International Finance
FINA 5331
Lecture 13:
Uncovered Interest Rate Parity,
Purchasing Power Parity
Aaron Smallwood Ph.D.
FRUH and UIP
• Ft = E(St+1) if investors are risk neutral.
• Since investors are assumed to be rational,
E(St+1) = St+1 + εt+1 where εt+1 is a random
(unforecastable) forecast error.
• Then Ft = St+1 + εt+1 and the forward rate is
an unbiased predictor of the future spot rate.
• From CIP Ft – St
(it – i*t)
=
St
(1 + i*t)
FRUH and UIP
• Then it must be the case that
E(St+1) – St
St
*)
(i
–
i
t
= t
(1 + i*t)
• or approximately
This is the Uncovered Interest Parity
condition. E(st+1) – st=it-it*
It will only hold if investors are risk neutral or
equivalently they do not care about the currency
denomination of the assets they hold
FRUH and UIP
• If uncovered interest parity (UIP) holds
then FRUH is true and investors are risk
neutral.
• Risk neutrality implies that investors
have no currency preference in which
their investments are denominated.
• Assets with identical risk characteristics
but denominated in different currencies
will be viewed as perfect substitutes.
Purchasing Power Parity
• Purchasing Power Parity and Exchange
Rate Determination
• PPP Deviations and the Real Exchange
Rate
• Evidence on PPP
Purchasing Power Parity
in a Perfect Capital Market
• Purchasing power parity (PPP) is built on
the notion of arbitrage across goods
markets and the Law of One Price.
• The Law of One Price is the principle that
in a PCM setting, homogeneous goods will
sell for the same price in two markets,
taking into account the exchange rate.
PUS,wheat  PUK,wheat  S$ / £
The Big Mac PPP Standard Reviewed
• Let’s review recent evidence related to the
Big Mac index:
• http://www.economist.com/content/big-mac-index
• Mexican peso price of the dollar in Jan,
2013 was: Peso 12.74. Big Mac costs 37
pesos in Mexico. Cost in US dollars:
37/12.74 = $2.90. Cost is $4.37 in US.
Purchasing Power Parity
• Let PUS and PUK represent the weighted
average price level for goods in the U.S.
and U.K. market baskets respectively.
• Absolute PPP predicts that these two price
measures will be equal after adjusting for
the exchange rate: PUS = S$/£  PUK
• Absolute PPP requires that the
consumption baskets are identical across
the two countries.
Purchasing Power Parity and Exchange Rate
Determination
• The exchange rate between two currencies should equal the
ratio of the countries’ price levels:
S($/£) =
P$
P£
For example, if an ounce of gold costs $300 in the U.S. and £150
in the U.K., then the price of one pound in terms of dollars
should be:
P$ $300
S($/£) =
=
= $2/£
P£ £150
Relative Purchasing Power Parity
Suppose absolute PPP is violated. Introduce K so that:
PUS, t +1 = K  S$/£, t +1  PUK, t +1
(a)
PUS, t = K  S$/£, t  PUK, t

(b)
%ΔpUS = %Δ s + %Δ pUK + %Δ s  %Δ pUK
S$/£, t 1  S$/£, t
PUS, t 1  PUS, t
PUK, t 1  PUK, t
%s 
, %pUS 
, %pUK 
S$/£, t
PUS, t
PUK, t
For small % changes, or when continuous rates are used, the
cross-product term %Δ s  %Δ pUK can be ignored.
% exchange rate = % U.S.prices – % U.K.prices
Relative Purchasing Power Parity
• Note that %Δp = π, the rate of inflation
• Relative PPP states that the rate of
change in the exchange rate is equal to
the differences in the rates of inflation:
%Δs =
($ – £)
(1 + £ )
≈  $ – £
If U.S. inflation is 5% and U.K. inflation is 8%, the pound
should depreciate by 2.78% or approximately 3%.
Ex-Ante PPP
• Ex-Ante PPP says that relative PPP will
hold in an expected value sense, i.e.
E (% st 1 )  E ( t 1 )  E (
*
t 1
)
Where E is the expectations operator signifying
that E(·) is an expected value.
Purchasing Power Parity
• The real exchange rate is calculated by correcting the
nominal exchange rate for the price levels in the two
countries.
• When absolute PPP holds:
$1.50/£ =
$1,500/US good
£ 1,000/British good
.
