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CMA Intermediate · Financial Management and Business Data Analytics · Data Analysis and Modelling

A firm's share price has a mean of ₹200 and standard deviation of ₹30, while a second firm's share price has a mean of ₹80 and standard deviation of ₹16. Which conclusion about relative variability is correct?

The second firm is more variable relatively. Its coefficient of variation is 16/80 = 20%, whereas the first firm's is 30/200 = 15%. Absolute standard deviation cannot compare series with different means, so the coefficient of variation is used.

  1. AThe first firm is more variable because its standard deviation is higher
  2. BBoth are equally variable since both have positive standard deviations
  3. CThe second firm is more variable because its coefficient of variation is 20% against 15%Correct
  4. DThe second firm is more variable because its mean is lower

Explanation

Coefficient of variation = SD/mean. First firm: 30/200 = 15%. Second firm: 16/80 = 20%. Relative variability is higher for the second firm; comparing absolute SD ignores the different means.

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