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1
Security Market Indicator Series
(Stock market indexes,
their construction
and use)
2
Stock Markets
• Most everyone ‘follows’ the stock markets
• Daily news media commonly report the daily value and the change in U.S. market indicator series such as the Dow Jones Industrial Average and the Down Jones Transportation Average and the NASDAQ Composite.
• In Canada we commonly hear about the TSE (Toronto Stock Exchange) 300 Composite Index and the CDNX (Canadian Venture Exchange)
• But what are these measures? How are they conceived? What do they measure? How can we use them?
3
Security-market Indicator Series
• The term “security-market indicator series” is a more correct term to use when describing the whole range of stock market ‘indices’ and ‘averages’– this is because not all indicator series is constructed as an index
• For example the DJIA (Dow Jones Industrial Average) is an average of 30 large ‘blue-chip’ stocks traded on the NYSE (New York Stock Exchange)
• The TSE (Toronto Stock Exchange) 300 is a composite index made of the the 300 largest ‘value-weighted’ stocks publicly traded on the Toronto Stock Exchange
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What is a ‘Blue Chip’ Stock?
• Blue chip stocks is a general term that is loosely applied to companies that are generally considered to be leaders in their industry, are typically very large in terms of market capitalization (the number of shares outstanding multiplied by their current market price), are considered to be ‘mature’ (ie. they are not necessarily rapidly growing in terms of sales or stock price) and often pay a substantial and consistent cash dividend.
• Examples include IBM, American Express, etc.
• Why not do an internet search and find out what 30 stocks are included in the DJIA?
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DJIA
• Companies included in the average are those selected by Dow Jones & Company, publisher of the Wall Street Journal
• The composition of the average changes over time as companies are dropped because of a merger or bankruptcy has occurred, because a company’s trading activity is low, or because a company not in the average becomes very prominent.
• When a company is replaced by another company, the average is readjusted in such a way as to provide comparability with earlier values.
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Use of Security Market Indexes
• As benchmarks to evaluate the performance of professional money managers
• to create and monitor an index fund
• to measure market rates of return in economic studies
• for predicting future market movements by technicians
• as a proxy for the market portfolio of risky assets when calculating the systematic risk of an asset
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Differentiating Factors in the Construction of Market Indexes
• Because the indicator series are intended to reflect overall market price changes of a group of securities, it is necessary to consider which factors are important in computing an index that is intended to represent a total population.
• Each indicator series will be built upon conscious choices on the following issues:– SAMPLE
– WEIGHTING SAMPLE MEMBERS
– COMPUTATIONAL PROCEDURE
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Differentiating Factors in the Construction of Market Indexes
• SAMPLE - the size of the sample, the breadth of the sample, and the source of the sample used to construct a series are all important
• WEIGHTING SAMPLE MEMBERS - three principal weighting systems are (1) price-weighted (2) value-weighted (3) unweighted (equally weighted)
• COMPUTATIONAL PROCEDURE - one alternative is to take a simple arithmetic average of the various member in the series. Another is to compute an index and have all changes, whether in price or value, reported in terms of the basic index. Finally, some prefer a geometric average of the components rather than an arithmetic average.
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Price-Weighted Series
• A price-weighted series is an arithmetic average of current prices, which means that index movements are influenced by the differential prices of the components.
• DJIA– the Dow Jones Industrial Average is the best-known
price-weighted series and is also the oldest and most popular stock-market indicator series.
– It is computed by totaling the current prices of the 30 stocks and dividing the sum by a divisor that has been adjusted to take account of stock splits and changes in the sample over time.
30
1
/i
adjit DpDJIA
Price-weighted series
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Example of Change in DJIA Divisor when a sample stock splits
After Three-for-One
Before Split Split by Stock A
Prices Prices
A $30 $10
B 20 20
C 10 10
60 3 = 20 40 X = 20
X = 2 = New Divisor• when a stock splits, the divisor becomes smaller as shown.• The cumulative effect of splits can be derived from the DJIA…it was originally
30…but as of July 1999 it was 0.197405
Price-weighted series
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Example of the Impact of Differently Priced Shares on a Price-Weighted Series
Period T + 1
Period T Case A Case BA 100 110 100.7
B 50 50 50
C 30 30 33
Sum 180 190 183
Divisor 3 3 3
Average 60 63.3 61
Percent Change 5.5 1.7
• because the series is price-weighted, a high-priced stock carries more weight than a low-priced stock.
