 Chapter 10
 Currency Exchange
Rates
Is a “strong” currency a “good” thing for an economy?
 On the one hand, a stronger currency for an economy,
by definition, means that the citizens of that economy
have achieved a greater claim on the world’s resources
outside of that economy. In effect, they are made
wealthier as foreign goods and holidays abroad are
made more affordable by the strength of their currency.
Is a “strong” currency a “good” thing for an economy? (cont)
 In addition, a stronger currency, by making imports
of raw materials cheaper, works to suppress price
rises in finished products, which works to curb
inflation and to keep interest rates low – which
generally works to promote economic growth.
Is a “strong” currency a “good” thing for an economy? (cont)
 On the other hand, a stronger currency
means that when goods are sold abroad in a
foreign country at a price determined by
that country’s currency, the price equates
with a reduced amount when converted
back to the exporting firm’s currency.
 A strong currency therefore works to
undermine the competiveness of a country’s
exports and, thereby, to undermine its
exporting companies.
Is a “strong” currency a “good” thing for an economy? (cont)
 The economy might appear more robust on paper with a stronger
currency, but that will be of little consolation when firms have to
reduce their work force due to falling orders from overseas.
 Developing countries, in particular, generally prefer to sustain a weak
currency aimed at building a manufacturing base with orders from
overseas.
Importance of Exchange Rates
 Movements in exchange rates can afford a
company a windfall gain when the currency
moves in its favor, while businesses have
been severely weakened and indeed
bankrupted by adverse exchange rate
movements.
The forces driving an exchange rate

(1) the demand for that economy’s currency from overseas
consumers seeking to purchase that economy’s goods and services
(banking and insurance services, for example),

(2) the demand for that economy’s currency from overseas
multinationals and overseas investors
economy,

seeking to invest in that
The forces driving an exchange rate (cont)
(3) the demand for that economy’s currency from the central banks of
overseas economies seeking to control their exchange rate with that
economy,
(4) speculation as to the currency’s “direction”,
and
(5) the currency’s inflation and interest rates.
Manipulating exchange rates
 Suppose we are changing 10 million Japanese Yen (¥) to US dollars at
an exchange rate of ¥120/$.
 Do we then multiply 10 million Yen by the exchange rate ¥120/$ to
determine the amount of dollars received?
 You can probably see that the answer is “No”.
 Rather, we must divide the 10 million Yen by 120 to determine the
amount of dollars received.
Manipulating exchange rates (cont)

We can see this in terms of the principle of dimensional consistency. If we were to
convert the 10 million Yen to US dollars by multiplying by ¥120/$, we would be
imposing the conversion:

P¥ x
¥
$
= P$,

where P¥ represents the 10 million Yen, and ¥/$ represents the exchange rate as ¥/$.

Note that the left-hand side of the above conversion has units of ¥-squared - ie, P¥ x ¥
- which is meaningless! - divided by $, equating with units of $ on the right-hand
side – ie, P$.
Manipulating exchange rates (cont)
Dimensional Consistency requires that
we have consistent units on both sides of the conversion.

The implication is that the units of ¥ in the ¥10 million number on the left-hand side must
“be allowed to cancel” with the units of in the divisor of $/¥, meaning that we require:

P¥ x
$
¥
= P$,
and not:
P¥ x
¥
$
= P$,

So the rule is simple: in calculations, ensure that the conversion complies with

the principle of dimensional consistency.
Direct and indirect quotes for currencies
 Quotes for assets can be “direct” or “indirect”.
 In everyday life, we generally prefer direct
quotes.
 For example, if a cake is priced at $2 per cake,
this represents a “direct” quote for the cake.
 It is a direct quote because we have the price
of the cake that is being bought or sold as the
price of a single cake.
 “One dollar will buy you half a cake” would
be an indirect quote for the cake.
Direct and indirect quotes for currencies (cont)
 Direct quotes are generally more intuitive
than indirect quotes. For example if last
week, cakes were trading at $2/cake (a
direct quote as the price of a single cake)
and the same cake is now priced at
$2.5/cake, it is immediately clear that the
price of the cake has increased.
Direct and indirect quotes for currencies (cont)
 This is because, with direct quotes, a higher
number implies a higher value for the
underlying object under the line – the cake
in this example – so that $2.5/cake implies
a more expensive cake that $2/cake.
 So, for example, if an exchange rate of
¥100/$ becomes ¥110/$, the dollar has
strengthened (and the Yen has accordingly
weakened).
Break Time
A model of exchange rates in response to interest rates
and inflation: the parity conditions
 Although it is not possible to construct a
mathematical model dependence of
exchange rate movements that has
generality, it is possible to construct a
mathematical dependence in relation to
interest rate and inflationary changes.
 The inputs are the parity conditions.
Purchasing Power Parity (PPP)
The law of one price gives us:


$
¥/$
𝑃0 x 𝑆0
¥
= 𝑃0
(10.1)
$
¥
¥/$
where the current price of the product is 𝑃0 in $, and is 𝑃0 in ¥ - and 𝑆0
is the current exchange rate (which is to say, the product costs the same in
both countries).

