Security-market indicator series




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CHAPTER 7
SECURITY-MARKET INDICATOR SERIES


Uses of Security Market Indexes

Benchmark to Judge Performance of Individual Portfolios

Develop an Index Portfolio

Examine Factors That Influence the Stock Market

Technical Analysis of the Market

Derivation of Systematic Risk for Securities



Differentiating Factors in Constructing Market Indexes

The Sample: Size, Breadth, and Source

Weighting of Sample Members:

price-weighted, value-weighted, unweighted

Computational Procedures

Stock-Market Indicator Series

Price Weighted Series

Dow Jones Industrial Average (30 stock average)

Nikkei-Dow Jones Average (Nikkei Stock Average Index)

Value Weighted Series

Standard and Poor's Indexes

New York Stock Exchange Index

NASDAQ Series

American Stock Exchange Market Value Index

Wilshire 5000 Equity Index

Russell Indexes

Financial Times Actuaries Indexes

Tokyo Stock Exchange Price Index

FT-Actuaries World Indexes

Morgan Stanley Capital International Indexes

Dow Jones World Stock Index

Euromoney-First Boston Global Stock Index

Salomon-Russell World Equity Index


Unweighted Price Indicator Series

Value Line Averages



Financial Times Ordinary Share Index

Style Indexes

Global Equity Indexes

FT/S&P - Actuaries World Indexes

Morgan Stanley Capital International (MSCI) Indexes

Dow Jones World Stock Index

Comparison of World Stock Indexes


Bond-Market Indicator Series

Investment-Grade Bond Indexes

Lehman Brothers

Merrill Lynch

Ryan Treasury

Salomon Brothers


High-Yield Bond Indexes

U.S. High-Yield Bond Indexes

Merrill Lynch Convertible Securities Indexes
Global Government Bond Market Indexes

Composite Stock-Bond Indexes

Merrill Lynch-Wilshire U.S. Capital Markets Index (ML-WCMI)

Brinson Partners Global Security Market Index (GSMI)


Comparison of Indexes Over Time

Correlations Among Monthly Equity Price Changes

Correlations Among Monthly Bond Series

Mean Annual Stock Price Changes




CHAPTER 7
Answers to Questions



  1. The purpose of market indicator series is to provide a general indication of the aggregate market changes or market movements. More specifically, the indicator series are used to derive market returns for a period of interest and then used as a benchmark for evaluating the performance of alternative portfolios. A second use is in examining the factors that influence aggregate stock price movements by forming relationships between market (series) movements and changes in the relevant variables in order to illustrate how these variables influence market movements. A further use is by technicians who use past aggregate market movements to predict future price patterns. Finally, a very important use is in portfolio theory, where the systematic risk of an individual security is determined by the relationship of the rates of return for the individual security to rates of return for a market portfolio of risky assets. Here, a representative market indicator series is used as a proxy for the market portfolio of risky assets.




  1. A characteristic that differentiates alternative market indicator series is the sample--the size of the sample (how representative of the total market it is) and the source (whether securities are of a particular type or a given segment of the population (NYSE, TSE). The weight given to each member plays a discriminatory role--with diverse members in a sample, it would make a difference whether the series is price-­weighted, value-weighted, or unweighted. Finally, the computational proce­dure used for calculating return--i.e., whether arith­metic mean, geometric mean, etc.




  1. A price-weighted series is an unweighted arithmetic average of current prices of the securities included in the sample--i.e., closing prices of all securities are summed and divided by the number of securities in the sample.

A $100 security will have a greater influence on the series than a $25 security because a 10 percent increase in the former increases the numerator by $10 while it takes a 40 percent increase in the price of the latter to have the same effect.




  1. A value-weighted index begins by deriving the initial total market value of all stocks used in the series (market value equals number of shares outstanding times current market price). The initial value is typically established as the base value and assigned an index value of 100. Subsequently, a new market value is computed for all securities in the sample and this new value is compared to the initial value to derive the percent change which is then applied to the beginning index value of 100.




  1. Given a four security series and a 2-for-1 split for security A and a 3-for-1 split for security B, the divisor would change from 4 to 2.8 for a price-weighted series.

Stock Before Split Price After Split Prices

A $20 $10

B 30 10

C 20 20


D 30 30

Total 100/4 = 25 70/x = 25

x = 2.8

The price-weighted series adjusts for a stock split by deriving a new divisor that will ensure that the new value for the series is the same as it would have been without the split. The adjustment for a value-weighted series due to a stock split is automatic. The decrease in stock price is offset by an increase in the number of shares outstanding.