Price-weighted series
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Citicisms of the DJIA
• Limited sample size– 30 nonrandomly selected blue-chip stocks make up the average
– the stocks selected are the largest and most pretigious companies in various industries.
– The DJIA, therefore, probably reflects price movements for large, mature, blue-chip firms rather than the typical company listed on the NYSE
– Several studies have pointed out that the DJIA has not been a volatile as other market indexes and that the long-run returns on the DJIA are not comparable to other NYSE stock indexes.
Price-weighted series
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Citicisms of the DJIA ...
• Weighting Scheme– because the DJIA is price weighted, when companies split their
stock, their prices decline, and therefore their weight in the DJIA is reduced - even though they may be large and important.
– Therefore, the weight scheme casues a downward bias in the DJIA, because the stocks that have higher growth rates will have higher prices, and because such stocks tend to split, they will consistently lose weight within the index.
Price-weighted series
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Value-Weighted Series
• A value-weighted series is generated by deriving the initial total
market value of all stocks used in the series:
Market Value = Number of Shares Outstanding ×
Current Market Price • This initial figure is typically established as the base and assigned an
index value (the most popular beginning index value is 100, but it can vary - say, 10, 50).
• Subsequently, a new market value is computed for all securities in the index, and the current market value is compared to the initial “base” value to determine the percentage change, which in turn is applied to the beginning index value:
ValueIndex BeginningIndex t
bb
tt
QP
QP
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Value-Weighted Series
• In a value-weighted series, there is an automatic adjustment for stock splits and other capital changes (since the decreased price of the share is offset by an equal and opposite effect of an increase in the number of shares outstanding).
• In a value-weighted index, the importance of individual stocks in the sample depends on the market value of the stocks. Therefore, a specified percentage change in the value of a large company has a greater impact than a comparable percentage change in a small company.
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Example of a Computation of a Value-weighted index
Stock Share Price Number of Shares Market ValueDecember 31, 1999
A $10.00 1,000,000 $10,000,000
B 15.00 6,000,000 90,000,000
C 20.00 5,000,000 100,000,000
Total $200,000,000
Base Value Equal to an Index of 100
December 31, 2000
A $12.00 1,000,000 $12,000,000
B (2 for 1 split) 10.00 12,000,000 120,000,000
C (10% stock dividend) 20.00 5,500,000 110,000,000
Total $242,000,000
New Index Value = [Current MV] / [Base Value] × Beginning Index Value
= [$242 M / $200 M] × 100 = 1.21
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Value-weight Indexes
• Price changes for the large market value stocks in a value-weighted index will dominate changes in the index over time.
• This value-weighted effect was prevalent on U.S. stock markets (NYSE, OTC) in 1998 when the market was being driven by large growth stocks - that is, almost all of the gain for the year was attributable to the largest 50 of the S&P 500 Index.
