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03-Indexes and Expectation

03-Indexes and Expectation - Indexes and Expectation...

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Indexes and Expectation
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Indexes Price weighted index Level is sum of prices divided by a “divisor”, D L E =(P 1 +P 2 +P 3 )/D Value weighted index Begin with arbitrary level (100). Call this level L0 The level next period is L1=L0(1+r vw1 )=100(1+r vw1 ) The level next period is L2=L1(1+r vw2 ) where r vwt is the return on the value-weighted portfolio of all stocks in the index at time t Equally weighted index Begin with arbitrary level (100). Call this level L0 The level next period is L1=L0(1+r ew1 )=100(1+r ew1 ) The level next period is L2=L1(1+r ew2 ) where r vwt is the return on the equally-weighted portfolio of all stocks in the index at
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Value Weighted Index Start with initial arbitrary value of 100 for some base year Level next period=100(1+r vw ) Need to find return on value-weighted portfolio. Value weighted portfolio: Weight on asset i is w i =(Market Cap i )/(Total Market Cap) Market Cap = Price*(Shares Outstanding) Total Market Cap = sum of individual market caps Weight measured at beginning of period.
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Value Weighted Index Total market cap at beginning (time 0)= (80 + 20 + 100 ) = $200 w 1 =40%, w 2 =10%, w 3 =50% r 1 =20%, r 2 =-20%, r 3 =50% Portfolio return = .4(0.2) + 0.1(-0.2) + 0.5(0.5) = 31% Index level next period is 100(1.31)=131 Price Shares Price Shares Stock 1 10 8 12 8 Stock 2 5 4 4 4 Stock 3 2 50 3 50 Time 0 Time 1
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Equally-Weighted Index Start with initial arbitrary value of 100 Level next period=100(1+r ew ) Equally-weighted portfolio Weight on asset i is w i =1 / n n is the number of assets in portfolio Equally Weighted Return Assume stocks pay no dividends r 1 =20%, r 2 =-20%, r 3 =50%, Portfolio return = 1/3(0.2 -0.2 + 0.5) = 16.67% Index level next period: 100(1.167)=116.7
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Stock Market Indices Dow Jones Industrial Average Price-weighted index Includes only 30 blue-chip companies Standard & Poor’s Composite 500 Index Value-weighted index Includes 500 firms Wilshire 5000 Index Value-weighted index Includes about 7,000 firms (despite its name)
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Investing
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