Index Methodology

What is stock market index and how does it construct?

A stock market index is a number that indicates the relative level of prices or value of securities in a market on a particular day compared with a base-day figure, which is usually 100 or 1000. There are many different ways of constructing an index. One of the most common methods is illustrated by the following simple example.The values of a market portfolio at the close of trading on Day 1 and Day 2 are recorded below:

Trading days	Value of portfolio	Index
DAY 1 (base day)	Tk 20,000	1000
DAY 2	Tk 21,000	1050

We take Day 1 as the base day. The index on that day will be taken as a standard. The value assigned to the base day index is 1000 in this example. On Day 2 the value of the portfolio has changed from Tk 20,000 to Tk 21,000, a 5% increase. Therefore, the value of the index on Day 2 will change to indicate a corresponding 5% increase in market value. The computation follows the procedure below:

 

                               2's portfolio value
Day 2's index = ------------------------------------------------- * Base Day's (Day 1) index
                               Base Day's (Day 1) portfolio value

                              Tk 21,000
                        = ---------------- * 1000
                              Tk 20,000
                        = 1050

 

Day 2's index is 1050 as compared to the 1000 of day 1. The above illustration only serves as an introduction to how a particular index is constructed. The daily computation of an index is more involved especially when there are changes in market capitalization of constituent stocks, e.g., rights offers, stock dividend etc. The primary objective of constructing market indices is to measure the performance of the market. The indices provide vital information about the current and historical behavior of the market. Stock market indices differ from one to another basically in their sampling and/or weighting methods.

Sampling Method

There are some market indices that are composed of all stocks listed in a market, e.g., the American Stock Market Index and the Hong Kong Stock Exchange All-Ordinaries Index etc.
In general, an index based on a larger percentage of the total number of listed stocks will be more representative than that one based on a smaller percentage. Although an index that consists of all listed stocks can be considered as more representative, a number of stocks may have very few transactions, the quoted price of these stocks may not reflect their true market value. An index may still be highly representative even if it consists of only a relatively small percentage of the total number of stocks. Here, the sample selection process plays an important role.
Most of well-known stock market indices of the major stock markets in developed countries are still considered as highly representative since their constituent stocks comprise a high percentage of total value of the market. For example, the Hang Seng Index (Hong Kong) is composed of 33 constituent stocks comprising approximately 70% of total value. FOX index (Finland) is composed of 25 most traded shares which is correspond to roughly 80% of the total market value and ATX 50 (Australia) comprises 84% of the capitalization and 97% of the turnover of all Australian stocks.

Weighting Method

There are, in general, three different weighting methods, namely, value-weighted, equally-weighted (or un-weighted), and price-weighted.

Value-weighted method may be considered as a most appropriate method than others for both the bourses of the country (DSE & CSE) since the existing indices of the bourses have been calculating under value-weighted method. For a value-weighted index, the weight of each constituent stock is proportional to its market share in terms of capitalization. We can assume that the amount of money invested in each of the constituent stocks is proportional to its percentage of the total value of all constituent stocks. Examples include all major stock market indices of Hong Kong, London and many others.

Computation of Value Weighted Indices and Adjustments for Changes in Market Capitalization

The computation of a value-weighted index is useful to think in terms of evaluating the performance of a portfolio of securities. Some adjustments need to be made due to changes in market capitalization of the portfolio's constituent stocks. The adjustment procedures are discussed in detail below.
To make our computation simple, we need to keep the number of constituent stocks small. Let us assume that the index is composed of only three stocks: A, B and C.