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Value-Weighted SeriesThe TSE 300 Composite
• TSE 300 Composite Index is a value-weighted series:
– 300 stocks (comprised of 14 subindexes)
– weights of the stocks is based on market capitalization adjusted for major shareholders
– Base year = 1975
– Base value of the index = 1000
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TSE 300 Composite Index Recent HistoryDate Closing Value
Dec-97 6699.4Jan-98 6700.2Feb-98 7092.5Mar-98 7558.5Apr-98 7665
May-98 7589.8Jun-98 7366.9Jul-98 6931.4
Aug-98 5530.7Sep-98 5614.1Oct-98 6208.3Nov-98 6344.2Dec-98 6485.9Jan-99 6729.6Feb-99 6312.7Mar-99 6597.8Apr-99 7014.7
May-99 6841.8Jun-99 7010.1Jul-99 7080.7
Aug-99 6970.8Sep-99 6957.7Oct-99 7256.2Nov-99 7519.5Dec-99 8413.8Jan-00 8481.1Feb-00 9129
6931.45530.75614.16208.36344.26485.96729.66312.76597.87014.76841.87010.17080.76970.86957.77256.27519.58413.8
TSE 300 Composite Index
0
2000
4000
6000
8000
10000
12000
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TSE 300 Composite Index The 14 sub-indexes - 04/06/01
1. Metals and Minerals:
2. Gold & Precious Metals
3. Oil & Gas
4. Paper & Forest Products
5. Consumer Products
6. Industrial Products
7. Real Estate
8. Transportation & Environmental Services
9. Pipelines
10.Utilities
11.Communications & Media
12.Merchandising
13.Financial Services
14.Conglomerates
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TSE 300 Composite Index Sub-indexes and components - 04/06/01
1. Metals and Minerals:integrated mines
mining
2. Gold & Precious Metals
3. Oil & Gasintegrated oils
oil & gas producers
oil & gas services
4. Paper & Forest Products
5. Consumer Productsfood processing
tobacco
Distilleries
breweries & Beverages
Household Goods
Biotechnology/Pharmaceuticals
6. Industrial Productssteel
fabricating & engineering
transportation equipment
technology-hardware
building materials
chemicals & fertilizers
technology -software
autos & parts
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TSE 300 Composite IndexSub-indexes - 04/06/01 ...
7. Real Estate
8. Transportation & Environmental Services
9. Pipelines
10.Utilitiestelephone utilities
gas/electrical utilities
11.Communications & Mediabroadcasting
cable & entertainment
publishing & printing
12.Merchandisingwholesale distributors
food stores
department stores
specialty stores
hospitality
13.Financial Servicesbanks & trusts
investment companies & funds
insurance
financial management companies
14.Conglomerates
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TSE 300 Composite IndexSub-indexes - 04/06/01 … examples
7. Real Estate– ACK - Acktion Corp
– BEI - Boardwalk Equities
– TZH - Trizec Hahn Corp
12.Merchandisingwholesale distributors
– FTT - Finning International Inc.
– RCH - Richelieu Hardware Ltd.
– UNS - Uni-select Inc.
14.Conglomerates– BNN.A - Brascan Corp
– CP - Canadian Pacific Ltd
– OCX - Onex Corporation SV
– POW - Power Corporation of Canada SV
24
TSE
• For further information on the Toronto Stock Exchange go to:
http://www.tse.com
• go to the periodicals in the Chancellor Patterson Library and go to Toronto Stock Exchange Review
25
Value-Weighted SeriesA TSE Problem - when a company’s market
capitalization gets too great
• This became a serious problem for the TSE 300 Composite in 2000 since BCE (Bell Canada Enterprises) has a large number of shares outstanding and their the individual share price rose to a point where the firm and its subsidiaries represented more than 20% of the TSE 300
• The reason this is a problem is that professionally-managed portfolios are not allowed to invest more than 10% of their value in any one stock (for proper diversification of risk…and the need as a professional fiduciary to ensure proper diversification)…hence, the usefulness of the TSE 300 as a benchmark of comparison has diminished considerably.
26
Unweighted Price Indicator Series
• In an unweighted index, all stocks carry equal weight regardless of their price or market value.
• A $20 stock is as important as a $40 stock, and the total market value of the company is unimportant.
• USE:– such an index can be used by individuals who randomly select
stock for their portfolio and invest the same dollar amount in each stock.
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Unweighted Price Indicator Series ...
• The actual movements in the index are typically based on the arithmetic average of the percent changes in price or value for the stocks in the index.
• The use of the percent price changes means that the price level or the market value of the stock does not make a difference - each percentage change has equal weight.
• The arithmetic average of percent changes procedure is used in academic studies when the authors specify equal weighting.
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Example of an Arithmetic and Geometric Mean of Percentage Changes
Share Price
Stock T T + 1 HPR HPY
X 10 12 1.20 0.20
Y 22 20 0.91 -0.09
Z 44 47 1.07 0.07
II = 1.20 × 0.91 × 1.07 sum = 0.18
= 1.168 0.18/3 = 0.06
1.1681/3 = 1.0531 = 6%
Index Value (T) × 1.0531 = Index Value (T + 1)
Index Value (T) × 1.06 = Index Value (T + 1)
29
Unweighted Series ...
