Suppose the following four stocks are to be combined into a stock index in January 2022 (perhaps a portfolio manager believes these stocks are an appropriate benchmark for their performance):

a. Calculate the initial value of the index if a price-weighting scheme is used. What is the rate of return on this index for the year ending December 31, 2022? For the year ending December 31, 2023?

b. Now assume that a value-weighted index is used and t hat it is scaled b y a factor of 10 million; that is, if the average firm’s market value is $5 billion, t he index would be quoted as 500.

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Brady Corporation Luck Industries Mahomes International Wentz Products Shares (millions) 375 430 550 275 1/1/22 $28 39 50 21 Price 1/1/23 $26 42 54 25 1/1/24 $32 46 62 23