Before Split

Stock Price/Share # of Shares Market Value

A $20 1,000,000 $ 20,000,000

B 30 500,000 15,000,000

C 20 2,000,000 40,000,000

D 30 3,500,000 105,000,000

Total $180,000,000



The $180,000,000 base value is set equal to an index value


of 100.

After Split

Stock Price/Share # of Shares Market Value

A $10 2,000,000 $ 20,000,000

B 10 1,500,000 15,000,000

C 20 2,000,000 40,000,000

D 30 3,500,000 105,000,000

Total $180,000,000


Current Market Value

New Index Value =                      x Beginning Index Value

Base Value
180,000,000

=             x 100

180,000,000
= 100
which is precisely what one would expect since there has been no change in prices other than the split.


  1. In an unweighted price indicator series, all stocks carry equal weight irrespective of their price and/or their value. One way to visualize an unweighted series is to assume that equal dollar amounts are invested in each stock in the portfolio, for example, an equal amount of $1,000 is assumed to be invested in each stock. Therefore, the investor would own 25 shares of GM ($40/share) and 40 shares of Coors Brewing ($25/share). a $100 stock. An unweighted price index which consists of the above three stocks would be constructed as follows:


Stock Price/Share # of Shares Market Value

GM $ 40 25 $1,000

Coors 25 40 1,000

Total $2,000


A 20% price increase in GM:
Stock Price/Share # of Shares Market Value

GM $ 48 25 $1,200

Coors 25 40 1,000

Total $2,200


A 20% price increase in Coors:
Stock Price/Share # of Shares Market Value

GM $ 40 25 $1,000

Coors 30 40 1,200

Total $2,200


Therefore, a 20% increase in either stocks would have the same impact on the total value of the index (i.e., in all cases the index increases by 10%. An alternative treatment is to compute percentage changes for each stock and derive the average of these percentage changes. In

this case, the average would be 10% (20% - 0%)). So in the case of an unweighted price-indicator series, a 20% price increase in GM would have the same impact on the index as a 20% price increase of Coors Brewing.




  1. Based upon the sample from which it is derived and the fact that is a value-weighted index, the Wilshire 5000 Equity Index is a weighted composite of the NYSE composite index, the AMEX market value series, and the NASDAQ composite index. We would expect it to have the highest correlation with the NYSE Composite Index because the NYSE has the highest market value. The AMEX index would have the lowest correlation with the Wilshire Index.




  1. The high correlations between returns for alternative NYSE price indicator series can be attributed to the source of the sample (i.e. stock traded on the NYSE). The four series differ in sample size, that is, the DJIA has 30 securities, the S&P 400 has 400 securities, the S&P 500 has 500 securities, and the NYSE Composite about 2330 stocks. The DJIA differs in computation from the other series, that is, the DJIA is a price-weighted series where the other three series are value-weighted. Even so, there is strong correlation between the series because of similarity of types of companies.




  1. The two stock price indexes (Tokyo SE and Nikkei) for the Tokyo Stock Exchange listed in Exhibit 7.15 show a high positive correlation (.868). However, the two indexes represent substantially different sample sizes and weighting schemes. The Nikkei-Dow Jones Average consists of 225 companies and is a price weighted series. Alternatively, the Tokyo SE encompasses a much large set of 1800 companies and is a value-weighted series.

Although the NYSE is the only index listed in Exhibit 7.15 that includes just NYSE stocks, the S&P 500 has a high concentration of NYSE stocks. Both indexes are value-weighted but are different in sample size. However, the two indexes are highly correlated (.993).


The correlation between the TSE indexes (Tokyo SE and Nikkei) and NYSE series (S&P 500 and NYSE) are substantially lower (between .306 and .391). These results support the argument for diversification among countries.


  1. Since the equal weighted series implies that all stocks carry the same weight, irrespective of price or value, the results indicate that on average all stocks in the index increased by 23 percent. On the other hand, the percentage change in the value of a large company has a greater impact than the same percentage change for a small company in the value weighted index. Therefore, the difference in results indicate that for this given period, the smaller companies in the index outperformed the larger companies.




  1. The bond-market series are more difficult to construct due to the wide diversity of bonds available. Also bonds are hard to standardize because their maturities and market yields are constantly changing. In order to better segment the market, you could construct five possible subindexes based on coupon, quality, industry, maturity, and special features (such as call features, warrants, convertibility, etc.).