We can express Eqn 10.1 as
¥/$
 𝑆0
¥
=
𝑃0
$
𝑃0
 which is the statement of purchasing power parity (PPP).
(10.2)
Relative Purchasing Power Parity (RPPP)
 Now suppose we have inflation per year on prices in the US at the rate
inf $ per annum and on prices in Japan at the rate inf ¥ per annum.
¥/$
Eqn 10.2 updated determines a revised exchange rate 𝑆1
as
¥/$
𝑆1
¥
=
after one year
¥
𝑃0 x (1 + 𝑖𝑛𝑓 )
$
$
𝑃0 x (1 + 𝑖𝑛𝑓 )
(10.3)
 Combining Eqn 10.3 with Eqn 10.2, we have:


¥/$
𝑆1
=
¥/$ 1+𝑖𝑛𝑓¥
𝑆0
1+𝑖𝑛𝑓$
Which is the law of relative purchasing power parity
(10.4)
Relative Purchasing Power Parity (RPPP) and “follow through”
 The following Illustrative Example demonstrates how
the terms of trade between countries actually remains
unaffected when (1) the sale price of the goods traded
adjusts to the local inflation, which we refer to as
“follow through”, combined with (2) the exchange rate
changes in compliance with relative purchasing power
parity (RPPP).
Relative Purchasing Power Parity (RPPP) and “follow through”(cont)
 Suppose a Japanese car company exports cars to the
US, where they sell at $100,000.
 If the exchange rate is 110 ¥/$, how much do the cars
sell for in Yen?
 We have:

$100,000 x 110 ¥/$ = 11,000,000 ¥.
Relative Purchasing Power Parity (RPPP) and “follow through”(cont)
 Suppose we now have 10% inflation in the US and zero
inflation in Japan over the coming year.
 What is the anticipated exchange rate at the end of a year?
 With Eqn 10.4, we have

 ///
¥/$
𝑆1
=
¥/$ 1+𝑖𝑛𝑓¥
𝑆0
1+𝑖𝑛𝑓$
=
110 𝑥
1.0
1.10
= 100 ¥/$.
Relative Purchasing Power Parity (RPPP) and “follow through”(cont)

Assuming follow through,

And what does that now equate to in Yen?

The idea of “follow through” is that if inflation is 10% in the US - meaning
How much do the cars now sell for in the US?
prices in the US increase by 10% - it is reasonable to assume that the above
cars sell for 10% more, which is to say:

$100,000 x 1.1 = $110,000.
Which in Yen provides the Japanese company with

$110,000 x 100 ¥ / $ = 11,000,000 ¥.

exactly as one year previous.
A reality check on Purchasing Power Parity (PPP)
 We know from experience that purchasing
power parity does not hold strictly.
 On travels abroad, goods and services will
inevitably appear either more or less
expensive to our pocket due to the currency
exchange.
 Purchasing power parity nevertheless
highlights at least one influence on the
changing valuation of a currency, namely, that
higher inflation in an economy in relation to
other economics, should tend to weaken the
exchange rate of the high inflation currency
against less inflated currencies.
Interest Rate Parity (IRP)
 We have the approximate form from Eqn 3.11:

int = r + inf
 where int = nominal interest rate, r = real interest rate and
inf = expected inflation.
Thus, we have the approximations:

Int$ = r$ + inf$
and
Int¥ = r¥ + inf¥.
Interest Rate Parity (IRP) (cont)
 The Fisher effect considers that real interest rates should
conform as to be equal with each other across currencies –
which we may think of as the “purchasing power parity” of the
“price” of borrowing across economies.
 Thus, allowing that r¥ and r$ are equal, we have from the
previous slide:

int¥ - int$ approximatel equal to inf¥- inf$
(10.8)
Interest Rate Parity (IRP) (cont)

1+int$ = (1+r$) x (1+inf$ )
More precisely, we have:
1+int¥ = (1+r¥) x (1+inf¥ )
and:
so that:



1+𝑖𝑛𝑡 ¥
1+𝑖𝑛𝑡 $
=
1+𝑖𝑛𝑓¥
1+𝑖𝑛𝑓$
(10.10)
which with Eqn 10.4 provides:
¥/$
𝑆1
=
¥/$ 1+𝑖𝑛𝑡 ¥
𝑆0 1+𝑖𝑛𝑡 $
which is the statement of interest rate parity (IRP).
(10.11)
A reality check on Interest Rate Parity (IRP)
 Interest Rate Parity is both counter-intuitive and unreliable, in that we
have the outcome that the lower the interest rate on, say, the dollar
against the Yen, the higher the anticipated value of the US dollar,
¥/$
𝑆1 , and the lower the anticipated value of the Yen.
 This is the necessary outcome of IRP, which simply assumes that real
interest rates (over and above inflation) remain equal, so that higher
interest rates occur in lock-step with higher inflation.
 Not always so in practice!
Forward rate parity (FRP)

A forward contract is a contract that today sets the terms of exchange for a
transaction in the future. So, for example, if the bank agrees to change my US
dollars into Yuan 12 months from now at the rate 6.25 Yuan to the US dollar
(which rate we agree on today), this is a forward contract.

