STOCK INDEX
N K JAIN
JAMIA HAMDARD
STOCK INDEX
Successful trading of the index contract
requires a thorough understanding of
construction of the indexes.
When the differences and interrelationships among the indexes are
understood, it is easier to understand the
differences among the future contracts
that are based on these indexes.
STOCK INDEX
Stock
market indexes can be:
Value Weighted Index: Each stock in
the index affects the index value in
proportion to the market value of all
shares outstanding.
Price Weighted Index: Weight of each
stock is proportional to its stock price.
Stock Index
In a price weighted index a small capitalisation
firm could have a much higher weight than a
much larger firm if the small capitalisation firm
had a high stock price but relatively few
outstanding shares.
MMI and Nikkei indexes are price weighted.
S&P 500 and NYSE indexes are value weighted.
Stock Index
All
four indexes exclude dividends.
The omission of dividends is very
important for understanding the pricing of
the future contracts.
Price Weighted Index
This index is computed as follows:
Index = Pi / Divisor
where, Pi is the price of stock i
This does not reflect the percentage change in
price of a share. If a stock doubles from Re 1 to
Rs. 2 and another stock moves from Rs. 100 to
Rs. 101, both the price changes have the same
effect on the index, because the index depends
on the sum of prices.
Price Weighted Index
Stock
Initial Price Next Price
ABC
70
80
DEF
30
50
XYZ
40
45
Total
140
175
Value of
Index
28
35
Divisor
Price Weighted Index
In case there is stock split than using old divisor
will distort the value of the index.
This can not be permitted or the index will
become meaningless as a barometer of stock
prices.
For the index to reflect the level of prices in the
market accurately, simply substituting one stock
for another should not change the index,
The same principle holds for stock dividends and
stock splits.
Price Weighted Index
To find the new divisor, compute the new sum
of prices that result from substituting one firm
for another. Then divide this sum by the original
index value
The value of new divisor is calculated as:
New sum of prices
New Divisor
=
-----------------------Index value before
substitution
Price Weighted Index
STOCK ABC IS SPLIT 2:1
Stock
ABC
Before Split After Split
Price
Price
80
40
Next Price
45
DEF
50
50
55
XYZ
45
45
50
Total
175
135
150
Value of
Index
35
With old 27
new 35
New135/35
or 3.8
30
39.4
Divisor
Old = 5
Price Weighted Index
Rebalancing a portfolio that mimics an index
It is easy to create such portfolio by having all the stocks
of the index in equal number
If a one stock is replaced by another, the composition of
the mimicking portfolio must be changed (rebalanced)
such that the portfolio would continue to mimic the
index.
Since the index divisor will change to preserve the
market value of the index, the transactions that
rebalance the portfolio must cancel each other out
The change in the index divisor tells us precisely how the
portfolio must be rebalanced
Price Weighted Index
Consider a stock portfolio whose value mimics the value
of the price weighted index (shown in table on next
slide)
Suppose XYZ stock is replaced by QRS which sells at 20.
Then the value of new divisor would be:
Index value after inclusion = Index value before
inclusion
120 * Old Divisor = 140 * New Divisor
In our example, the sum of old prices is 140, while that
of new prices is 120
If the old divisor is set at 5 the new divisor would be
4.2857
Price Weighted Index
Stock
Price
Number
Value
ABC
70
20,000
14,00,000
DEF
30
20,000
6,00,000
XYZ
40
20,000
8,00,000
Total
140
28,00,000
Price Weighted Index
This change in index divisor will indicate us how many
shares of each stock we must hold
New number of shares
=
Old Divisor * Old no. of shares =
5 * 20000
New Divisor
4.2857
= 23,333.41 shares
Thus we must purchase 23333.41 shares of QRS and
3333.41 shares each of ABC and DEF
The total cost of rebalancing portfolio is financed by
selling 20,000 shares of XYZ
In case of a stock split, we must sell off the stock that
split and increase the shares held of all other stocks
Price Weighted Index
Stock
Price
Number
Value
ABC
70
23,333.41
16,33,338
DEF
30
23,333.41
7,00,002
QRS
20
23,333.41
4,66,668
Total
~28,00,000
Price Weighted Index
Disadvantages:
1. Change in the price of small firm stocks
have the same effect on index as do
changes in the price of large firm stock
2. The effect of a given percentage stock
price change on a price-index depends
on the initial price of the stock
Value Weighted Index
In
this index each of the stock has a
different weight in the calculation of the
index. The weight is proportional to the
total market value of the stock i.e. the
price per share times the number of
shares outstanding
Consider the example on next slide: if we
want to set index at 100, then divisor
would be 147.5
Value Weighted Index
Stock
Price
Market cap
30
Shares in
the market
175
A
B
90
50
4500
50
100
5000
Total
5250
14750
Value Weighted Index
Divisor does not have to be changed in case of stock
splits because the price is adjusted automatically
