International Parity
Relationships and Forecasting
Foreign Exchange Rates
6
Chapter Six
Chapter Objective:
This chapter examines several key international
parity relationships, such as interest rate parity and
purchasing power parity.
6-0
Chapter Outline
Covered
Interest
InterestRate
Interest
RateParity
Parity
Rate
Parity (CIRP)

Covered Interest
Arbitrage
Purchasing
Purchasing
Power
Power
Parity
Parity(PPP): absolute & relative

IRP
and
Exchange
Determination

PPP
Deviations
and:Rate
the Real
Exchange
Rate
The
The
Fisher
Fisher
Effects
Effects
Domestic
& International

for
Deviations
from
IRP
 Reasons
Evidence
on
Purchasing
Power
Forward
Forecasting
Forecasting
Parity
Exchange
ExchangeRates
Rates Parity

PowerApproach
Parity
 Purchasing
The
Fisher
Effects

Efficient
Market
 Forecasting Exchange Rates

Fisher Effects
 The
Forecasting
Exchange
 Fundamental
ApproachRates
 Forecasting
Exchange Rates
 Technical Approach

6-1
Performance of the Forecasters
Covered Interest Rate Parity Defined




Idea: $1 (or any amount in $ or in any FC) invested in
anywhere should yield the same $ return (or FC return)
if the world investment market is perfect! Competitive
returns! Otherwise?
CIRP is an “no arbitrage” condition.
If CIRP did not hold, then it would be possible for an
astute trader to make unlimited amounts of money
…almost
all opportunity.
of the time!
exploiting the
arbitrage
Since we don’t typically observe persistent arbitrage
conditions, we can safely assume that CIRP holds.
6-2
A Simple Covered Interest Rate Arbitrage
Example


BOA 4% vs Nations Bank 5%
Identify L and H, Borrow Low & Invest (Deposit) High




A few issues:



Borrow say $1 from BOA and Deposit at NB
Cash Flow at 0: +$1 from BOA -$1 to NB => Net CF= $0
Cash Flow at1: +$1.05 from NB -$1.04 to BOA => $0.01
arbitrage gain.
1) Bid-Asked? How about 3.99~3.01% vs 4.99~5.01%
2) Can it be sustained?
What is the equilibrium situation, then?
What about




4% in the US vs 5% in the UK?
Well, we need more info to determine the
arbitrage opportunity. Why?
Why? US interest rate, i$, is a $ interest rate and
the UK rate, i£, is a £ interest rate. It is like
comparing apples and oranges.
What do you need? Exchange rates!
.

A Box Diagram to show





$ interest rate investing in the UK is 5.5% > 4%


Why 5.5% > 5.0%? Investing in UK involves two transactions
(or investments)!
Borrow from the US and Invest in UK!


$1 invested in the US => $1.04
$1 => 0.5 £s at So = $2/ £, or (1/So) £ s
Then 0.5 £ s => 0.5*(1.05) = 0.525 £ s, or (1/So)*(1+iBP) £ s
To convert £ s to $s, we need the future exchange rate. To have
no risks, we use a forward contract with the forward rate, say
F=$2.01/ £. Then $ amount is $1.055, or $(1/S0)*(1+i £)*F
Arbitrage strategy: Arbitrage profit = $0.015
In equilibrium with no arbitrage opportunity, 1+i$ =
(1/So)*(1+i£)*F. CIRP (why Covered?)
Covered Interest Rate Parity Defined
Consider alternative one-year investments for $1:
1.
Invest in the U.S. at i$. Future value = $ (1 + i$)
Trade your $ for £ at the spot rate, invest (1/So ) £s in Britain
at i£ while eliminating any exchange rate risk by selling the
future value of the British investment forward.
2.
F
Future value = $(1 + i£) ×
So
Since these investments have the same risk, they must have
the same future value (otherwise an arbitrage would exist)
F
(1 + i$)
F$/£ = S$/£ × (1 + i )
(1 + i£) ×
= (1 + i$)
So
£
6-6
Alternative 2:
Send your $ on a
round trip to
Britain
$1,000
So
Step 2:
Invest those
pounds at i£
Future Value =
$1,000
Alternative 1:
invest $1,000 at i$
CIRP
Step 3: repatriate
future value to the
U.S.A.
$1,000
 (1+ i£)
So
$1,000
 (1+ i£) × F
$1,000×(1 + i$) =
So
6-7
Since both of these investments have the same risk, they must
have the same future value—otherwise an arbitrage would exist
CIRP Defined
Formally,
1 + i$
F
=
1 + i¥
So
CIRP is sometimes approximated as
i$ – i¥ ≈ F – So
So
6-8
CIRP and Covered Interest Arbitrage
If CIRP failed to hold, an arbitrage would exist. It’s
easiest to see this in the form of an example.
Consider the following set of foreign and domestic
interest rates and spot and forward exchange rates.
Spot exchange rate
360-day forward rate
6-9
So = $2.0000/£
F360 = $2.0100/£
U.S. discount rate
i$ = 3.00%
British discount rate
i£ =
2.49%
CIRP and Covered Interest Arbitrage
A trader with $1,000 could invest in the U.S. at 3.00%, in one
year his investment will be worth
$1,030 = $1,000  (1+ i$) = $1,000  (1.03)
Alternatively, this trader could
1. Exchange $1,000 for £500 at the prevailing spot rate,
2. Invest £500 for one year at i£ = 2.49%; earn £512.45
3. Translate £512.45 back into dollars at the forward rate
F360($/£) = $2.01/£, the £512.45 will be worth $1,030.
6-10
Alternative 2:
Arbitrage I
buy pounds
£500
£1
£500 = $1,000×
$2.00
$1,000
Alternative 1:
invest $1,000
at 3%
FV = $1,030
6-11
Step 2:
Invest £500 at
i£ = 2.49%
£512.45 In one year £500
will be worth
Step 3: repatriate
£512.45 =
to the U.S.A. at
£500  (1+ i£)
F360($/£) =
$2.01/£
$1,030
F£(360)
$1,030 = £512.45 ×
£1
CIRP & Exchange Rate Determination
According to CIRP only one 360-day forward rate,
F360, can exist. It must be the case that
F360 = $2.01/£
Why?
If F360  $2.01/£, an astute trader could make money
with one of the following strategies:
6-12
Arbitrage Strategy I
If F360 > $2.01/£ => then LHS<RHS
i. Borrow $1,000 at t = 0 at i$ = 3%.
ii. Exchange $1,000 for £500 at the prevailing spot
rate, (note that £500 = $1,000 ÷ $2/£) invest £500 at
2.49% (i£) for one year to achieve £512.45
iii. Translate £512.45 back into dollars, if
F360 > $2.01/£, then £512.45 will be more than
enough to repay your debt of $1,030.
6-13
Arbitrage Strategy II
If F360 < $2.01/£
i. Borrow £500 at t = 0 at i£= 2.49% .
ii. Exchange £500 for $1,000 at the prevailing spot
rate, invest $1,000 at 3% for one year to achieve
$1,030.
iii. Translate $1,030 back into pounds, if
F360 < $2.01/£, then $1,030 will be more than
enough to repay your debt of £512.45.
6-14
Reasons for Deviations from CIRP

