Security Market Indexes

• Security Market Indexes: A statistical measure of change in a securities market.

• An index is an imaginary portfolio of securities representing a particular market or a portion of it. Each index has its own calculation methodology and is usually expressed in terms of a change from a base value.

Uses 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 substitute for the market portfolio of risky

assets when calculating the systematic risk of an asset

Differentiating Factors in Constructing Market Indexes

Weighting of sample members• price-weighted series

• value-weighted series

• unweighted (equally weighted) series

Stock-Market Indicator Series

Price Weighted Series• Dow Jones Industrial Average (DJIA)• Nikkei-Dow Jones AverageValue-Weighted Series• NYSE Composite• S&P 500 Index and more…Unweighted Price Indicator Series• Value Line Averages• Financial Times Ordinary Share Index

Dow Jones Industrial Average (DJIA)

• Best-known, oldest, most popular series

• Price-weighted average of thirty large well-known industrial stocks, leaders in their industry, and listed on NYSE

• Total the current price of the 30 stocks and divide by a divisor (adjusted for stock splits and changes in the sample)

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)

Exhibit 5.1

Demonstration of the Impact of Differently Priced Shares on a Price-Weighted

Indicator Series PERIOD T+ 1 .

Period T Case A Case B

A 100 110 100

B 50 50 50

C 30 30 33

Sum 180 190 183

Divisor 3 3 3

Average 60 63.3 61

Percentage Change 5.5% 1.7%

Exhibit 5.2

Criticism of the DJIA

• Limited to 30 non-randomly selected blue-chip stocks

• Does not represent a vast majority of stocks

• The divisor needs to be adjusted every time one of the companies in the index has a stock split

Nikkei-Dow Jones Average

• Arithmetic average of prices for 225 stocks on the First Section of the Tokyo Stock Exchange (TSE)

• Best-known series in Japan

• Price-weighted series formulated by Dow Jones and Company

• The 225 stocks represent 15 percent of all stocks on the First Section

Value-Weighted Series

• Derive the initial total market value of all stocks used in the seriesMarket Value = Number of Shares Outstanding

X Current Market Price

• Assign an beginning index value (100) and new market values are compared to the base index

• Automatic adjustment for splits

• Weighting depends on market value

Value-Weighted Series

where:

Indext = index value on day t

Pt = ending prices for stocks on day t

Qt = number of outstanding shares on day t

Pb = ending price for stocks on base day

Qb = number of outstanding shares on base day

ValueIndex BeginningIndex t

bb

tt

QP

QP

Value-Weighted Series

December 31, 2005

Stock Price No of share Market value

A 10 1000 $10,000

B 15 6000 90,000

C 20 5000 100,000

200,000

Base value equal to an index is 100

Value-Weighted Series

December 31, 2006

Stock Price No of share Market value

A 12 1000 $12,000

B 10 12000 120,000

C 20 5500 110,000

242,000

New index value = (242,000/200,000)*100 = 121

Unweighted Price Indicator Series

• All stocks carry equal weight regardless of price or market value

• May be used by individuals who randomly select stocks and invest the same dollar amount in each stock

• Some use arithmetic average of the percent price changes for the stocks in the index

Unweighted Price Indicator Series

• 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

Unweighted Price Indicator Series

• GM=[1.2*.91*1.07]^(1/3) AM = (.2-.09+.07)/ 3 = 1.0531 = 0.06

Index value (T+1)=Index value (T)*1.053

= 100*1.053 or 100*1.06

= 105.3 or 106

Stock T T+1 HPR HPY

X 10 12 1.2 0.20

Y 22 20 0.91 -0.09

Z 44 47 1.07 0.07