future S t +1 is small and near zero, then the forward rate is an unbiased predictor of the future spot rate.
McGraw Hill / Irwin  2001 by The McGraw-Hill Companies, Inc. All rights reserved.

The Forward Rate Unbiased Condition
5 - 27

A forward rate bias may imply market inefficiency, or it may reflect a risk premium.

Empirical data reveals that the forward rate and future spot rate track along a very similar path, though F tracks “below” the future
S when the spot rate is rising, and vice versa.

On the other hand, actual exchange rate changes form a volatile series, while the forward premium is relatively smooth and calm.
McGraw Hill / Irwin  2001 by The McGraw-Hill Companies, Inc. All rights reserved.

5 - 28
Policy Matters - Private Enterprises

Managers may make profit maximizing decisions by exploiting deviations from the parity conditions, or they may want to avoid or hedge the risks of such deviations.

Application 1: IRP & One-Way Arbitrage
 One-way arbitrage is picking the better-priced alternative for a transaction in the presence of transaction costs.
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5 - 29
Example of One-Way Arbitrage
A manager who holds US$ now wants € in the future.
time dimension
US$
Jan 1
B
Invest US$ at i
$
Jul 1
A
Buy € spot at S
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€
C
Path 1
By taking the lower cost path, the manager is engaging in one-way arbitrage.
Buy € forward at F
Path 2
D
Invest € at i
€
 2001 by The McGraw-Hill Companies, Inc. All rights reserved.

5 - 30
Policy Matters - Private Enterprises

Application 2: Credit Risk & Forward Contracts
 The costs of using an outright forward versus a synthetic forward for hedging may differ for firms because credit risk is usually priced in bank loans but not in forward contracts.

Application 3: IRP & the Country Risk Premium
 The deviations of government securities from IRP provides a measure of the political risk differences among countries.
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5 - 31
Policy Matters - Private Enterprises

Appln 4: Are Deviations from IFE Predictable?
 Even if the deviations are zero on average, a nonrandom pattern can present a profit opportunity.

Appln 5: Are Deviations from IFE Excessive?
 Under a system of pegged exchange rates, any interest rate differential represents a deviation.
 A speculator may (1) invest in the high i currency when the peg is expected to hold, or (2) borrow the high i currency when the peg is expected to change by more than the interest differential.
McGraw Hill / Irwin  2001 by The McGraw-Hill Companies, Inc. All rights reserved.

5 - 32
Policy Matters - Private Enterprises

Appln 6: IFE and Diversification Possibilities
 Can passive investors gain by holding a diversified portfolio of international currencies on an unhedged basis?

Appln 7: IFE, Long-Term Bonds & Exchange
Rate Predictions
 When IFE is extended to long-term bonds ( n -period investments) :
E
  t n



1
1

 i
$, n i
£, n
 n n


S t
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5 - 33
Policy Matters - Public Policymakers

The Fisher parities can provide information regarding how closely national financial markets are linked to one another, and what price, if any, a nation is paying for perceived political and economic risks.

The interest rate differential may be a useful indicator of policy credibility for countries following pegged exchange rate policies.
McGraw Hill / Irwin  2001 by The McGraw-Hill Companies, Inc. All rights reserved.