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Coefficient of variation (CV)
Introduction
The coefficient of variation is used to determine the degree of dispersion of data points (returns) in a series around the mean. This measure can be particularly useful in the context of portfolio management as it allows an investor to compare data sets (investments) expressed in different units.
Usage And Applications
The coefficient of variation calculation is simple and easy to apply:
Standard deviation / Mean
The calculation expresses the variability (risk) of an investment relative to its mean (expected) return. When comparing two investments, the preference would be for the investment which exhibits the lower CV.
Examples Of Use
Mr. Client wishes to compare the performance of two stocks that he has been following. One is a Japanese software company and the other is an American consumer non-discretionary goods company.
Over the past 5 years
Japanese company
Year 1 finishing price: 20,076 JPY
Year 2 finishing price: 24,088 JPY
Year 3 finishing price: 17,120 JPY
Year 4 finishing price: 27,880 JPY
Year 5 finishing price: 27,010 JPY
Japanese company annualized mean: 7.39%
Japanese company annualized volatility: 17.59%
Coefficient of variation= 2.38
American company
Year 1 finishing price: 3.28 USD
Year 2 finishing price: 3.78 USD
Year 3 finishing price: 2.44 USD
Year 4 finishing price: 6.78 USD
Year 5 finishing price: 3.80 USD
American company annualized mean: 3.86%
American company annualized volatility: 37.81%
Coefficient of variation= 9.79
Despite the Japanese company appearing very volatile due to the large JPY denominated stock price, the coefficient of variation shows that the American company is considerably riskier given its poor risk/reward profile.
Sources & Further Reading
- Organizing, Visualizing, and Describing Data 2022 Curriculum CFA Program Level I Quantitative Methods – Portfolio Management and Wealth Planning