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 Average Value-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 B C = 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 B C Sum Divisor Average 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 series Market 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: Index t = index value on day t P t = ending prices for stocks on day t Q t = number of outstanding shares on day t P b = ending price for stocks on base day Q b = number of outstanding shares on base day

Value-Weighted Series December 31, 2005 Stock PriceNo of share Market value A $10,000 B ,000 C , ,000 Base value equal to an index is 100

Value-Weighted Series December 31, 2006 Stock PriceNo of share Market value A $12,000 B ,000 C , ,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 = ( )/ 3 = = 0.06 Index value (T+1)=Index value (T)*1.053 = 100*1.053or100*1.06 = or106 StockTT+1HPRHPY X Y Z