02-Compounding

# The level next period is l2l11r vw2 where r vwt is

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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 time t

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Index Example: Example: Index with 3 stocks Price-Weighted Index L 0 =1/3(10+5+2)=5.67 L 1 =1/3(12+4+3)=6.33 Percent Change=(6.33/5.67)-1=11.64% 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
Price Weighted Index and Splits What if stock 1 split in the second period? Index Level at time 1: If no split occurs: ( 12 +4+3)/3=6.33 If split occurs and we don’t adjust: ( 6 +4+3)/3 = 4.33 To adjust for split need to come up with a new divisor With no split, index level would have been 6.33 6.33=(6+4+3)/D D=2.0537 Price Shares Price Shares Price Shares Price Shares Stock 1 10 8 12 8 Stock 1 10 8 6 16 Stock 2 5 4 4 4 Stock 2 5 4 4 4 Stock 3 2 50 3 50 Stock 3 2 50 3 50 Time 0 Time 1 Time 0 Time 1 With No Split With Split
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