KSE Index Computation

COMPUTATION METHOD

1. OBJECTIVE & DESCRIPTION

The primary objective of the KSE100 index is to have a benchmark by which the stock price performance can be compared to over a period of time. In particular, the KSE 100 is designed to provide investors with a sense of how the Pakistan equity market is performing. Thus, the KSE100 is similar to other indicators that track various sector of the Pakistan economic activity such as the gross national product, consumer price index, etc.

2. COMPOSITION OF THE KSE100 INDEX

The KSE100 contains a representative sample of common stock that trade on the Karachi Stock Exchange. The KSE stocks that comprise the index have a total market value of around Rs. 1,197 Billion compared to total market value of Rs. 1,365 Billion for over 679 stocks listed on the Karachi Stock Exchange. This means that the KSE100 Index represents 88 percent of the total market capitalization of the Karachi Stock Exchange, as of 27th February, 2004.

LIST OF SECTORS
1.
  Open-end Mutual Funds
19.
  Oil & Gas Marketing Companies
2.
  Close-end Mutual Funds
20.
  Oil & Gas Exploration Companies
3.
  Modarabas
21.
  Engineering
4.
  Leasing Companies
22.
  Automobile Assembler
5.
  Investment Banks/Investment Cos./Securities Cos.
23.
  Automobile Parts & Accessories
6.
  Commercial Banks
24.
  Cable & Electrical Goods
7.
  Insurance
25.
  Transport
8.
  Textile Spinning
26.
  Technology & Communication
9.
  Textile Weaving
27.
 &nbspFertilizer
10.
  Textile Composite
28.
  Pharmaceuticals
11.
  Woollen
29.
  Chemical
12.
  Synthetic & Rayon
30.
  Paper & Board
13.
  Jute
31.
  Vanaspati & Allied Industries
14.
  Sugar & Allied Industries
32.
  Leather & Tanneries
15.
  Cement
33.
  Food & Personal Care Products
16.
  Tobacco
34.
  Glass & Ceramics
17.
  Refinery
35.
  Miscellaneous
18.
  Power Generation & Distribution
 
3. STOCK SELECTION RULES

The selection criteria for stock inclusion in the recomposed KSE100 Index are:

Rule # 1: Largest market capitalisation in each of the 34 Karachi Stock Exchange sectors excluding open-end Mutual Fund Sector.

Rule # 2: The remaining index places (in this case 66) are taken up by the largest market capitalisation companies in descending order.

A number of the 34 top sector companies may also qualify for inclusion on the basis of their market capitalisation. In other words, companies may qualify solely under rule 1, solely under rule 2, or under both.

The fact that the sector rule is identified as Rule 1 does not imply that it is more important, only that the nature of the selection process is such that it is the screening that is done first.

4. CALCULATION METHODOLOGY *

In the simplest form, the KSE100 index is a basket of price and the number of shares outstanding. The value of the basket is regularly compared to a starting point or a base period. In our case, the base period is 1st November, 1991. To make the computation simple, the total market value of the base period has been adjusted to 1000 points. Thus, the total market value of the base period has been assigned a value of 1000 points.

An example of how the KSE100 Index is calculated can be demonstrated by using a three-stock sample. Table 1 illustrates the process. First, a starting point is selected and the initial value of the three-stock index set equal to 1000.

Taking stock A's share price of Rs. 20 and multiplying it by its total common shares outstanding of 50 million in the base period provides a market value of one billion Rupees. This calculation is repeated for stocks B and C with the resulting market values of three and six billion Rupees, respectively.

The three market values are added up, or aggregated, and set equal to 1000 to form the base period value. All future market values will be compared to base period market value in indexed form.

CALCULATING THE KSE100

Step 1: The Base Period Day 1 TABLE 1

Stock
Share Price (in Pak Rs.)
Number of Shares (in Rs.)
Market Value
A
20.00
50,000,000
1,000,000,000.00
B
30.00
100,000,000
3,000,000,000.00
C
40.00
150,000,000
6,000,000,000.00
Total Market Capitalisation 10,000,000,000.00

Note: Base Period Value/Base Divisor = Rs. 10,000,000,000.00 = 1000.00 Base Period Value/Base Divisor = Rs. 10,000,000,000.00 = 1000.00 * All figures taken are only hypothetical