To differentiate between today’s rate and a rate negotiated forward from
today, we call the current rate the “spot” rate and the forward negotiated rate
the “forward” rate.

The actual exchange rate in the future, which is currently unknown, is at the
present time referred to as the “future spot rate”.
Forward rate parity (FRP) (cont)
Suppose, as an example, that the current spot rate is ¥120/$, and
that the 12 months forward rate (F¥/$) is F¥/$ = ¥119/$.
Suppose, also, that the 12-month interest rate on a Yen deposit
is 0.4% and on a US dollar deposit is 5%.
 To see how the forward rate is expected to interact with
inflation and interest rates, consider that I have, say,

¥10 million today.
Forward rate parity (FRP) (cont)
I have a choice between:

Strategy A: depositing my ¥10 million at the interest rate currently being offered for
a 1-year deposit, 0.4%,

or

Strategy B: converting the ¥10 million into US dollars today (at the spot rate 𝑆0
¥/$
=
¥120/$) and depositing the dollars at the interest rate currently being offered for a 1year deposit on the US dollar (5%) and then (to compare like with like, which is to
say, ¥ with ¥), at the end of the 12-month period, changing the accumulated dollars
into Yen (at the forward rate F¥/$ = ¥119/$).
Forward rate parity (FRP) (cont)

Strategy A:
At the end of 12 months, Strategy A will deliver:
¥10 million x (1+ int¥)

Strategy B:
=
¥10 million x 1.004
Strategy B will today deliver ¥10 million converted to US dollars as
$/¥

¥10 million x 𝑆0
¥10 million
→ US $
¥10 million
120

which is to say,

We can then deposit this amount in a US account to deliver
¥/$
𝑆0
=
$83,333.33 x (1+ int$) at the end of 12 months =

= ¥10,040,000,
= $83,333.33 today.
$83,333.33 x 1.05 = $87,500.
In addition, we can today use the forward rate to guarantee the conversion of the $87,500 into
Yen 12 months forward, which is to say,
$87,500.00 x F¥/$ = $87,500.00 x 119¥/$
= ¥10,412,500.
Forward rate parity (FRP) (cont)
Forward rate parity (FRP) (cont)
 Thus, Strategy B delivers ¥10,412,500,
as compared with ¥10,040,000 following Strategy A.
 In other words, it is possible to arbitrage the situation by borrowing
¥10 million Yen today and, following Strategy B, accumulate
¥10,412,500 12 months forward. We would then pay back the loan
plus interest (¥10,040,000) and retain a ¥372,500 risk-free profit. In
effect, the market is offering a risk-free money machine.
In such a situation,
“everyone” should be changing Yen into dollars!!
///
Forward rate parity (FRP) (cont)
Equilibrium demands that the outcomes of Strategies A and B above
must be equal.
Which is to say, following through the steps of Strategies A and B and
ensuring that they equate with each other, we require:
$/¥

1+ int¥ = 𝑆0
(1+ int$) / F$/¥
¥
 which provides

𝐹
¥/$
=
¥/$ 1+ 𝑖𝑛𝑡
𝑆0 1+𝑖𝑛𝑡 $
(10.13)
which is the statement of forward rate parity (FRP).
The forward currency premium
(discount)
 Investors refer to the “premium”
(alternatively the “discount”) on a currency
by calculating the percentage difference
between the forward rate and the current
spot rate; which we estimate (with Eqn
10.13) as:
¥/$
𝐹1
¥/$
− 𝑆0
¥/$
𝑆0
approximately equal to
int¥ - int$
(10.16)
Combining the parity conditions

Combining the parity conditions (Eqns 10.4, 10.12 and 10.13) we have
𝐹
/
¥ $
=
¥/$
𝑆1
=
¥/$ 1+𝑖𝑛𝑡 ¥
𝑆0
1+𝑖𝑛𝑡 $
=
¥/$ 1+𝑖𝑛𝑓¥
𝑆0
1+𝑖𝑛𝑓$
(10.14)

Equation 10.14 is the statement that the forward rate (F) is actually investors’
expectation for the future spot rate (S1), both of which can be identified with the impact
of the relative inflation and interest rates.

///
Review
 One way in which we may attempt to accommodate
what might appear to be independent conclusions, is to
remark that in the short to medium term (looking
forward up to twelve months or so), changes in
inflationary expectations combined with government
intervention (Forces 4 and 5 in slide 8) impact on a
currency’s exchange rate.
 Over this period, speculative forces (Force 4 in slide 8)
are likely to move a currency’s exchange rate with selfsustaining movements.
 Over a currency’s longer-term (looking forward beyond
eighteen months or more), the fundamentals for the
economy - the economy’s provision of goods and
services, as well as investment opportunities into its
economy - can be expected to determine the currency’s
exchange rate (Forces 1 – 2 in slide 7).