7 stock index

STOCK INDEXSTOCK INDEX

N K JAINN K JAIN

JAMIA HAMDARDJAMIA HAMDARD


Successful trading of the index contract Successful trading of the index contract

requires a thorough understanding of requires a thorough understanding of

construction of the indexes.construction of the indexes.

When the differences and interWhen the differences and inter--

relationships among the indexes are relationships among the indexes are

understood, it is easier to understand the understood, it is easier to understand the

differences among the future contracts differences among the future contracts

that are based on these indexes.that are based on these indexes.


Stock market indexes can be:Stock market indexes can be:

Value Weighted IndexValue Weighted Index: Each stock in : Each stock in

the index affects the index value in the index affects the index value in

proportion to the market value of all proportion to the market value of all

shares outstanding.shares outstanding.

Price Weighted IndexPrice Weighted Index: Weight of each : Weight of each

stock is proportional to its stock price.stock is proportional to its stock price.

Stock IndexStock Index

In a price weighted index a small In a price weighted index a small capitalisationcapitalisation

firm could have a much higher weight than a firm could have a much higher weight than a

much larger firm if the small much larger firm if the small capitalisationcapitalisation firm firm

had a high stock price but relatively few had a high stock price but relatively few

outstanding shares.outstanding shares.

MMI and Nikkei indexes are price weighted.MMI and Nikkei indexes are price weighted.

S&P 500 and NYSE indexes are value weighted.S&P 500 and NYSE indexes are value weighted.

Stock IndexStock Index

All four indexes exclude dividends.All four indexes exclude dividends.

The omission of dividends is very The omission of dividends is very

important for understanding the pricing of important for understanding the pricing of

the future contracts.the future contracts.

Price Weighted IndexPrice Weighted Index

This index is computed as follows:This index is computed as follows:

Index = Index = ∑∑ PPi i / Divisor/ Divisor

where, Pwhere, Pii is the price of stock iis the price of stock i

This does not reflect the percentage change in This does not reflect the percentage change in

price of a share. If a stock doubles from Re 1 to price of a share. If a stock doubles from Re 1 to

RsRs. 2 and another stock moves from . 2 and another stock moves from RsRs. 100 to . 100 to

RsRs. 101, both the price changes have the same . 101, both the price changes have the same

effect on the index, because the index depends effect on the index, because the index depends

on the sum of prices.on the sum of prices.


35352828Value of Value of

IndexIndex

55175175140140TotalTotal

45454040XYZXYZ

50503030DEFDEF

80807070ABCABC

DivisorDivisorNext PriceNext PriceInitial PriceInitial PriceStock Stock


In case there is stock split than using old divisor In case there is stock split than using old divisor

will distort the value of the index.will distort the value of the index.

This can not be permitted or the index will This can not be permitted or the index will

become meaningless as a barometer of stock become meaningless as a barometer of stock

prices.prices.

For the index to reflect the level of prices in the For the index to reflect the level of prices in the

market accurately, simply substituting one stock market accurately, simply substituting one stock

for another should not change the index,for another should not change the index,

The same principle holds for stock dividends and The same principle holds for stock dividends and

stock splits.stock splits.


To find the new divisor, compute the new sum To find the new divisor, compute the new sum

of prices that result from substituting one firm of prices that result from substituting one firm

for another. Then divide this sum by the original for another. Then divide this sum by the original

index valueindex value

The value of new divisor is calculated as:The value of new divisor is calculated as:

New sum of pricesNew sum of prices

New DivisorNew Divisor == ------------------------------------------------

Index value before Index value before

substitutionsubstitution


STOCK ABC IS SPLIT 2:1STOCK ABC IS SPLIT 2:1

DivisorDivisor

Value of Value of

IndexIndex

TotalTotal

XYZXYZ

DEFDEF

ABCABC

Stock Stock

Old = 5Old = 5

3535

175175

4545

5050

8080

Before Split Before Split

PricePrice

New135/35 New135/35

or 3.8or 3.8

With old 27With old 27

new 35new 35

135135

4545

5050

4040

After Split After Split

PricePrice

3030

39.4 39.4

150150

5050

5555

4545

Next PriceNext Price


Rebalancing a portfolio that mimics an indexRebalancing a portfolio that mimics an index

It is easy to create such portfolio by having all the stocks It is easy to create such portfolio by having all the stocks

of the index in equal numberof the index in equal number

If a one stock is replaced by another, the composition of If a one stock is replaced by another, the composition of

the �mimicking� portfolio must be changed (rebalanced) the �mimicking� portfolio must be changed (rebalanced)

such that the portfolio would continue to mimic the such that the portfolio would continue to mimic the

index.index.

