Exchange Rate Theories: Purchasing Power Parity
Forecasting exchange rate is easier
said than done. In the market, there are thousands of trading software known as
“forex robots” ( described in Session 4.3) are available which help
in forecasting forex rates and promise to get rich quick!! However, until now
nobody is known to have been amassed great riches by predicting forex rates and
making a killing. Interestingly we know of the many traders have companies
which have gone kaput on account forex trading going horribly wrong.
Irrespective of this fact, all and sundry anything remotely to do with forex
rates wants to learn the tools to predict forex rates. Significant research
work is also being carried out to find out newer models to predict forex rates
and make a killing!
A person interested on forecasting
forex would get to hear simpler techniques based one age old basics like “Fibonacci series” and “time series analysis” to complex
models based on neural network, artificial intelligence and genetic algorithms etc.
In fact, while browsing through the
web, the author comes across an interesting write up. A researcher has claimed
to develop a theory, which he is intending to sale/license, and generate
revenue from the sale/license. The researcher also mentions that the theory
would help users “24 hrs non-stop wealth
building”!! The website content goes like this … “The brand new theory towards analyzing and forecasting the forex
market and it has come after 700
years of Fibo and 150 years of Elliot waves, the two most popular indicators”.
Anybody will be quite intrigued by the phrases like “700 years of Fibo and 150
years of Elliot waves” – how on the earth he got a time series data for 700 years forex quotations!!
As there is no end to the number of
theories developed based on mathematical model, let us focus more on
understating macroeconomic parameters like interest
rate, inflation etc, those that have bearing on forex rate.
There are certain fundamental
macroeconomic conditions which influence the exchange rates. One of the
fundamental parity conditions is known as “Purchasing
Power Parity” and the Law of One Price (LOOP). These
aspects are discussed in detail.
17.2: Purchasing Power Parity and Law of One
Price:
One of the basic theories on exchange
rate relates the price level in a country to the exchange rate. Purchasing power parity (PPP) is a
theory of exchange rate determination which compares the average costs of goods
and services between countries. It proposes that if identical products are
services are sold in two different markets at two different prices, the
exchange rate would be such that the price of the product/service is still same
even if product/service price may be stated in two different currencies. In
other words, exchange rate between currency pairs is in equilibrium when
purchasing power is same.
PPP indicates that exchange rate
between two countries should equal to the ratio of similar goods and services
in both countries.
For example, if one kg of Potato costs
INR 18 in India and similar quality of potato costs 50 cents in USA, then the
PPP exchange rate would be INR 36 per USD. This is the absolute version of
theory of purchasing power of parity.
In
other words, the exchange rate between two currencies can be represented as
.......
E q (1
7 .1)
The concept of purchasing power parity
is quite old. It is believed to have been propounded by the sixteenth-century
scholars of the University of Salamanca of Spain. Though lots of empirical
research have been undertaken to test whether PP holds or not, the Big Mac Index calculated by the Economist
is the most well known test on PPP.
The “Big Mac index” published by Economist tries to find out what
should have been the PPP governed exchange rate. As McDonald burgers offered in
many countries are standardized, PPP governed exchange rate is found out by
comparing the prices of burgers between two countries and comparing the
exchange calculated to the actual exchange rate. The paragraph given in Box 17.1 succinctly explains the
purchasing Power Parity.(source: http://www.economist.com/markets/bigmac/about.cfm)
For example, Price of a Big Mac is
USD3.57 in the USA and price of a Big Mac is INR 99 in India. This means that
the implied purchasing power parity is INR 27.73 per USD. However the actual
exchange rate is INR 48 per USD. This indicates that INR is undervalued valued by [(27.73- 48)/48]*100=
-42.29%. It indicates that INR should
appreciate in near future.
Let us take another example. Suppose a
Big Mac costs about $2.99 in in USA and costs €2.5 in UK. The prevailing
exchange rate is GBPUSD 1.5371(USD 1.5371 per GBP). As per the Big Mac exchange
rate, the GBPUSD rate should be USD 0.8361 per GBP. As per the actual exchange
rate, USD is undervalued by 45.6%. USD should appreciate by 45.6%.
Box 17.1:
Burgernomics is
based on the theory of purchasing-power parity Source: http://www.economist.com/markets/bigmac/about.cfm
“Burgernomics
is based on the theory of purchasing-power parity, the
notion that a dollar should buy the
same amount in all countries. Thus in the long run, the exchange rate between
two countries should move towards the rate that equalizes the prices of an
identical basket of goods and services in each country.
Our
"basket" is a McDonald's Big Mac, which is produced in about 120
countries. The Big Mac PPP is the
exchange rate that would mean
hamburgers cost the same in America
as abroad. Comparing actual exchange rates with PPPs indicates whether a currency is under or overvalued.”
