Transcript Course Objective - Chandigarh University

Fundamental equilibrium
relations: parity conditions
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What are Parity Conditions?
 Parity Conditions are a set of equilibrium relationships that
should apply to product prices, interest rates and spot and
forward exchange rates if markets are not impeded. They
are
• Pricing relationships based on the law of one price
• Hold if no arbitrage opportunities exist
 Law of One Price
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Identical products should sell for the same price everywhere
Otherwise, arbitrage opportunities will exist
Seldom holds for non traded assets
Can’t compare assets that vary in quality
May not hold precisely when there are market frictions
An example: The world price of gold
Suppose
P£
P€
= £250/oz in London
= €400/oz in Berlin
The law of one price requires:
Pt£ = Pt€ St£/€
 £250/oz = (€400/oz) (£0.6250/€)
or 1/(£0.6250/€) = €1.6000/£
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If this relation does not hold, then there is an
opportunity to lock in a riskless arbitrage profit.
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Fundamental equilibrium
relations: parity conditions
 Arbitrage
• Profit-guaranteeing strategy of “Buy low, sell
high”
• No investment and no risk
• Why Study Parity Conditions?
 They provide the foundation of international
finance.
 They are useful in:
• Explaining the determinants of foreign
exchange rates.
• Forecasting the long-run trend in an exchange
rate.
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International Parity Conditions
• Purchasing Power Parity (PPP)
 Absolute PPP
 Relative PPP
• Fisher Effect (FE)
 Generalized Fisher Effect (GFE)
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International Fisher Effect (IFE)
Interest Rate Parity (IRP)
Unbiased Forward Rate (UFR)
Purchasing Power Parity
 Absolute PPP
• Asks what should be the current exchange rate
• Is based on price levels
 Relative PPP
• Asks how the exchange rate should change
• Is based on price changes
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Absolute PPP
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It states that exchange adjusted price levels should be
identical world wide.
In other words a unit of home currency should have the
same purchasing power around the world.
Application of the “law of one price” to national price
levels rather than individual prices
Assumptions:
 Free trade will equalize the price of any good in all
countries
 Otherwise there will be arbitrage opportunities
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Criticisms
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 Ignores effects on free trade of transportation costs
 Tarrifs
 Quotas and other restrictions
 Product differentiations
The Big Mac Hamburger Standard
 The Economist developed the Big Mac Standard to track PPP:
• Assuming that the Big Mac is identical in all countries, it
serves as a comparison point as to whether or not currencies
are trading at market prices
• Big Mac in Switzerland costs Sfr6.30 while the same Big Mac
in the US costs $2.54
• The implied PPP of this exchange rate is Sfr2.48/$
 However, on the date of the survey, the actual exchange rate was
Sfr1.73/$
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How Well Does the Absolute
PPP Work?
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Based on the assumption of free trade
It has limited usefulness due to:
 Differentiated goods
 Costly information
 Transportation costs
 Differential tariffs, quotas, and other restrictions on free trade
Thus, the Relative PPP is more commonly used today because it has
more reasonable assumptions
Relative PPP
 States the exchange rate between home currency and any foreign
currency will adjust to reflect price levels in any two countries
 For ex. If inflation is 5 % in Us and 1 % in Japan, then in order to
equalize the dollar price of goods in the two countries, the dollar
value of the Japanese Yen will have to rise by 4 %
 et
=
(1 + ih)t
eo
(1 + if)t
• Where ih and if price level increases for home currency and
foreign currency
• eo is the dollar value of one unit of home currency at the
beginning of the period and et is the spot exchange rate in
period t
For ex. If the US and Germany are running annual inflation rates of 5 % and 3 %
respectively, and initial exchange rate was Euro 1 = $0.75, then according to the
equation, the value of the euro in 3 years should be
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e3 = 0.75(1.05/1.03) = $0.7945
PPP states that currencies with high rates of inflation should
devalue relative to currencies with low rates of inflation
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How Well Does Relative PPP
Work?
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Illustration Between June 1979 and June 1980 the US rate of inflation
was 13.6% and the German rate of inflation was 7.7 %. In line with the
higher rate of inflation in the US, the DM revalued from $0.54 in June
1979 to $0.57 in June 1980. thus the real rate of exchange in June
1980 equaled $0.57(1.077/1.136) = $0.54. In other words the inflation
adjusted $ / DM exchange rate held constant at $0.54. During the same
period, UK experienced a 17.6% rate of inflation and the Pound Sterling
revalued from $2.09 to $2.17. Thus the real value of the pound in June
1980 (relative to June 1979) was 2.17(1.176/1.136) = $2.25 a real
appreciation 7.6%
PPP does not hold over the short-run
 Sticky goods prices (lagged changes)
 Changes in exchange rates precede changes in prices.
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PPP holds over the long-run
 Clear relationship between relative inflation rates and changes in nominal
exchange rates
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PPP holds more closely when price indices cover tradable goods.