However, if a stock alters its capitalisation in a manner
that is not reflected by an automatic adjustment in its
price, then the divisor must be changed
Say, a company issues more stocks in a secondary
offering
To produce continuity in the value of index between the
day secondary is issued and the day after it is issued,
the divisor is changed to keep the index value the same
Consider price change as shown in the table:
Value Weighted Index
Stock
Price
Market cap
40
Shares in
the market
175
A
B
80
50
4000
60
100
6000
Total
7000
17000
Value Weighted Index
Suppose stock A issues 2 million shares
increasing total float to 177 million. Such an
action would change the value of the index
Index value before secondary
= 17000 / 147.5 = 115.25
Index value after secondary
= 17080 / 147.5 = 115.80
It makes no sense to change the value of the index
from 115.25 to 115.80 when nothing actually
happened in the market place
Value Weighted Index
Stock
Price
Market cap
40
Shares in
the market
177
A
B
80
50
4000
60
100
6000
Total
7080
17080
Value Weighted Index
In order to keep the value of the index the same
on the morning after the secondary is issued,
the divisor must be changed to reflect the extra
2 million shares
The new divisor would be equal to the new total
capitalisation (17080) divided by old index value
(115.2542373)
So new divisor is = 148.19412
The divisor of the value weighted index can
change quite often. In a value weighted index ,
the stocks with the largest market value have
the most weight within the index.
Value Weighted Index
Stock
Price
Market
cap
%age
40
Shares in
the
market
177
7080
41.5
80
50
4000
23.4
60
100
6000
35.1
17080
100.0
Total
Value Weighted Index
Another
interesting statistics to know
regarding any index is how many shares
of each stock are in the index. In a value
weighted index, the number of shares of
each stock are determined by dividing the
stocks float by the divisor of the index
In our example Divisor is 148.19412
Index value is 115.25
Value Weighted Index
Stock
Price
Market
cap
Shares
40
Shares in
the
market
177
7080
1.19437
80
50
4000
0.33739
60
100
6000
0.67479
Total
17080
Value Weighted Index
Thus if stock A goes up by one point, then the
value of index would increase by 1.20 points
because there are 1.2 shares of stock A in the
index.
It readily allows an investor to see how any
stocks movement will affect the index
movement in a trading day.
Number of shares in a VWI do not change on a
daily basis
VWI are the most prevalent type
Sub-Indices
It
refers to an index of stocks in which all
the stocks are members of the same
industry group
They may be PWI or VWI
They consist of fewer stocks
Large indices are known as broad based
while sub-indices are narrow based
Simulating an Index
1.
2.
It is not possible to replicate the entire index
because:
Individual investors lack execution capability
Capital required is huge
Some traders try to take advantage of
theoretical price discrepancies
They set up a basket of small number of
stocks to duplicate the performance of the
entire index
Tracking Error
It
is the difference in performance of the
actual index and the simulated index
portfolio
It may be statistically possible to predict
how closely a portfolio will simulate a
given index
Tracking error is less if simulated index
has a high correlation to the main index
Uses of Security Market Indexes
To compute market return over a
specified time period
2. To use it as a benchmark to judge the
performance of a portfolio
3. Indicator series are used to develop an
index portfolio
4. To examine the factors that influence
aggregate security price movements
1.
Uses of Security Market Indexes
5. Technical analysts use them to plot and
analyse price and volume changes for a
stock market series to predict future price
movements
6. Capital market theory has developed
relationship between the rates of return
for a risky asset and the rates of return
for a market portfolio of risky assets.
Importance of Stock Market
Index
It
is a standard of comparison to judge
the performance of individual investor
To evaluate alternative investments
To measure the market rates of return
To predict the market movements
Factors affecting the construction
of stock market index
Sample
size
Sample should be large enough to be
statistically significant
Representativeness
It should be representative of total
population and should possess
characteristics of interest
Base
year
It should be a normal year
Factors affecting the construction of
stock market index
Economical
Computational costs are low but one should keep in
mind economies in gathering and updating data
Timeliness
A price indicator should reflect all changes in the
underlying prices immediately
Descriptive title
A price indicator should bear a title that suggests
what it represents unambiguously
Popular Stock Market Indexes in India
Index
Sample
size
Base
Year
BSE sensex
30
CNX Nifty
50
1978100
79
Nov 3, 100
1995
Value
weighted
-do-
Economic
times
Financial Exp
72
198485
197980
100
100
Equal
weighted
Value
RBI Index
338
198182
100
Un-weighted
BSE National
100
198384
100
Value
100
Base
Value
Weighting
type
