6.29.2005

Q&A: In an equal-weighted market index...

composed stock A and stock B, what's the rate of return if stock A increases by 10%, and B increases by 20%?

  • An equally weighted arithmetic average of these returns would be: (10% + 20%) / 2 = 15%. Or
  • for the geometric mean: 1 + r = [( 1 + 0.1) x (1 + 0.2)]^(1/2)
    • r = 1.1489. So the geometric average = 14.89% < the arithmetic average.

Bonus Points

  • In an unweighted/equal-weighted series, all stocks carry equal weight regardless of their price or market value. It assumes that equal dollar amounts are invested in each stock in the index at the beginning of the period.
    • Value Line Index: It is equally weighted geometric average of the performance of about 1,700 firms.
  • It is typically generated by taking the arithmetic or geometric mean of the percentage changes in the value for the stocks in the index.
    • Whenever there is variation in performance among the stocks in an index, the geometric average will be less than the arithmetic average (For this reason value Line index provides a downward-biased measure of the rate of return that would be earned by an investor purchasing an equally weighted portfolio of all the stocks in the index.)

Category: C++ Quant > Financial Markets

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