  1. Since the Merrill Lynch-Wilshire Capital Markets index is composed of a distribution of bonds as well as stocks, the fact that this index increased by 15 percent, compared to a 5 percent gain in the Wilshire 5000 Index indicates that bonds outperformed stocks over this period of time.




  1. The Russell 1000, and Russell 2000 represent two different population sample of stocks, segmented by size. The fact that the Russell 2000 (which is composed of the smallest 2,000 stocks in the Russell 3000) increased more than the Russell 1000 (composed of the 1000 largest capitalization U.S. stocks) indicates that small stocks performed better during this time period.




  1. One would expect that the level of correlation between the various world indexes should be relatively high. These indexes tend to include the same countries and the largest capitalization stocks within each country.




  1. High yield bonds (ML High Yield Bond Index) have definite equity characteristics. Consequently, they are more highly correlated with the NYSE composite stock index rather than the ML Aggregate Bond Index.




  1. Based on Exhibit 7.16, MLJA – Japan Government bonds would be the best choice for diversification with U.S Government bonds (LBGC), because the correlation between LBGC and MLJA is 0.113, suggesting that this investment affords the best opportunity to diversify risk.

CHAPTER 7
Answers to Problems

1(a). Given a three security series and a price change from period T to T+1, the percentage change in the series would be 42.85 percent.


Period T Period T+1

A $ 60 $ 80

B 20 35

C 18 25


Sum $ 98 $140

Divisor 3 3

Average 32.67 46.67
46.67 - 32.67 14.00

Percentage change =               =       = 42.85%

32.67 32.67

1(b). Period T



Stock Price/Share # of Shares Market Value

A $60 1,000,000 $ 60,000,000

B 20 10,000,000 200,000,000

C 18 30,000,000 540,000,000

Total $800,000,000

Period T+1

Stock Price/Share # of Shares Market Value

A $ 80 1,000,000 $ 80,000,000

B 35 10,000,000 350,000,000

C 25 30,000,000 750,000,000

Total $1,180,000,000

1,180 - 800 380

Percentage change =             =     = 47.50%

800 800


1(c). The percentage change for the price-weighted series is a simple average of the differences in price from one period to the next. Equal weights are applied to each price change.
The percentage change for the value-weighted series is a weighted average of the differences in price from one period T to T+1. These weights are the relative market values for each stock. Thus, Stock C carries the greatest weight followed by B and then A. Because Stock C had the greatest percentage increase and the largest weight, it is easy to see that the percentage change would be larger for this series than the price-weighted series.

2(a). Period T



Stock Price/Share # of Shares Market Value

A $ 60 16.67 $1,000.00

B 20 50.00 1,000.00

C 18 55.56 1,000.00

Total $3,000.00

Period T+1

Stock Price/Share # of Shares Market Value

A $ 80 16.67 $1,333.60

B 35 50.00 1,750.00

C 25 55.56 1,389.00

Total $4,472.60

4,472.60 - 3,000 1,472.60

Percentage change =                  =          = 49.09%

3,000 3,000

2(b). 80 - 60 20

Stock A =         =     = 33.33%

60 60

35 - 20 15



Stock B =         =     = 75.00%

20 20


25 - 18 7

Stock C =         =     = 38.89%

18 18

33.33% + 75.00% + 38.89%



Arithmetic average =                         

3

147.22%



=         = 49.07%

3

The answers are the same (slight difference due to rounding). This is what you would expect since Part A represents the percentage change of an equal-weighted series and Part B applies an equal weight to the separate stocks in calculating the arithmetic average.


2(c). Geometric average is the nth root of the product of n items.

Geometric average = [(1.3333)(1.75)(1.3889)]1/3 - 1

= [3.2407]1/3 - 1

= 1.4798 - 1
= .4798 or 47.98%
The geometric average is less than the arithmetic average. This is because variability of return has a greater affect on the arithmetic average than the geometric average.