Step 2: Index Value as on Day 2 TABLE 2

Stock
Share Price (in Pak Rs.)
Number of Shares (in Rs.)
Market Value
A
22.00
50,000,000
1,100,000,000.00
B
33.00
100,000,000
3,300,000,000.00
C
44.00
150,000,000
6,600,000,000.00
Total Market Capitalisation 11,000,000,000.00

Index = (11,000,000,000.00/10,000,000,000.00)*1000= 1.10 * 1000 = 1100

Thus, the formula for calculating the KSE100 Index is :

{(Sum of Shares Outstanding * Current Price)/Base Period Value}*1000

OR


(Market Capitalization/Base Divisor) * 1000
Base Divisor

The KSE100 Index calculation at any time involves the same multiplication of share price and shares outstanding for each of the KSE100 Index component stocks. The aggregate market value is divided by the base value and multiplied by 1000 to arrive at the current index number.

 

5. RECOMPOSITION OF THE KSE-100 INDEX

Maintenance of the index over time will require an on-going semi-annual recomposition process, internal and external- buffer files of shares that exceed (shares outside the index) or fall below (shares inside the index) the above criteria will be maintained under the jurisdiction of the recomposition committee.

Maintaining adequate representation of the under-lying stock market through all of its future development and changes is dependent upon the establishment of an appropriate recomposition process. Recomposition rules fall into two general categories: Sector rules and market capitalisation rules.

5.1 Sector Rules

Sector rules govern the selection (or deletion) of companies on the basis of being the top capitalisation stock in each of the 34 KSE sectors. Two rules are recommended to undertake selection in this area-one, a time based rule and the other a value-based rule. Application can be triggered by compliance with either rule.

5.1.1 Time-based rule:

A company (not in the index) which becomes the largest in its sector (by any amount of value) will enter the index after maintaining its position as largest in the sector for two consecutive recomposition periods (i.e., one year).

5.1.2 Value-based rule:

A company (not in the index) which becomes the largest in its sector by a minimum of 10% greater in capitalisation value than the present largest in the sector (in the index) will enter the index after one recomposition period (i.e., 6 months).

5.2 Capitalisation Rule Capitalisation Rule

Capitalisation rules govern the selection (or deletion) of companies on the basis of being among the largest capitalisation companies in the stock market. Only one rule applies here-time based rule.

5.2.1 Time-based rule:

A company (not in the index) may qualify for entry if it exceeds the market cap value of the last stock in the index selected on the basis of market cap for two recomposition periods (i.e. one year). A qualifying company automatically pushes out the lowest cap selected stock in the index.

5.3 Rules for new issues:

A newly listed company or a privatized company shall qualify to be included in the existing index (after one recomposition period) if the market capitalisation of the new or privatized company is at least 2% of the total market capitalization.

5.4 Recomposition Time table

The recomposition committee will meet semi-annually, with meetings scheduled to take place at least two weeks before the end of the last trading day of the month in which they occur. This is to allow for a minimum announcement period of two weeks, commencing the day following the recomposition meeting, when the results of the meeting are made public, at the end of the last trading day of the month, when changes are implemented into the index.

5.5 Recomposition Committee

The recomposition committee has two broad function:

  1. Overseeing implementation of the index rules at the semi-annual recomposition sessions.

  2. Reviewing the index rules and altering them as necessary.

AN EXAMPLE OF THE RECOMPOSTION OF THE KSE100

The base divisor adjustment process can easily be understood by an example mentioned below. It is important to understand that all divisor adjustment are made after the close of trading.

DIVISOR CHANGES

KSE-100 Index as on Day 2 = 1100

Index Market Capitalization on Day 2 = 11,000,000,000.00

Divisor as on Day 2 = 10,000,000,000.00

Revised Market Capitalization due to addition and Delition of companies on the basis of Sector Base

Rule and Market Capitalization Rule.- Say = Rs. 12,000,000,000.00

As mentioned earlier the Revised Market Capitalization are the market capitalization of those companies which would constitute the KSE-100 Index on the next day (Day 3). The Revised Market Capitalization calculated after the end of closing of trading session of Day 2 by using closing prices of the same day. 

The key to making this adjustment, as with any divisor adjustment, is that the index value is temporarily 'frozen' at the close of trading, while the divisor is adjusted for the increase or decrease in market value of the numerator in the formula.