Day 1 (base day)

Market Data of Constituent Stocks on Day 1

Stock	Shares Outstanding	Closing Price	Market Value
A	20	10	200
B	5	8	40
C	10	5	50
Aggregate Market Value (AMV) = 290

The market value of each stock at closing is given by the product of the number of shares outstanding and the closing price. For stock A, for instance, it is 20 shares times Tk.10 which yields Tk.200. The aggregate market value (AMV) of all constituent stocks is the sum of the market value of each stock. The AMV of day 1 is Tk.290. Day 1 will be taken as the base day on which the index is set at 1000

Day 2

Market Data of Constituent Stocks on Day 2

Stock	Shares Outstanding	Closing Price	Market Value
A	20	10	200
B	5	9	45
C	10	5.5	55
Aggregate Market Value (AMV) = 300

As there is no change in capitalization, no adjustment is needed on Day 2. The AMV is equal to Tk.300. The computation of the index on Day 2 follows the procedure below:

  

                          Day 2's AMV
Day 2's index = -------------------- * Day 1's index
                            Day 1's AMV

                             300
                        = ------- * 1000
                             290
                       = 1034.4828

 

It should be clear that the change in the index value shows the relative change in the aggregate market value of the constituent stocks. There is a 3.45% increase in AMV (also in index) on Day 2 relative to Day 1 (the base day).

Adjustment to Changes in Capitalization

Adjustments need to be made from time to time as a result of changes in capitalization of the constituent stocks. They are discussed in detail below:

Day 3 (Ex-Bonus)

Company Aissues 50% bonus shares. Its shares are to be traded ex-bonus at the ratio of "1 for 2", i.e., one share will be given as bonus for every 2 shares held. This issue of shares is going to change the total number of shares outstanding on Day 3. The adjustment is shown below:

 

                                                                                                   20(1+2)
New Total No. of Shares Outstanding of Company A = ------------
                                                                                                        2
                                                                                                 = 30

Market Data of Constituent Stocks on Day 3

Stock	Shares Outstanding	Closing Price	Market Value
A	30	7	210
B	5	8	40
C	10	6	60
Aggregate Market Value (AMV) = 310

Therefore,

                             Day 3's AMV
Day 3's index = ---------------------- * Day 2's index
                             Day 2's AMV
                                310
                        = ----------- * 1034.4828
                               300

                        = 1068.9656

Note that the closing price of Company A on day 3 is Tk. 7/- determined by demand and supply factors in the market against the theoretically adjusted price (to the extent of disclosure) of Tk. 6.67 made on day 2 after closing market / on day 3 before starting market.

If the company issuing bonus share also recommends / declares cash dividend, then the cash dividend (to the extent of disclosure) should also be adjusted in the aforesaid theoretical price.

Day 4 (Ex-Rights)

Stock C has declared 40% rights share at the ratio of "2 for 5" at Tk.1.50 each including a premium of Tk. 0.5 each. The offer expires on Day 4 (i.e. ex-rights). As mentioned earlier, it is useful to treat the constituent stocks as a portfolio held by an investor. In the computation of the index on Day 4, the investor is assumed to exercise the rights. Therefore, the new number of shares outstanding for stock Cis given below:

                                                                                   10(2+5)
New Number of Shares Outstanding for Stock C = ----------
                                                                                        5
                                                                              = 14

 

Market Data of Constituent Stocks on Day 4

Stock	Shares Outstanding	Closing Price	Market Value
A	30	6.5	195
B	5	9.2	46
C	14	4.5	63
Aggregate Market Value (AMV) = 314

Since all rights are exercised, capitalization adjustment needs to be made on day 3 after closing market / on day 4 before starting market. The number of shares outstanding increases by 4. This will cause an increase in capitalization by Tk.6 (= 4*1.50). The adjusted AMV on Day 3 after closing market / on day 4 before starting market in the index computation on Day 4 will be:
310 + 6 = 316
Therefore,

                             Day 4's AMV
Day 4's index =--------------------------------- * Day 3's index
                           Adjusted Day 3's AMV     
                              304
                        = ---------- * 1068.9656
                             316
                        = 1028.3720


                                     1028.3720 - 1068.9656
Percentage change = ------------------------------- * 100%
                                            1068.9656

                                = -3.80%

The index dropped from 1068.9656 to 1028.3720. This can be interpreted as a 3.80% decrease in AMV.

