5
International Parity Relationships
and Forecasting FX Rates
Chapter five
Chapter Objective:
• This chapter examines several key international parity
relationships, such as interest rate parity and
purchasing power parity.
Chapter Outline
 Interest Rate Parity
 Purchasing Power Parity
 The Fisher Effects
 Forecasting Exchange Rates
1
Interest Rate Parity
 IRP: Relationship between nominal interest rates and
forward/spot exchange rates or forward premiums
 IRP is an zero arbitrage condition.
 Arbitrage = the act of buying and selling simultaneously the same
or equivalent assets to make a guaranteed (riskless) profit.
 If IRP did not hold, then it would be possible for an
astute trader to make unlimited amounts of money
exploiting the arbitrage opportunity.
 Since we don’t typically observe persistent arbitrage
conditions, we can safely assume that IRP holds.
2
Interest Rate Parity
Suppose you have $100,000 to invest for one year.
1) invest in Canada at i$ : Future value = $100,000(1 + i$),
or
2) trade your dollars for pound at the spot rate, invest in UK at
i£ and hedge your exchange rate risk by selling the future
value of the British investment forward.
Future value = $100,000(F/S)(1 + i£)
Since both investments have the same risk, they must have the
same future value—otherwise an arbitrage would exist.
Therefore,
$100,000(F/S)(1 + i£) = $100,000(1 + i$)
(F/S)(1 + i£) = (1 + i$)
(F/S) = (1 + i$) / (1 + i£)
3
Interest Rate Parity
Formally,
(F/S)(1 + i£) = (1 + i$)
or if you prefer,
1 + i$
1 + i£
=
F
S
IRP is sometimes approximated as
i$ – i£
=
F–S
S
If i$ > i £ then F>S
4
Interest Rate Parity Carefully Defined
 Depending upon how you quote the exchange rate:
(1) direct quote is $ per £
(2) indirect quote is £ per $ we have:
(2)
1 + i£
F£/$
=
1 + i$
S£/$
(1)
or
1 + i$
F$/£
=
1 + i£
S$/£
5
IRP and Covered Interest
Arbitrage
 If IRP 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
S($/£) = $1.25/£
F360($/£) = $1.20/£
Canadian interest rate
i$ = 7.10%
British interest rate
i£ = 11.56%
6
Interest Rate Parity
$1,000
1. Trade $1000 for £800
2. Invest £800 at 11.56% = i£
$1,071
$1,071
3. One year later, trade
£892.48 for $ at
F360($/£) = $1.20/£
7
IRP and Covered Interest
Arbitrage (CIA)
(1) $1,000 invested in Canada:
One-year result: $1,000(1+ i$) = $1,000(1.071) = $1,071
(2) - Exchange $1,000 for £800 at the prevailing spot rate,
(£800 = $1,000 ÷ $1.25/£)
- Invest £800 at i£ = 11.56% for one year.
One-year result: £800 (1+ i£)= £800 (1.1156) = £892.48
-Translate £ back into dollars at F360($/£) = $1.20/£,
$1.20/£  £892.48 = $1,071.
8
Interest Rate Parity & Exchange
Rate Determination
 According to IRP only one 360-day forward rate, F360($/£),
can exist.
 It must be the case that
F360($/£) = $1.20/£
Why?
 If F360($/£)  $1.20/£, an astute trader could make money with
one of the following strategies:
9
Arbitrage Strategy I
If F360($/£) > $1.20/£
i. Borrow $1,000 at t = 0 at i$ = 7.1%.
ii. Exchange $1,000 for £800 at the prevailing spot rate, (note
that £800 = $1,000÷$1.25/£) invest £800 at 11.56% (i£) for
one year to achieve £892.48
iii. Translate £892.48 back into dollars, if
F360($/£) > $1.20/£ , £892.48 will be more than enough to
repay your dollar obligation of $1,071.
10
Arbitrage Strategy II
If F360($/£) < $1.20/£
i. Borrow £800 at t = 0 at i£= 11.56% .
ii. Exchange £800 for $1,000 at the prevailing spot rate,
invest $1,000 at 7.1% for one year to achieve $1,071.
iii. Translate $1,071 back into pounds, if
F360($/£) < $1.20/£ , $1,071 will be more than enough to
repay your £ obligation of £892.48.
11
Covered Interest Arbitrage (CIA)
 Because the spot and forward markets are not always in a
state of equilibrium opportunity for arbitrage exists.
 The arbitrager who recognizes this imbalance can invest in
the currency that offers the higher return on a covered basis,
i.e., exchange rate back to $, for example, is guaranteed at
the current forward rate.
 CIA opportunities continue until IRP is reestablished.
12
CIA Example - 2
Dollar rate = 8.00 % per year
Start
End
 1.04
$1,000,000
$1,040,000
$1,044,638
Arbitrage
Potential
Dollar money market
S =¥ 106.00/$
180 days = 6 months
F180 = ¥ 103.50/$
Yen money market
¥ 106,000,000
 1.02
¥ 108,120,000
Yen rate = 4.00 % per year
13
IRP and Exchange Rate
Determination
(1  i£ )
xF
 According to IRP: S 
(1  i$ )
 Given F, S depends on relative interest rates
 All else equal, an increase in i$ will lead to a
higher foreign exchange value of the dollar.
 i.e. when i$  => S
14
IRP and Exchange Rate
Determination
 Under certain conditions F can be viewed as the expected
future S conditional on all relevant information being
available. F  E ( St 1 I t )
 Then
(1  i£ )
S
x E ( St 1 I t )
(1  i$ )
 using the approximation formula:
(i$  i£ )  E (e)
 where E(e) is the expected rate of change in the exchange
rate that is [E(St+1)-St]/St
15
Reasons for Deviations from IRP
 Arbitrage Profit exists when (F/S)(1 + i£)  (1 + i$ )> 0
 Transactions Costs




