Stock Market Index

Definition

• A stock market index is a hypothetical basket of securities designed to track market changes.

• The most widely followed US stock market indexes are:

• DJIA

• S&P 500

• NASDAQ Composite

Important international stock market indexes are the Nikkei 225 (Japan)

Index differ from one another with respect to:

• The securities included in the index

and

• The method used in calculating the value of index

Types

• Price-Weighted Index

• Value –Weighted Index

• Equal- Weighted

• Geometric Mean

Price-Weighted Index• Definition:• Suppose there are two stocks A & B

• Average = A+B / d (Where d is divisor)

• Formula: I1 = I o * AP1 / APo

Title NO Price To

Price T1

A 1500 10 13

B 2000 20 22

Adjusting the Divisor with stock Split

• At T1 B splits (two of one)

• Number of share has increased

• To Price: 20

• T1 Price: 11 -------- (*2)= 22

Value –Weighted Index• Definition:• Suppose there are two stocks A & B

• Formula: I1 = I o * MV1 / MV0

Title No. of shares

Price at To

Price at T1

A 1500 10 13

B 2000 20 22

Equal–Weighted IndexDefinition: This index is computed by multiplying the level of the index

on the previous day by the arithmetic mean of the daily price

relatives of the relevant stocks in the index.

Daily Price relatives Today’s price dived by yesterday’s price

• Suppose there are two stocks A & BTitle NO Price

ToPrice T1

A 1500 10 13

B 2000 20 22

Calculation• Suppose there are two stocks A & B

• A: 13 / 10 = 1.3• B: 22 / 20 = 1.1

Now calculate the arithmetic mean

• 1.3 + 1.1 / 2 = 1.20

Title NO Price To

Price T1

A 1500 10 13

B 2000 20 22

• Consider the value of index on day To =100Then ,

I1 = Arithmetic Mean * I0 I1 = 1.20 * 100

= 120

*The value line Composite (Arithmetic) index, based

on more than 1500 stocks is prepared in this manner

Geometric Mean IndexDefinition: This index is computed by multiplying the level of the index

on the previous day by the geometric mean of the daily price

relatives of the relevant stocks in the index.

• Suppose there are two stocks A & B

Geometric Mean Index• Definition:• Suppose there are two stocks A & B

• A: 13 / 10 = 1.3• B: 22 / 20 = 1.1• Now calculate the Geometric mean

• (1.3 * 1.1) = 1.1958

Title NO Price To

Price T1

A 1500 10 13

B 2000 20 22

1/2

• Consider the value of index on day To =100

• Then ,

• I1 = I0 * Geometric mean

• I1 = 100 * 1.1958

• = 119.58

Comparing the Indices

• P-W I = 16.67 %

• V-W I = 15.45 %

• E-W I = 20 %

• GM = 19.58 %

Stock Split• A corporate action in which a company's existing

shares are divided into multiple shares.

• The number of shares outstanding increases by a specific multiple, the total dollar value of the shares remains the same compared to pre-split amounts.

• Because no real value has been added as a result of the split.

In the U.K., a stock split is referred to as:• "scrip issue", "bonus issue", "capitalization

issue" or "free issue".

• For example, in a 2-for-1 split, each stockholder receives an additional share for each share he or she holds.

Why stock splits are performed?• A company's share price has grown so high that to

many investors, the shares are too expensive to buy in round lots.

For example, if a XYZ Corp.'s shares were worth $1,000 each

• Investors would need to purchase $100,000 in order to own 100 shares.

• If each share was worth $10, investors would only need to pay $1,000 to own 100 shares.