LHS = 1 US good / British good
RHS
• When PPP holds, the real exchange rate is constant.
PPP Deviations and the Real Exchange Rate
The real exchange rate is
St Pt
t 
Pt
*
Pt
If absolute PPP holds then St  *   t  1
Pt
Absolute PPP implies that price indices in all countries are
computed with the same weights and the same basket of
goods. Since this is never true, relative PPP is the more
appropriate form. Under relative PPP, ρt will be constant but
differ from unity.
Purchasing Power Parity and Overvalued or
Undervalued Currencies
As we have seen, nominal exchange rates
greater than the PPP implied exchange rate
represent foreign currency overvaluation,
while nominal exchange rates less than the
PPP implied exchange rate represent domestic
overvaluation (or foreign undervaluation).
How useful is 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.
– Film, 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.
– Productivity differences in traded and non-traded
goods. (more on this in a minute)
• PPP-determined exchange rates still provide a
valuable benchmark.
The Balassa-Samuelson Effect
• How do productivity differences affect PPP?
• Assume that PPP holds initially, i.e. st = pt – pt*.
• LOP always holds for traded goods, i.e. st = ptT – ptT*.
• Labor is perfectly mobile within a nation between the traded goods sector
and the non-traded goods sector.
• The non-traded goods sector is more labor intensive.
• Output and labor markets are competitive.
• National price indices are a weighted average of traded goods prices and
non-traded goods prices, i.e. pt = θptT + (1-θ)ptN, where the weights are
fixed.
• Productivity growth is higher in the traded goods (capital intensive) sector.
The Balassa-Samuelson Effect
• Productivity increases in the traded goods sector mean that wages in that
sector will rise without prices in that sector rising (a real wage increase).
• Traded goods prices do not change, so the exchange rate does not change
because LOP holds for traded goods.
• Since labor is mobile between sectors, wages in each sector must be
equalized.
• Since wages are rising in the non-traded goods sector but productivity is
not, prices of non-traded goods must rise.
• The rise in the price of non-traded goods causes the overall price index to
rise since pt = θptT + (1-θ)ptN.
• PPP no longer holds since st and pt* stay the same while pt rises so that st <
p t – p t* .
• The domestic currency is overvalued!
Relaxing the Perfect Capital Market Assumptions
• Transaction Costs
– Transport and menu costs lead to a neutral band
around the PPP line, within which it is not profitable to
execute arbitrage transactions.
• Taxes
– Tariffs have an effect similar to transaction costs.
• Uncertainty
– Arbitrageurs will seek a greater profit to compensate for
risks, thus leading to a wider band around the PPP line
before arbitrage becomes profitable.
Empirical Evidence on Prices and Exchange Rates
• It seems that PPP is a poor explanation of
exchange-rate changes on a period-byperiod basis.
• However, there is a tendency for PPP to
reassert itself as time passes (mean
reversion).
Empirical Evidence on
Prices and Exchange Rates
• Note that the real exchange rate itself may
not be constant.
– It may change on a permanent basis if a real
shock affected one country but not its trading
partners.
– The Balassa-Samuelson hypothesis states
that countries that have experienced high
productivity gains, higher real income growth
and higher real incomes should have
appreciating real exchange rates.
Empirical Evidence on
Prices and Exchange Rates
• Empirical tests confirm that ...
– PPP is a poor descriptor of exchange rate
behavior in the short run, where the rates are
quite volatile and domestic prices are
somewhat sticky.
– But in longer-run analysis, it appears that PPP
offers a reasonably good guide.
Policy Matters - Private Enterprises
• If managers can identify the deviations
from parity that are growing larger or likely
to persist, then profit-maximizing decisions
can be made.
• Knowing that deviations from parity occur,
managers may adopt strategies that
reduce their exposure to the risks of such
deviations.
Policy Matters - Private Enterprises
• In a number of instances, international
price differentials in some commodities
have been both large and persistent.
• More interesting perhaps are the
international price differentials across
“branded goods” like McDonald’s Big Mac
and The Economist, whose prices are set
by brand managers rather than by market
forces.
Policy Matters - Public Policymakers
• Deviations from PPP, by definition,
measure changes in a country’s
international competitiveness, and reveal
whether a currency is overvalued or
undervalued relative to a simple standard.
• However, there are limitations on the
usefulness of PPP in policy decisions, as
real macroeconomic disturbances call for
a change in the real exchange rate.