Index numbers (lecture 4)

LECTURE 4
INDEX NUMBERS
Temur Makhkamov
Indira Khadjieva
QM Module Leaders
[e-mail]
[e-mail]
Office hours: by appointment
Room IB 205
EXT: 546

Lecture Outline
To understand the concept of index number and its use in economics, finance and business
To Represent data in terms of index numbers
To understand some well-known indices sush as Consumer Price Index, Dow Jones Industrial Averages and the Nasdaq Index

Index Numbers
Index number is the measure of change in a variable over time
Index numbers allows relative comparisons over time
They are typically used in economics to measure trends in a wide variety of areas including: stock market prices, cost of living, imports, exports, industrial or agricultural production and etc,.

Simple Index numbers
When an item is considered:
1) Fixed base index
2) Chain base index
When a group of items are considered:
1) Simple mean index
2) Simple aggregate index

AAPL Income Statement

Fixed Base Index
Definition: each value is compared with a value in the same (fixed) base period.
Where
Iy = index number of variable ‘y’
Yt = value of variable ‘y’ at time t
Y0 = value of variable ‘y’ in the base period

AAPL Income statement: Fixed Base Index

Chain Base Index
Definition each value is compared with a value in the preceding period
Where
Iy = index number of commodity ‘y’
Yt = value of commodity ‘y’ at time t
Y0 = value of commodity ‘y’ in the base period

AAPL Income statement: Chain Base Index

Hypothetical Index Composites

Simple Aggregate Index

Simple Aggregate Index
Definition the index is calculated by finding the ratio of the sum of the current values to the sum of the base values.
Where
Pc = the current value of an item,
P0 = the base value of the item
n = number of items

Simple Mean Index
Definition the index is calculated by finding the average (mean) of all the individual price relatives
Where
Pc = the current value of an item,
Pc = the base value of the item
n = number of items

Simple Mean Index

The Consumer Prices Index
Consumer Price Index (CPI) - is defined as the change in the prices of a basket of goods and services that are typically purchased by specific groups of households.
CPI is the main index used
to measure Inflation

Dow Jones Industrial Averages
The Dow Jones Industrial Average (DJIA) - price-weighted average of 30 blue-chip stocks that are generally the leaders in their industry.
Widely followed indicator of the stock market since October 1, 1928.
30 most important market-leading companies on the American stock exchange and reflects their growth

The Nasdaq Index
The Nasdaq 100 includes the shares of the 100 largest American and international companies as measured by their market capitalization which do not come from the financial sector and which are traded on the largest electronic stock exchange in the USA.
The shares included in it are weighted according to market capitalization
The index level represents the average of the shares included in it.
Dividend payments are not considered when calculating the index.

Concluding remarks
Today, you learnt:
The method of indexing data
The different types of indices used to show the change of the data over time