PPP holds better in high-inflation cases
Expected Inflation and Exchange Rate Changes
 Changes in expected as well as actual inflation will cause exchange rate
changes
 An increase in a currency’s expected rate of inflation, all other things being
equal, makes that currency more expensive to hold over time (as its value is
being eroded at a faster rate) and less in demand at the same price
 Consequently, the value of the higher inflation currencies will tend to be
depressed relative to the lower inflation currencies, other things remaining
same
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To summarize, despite often lengthy departures from PPP, there is a
clear correspondence between relative inflation rates and changes in
the nominal exchange rate
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Nominal versus Real Exchange
Rates
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Nominal exchange rate
 Price of one currency in terms of another
Real exchange rate
 Real purchasing power of one currency relative to another
The difference between real exchange rate and nominal exchange rate
has important implications for foreign exchange risk measurement and
management. If the real exchange rate remains constant, i.e. if PPP
holds, currency gains or losses from nominal exchange rate changes
will generally be offset over time by effects of differences in relative
rates of inflation thereby reducing the impact of nominal devaluation
and revaluation. Deviations from PPP will lead to real exchange gains
and losses
PPP and real exchange rates
 If an exchange rate adjusts fully to the inflation differential
according with PPP, the real exchange rate remains constant.
 PPP holds if real exchange rates are stable over time.
Real Exchange Rate
 Quoted exchange rate adjusted for the country’s inflation rate.
 The real exchange rate is equal to:
et’ =
et (1 + if)t
(1 + ih)t
If Purchasing power holds exactly, that is
et
eo (1 + ih)t
(1 + if)t
then et’ equals eo. In other words, if changes in the nominal exchange
rate are fully offset by changes in the relative price levels between two
countries, then the real exchange rate remains unchanged.
Alternatively, a change in the real exchange rate is equivalent to a
deviation from PPP.
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Fisher Effect
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Describes the relationship between the nominal interest rate,
real interest rate, and the inflation rate.
The Fisher effect states that nominal interest rate r is made of
two components
 (1) real required rate of a and
 (2) an inflation premium equal to the expected amount of inflation i
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Fisher equation states that
 1 + Nominal rate = (1 + Real Rate)(1 + Expected inflation
rate)
= 1 + r = (1+a)(1+r)
Or r = a + i + ai
Often approximated by the equation
r=a+i
The Fishers equation states that if the required real return is 3
% and the expected inflation rate is 10%, then the nominal
interest rate will be about 13 % (13.3% to be exact)
The logic behind this result is that $1 will have the purchasing
power of $0.90 in terms of today’s dollar. Thus the borrower
must pay the lender $ 0.103 to compensate for the erosion in
the purchasing power of the $1.03 in principal and interest
payments, in addition to the $0.03 necessary to provide a 3 %
return
The Brazilian govt. in 1980 spent $10 million on an
advertisement campaign to boost savings. However the
savings dropped because the interest rates on saving deposits
and treasury bills in 1980 were far below the inflation rate of
110%
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Generalized Fisher effect
• GFE says that real rates are equal among
countries through arbitrage
 i.e ah = af where hand f refer to home currency and
foreign currency
 If expected real returns in one currency is higher
than another, capital would flow from the second to
the first currency. This will continue in the absence
of govt. intervention till the real returns are
equalized
 In equilibrium, it should follow that nominal interest
rate differential will approximately the anticipated
inflation rate differential
 Or
1 + rh = 1+ ih
1 + rf
1 +if
Where rh and rf are the nominal home and foreign
currency interest rates
• For ex. If inflation rates in US and UK are 4 % and
7% respectively, then Fisher effect says the
nominal interest rates should be 3 % higher in UK
than in US
• GFE states that currencies with high rates of
inflation should bear higher interest rates than
countries with lower rates of inflation.
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How Well Does the FE (GFE)
Work?
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The FE (GFE) generally holds.
However, real interest rate differentials exist due to:
 Currency risk
 Inflation risk
 Political risk
• Differing tax policies
• Regulatory barriers to free flow of capital
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For ex. If political risk in Argentina causes foreign
investors to demand a 7 % higher interest rate than
they demand elsewhere, then foreign investors will
consider a 10 % expected real return in Argentina to be
equivalent to 3 % return elsewhere.
Hence real interest rates in developing countries can
exceed those in developed countries without presenting
attractive arbitrage opportunities to foreign investors
As the rate on bank deposits will not be the same as
rate on treasury bonds, while computing interest
differentials identical risk characteristics must be borne
in mind save currency risk, otherwise one will be
comparing apples and oranges
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International Fisher Effect
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Similar to Relative PPP except it uses interest rate rather than inflation
rate differentials to explain exchange rate changes.
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For ex. A rise in US inflation rate relative to those in other countries will
be associated with a fall in the $ value. It will be also associated with a
rise in the interest rate in the US relative to foreign interest rates.
