This article is the first in a series dealing with the complexities of indices as a tool for making investment decisions.

As a general definition in financial or economic terms, an index number shows the increase or decrease in a magnitude from one period to another.

The magnitude could vary from prices (shares, consumer prices, etc.) to quantity indicators (sales, production, etc.). One could also define an index number as a summary measure of the change in the level of activity of a single item or a basket of related items from one time period to another.

Price indices are mostly used in the investment industry, whereas quantity indices are important for the investment decision, e.g. the expected sales in a particular industry.

Index numbers are constructed by expressing the value of an item in the current period as a ratio of its value in the base period.

Index number = Current Period Value x 100

Base Period Value 1 %

There are two major categories of index numbers. In each of these categories, an index can be computed for either a single item or a basket of related items. The categories are:

• Price indices:

• single price index

• composite price index

• Quantity indices:

• single quantity index

• composite quantity index

Index numbers measure the percentage changes from a base period which has an index of 100. An index number above 100 indicates an increase in the level of activity being monitored, while an index number below 100 reflects a decrease.

The magnitude of the change is shown by the difference between the index number and the base index of 100. Examples of index numbers and composite indices in South Africa include:

•
The JSE Actuaries Index: Overall (All Share Index)

• The JSE Actuaries Index: Gold Index

• The JSE Actuaries Index: Fini 15

• The JSE Actuaries Index: Indi 25

• Consumer Price Index (CPI)

• Production Price Index (PPI)

• Business Confidence Index (Sacob BCI).

The first step in interpreting a price index is to note the base period with which the comparison is made. The absolute value of any single figure in a price index is meaningless unless the base period is known.

Below is an example of a share’s price movement over a period of five days, using:

• the price as on day one (1350) as the basis (=100)

• the prices of the next four days expressed as a relative to the base price.

The base price equals an index of 100 on day one and the percentage movement for days two to five is then either added or subtracted from 100.

The index for day two is calculated as 1355/1350 x 100 = 100.4, for day three it is 1375/1350 x 100 = 101.8, etc. The above table shows a 10% increase in the share price by day four (110.0 – 100) and by day five the share price increased by 29.6% (129.6 – 100).

Indices used in the investment world are usually composite indices, i.e. the index consists of share prices of more than a single share. When calculating and comparing day-to-day values, the market capitalisation (market value) of the company involved is used. Market value is simply the shares in issue multiplied by the share price.

Consider the following example:

An index consists of the following shares:

• company X: issued 1 million shares

• company Y: issued 3 million shares

• company Z: issued 5 million shares.

The table on the left shows the share prices and subsequent market capitalisations of the shares.

In this example, indices are calculated on the combined market capitalisation. By employing this method, companies are weighted in terms of their contribution to the index according to their respective market capitalisation.

The JSE of Actuarial indices are arithmetically weighted indices based on the market capitalisation weight of each company. The price index is the summation of the market values of all companies within the index and each company is weighted by its market value. The index value is a number that represents the otal value of all companies within the index at a particular point compared to a comparable calculation at the starting point.

The index value is calculated daily by dividing the total market value of all constituent companies by a number known as the divisor. The divisor is an arbitrary number chosen as the starting point of the index (the index starting value).

The index value equals the total market capitalisation of constituents divided by the current index divisor. It is important to know how to use the index as an investment tool.

Fund managers often structure their portfolios in a way so as to outperform indices. Outperforming an index translates into beating inflation by a substantial margin and making money in the process.

It’s also worth noting that indices around the globe often react out of synchronisation with the overall market. This would depend on the individual shares and their relative weightings within an index. A heavy-weight like Anglo American may have a substantial influence on the All Share index, which may at times cause the index to rise, while the rest of the shares within that index could actually fall.

In the next issue of Blue Chip we will continue our focus on composite indices and two approaches to determining weights:

•The Laspeyres approach: advocating holding quantities/prices constant at base period levels

•The Paasche approach: holding quantities/prices constant at current period levels.

We will also look at two methods for constructing a composite price index: weighted aggregates and weighted average of price relatives. We end this series by looking at problems of index number construction, limitation on the interpretation of index numbers, and applications of index numbers.

(Mark Fortuin is Project Manager of Blue Chip Journal)