Since the index divisor will change to preserve the Since the index divisor will change to preserve the

market value of the index, the transactions that market value of the index, the transactions that

rebalance the portfolio must cancel each other outrebalance the portfolio must cancel each other out

The change in the index divisor tells us precisely how the The change in the index divisor tells us precisely how the

portfolio must be rebalancedportfolio must be rebalanced


Consider a stock portfolio whose value mimics the value Consider a stock portfolio whose value mimics the value

of the price weighted index (shown in table on next of the price weighted index (shown in table on next

slide)slide)

Suppose XYZ stock is replaced by QRS which sells at 20.Suppose XYZ stock is replaced by QRS which sells at 20.

Then the value of new divisor would be:Then the value of new divisor would be:

Index value after inclusion = Index value before Index value after inclusion = Index value before

inclusion inclusion

120 * Old Divisor = 140 * New Divisor120 * Old Divisor = 140 * New Divisor

In our example, the sum of old prices is 140, while that In our example, the sum of old prices is 140, while that

of new prices is 120of new prices is 120

If the If the old divisorold divisor is set at is set at 55 the the new divisornew divisor would be would be

4.28574.2857


28,00,00028,00,000140140TotalTotal

8,00,0008,00,00020,00020,0004040XYZXYZ

6,00,0006,00,00020,00020,0003030DEFDEF

14,00,00014,00,00020,00020,0007070ABCABC

ValueValueNumberNumberPricePriceStockStock


This change in index divisor will indicate us how many This change in index divisor will indicate us how many shares of each stock we must holdshares of each stock we must hold

New number of shares New number of shares ==

Old Divisor * Old no. of shares Old Divisor * Old no. of shares = = 5 * 200005 * 20000

New Divisor New Divisor 4.28574.2857

= 23,333.41 shares= 23,333.41 shares

Thus we must purchase 23333.41 shares of QRS and Thus we must purchase 23333.41 shares of QRS and 3333.41 shares each of ABC and DEF3333.41 shares each of ABC and DEF

The total cost of rebalancing portfolio is financed by The total cost of rebalancing portfolio is financed by selling 20,000 shares of XYZselling 20,000 shares of XYZ

In case of a stock split, we must sell off the stock that In case of a stock split, we must sell off the stock that split and increase the shares held of all other stockssplit and increase the shares held of all other stocks


~~28,00,00028,00,000TotalTotal

4,66,6684,66,66823,333.4123,333.412020QRSQRS

7,00,0027,00,00223,333.4123,333.413030DEFDEF

16,33,33816,33,33823,333.4123,333.417070ABCABC

ValueValueNumberNumberPricePriceStockStock


Disadvantages:Disadvantages:

1.1. Change in the price of small firm stocks Change in the price of small firm stocks

have the same effect on index as do have the same effect on index as do

changes in the price of large firm stockchanges in the price of large firm stock

2.2. The effect of a given percentage stock The effect of a given percentage stock

price change on a priceprice change on a price--index depends index depends

on the initial price of the stockon the initial price of the stock

Value Weighted IndexValue Weighted Index

In this index each of the stock has a In this index each of the stock has a

different weight in the calculation of the different weight in the calculation of the

index. The weight is proportional to the index. The weight is proportional to the

total market value of the stock i.e. the total market value of the stock i.e. the

price per share times the number of price per share times the number of

shares outstandingshares outstanding

Consider the example on next slide: if we Consider the example on next slide: if we

want to set index at 100, then divisor want to set index at 100, then divisor

would be 147.5would be 147.5



500050001001005050CC

4500450050509090BB

525052501751753030AA

Market capMarket capShares in Shares in

the marketthe market

PricePriceStockStock


Divisor does not have to be changed in case of stock Divisor does not have to be changed in case of stock

splits because the price is adjusted automaticallysplits because the price is adjusted automatically

