1. STOCK INDEX
N K JAIN
JAMIA HAMDARD

2. STOCK INDEX
Successful trading of the index contract
requires a thorough understanding of
construction of the indexes.
When the differences and inter-
relationships among the indexes are
understood, it is easier to understand the
differences among the future contracts
that are based on these indexes.

3. 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.

4. 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.

5. Stock Index
 Allfour indexes exclude dividends.
 The omission of dividends is very
important for understanding the pricing of
the future contracts.

6. 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.

7. Price Weighted Index
Stock Initial Price Next Price Divisor
ABC 70 80
DEF 30 50
XYZ 40 45
Total 140 175 5
Value of 28 35
Index

8. 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.

9. 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

10. Price Weighted Index
STOCK ABC IS SPLIT 2:1
Stock Before Split After Split Next Price
Price Price
ABC 80 40 45
DEF 50 50 55
XYZ 45 45 50
Total 175 135 150
Value of 35 With old 27 30
Index new 35 39.4
Divisor Old = 5 New135/35
or 3.8

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. Value Weighted Index
Stock Price Shares in Market cap
the market
A 30 175 5250
B 90 50 4500
C 50 100 5000
Total 14750

19. 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:

20. Value Weighted Index
Stock Price Shares in Market cap
the market
A 40 175 7000
B 80 50 4000
C 60 100 6000
Total 17000

21. 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

22. Value Weighted Index
Stock Price Shares in Market cap
the market
A 40 177 7080
B 80 50 4000
C 60 100 6000
Total 17080

23. 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.

24. Value Weighted Index
Stock Price Shares in Market %age
the cap
market
A 40 177 7080 41.5
B 80 50 4000 23.4
C 60 100 6000 35.1
Total 17080 100.0

25. 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
stock’s float by the divisor of the index
 In our example Divisor is 148.19412
 Index value is 115.25

26. Value Weighted Index
Stock Price Shares in Market Shares
the cap
market
A 40 177 7080 1.19437
B 80 50 4000 0.33739
C 60 100 6000 0.67479
Total 17080

27. 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
stock’s 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

28. Sub-Indices
 Itrefers 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

29. Simulating an Index
 It is not possible to replicate the entire index
because:
1. Individual investors lack execution capability
2. 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

30. 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

31. Uses of Security Market Indexes
1. 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

32. 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.

33. Importance of Stock Market
Index
 Itis 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

34. 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

35. 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

36. Popular Stock Market Indexes in India
Index Sample Base Base Weighting
size Year Value type
BSE sensex 30 1978- 100 Value
79 weighted
CNX Nifty 50 Nov 3, 100 -do-
1995
Economic 72 1984- 100 Equal
times 85 weighted
Financial Exp 100 1979- 100 Value
80
RBI Index 338 1981- 100 Un-weighted
82
BSE National 100 1983- 100 Value
84