 

Day 5 (Replacement)

Stock B is replaced by stock D, which has a closing price at Tk.11.5 on Day 4 and its number of shares outstanding is 20. Market Data of Constituent Stocks on Day 5

Stock	Shares Outstanding	Closing Price	Market Value
A	30	7	210
D	20	11	220
C	14	5	70
Aggregate Market Value (AMV) = 500

The adjustment on Day 4's AMV in computing Day 5's Index follows a procedure as if the stock replacement had taken place on Day 4. The adjusted AMV on Day 4 is given as:

Stock	Shares Outstanding	Closing Price	Market Value
A	30	6.5	195
D	20	11.5	230
C	14	4.5	63
Aggregate Market Value (AMV) = 488

Therefore,                  Day 5's AMV
Day 5's index = --------------------------------- * Day 4's index
                            Adjusted Day 4's AMV

                          500
                       = ------ * 1028.3720
                         488

                       = 1053.6598

Day 6 (Addition)

Stock Eis added to the index as a constituent stock on Day 6. Stock E has a closing price of Tk.4 and the number of shares outstanding is 40 on Day 5.
Market Data of Constituent Stocks on Day 6

Stock	Shares Outstanding	Closing Price	Market Value
A	30	7.2	216
C	14	4.8	67.2
D	20	12	240
E	40	4.5	180
Aggregate Market Value (AMV) = 703.2

Since the number of stocks has changed, we need to compute the adjusted AMV for Day 5 in computing Day 6's index. Day 5's adjusted AMV will be equal to the original AMV plus the market value of stock E on Day 5. This is equal to Tk.500 + 160 (4*40) = 660.

                                  Day 6's AMV
Day 6's index = ---------------------------------- * Day 5's index
                             Adjusted Day 5's AMV

                           703.2
                         = ------- * 1053.6598
                            660

                        = 1122.6266

Any new issue should not be considered in the computation of index for “x” days from the date of first trade. “x” may be a single digit parameter e.g. x = 1, 2, 3...... days. Here, in DSE and CSE, “x” is equal to 1.

Shares issued under Repeat Public Offer (RPO), conversion, amalgamation, acquisition etc. should be treated as new issue (addition) and adjusted to give effect in the index on the following day of crediting/ issuing of those shares as per the guideline of “Day 6”.

Day 7 (Deletion)

Stock C is deleted from the index's constituent stocks. The new total number of stocks is reduced to 3. Market Data of Constituent Stocks on Day 7

Stock	Shares Outstanding	Closing Price	Market Value
A	30	7	210
D	20	12.3	246
E	40	5	200
Aggregate Market Value (AMV) = 656

The adjusted AMV on Day 6 will be a reduction by the amount of market value of stock C on Day 6. Day 6's adjusted AMV will be equal to Tk 703.2 - 67.2 = 636.

                                Day 7's AMV
Day 7's index = --------------------------------- * Day 6's index
                             Adjusted Day 6's AMV

                           656
                         = ----- * 1122.6266
                          636

                        = 1157.9293

Day 8 (Ex-Dividend)

Cash dividends of Tk .50 per share are declared for stock E and Day 8 is to be ex-dividend. Market Data of Constituent Stocks on Day 7

Stock	Shares Outstanding	Closing Price	Market Value
A	30	7.2	216
D	20	12.3	246
E	40	4.6	184
Aggregate Market Value (AMV) = 646

No adjustment is needed, as there is no change in capitalization.

                              646
Day 8's index = ------- * 1157.9293
                              656

                         = 1140.2779

Note that the price of stock E drops. This is a normal phenomenon as a stock goes ex-dividend. Day 8’s index records a decrease as well.
Note that the closing price of Company E on day 8 is Tk. 4.6 determined by demand and supply factors in the market against the theoretically adjusted price (to the extent of corporate disclosure) of Tk. 4.50 made on day 7 after closing market / on day 8 before starting market.