Transactions Costs


Capital Controls


There may be bid-ask spreads to overcome
Governments sometimes restrict import and export of
money through taxes or outright bans.
Different risks
6-15
Transactions Costs Example

Will an arbitrageur facing the following prices be
able to make money?
Borrowing
Lending
$
5.0%
4.50%
€
5.5%
5.0%
Spot
Bid
$1.42 = €1.00
Forward $1.415 = €1.00
6-16
Ask
$1.45 = €1,00
$1.445 = €1.00
Purchasing Power Parity



Purchasing Power Parity and Exchange Rate
Determination
PPP Deviations and the Real Exchange Rate
Evidence on PPP
6-17
Purchasing Power Parity and
Exchange Rate Determination


The exchange rate between two currencies
should equal the ratio of the countries’ price
levels (Absolute PPP):
 So = P$/P£
Alternatively, P$ = So*P£, Price level in each
country determined in the same currency ($)
should be the same in both countries. What you
can buy with $100 should be the same anywhere
in the world. => Living costs are the same!
Relative PPP





If Absolute PPP holds at each point in time, say at t=0
and t=1, then
We can show that %chg in the exchange rate (=(S1So)/So, FC appreciation rate relative to $) is equal to the
difference between the %chg in the US price level (=US
inflation rate) and the %chg in the UK price level (=UK
inflation rate), E(e) = E(π$) – E(π£)
If the inflation rate in the U.S. is expected to be 5% in
the next year and 3% in the euro zone,
Then the expected change in the exchange rate in one
year should be 5 - 3=2%, euro is expected to be 2%
stronger against $
Make sense?
Fisher Equations



Domestic (Closed)
i$ = ρ$ + E(π$), 1+i$ = (1+$)*(1+E($)) to be
exact
International (Open)

- i£ = E(π$) – E(π£)
Relative PPP + International Fisher
E(e) = E(π$) – E(π£) = i$ - i£
 i$


Assuming that ρ$ = ρ£ ,
Evidence on PPP

PPP probably doesn’t hold precisely in the real
world for a variety of reasons.




Non-tradable goods like services, perishable products
Transactions & Transportation costs including tariffs,
etc.
Different consumption baskets
PPP-determined exchange rates still provide a
valuable benchmark.
6-21
Forward Parity


F = E(S1)
(F – So)/So = (E(S1) – So)/So = E(e)
Approximate Equilibrium Exchange
Rate Relationships
E(e)
(i$ – i¥)
≈ Rel PPP
≈ CIRP
≈ Int
Fisher
6-23
E($ – £)
≈ Fwd
Parity
F–S
S
Forecasting Exchange Rates




Efficient Markets Approach
Fundamental Approach
Technical Approach
Performance of the Forecasters
6-24
Efficient Markets Approach



Financial Markets are efficient if prices reflect all
available and relevant information.
If this is so, exchange rates will only change when
new information arrives, thus:
St = E[St+1| It]
and/or
Ft = E[St+1| It]
Predicting exchange rates using the efficient
markets approach is affordable and is hard to beat.
6-25
Fundamental Approach

Involves econometrics to develop models that use a
variety of explanatory variables. This involves
three steps:




step 1: Estimate the structural model.
step 2: Estimate future parameter values.
step 3: Use the model to develop forecasts.
The downside is that fundamental models do not
work any better than the forward rate model or the
random walk model.
6-26
Technical Approach



Technical analysis looks for patterns in the past
behavior of exchange rates.
Clearly it is based upon the premise that history
repeats itself.
Thus it is at odds with the EMH
6-27
Performance of the Forecasters



Forecasting is difficult, especially with regard to
the future.
As a whole, forecasters cannot do a better job of
forecasting future exchange rates than the forward
rate.
The founder of Forbes Magazine once said:
“You can make more money selling financial
advice than following it.”
6-28