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QUESTION 01 (10 points) ‐ Coefficient of Variation (CV) We need to compare volatility of multiple assets. As the assets have different variation ranges, e.g. a big stock versus a penny stock, it is useful to look at the coefficient of variation, not the standard deviation, as a measure of volatility. We have the following population data:

Asset A Asset B Asset C
Mean ($) 181.92 0.38 247.19
Standard deviation ($) 23.48 0.09 27.31

(a) Give an equation for the coefficient of variation in percentage terms.
(b) Find volatility of the three assets. Use two decimals for percentages, e.g. 23.76%.
(c) Which asset is the least volatile? Which asset is the most volatile?

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Answer:

a, Coefficient of variation

   = Standard deviation x 100

          Mean

b, Coefficient of variation

  Asset A

   Coefficient of variation

   = $23.48   x 100

      $181.92

  = 12.91%

   Asset B

  Coefficient of variation

  = $0.09 x 100

     $0.38

 = 23.68%

  Asset C

   Coefficient of variation

  = $27.31  x 100

     $247.19

  = 11.05%

Asset C is least volatile while Asset B is most volatile

Explanation:

Coefficient of variation is the ratio of standard deviation to mean (expected return) multiplied by 100. It is used to measure the volatility of assets. Asset  C has the least coefficient of variation, thus, it is the least volatile. Asset B has the highest coefficient of variation, which implies that it is the most volatile.

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