3. Student Exercise


30


4(a). DJIA = ð Pit/Dadj

i=1


Day 1

Company Price/Share
A 12 12 + 23 + 52 87

B 23 DJIA =              =     = 29

C 52 3 3


Day 2

(Before Split) (After Split)



Company Price/Share Price/Share

A 10 10


B 22 44

C 55 55
10 + 22 + 55 10 + 44 + 55

DJIA =              DJIA =             

3 X
87 109

=     = 29 29 =    

3 X
X = 3.7586 (new divisor)



Day 3

(Before Split) (After Split)



Company Price/Share Price/Share

A 14 14


B 46 46

C 52 26


14 + 46 + 52 14 + 46 + 26

DJIA =              = 29.798 DJIA =             

3.7586 Y
112 86

=        29.798 =    

3.7586 Y
Y = 2.8861 (new divisor)

Day 4

Company Price/Share

A 13 13 + 47 + 25

B 47 DJIA =             

C 25 2.8861


85

=        = 29.452

2.8861

Day 5

Company Price/Share

A 12 12 + 45 + 26

B 45 DJIA =             

C 26 2.8861


83

=        = 28.759

2.8861

4(b). Since the index is a price-weighted average, the higher priced stocks carry more weight. But when a split occurs, the new divisor ensures that the new value for the series is the same as it would have been without the split. Hence, the main effect of a split is just a repositioning of the relative weight that a particular stock carries in determining the index. For example, a 10% price change for company B would carry more weight in determining the percent change in the index in Day 3 after the reverse split that increased its price, than its weight on Day 2.



4(c). Student Exercise

5(a). Base = ($12 x 500) + ($23 x 350) + ($52 x 250)

= $6,000 + $8,050 + $13,000

= $27,050


Day 1 = ($12 x 500) + ($23 x 350) + ($52 x 250)

= $6,000 + $8,050 + $13,000

= $27,050

Index1 = ($27,050/$27,050) x 10 = 10


Day 2 = ($10 x 500) + ($22 x 350) + ($55 x 250)

= $5,000 + $7,700 + $13,750

= $26,450
Index2 = ($26,450/$27,050) x 10 = 9.778
Day 3 = ($14 x 500) + ($46 x 175) + ($52 x 250)

= $7,000 + $8,050 + $13,000

= $28,050
Index3 = ($28,050/$27,050) x 10 = 10.370
Day 4 = ($13 x 500) + ($47 x 175) + ($25 x 500)

= $6,500 + $8,225 + $12,500

= $27,225
Index4 = ($27,225/$27,050) x 10 = 10.065
Day 5 = ($12 x 500) + ($45 x 175) + ($26 x 500)

= $6,000 + $7,875 + $13,000

= $26,875
Index5 = ($26,875/$27,050) x 10 = 9.935

5(b). The market values are unchanged due to splits and thus stock splits have no effect. The index, however, is weighted by the relative market values.

6. Price-weighted index(PWI)2002 = (20 + 80+ 40)/3 = 46.67

To accounted for stock split, a new divisor must be


calculated:

(20 + 40 + 40)/X = 46.67

X = 2.143 (new divisor after stock split)
Price-weighted index2003 = (32 + 45 + 42)/2.143 = 55.53

VWI2002 = 20(100,000,000) + 80(2,000,000) + 40(25,000,000)

= 2,000,000,000 + 160,000,000 + 1,000,000,000

= 3,160,000,000

assuming a base value of 100 and 2002 as base period,

then 3,160,000,000/3,160,000,000 x 100 = 100


VWI2003 = 32(100,000,000) + 45(4,000,000) + 42(25,000,000)

= 3,200,000,000 + 180,000,000 + 1,050,000,000

= 4,430,000,000

assuming a base value of 100 and 2002 as period, then

4,430,000,000/3,160,000,000 x 100= 1.4019 x 100 = 140.19
6(a). Percentage change in PWI = (55.53 - 46.67)/46.67 = 18.99%
Percentage change in VWI = (140.19 - 100)/100 = 40.19%
6(b). The percentage change in VWI was much greater than the change in the PWI because the stock with the largest market value (K) had the grater percentage gain in price (60% increase).
6(c). December 31, 2002

Stock Price/Share # of Shares Market Value

K $ 20 50.0 $1,000.00

M 80 12.5 1,000.00

R 40 25.0 1,000.00

Total $3,000.00

December 31, 2003

Stock Price/Share # of Shares Market Value

A $ 32 50.0 $1,600.00

B 45 25.0* 1,125.00

C 42 25.0 1,050.00

Total $3,775.00
(*Stock-split two-for-one during the year)
3,775.00 - 3,000 775.00

Percentage change =                  =          = 25.83%

3,000 3,000
(As a geometric average = [(1.60)(1.125)(1.05)]1/3 - 1

= [1.89]1/3 - 1

= 1.2364 - 1
= .2364 or 23.64%
Unweighted averages are not impacted by large changes in stocks prices (i.e. price-weighted series) or in market values (i.e. value-weighted series).

CHAPTER 7

Answers to Combined Web and Spreadsheet Exercises


Student Exercise.








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