• Both Value Line and the Financial Times Ordinary Share Index compute a geometric mean of the holding period returns and derive the holding period yield from this calculation.
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Summary of Stock Market Indexes
Number ofName of Index Weighting Stocks SourceDow Jones Industrial Average Price 30 NYSE
Nikkei-Dow Jones Average Price 225 Tokyo
S&P 400 Industrial Market Value 400 NYSE, OTC
S&P Composite Market Value 500 NYSE, OTC
NASDAQ Composite Market Value 4,879 OTC
Wilshire 5000 Equity Value Market Value 5,000 NYSE, AMEX, OTC
Russell 3,000 Market Value 3,000 NYSE, AMEX, OTC
Value Line Industrial Average Equal (geo) 1,499 NYSE, AMEX, OTC
TSE 300 Composite Market Value 300 TSE
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Bond-Market Indicator Series
• Investors know little about the several bond-market series because these bond series are relatively new and not widely published.
• Knowledge regarding these bond series is becoming more important because of the growth of fixed-income mutual funds and the consequent need to have a reliable set of benchmarks to use in evaluating performance.
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Bond-Market Indicator SeriesChallenges
• The creation and computation of bond-market indexes is more difficult than stock-market series for several reasons:– the universe of bonds is much broader than that of stocks, ranging from
Federal Government bonds to bonds in default.
– The universe of bonds is constantly changing because numerous new issues, bonds maturing, calling of outstanding bonds, and bond sinking funds.
– The volatility of prices for individual bonds and bond portfolios change because bond price volatility is affected by duration, which is likewise constantly changing because of changes in maturity, coupon, and market yield.
– Pricing of bonds correctly especially in the case of corporates.
33
Composite Stock-Bond Indexes
• A composite series is intended to measure the performance of all securities in a given country.
• Use of a composite series of stocks and bonds makes it possible to examine the benefits of diversifying with a combination of asset classes such as stocks and bonds in addition to diversifying within the asset classes of bonds or stocks.
• Examples:– Merrill Lynch - Wilshire U.S. Capital Markets Index
– Brinson Partners Global Security Market Index (GSMI) - this index contains both U.S. stocks and bonds, but also includes non-U.S. equities and nondollar bonds as well as an allocation to cash.
34
Mean and Standard Deviation of Annual Percentage Price Change for Stock Price Series 1972 - 1997
Geometric Arithmetic Standard Coefficient
Mean Mean Deviation of Variation
DJIA 8.79 10.09 16.70 1.66
S&P 500 9.06 10.35 16.49 1.59
NASDAQ 11.89 13.94 20.81 1.49
Wilshire 5000 9.29 10.69 17.07 1.60
TSE 300 11.32 12.54 16.52 1.32
FT All-share 10.37 14.36 31.94 2.22
Nikkei 6.97 9.74 25.77 2.65
This gives you an idea of the mean return and volatility of returns for the universe of securities measured by the respective index.
This gives you an idea of the mean return and volatility of returns for the universe of securities measured by the respective index.
35
Mean and Standard Deviation of Annual Rates of Return for Lehman Brothers Bond Indexes 1972 - 1997
Geometric Arithmetic Standard CoefficientMean Mean Deviation of Variation
Government/Corporate 9.68 9.95 8.04 0.81
Government 9.65 9.77 7.15 0.73
Corporate 10.17 10.60 10.25 0.97
Mortgage-Backed9.94 10.35 10.07 0.97
36
Correlation Coefficients Among Monthly Percentage Price Changes In Alternative Equity Indices 1972 - 1997
S&P NASDAQ Wilshire TSE500 NYSE Composite 5000 300
S&P 500 -
NYSE 0.919 -
NASDAQ 0.783 0.881 -
Wilshire 5000 0.906 0.987 0.906 -
TSE 300 0.687 0.761 0.740 0.870 -
Nikkei 0.358 0.350 0.308 0.335 0.293
FT All-Share 0.615 0.712 0.620 0.693 0.627