Annexure
17.1 details
the exchange rate between USD and many other country currency based on the burger price. If a currency is undervalued, it is
expected to appreciate and if a
currency is overvalued, it is expected to depreciate in future. Hence, by analyzing the Big Mac price prevailing
in two countries, we can determine the exchange rate. If the actual exchange
rate differs from the Big Mac rate, then either currency will appreciate or
depreciate.
However, Big Mac index as a universal
product which can be compared across countries has been debatable. Bag Mac is
considered as daily consumable staple food in US unlike a luxury product in
many countries. Hence in many countries, people do not mind paying a premium to
buy a Big Mac. Hence the premium is in-built into Big Mac price itself makes
foreign currency undervalued.
Starbucks
Tall Latte index is
also another index which compares the price of Starbucks Latte in different countries, exactly like the Big Max Index. But
yet to enjoy the cult status likes Big Mac Index.
PPP calculated by comparing price of
one good across in different currencies is known as Absolute PPP. However the absolute law of one price never holds
good when prices of one commodity is
compared. (For example, price of one KG of Potato, Price of a similar brand
car, price of a mobile phone etc.)
Another form of less stringent PPP
stresses on comparing price index of
basket of goods in both countries
rather than comparing any one good/service.
It indicates that if a country is
experiencing higher inflation (higher price level) compared to another country,
its currency will depreciate relative to other currency.
In other words, the spot rate between two
countries can be determined by comparing the price index of a basket of similar goods and services. It is
very important to understand at this
point is that price index should comprise of “similar” goods & services”
consumed by residents of both countries.
On a given date, suppose a basket of
goods & services costs INR 5000 and a similar basket of goods &
services cots USD300, the spot exchange rate on that date should be
Spot Rate =
|
INR
|
5000
|
= INR 16.67
/USD
|
|
USD
|
300
|
|||
If the actual spot exchange rate equals the
rate calculated by PPP, then PPP holds true. However, it is empirically proved
that PPP in absolute form based on
single product or
based on a price index does not hold
good.
17.3: Purchasing Power Parity and Law of One
Price (LOOP):
PPP is based on the concept of “Law of One Price”. The LOOP indicates
that identical good/services should sell for the same price in two separate
markets when there are no transportation costs and no differential tax rates
exists in the two markets. If there is a price difference, then exchange rate
would move in such a manner so that, in both markets the product will sell at
same price.
For example, Nokia E75 model mobile
phone costs INR 26,000 in India. The same model costs Bangladeshi Taka of
35000. Suppose the exchange rate between BTKINR is INR0.642/BTK. With this
exchange rate, mobile handset costs INR 22470 at Bangladesh. So why anybody
would buy the handset in India? Indian people would sell INR and buy BTK and
purchase the mobile in Bangladesh and sell the handset in India at a price of
INR26000. For every handset sold in India, the trader makes a profit of
INR3530. This profit is the arbitrage profit i.,e buying low and selling high
and no risk. So many people would flock to sell INR to buy BTK. Suppose
exchange moves to INR0.713/BTK. The mobile handset now costs INR 24967. Still
there is possibility of arbitrage opportunity. The exchange rate would keep on
adjusting so that the arbitrage opportunity is completely done away with.
Suppose the exchange rate moves to INR
0.746/BTK, then buying in Bangladesh and selling in India becomes a loss making
proposition. In this case, the traders would buy the handset in India and start
selling Bangladesh. This process will go on till the price of the handset is
same in both countries.
In this example, we have ignored, the
transaction cost, the import duty, the sales tax and cost associated with
conversion of INR to BTK etc. have been ignored. With inclusion of these
duties/taxes and levies, the arbitrage opportunity may not exists, Also another
inherent assumption in this example is that the Nokia E75 model is demanded in
both India and Bangladesh.
The
LOOP holds well only if three conditions are satisfied. These three are
•
Transportation costs, barriers to trade
(import-export levies, customs duty etc) and other transaction costs (currency
conversion fee) are insignificant.
•
There must be competitive markets for
the goods and services in both countries.
•
The LOOP applies only to tradable
goods. LOOP is not applicable to immobile goods such as houses, and many
services that are local
Many
tests have been conducted by researchers to test whether the PPP holds true or
not.
17.4: Relative Purchasing Power Parity
Relative PPP postulates that the change
in inflation rate governs the change in exchange rate.
Where St is the spot rate of foreign
currency/domestic currency and P(t) is tej price level prevailing now and P(t-1) price level prevailing before one
period
For example, the inflation rate in 2008
is 8.39% in India. Let us assume that Inflation rate in USA during 2008.is 4%.
The right hand side of the Eq. (17.3)
is 1.04/1.0839 is 0.96. This indicates that INR should depreciate by 4%. IF the
spot exchange rate was USD0.0217/INR (INR 45 per USD) at S(t-1) then St should be USD0.0208/INR ( INR
(47.91 per USD).