However, if a stock alters its However, if a stock alters its capitalisationcapitalisation in a manner in a manner

that is not reflected by an automatic adjustment in its that is not reflected by an automatic adjustment in its

price, then the divisor must be changedprice, then the divisor must be changed

Say, a company issues more stocks in a secondary Say, a company issues more stocks in a secondary

offeringoffering

To produce continuity in the value of index between the To produce continuity in the value of index between the

day secondary is issued and the day after it is issued, day secondary is issued and the day after it is issued,

the divisor is changed to keep the index value the samethe divisor is changed to keep the index value the same

Consider price change as shown in the table:Consider price change as shown in the table:



600060001001006060CC

4000400050508080BB

700070001751754040AA





Suppose stock A issues 2 million shares Suppose stock A issues 2 million shares

increasing total float to 177 million. Such an increasing total float to 177 million. Such an

action would change the value of the index action would change the value of the index

Index value before secondary Index value before secondary

= 17000 / 147.5 = 115.25= 17000 / 147.5 = 115.25

Index value after secondary Index value after secondary

= 17080 / 147.5 = 115.80= 17080 / 147.5 = 115.80

It makes no sense to change the value of the index It makes no sense to change the value of the index

from 115.25 to 115.80 when nothing actually from 115.25 to 115.80 when nothing actually

happened in the market placehappened in the market place



600060001001006060CC

4000400050508080BB

708070801771774040AA





In order to keep the value of the index the same In order to keep the value of the index the same on the morning after the secondary is issued, on the morning after the secondary is issued, the divisor must be changed to reflect the extra the divisor must be changed to reflect the extra 2 million shares2 million shares

The new divisor would be equal to the new total The new divisor would be equal to the new total capitalisationcapitalisation (17080) divided by old index value (17080) divided by old index value (115.2542373)(115.2542373)

So new divisor is = 148.19412So new divisor is = 148.19412

The divisor of the value weighted index can The divisor of the value weighted index can change quite often. In a value weighted index , change quite often. In a value weighted index , the stocks with the largest market value have the stocks with the largest market value have the most weight within the index.the most weight within the index.


TotalTotal

CC

BB

AA

StockStock

6060

8080

4040

PricePrice

100100

5050

177177

Shares in Shares in

the the

marketmarket

1708017080

60006000

40004000

70807080

Market Market

capcap

100.0100.0

35.135.1

23.423.4

41.541.5

%age%age


Another interesting statistics to know Another interesting statistics to know

regarding any index is how many shares regarding any index is how many shares

of each stock are in the index. In a value of each stock are in the index. In a value

weighted index, the number of shares of weighted index, the number of shares of

each stock are determined by dividing the each stock are determined by dividing the

stock�s float by the divisor of the indexstock�s float by the divisor of the index

In our example Divisor is 148.19412In our example Divisor is 148.19412

Index value is 115.25Index value is 115.25


TotalTotal

CC

BB

AA

StockStock

6060

8080

4040

PricePrice

100100

5050

177177

Shares in Shares in

the the

marketmarket

1708017080

60006000

40004000

70807080

Market Market

capcap

0.674790.67479

0.337390.33739

1.194371.19437

SharesShares


Thus if stock A goes up by one point, then the Thus if stock A goes up by one point, then the

value of index would increase by 1.20 points value of index would increase by 1.20 points

because there are 1.2 shares of stock A in the because there are 1.2 shares of stock A in the

index.index.

It readily allows an investor to see how any It readily allows an investor to see how any

stock�s movement will affect the index stock�s movement will affect the index

movement in a trading day.movement in a trading day.