As the Formula for KSE-100 Index is:
Market Capitalization
Index = —————————————— x 1000
Divisor


Therefore, in order to get the new divisor than formula is reframed as:
Revised Market Cap.
New Divisor = ————————————— x 1000
Index (Day 2)
12,000,000,000
= ——————————— x 1000
1100
= 10,909,090,909

Note: The formula for Re-composition of the KSE100 Index is same as mentioned in Table 2, except that the treatment of Base Divisor changes from Base Period Value to an arbitrary number, set such that there is no break in the index series. This will be adjusted for any capital changes in indexed stocks.

 

5. RECOMPOSITION OF THE KSE-100 INDEX

Maintenance of the index over time will require an on-going semi-annual recomposition process, internal and external- buffer files of shares that exceed (shares outside the index) or fall below (shares inside the index) the above criteria will be maintained under the jurisdiction of the recomposition committee.

Maintaining adequate representation of the under-lying stock market through all of its future development and changes is dependent upon the establishment of an appropriate recomposition process. Recomposition rules fall into two general categories: Sector rules and market capitalisation rules.

5.1 Sector Rules

Sector rules govern the selection (or deletion) of companies on the basis of being the top capitalisation stock in each of the 34 KSE sectors. Two rules are recommended to undertake selection in this area-one, a time based rule and the other a value-based rule. Application can be triggered by compliance with either rule.

5.1.1 Time-based rule:

A company (not in the index) which becomes the largest in its sector (by any amount of value) will enter the index after maintaining its position as largest in the sector for two consecutive recomposition periods (i.e., one year).

5.1.2 Value-based rule:

A company (not in the index) which becomes the largest in its sector by a minimum of 10% greater in capitalisation value than the present largest in the sector (in the index) will enter the index after one recomposition period (i.e., 6 months).

5.2 Capitalisation Rule Capitalisation Rule

Capitalisation rules govern the selection (or deletion) of companies on the basis of being among the largest capitalisation companies in the stock market. Only one rule applies here-time based rule.

5.2.1 Time-based rule:

A company (not in the index) may qualify for entry if it exceeds the market cap value of the last stock in the index selected on the basis of market cap for two recomposition periods (i.e. one year). A qualifying company automatically pushes out the lowest cap selected stock in the index.

5.3 Rules for new issues:

A newly listed company or a privatized company shall qualify to be included in the existing index (after one recomposition period) if the market capitalisation of the new or privatized company is at least 2% of the total market capitalization.

5.4 Recomposition Time table

The recomposition committee will meet semi-annually, with meetings scheduled to take place at least two weeks before the end of the last trading day of the month in which they occur. This is to allow for a minimum announcement period of two weeks, commencing the day following the recomposition meeting, when the results of the meeting are made public, at the end of the last trading day of the month, when changes are implemented into the index.

5.5 Recomposition Committee

The recomposition committee has two broad function:

  1. Overseeing implementation of the index rules at the semi-annual recomposition sessions.

  2. Reviewing the index rules and altering them as necessary.

AN EXAMPLE OF THE RECOMPOSTION OF THE KSE100

The base divisor adjustment process can easily be understood by an example mentioned below. It is important to understand that all divisor adjustment are made after the close of trading.

DIVISOR CHANGES

KSE-100 Index as on Day 2 = 1100

Index Market Capitalization on Day 2 = 11,000,000,000.00

Divisor as on Day 2 = 10,000,000,000.00

Revised Market Capitalization due to addition and Delition of companies on the basis of Sector Base

Rule and Market Capitalization Rule.- Say = Rs. 12,000,000,000.00

As mentioned earlier the Revised Market Capitalization are the market capitalization of those companies which would constitute the KSE-100 Index on the next day (Day 3). The Revised Market Capitalization calculated after the end of closing of trading session of Day 2 by using closing prices of the same day. 

The key to making this adjustment, as with any divisor adjustment, is that the index value is temporarily 'frozen' at the close of trading, while the divisor is adjusted for the increase or decrease in market value of the numerator in the formula.

As the Formula for KSE-100 Index is:
Market Capitalization
Index = —————————————— x 1000
Divisor


Therefore, in order to get the new divisor than formula is reframed as:
Revised Market Cap.
New Divisor = ————————————— x 1000
Index (Day 2)
12,000,000,000
= ——————————— x 1000
1100
= 10,909,090,909

Note: The formula for Re-composition of the KSE100 Index is same as mentioned in Table 2, except that the treatment of Base Divisor changes from Base Period Value to an arbitrary number, set such that there is no break in the index series. This will be adjusted for any capital changes in indexed stocks.

 

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