Security Market Indexes Security Market Indexes A statistical

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 wellknown 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 Exhibit 5. 1 Before Split by Stock A Prices A 30 10 B 20 20 C 10 10 60 3 = 20 40 X = 2 (New Divisor)

Demonstration of the Impact of Differently Priced Shares on a Price-Weighted Exhibit 5. 2 Indicator Series Period T A 100 B 50 C 30 Sum 180 Divisor 3 Average 60 Percentage Change PERIOD T+ 1 Case A Case B 110 100 50 50 30 33 190 183 3 3 63. 3 61 5. 5% 1. 7% .

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: 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

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 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 • 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