Number of shares in a VWI do not change on a Number of shares in a VWI do not change on a

daily basisdaily basis

VWI are the most prevalent typeVWI are the most prevalent type

SubSub--IndicesIndices

It refers to an index of stocks in which all It refers to an index of stocks in which all

the stocks are members of the same the stocks are members of the same

industry groupindustry group

They may be PWI or VWIThey may be PWI or VWI

They consist of fewer stocksThey consist of fewer stocks

Large indices are known as �broad based� Large indices are known as �broad based�

while subwhile sub--indices are ��narrow basedindices are ��narrow based

Simulating an IndexSimulating an Index

It is not possible to replicate the entire index It is not possible to replicate the entire index

because:because:

1.1. Individual investors lack execution capabilityIndividual investors lack execution capability

2.2. Capital required is hugeCapital required is huge

Some traders try to take advantage of Some traders try to take advantage of

theoretical price discrepanciestheoretical price discrepancies

They set up a basket of small number of They set up a basket of small number of

stocks to duplicate the performance of the stocks to duplicate the performance of the

entire indexentire index

Tracking ErrorTracking Error

It is the difference in performance of the It is the difference in performance of the

actual index and the simulated index actual index and the simulated index

portfolioportfolio

It may be statistically possible to predict It may be statistically possible to predict

how closely a portfolio will simulate a how closely a portfolio will simulate a

given indexgiven index

Tracking error is less if simulated index Tracking error is less if simulated index

has a high correlation to the main indexhas a high correlation to the main index

Uses of Security Market IndexesUses of Security Market Indexes

1.1. To compute market return over a To compute market return over a

specified time period specified time period

2.2. To use it as a benchmark to judge the To use it as a benchmark to judge the

performance of a portfolioperformance of a portfolio

3.3. Indicator series are used to develop an Indicator series are used to develop an

index portfolioindex portfolio

4.4. To examine the factors that influence To examine the factors that influence

aggregate security price movementsaggregate security price movements

Uses of Security Market IndexesUses of Security Market Indexes

5.5. Technical analysts use them to plot and Technical analysts use them to plot and

analyseanalyse price and volume changes for a price and volume changes for a

stock market series to predict future price stock market series to predict future price

movementsmovements

6.6. Capital market theory has developed Capital market theory has developed

relationship between the rates of return relationship between the rates of return

for a risky asset and the rates of return for a risky asset and the rates of return

for a market portfolio of risky assets.for a market portfolio of risky assets.

Importance of Stock Market Importance of Stock Market

IndexIndex

It is a standard of comparison to judge It is a standard of comparison to judge

the performance of individual investorthe performance of individual investor

To evaluate alternative investmentsTo evaluate alternative investments

To measure the market rates of return To measure the market rates of return

To predict the market movementsTo predict the market movements

Factors affecting the construction Factors affecting the construction

of stock market indexof stock market index

Sample sizeSample size

�� Sample should be large enough to be Sample should be large enough to be

statistically significantstatistically significant

RepresentativenessRepresentativeness

�� It should be representative of total It should be representative of total

population and should possess population and should possess

characteristics of interestcharacteristics of interest

Base yearBase year

�� It should be a normal yearIt should be a normal year

Factors affecting the construction of Factors affecting the construction of

stock market indexstock market index

EconomicalEconomical

�� Computational costs are low but one should keep in Computational costs are low but one should keep in

mind economies in gathering and updating datamind economies in gathering and updating data

TimelinessTimeliness

�� A price indicator should reflect all changes in the A price indicator should reflect all changes in the

underlying prices immediatelyunderlying prices immediately

Descriptive titleDescriptive title

�� A price indicator should bear a title that suggests A price indicator should bear a title that suggests

what it represents unambiguouslywhat it represents unambiguously

Popular Stock Market Indexes in India

ValueValue10010019831983--

8484

100100BSE NationalBSE National

UnUn--weightedweighted10010019811981--

8282

338338RBI IndexRBI Index

ValueValue10010019791979--

8080

100100Financial ExpFinancial Exp

Equal Equal

weightedweighted

10010019841984--

8585

7272Economic Economic

timestimes

--dodo--100100Nov 3, Nov 3,

19951995

5050CNX NiftyCNX Nifty

Value Value

weightedweighted

10010019781978--

7979

3030BSE BSE sensexsensex

Weighting Weighting

typetype

Base Base

ValueValue

Base Base

YearYear

Sample Sample

sizesize

IndexIndex

7 stock index

Economy & Finance