Combine these two we get the IFE
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IFE states that
 (1 + rh)t = et
(1 + rf)t eo
Where et is the expected exchange rate in period t
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IFE states that currencies with low interest rates should appreciate
relative to currencies with high interest rates
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How Well Does IFE Work?
 Nominal interest rate equals real interest rate plus expected
inflation.
 If real interest rate increases, the nation’s currency appreciates.
 If expected inflation increases, the nation’s currency depreciates.
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Considerable short-run deviations do occur.
 Uncovered interest arbitrage
 Arbitrage between financial markets in the form of capital flows,
should ensure that interest differential between any two countries
is an unbiased predictor in future change of spot rate of exchange
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If real rates of interest are equal across countries (d = f ), then interest
rate differentials merely reflect inflation differentials
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This relation is unlikely to hold at any point in time, but should hold in
the long run
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Interest Rate Parity
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Spot and forward rates are related by IRP
IRP states that
Ftd/f/S0d/f = [(1+id)/(1+if)]t
Where S d/f = today’s spot exchange rate
0
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E[Std/f]
= expected future spot rate
Ftd/f = forward rate for time t exchange
i
= a country’s nominal interest rate
p
= a country’s inflation rate
Forward premiums and discounts are entirely
determined by interest rate differentials.
This is a parity condition that you can trust.
Interest rate parity:
Which way do you go?
If Ftd/f/S0d/f > [(1+id)/(1+if)]t
then
Ftd/f must fall
S0d/f must rise
id must rise
if must fall
so...
Sell f at Ftd/f
Buy f at S0d/f
Borrow at id
Lend at if
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Interest rate parity:
Which way do you go?
If Ftd/f/S0d/f < [(1+id)/(1+if)]t
then
so...
Ftd/f must rise
Buy f at Ftd/f
S0d/f must fall
Sell f at S0d/f
id must fall
Lend at id
if must rise
Borrow at if
• Interest rate parity is enforced through “covered
interest arbitrage
An Example:
Given: i$ = 7% S0$/£ = $1.20/£
i£ = 3% F1$/£ = $1.25/£
F1$/£ / S0$/£ > (1+i$) / (1+i£)
1.041667 > 1.038835
The fx and Eurocurrency markets are not in
equilibrium.
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Interest Rate Parity (IRP):
Example
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Suppose you have $1 million to invest for 90 days and
the following choices:
 Invest in dollar-denominated securities for 90 days
earning 8.00% per annum, or
 Invest in Swiss franc-denominated securities of similar
risk and maturity earning 4.00% per annum
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Suppose you have the following quotes:
 Spot rate of SF1.4800/$
 90-day forward rate of SF1.4655/$
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Would you invest in the U.S. or Switzerland?
Covered Interest Arbitrage
 Spot and forward market are not in equilibrium.
 Relative forward differential does not equal relative
interest differential
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How Well Does IRP Work?
Small deviations from IRP do occur.
 Covered interest arbitrage opportunities
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Lack of arbitrage profit opportunities due to:
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Transactions costs
Differential tax rates
Government controls
Political risk
Time lag
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Forward rates as predictors
of future spot rates
• Ftd/f = E[Std/f]
or
Ftd/f / S0d/f = E[Std/f] / S0d/f
• Forward rates are unbiased estimates of
future spot rates.
 Speculators will force this relation to hold on
average
 For daily exchange rate changes, the best estimate
of tomorrow's spot rate is the current spot rate
 As the sampling interval is lengthened, the
performance of forward rates as predictors of future
spot rates improves
• Are Forward Prices Unbiased?
 Evidence that forward rates are biased predictors of
future spot rates.
• Risk premium
– Appears to change signs
– Averages near zero
• Market efficiency
 It appears that it does pay to use resources to
forecast exchange rates
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Currency Forecasting
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Successful currency forecasting is difficult.
Currency forecasting can lead to consistent profits only
if forecaster has:
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Superior forecasting model
Access to information before other investors
Exploit small, temporary deviations from equilibrium
Ability to predict government intervention in foreign
exchange market
Forecasting Fixed Exchange Rates
 Forecasters must focus on predicting government action,
since devaluations and revaluations are political
decisions.
 Basic forecasting methodology involves:
• Determine pressure on a currency to devalue or revalue
• Determine political will of leaders to persist with current level
of disequilibrium
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Forecasting Floating Exchange Rates
 Market-Based Forecasts
• Forward rate
• Interest rate
 Model-Based Forecasts
• Fundamental analysis
• Technical analysis
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International Parity Conditions
FE
Interest Rate
Differential
(1  ih )
(1  i f )
Expected Inflation
Rate Differential
E (1  I h )
E (1  I f )
IFE
PPP
IRP
Forward
Differential
f1
e0
Expected Change
in Spot Rate
e1
e0
UFR
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