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WilliamMary $10 James $20 Price per share before 8/1 closing $40 Shares outstanding before 8/1 closing 5 million 8 million 10 million Shares outstanding before 9/1 closing 10 million 8 million 10 million The Tribe Index starts with only two stocks, William Incorporated and Mary Holdings Price per share before 9/1 closing $25 $15 $20 At the market closing on 8/1, William conducts a 2-for-1 split. At the market closing on 9/1, the Tribe Index begins to include a third stock, James Development. (a) Suppose the index is price-weighted like the DJIA, and begins with a divisor of 2 prior to 8/1. What is the index level immediately before the split? What should be the new divisor immediately after the split? What is the index level immediately before James is added? What should be the new divisor immediately after James is added? (b) Suppose the index is market capitalization-weighted like the S&P500, and begins with a divisor of 1 million prior to 8/1. Answer the same questions above.

Explanation / Answer

Ans 3 a) Price weighted index level before split = ($40 + $10)/2 = $25

let new devisor be x

(25 + 15)/x = (50+15)/2

x = 40*2/65 = 1.23

Index level before James is added = (25+15)/1.23 = 32.5

Devisor before James is added = 3

Devisor after James is added is given by x

(25 + 15 + 20)/x = (50 + 15 + 20)/3

x = 60 * 3/85 = 2.12

Asn b) Lets take intial value of market capitalization index as 100 and it is equal to (40*5 + 10*8) = 280

will use devisor of 2.8 for the calculation

at 9/1 market capitalization increase to (25*10 + 15*8) = 370

index value = 370/250 *100 = 148

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