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# 7 Stock Index

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### 7 Stock Index

1. 1. STOCK INDEX N K JAIN JAMIA HAMDARD
2. 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. 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. 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. 5. Stock Index  Allfour indexes exclude dividends.  The omission of dividends is very important for understanding the pricing of the future contracts.
6. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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