With two countries having different
inflation rate, the relative prices of goods in the two countries, will change
so that the goods and services offered in these countries are priced same.
17.5: Inflation and Measurement of Rate of
Inflation:
Inflation rate measures the rate of
change of increase in prices of goods and services during a given time period.
Normally the prices of goods and services are measured by construction of an
index. The index can be Consumer price
index (CPI) or Wholesale
price index(WPI).
Composition
of CPI: The
basket of goods and services consumed by different classes of consumers in India varies. Hence based
on economic groups, 4 different CPIs are calculated. These 4 indices are CPI
for Industrial Workers [CPI(IW)] CPI for Urban Non-Manual Employees
[CPI(UNME)], CPI for Agricultural Labourers [CPI(AL)], and CPI for Rural Labourers
[CPI(RL)].
Composition
of WPI: The
WPI for all-India consists of 435 commodities. The 435 items details are given in Table 17.5. Basically it consists of 98
primary articles, 19 articles on fuel, power etc, and 318 items of manufactured products. The base year
for calculation of WPI is 1993-94. These three major groups have 22.025%,
14.226% and 63.749% respectively.
Table17.5: Composition of Wholesale Price
Index in India.
Number of items in
|
Weight in the
|
|||
the index
|
index
|
|||
Primary
Articles(1+2+3)
|
98
|
22.025
|
||
(1)Food
|
17.386
|
|||
(2)Non-food
|
10.081
|
|||
(3)Minerals
|
4.828
|
|||
Fuel, power,
light and lubricants
|
19
|
14.226
|
||
Manufactured
|
Products
|
318
|
63.749
|
|
( 4+5+6+7+8)
|
||||
(4)
|
Food Products
|
10.143
|
||
(5)
|
Beverages, Tobacco & Tobacco Products
|
2.149
|
||
( 6) Textiles
|
11.545
|
|||
(7)
|
Leather & Leather Products
|
1.018
|
||
(8)
|
Others
|
32.187
|
||
WPI is calculated on weekly basis. The
data for these 435 items are collected from both official and unofficial
sources—primarily wholesale prices. Data from Directorate of
Economics
and Statistics, Ministry of Agriculture etc are taken. Also data from various mandies, trade associations,
and manufacturers are taken to calculate the WPI.
Calculation
of WPI: Suppose
price of rice in January 2009 is Rs. 17 per kg. The price of same rice increases to Rs.20 in
January 2010. The WPI for Rice in 2010 would be 18% given by (20 – 17)/17 x 100
=18%.
Hence WPI for Rice for January 2010
would be 118. Similarly the WPI for all 435 items are calculated. Individual
WPI are multiplied with the respective weights given in Table17.5 to get the WPI for the period ending 2010. This amount is
compared with WPI figure in January
2009 to get the inflation rate. For example, if WPI in January 2009 is 112.25
and it is 120.35 in January 2010, the inflation rate would be (120.35 –
112.25)/112.25 x 100 =7.22%.
The same process can go on for next
week or next month. Suppose by end of February 2010, WPI is 118.75 compared to
120.35 in January 2010. This means Inflation has gone down by 1.33% compared to
January 2010.
Government of India changes the
composition of all indices from time to time. The change in composition of
index is done so as to reflect the changing profile of the consumption pattern
of people. Suring September 2010, government of India included items like
ice-cream, mineral water, computers, gold, construction machinery and TV sets
etc to the WPI.
Besides changing the composition of
commodities to be part of the index, government also changes the base year. The
WPI composition given in Table 17.5
has the base year of 1994-95. The previous base year was 1981-82.
The changing composition of the WPI
index and base year throws some interesting lights on the consumption pattern
of a country. As the country develops, people tend to consume more fuel &
power, and more manufactured products compared to primary articles. This trend
can be observed from the details given in Table
17.6.
Base year
|
Base Year
|
|
1981-82
|
1994-95.
|
|
Primary Article
|
32.30
|
22.03
|
Fuel, power,
light and lubricants
|
10.66
|
14.03
|
Manufactured
Products
|
57.04
|
63.75
|
Box 17.2: Measurement of Inflation
Inflation
rate in India is measured by the wholesale
price index (WPI). Currently,
WPI
(Base year 1993-94 =100) is
a combined index of 435 articles/items, comprising
98 ‘primary articles’, 19 items of ‘fuel,
power, light and lubricants’ variety and 318
‘manufactured products’. This index is the most commonly
quoted measure of inflation in India
mainly because of its availability on a weekly basis and also the absence of a
representative retail price index at such regular high frequency.
I n
India, 4 consumer price indices viz.,
consumer price index for industrial workers (CPI-IW), consumer price index for urban non-manual employees (CPI-UNME),
consumer price index for agricultural
labourers (CPI-AL) and consumer price index for rural labourers (CPI-RL) are compiled officially with reference
to four different population groups.
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