The interest rate available to an arbitrageur for borrowing, ia, may
exceed the rate he can lend at, ib.
There may be bid-ask spreads to overcome, Fb/Sa < F/S
Thus (Fb/Sa)(1 + i£b)  (1 + i$ a)  0 because
(Fb/Sa)< (Fb/Sa) ; (1 + i£b)< (1 + i£); (1 + i$ a)> (1 + i$ )
 Capital Controls

Governments sometimes restrict import and export of money
through taxes or outright bans.
16
Purchasing Power Parity (PPP)
 PPP : Law of one price applied internationally to a standard
commodity basket.
 Absolute PPP : The exchange rate between two currencies
should equal the ratio of the countries’ price levels:
P$
S($/£) =
P£
For example, if the standard commodity basket costs $300 in the U.S. and £150
in the U.K., then the price of one pound sterling in terms of dollars should be:
S($/£) =
P$
P£
$300
= £150
= $2/£
• Spot exchange rate is determined by relative prices of similar basket of goods
Relative Purchasing Power Parity
 If the assumptions of absolute PPP theory are relaxed,
we observe relative purchasing power parity

This idea is that PPP is not particularly helpful in
determining what the spot rate is today, but that the relative
change in prices between countries over a period of time
determines the change in exchange rates.

Moreover, if the spot rate rate between 2 countries starts in
equilibrium, any change in the differential rate of inflation
between them tends to be offset over the long run by an equal
but opposite change in the spot rate.
18
Relative Purchasing Power Parity
and Exchange Rate Determination
 Relative PPP states that the rate of change in the
exchange rate is equal to the differences in the rates
of inflation:
e=
($ – £)
(1 + £ )
≈ $ –  £
 If Canadian inflation is 5% and U.K. inflation is 3.5%,
the dollar should depreciate by 1.45% or around 1.5%
19
PPP Deviations and the
Real Exchange Rate
The real exchange rate is
(1 + $)
q =
(1 + e)(1+ £)
If PPP holds,
(1 + e) =
(1 + $ )
(1 + £ )
then q = 1.
If q < 1 competitiveness of domestic country improves with currency
depreciations (if dollar depreciates by more than is warranted by PPP)
If q > 1 competitiveness of domestic country deteriorates with currency
depreciations (if dollar depreciates by less than the inflation differential)
20
Evidence on PPP
 PPP probably doesn’t hold precisely in the real
world for a variety of reasons.



Haircuts cost 10 times as much in the developed world as
in the developing world.
Ipod, on the other hand, is a highly standardized
commodity that is actively traded across borders.
Shipping costs, as well as tariffs and quotas can lead to
deviations from PPP.
 PPP-determined exchange rates still provide a
valuable long-run benchmark.
21
The Fisher Effects
 An increase (decrease) in the expected rate of inflation will
cause a proportionate increase (decrease) in the interest rate
in the country.
 For Canada, the Fisher effect is written as:
1 + i$ = (1+ $)(1 + E[$]) = 1 + $ + E[$] + $E[$]
i$ = $ + E($) + $E[$] ≈ $ + E[$]
Where
$ is the equilibrium expected “real” Canadian interest rate
E[$] is the expected rate of Canadian inflation
i$ is the equilibrium expected nominal Canadian interest rate
22
Expected Inflation
 The Fisher effect implies that the expected inflation
rate is approximated as the difference between the
nominal and real interest rates in each country, i.e.
i$ = $ + (1 + $)E[$] ≈ $ + E[$]
E[$] =
(i$ – $)
(1 + $)
≈ i$ – $
23
International Fisher Effect
If the Fisher effect holds in Canada
i$ = (1+ $)(1 + E[$]) ≈ $ + E[$]
and the Fisher effect holds in Japan,
i¥ = (1+ ¥ )(1 + E[¥]) ≈ ¥ + E[¥]
and if the real rates are the same in each country (i.e.
$ = ¥ ), then we get the International Fisher Effect
E(e) =
(i$ – i¥)
(1 + i¥)
≈ i$ – i¥
24
International Fisher Effect
If the International Fisher Effect holds,
(i$ – i¥)
E(e) =
(1 + i¥)
and if IRP also holds
F–S
S
=
(i$ – i¥)
(1 + i¥)
then Forward Expectations parity holds. E(e) =
F–S
S
25
Approximate Equilibrium
Exchange Rate Relationships
E(e)
≈ IFE
(i$ – i¥)
≈ FEP
≈ PPP
F–S
≈ IRP
S
≈ FE
≈ FPPP
E($ – £)
26
Forecasting Exchange rates
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]
and
Ft = E[St+1| It]
 Predicting exchange rates using the efficient markets
approach is affordable and is hard to beat.
27
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.
28
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
29
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.”
30