International FinanceFINA 5331

Lecture 13:

Uncovered Interest Rate Parity,

Purchasing Power ParityAaron 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 = (1 + i*

t)

(it – i*t)

St

Ft – St

FRUH and UIP

• Then it must be the case that

• or approximately

This is the Uncovered Interest Parity condition.

It will only hold if investors are risk neutral or equivalently they do not care about the currency denomination of the assets they hold

= (1 + i*

t)(it – i*

t)St

E(St+1) – St

E(st+1) – st=it-it*

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 Parityin 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.

£/$wheatUK,wheatUS, SPP

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$

S($/£) = P£

P$

£150$300

= = $2/£

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:

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

$/£, 1 $/£, US, 1 US, UK, 1 UK, US UK

$/£, US, UK,

% , % , %t t t t t t

t t t

S S P P P Ps p p

S P P

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

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.

*1 1 1(% ) ( ) ( )t t tE s E E

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

If absolute PPP holds then

*t t

tt

S P

P

*1t

t tt

PS

P

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 – pt

T*.• 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)pt

N, 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)pt

N.• PPP no longer holds since st and pt

* stay the same while pt rises so that st < pt – pt

*.• 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.

• It seems that PPP is a poor explanation of exchange-rate changes on a period-by-period basis.

• However, there is a tendency for PPP to reassert itself as time passes (mean reversion).

Empirical Evidence on Prices and Exchange Rates

Empirical Evidence onPrices 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 onPrices 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.