Purchasing Power Parity

Akshay SawantMMS Finance

Currency Basics

55 Rs/$ 52 Rs/$ Rupee Appreciated & Dollar Depreciated

Dollar depreciated by (52/55)-1 i.e. 5.4 %

Rupee appreciated by [ (1/52)/(1/55) ] – 1 i.e. (0.01923)/(0.01818) – 1 = 5.769 %

Law of One Price

The law of one price says that the same

good in different competitive markets

must sell for the same price, when

transportation costs and barriers between

markets are not important.

Purchasing Power Parity

Japan cheapest, UK most expensive

Yen is undervalued, Pound overvaluedEXCHANGE RATE

(US)US$ VALUE

$29.99

$1 = ¥ 114.57 2500/114.57 = $21.82

$1 = £ 0.5591 25/.5591 = $44.72

COUNTRY LOCALCURRENCY

US $ 29.99

Japan ¥ 2500

UK £ 25

Absolute Purchasing Power Parity

The exchange rate between two countries will be identical to the ratio of the price levels for those two countries

. E (Rs/$) = P (Rs) / P ($)

EG Price of a product in India = 250 Rs

Price of same product in US = 5 $

Thus E (Rs/$) = 250/5 = 50 Rs/$

The following conditions must be met for this relationship to be true: 

1.The goods of each country must be freely tradable on the international market.

2.The price index for each of the two countries must be comprised of the same basket of goods.

3.All of the prices need to be indexed to the same year.

Relative Purchasing Power Parity

Relative purchasing power parity relates the change in two countries' expected inflation rates to the change in their exchange rates.

E(N)  = E(0) (DC/FC) (1 + IDC) / (1 + IFC)

Where,

E(0) is the spot exchange rate at the beginning of the time period.

E(N) is the spot exchange rate at the end of the N years.

IFC is the expected annualized inflation rate for foreign country.

IDC is the expected annualized inflation rate for domestic country.

Example

E(0) = 55 Rupees per dollar .   Consider annual inflation rate for the

U.S. to be 1.4 % The annual expected Indian inflation rate

is 6.87 % E(0) = 55 Rs per dollar.  (1 + IFC) = 1.014 (1 + IDC) = 1.0687. S1 = (1.0687) / (1.014) × 55   =   57.9669 Rupees per $

Basket Example PRODUCTS USA IN $ INDIA

RUPEE/DOLLAR

Coke, Pepsi 1 20 20

Candy bars & chocolates- snickers,

1 20 20

1 tin of frozen yogurt( 2 tins

from Wal-Mart)

1 15 15

1 small packet of lays

1 10 10

500 ml purified water

1 10 10

20 -30 strips of chewing gum

1 20 20

PPP Conversion

factor

15.83

Big Mac Index

Introduced in The Economist in September 1986 by Pam Woodall

Informal way of measuring the Purchasing Power Parity (PPP) between two currencies

Big Mac was chosen because it is available to a common specification in many countries around the world

Contd…

Big Mac PPP exchange rate between two countries is obtained by dividing the price of a Big Mac in one country by the price of a Big Mac in another country.

This value is then compared with the actual exchange rate; if it is lower, then the first currency is under-valued compared with the second, and conversely, if it is higher, then the first currency is over-valued.

Arbitrage Opportunities

1$ = 55 Rs Big Mac price in US 4.33 $...So price

in India should be 238 Rs But in India Price is 89 Rs Thus PPP exchange rate is 20.57

(89/4.33) Indians would produce in India and

sell in US for the arbitrage opportunity

Thus Rupee will appreciate

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