Which of the following statements about the coefficient of variation (CV) are correct?
Understanding Coefficient of Variation (CV)
Statements correct:
- CV is measure of relative dispersion.
- CV is useful in comparing risk of assets with differing average or expected returns.
- CV is calculated by dividing standard deviation by average/expected return.
The coefficient of variation (CV) is a statistical measure used to assess the relative dispersion or variability of a dataset. It provides a standardized measure of risk that allows for comparisons between assets or investments with differing average or expected returns. The CV is particularly useful when comparing investments with different units of measurement or scales. To calculate the CV, the standard deviation is divided by the average or expected return. This normalization process allows for a direct comparison of risk levels, as it accounts for the differences in variability relative to the mean or expected value.
Interpreting Coefficient of Variation
The interpretation of the CV in terms of risk depends on the context and underlying dataset. While a higher CV generally suggests a greater relative dispersion or variability, indicating a higher level of risk, it is important to consider multiple factors in risk assessment. These factors include the specific characteristics of the investment, the investment horizon, and the investor's risk tolerance.
In summary, the CV is a valuable tool for comparing the risk of assets with differing average or expected returns. By normalizing the standard deviation relative to the mean or expected value, it provides a relative measure of dispersion that aids in risk assessment and investment decision-making.
What is the final answer regarding the statements about the coefficient of variation (CV)?
Final Answer on Coefficient of Variation (CV)
The Coefficient of Variation (CV) does measure relative dispersion and is useful in comparing differing assets' risks. It is calculated by dividing the standard deviation by the mean. However, a higher CV indicates higher risk, not lower.
Explanation:
All the mentioned statements about the coefficient of variation (CV) are almost correct except for the last one. Absolutely, the Coefficient of Variation (CV) is a measure of relative dispersion. This means it describes the level of variability relative to the mean of a data set. The CV is indeed useful in comparing the risk of assets with differing average or expected returns. It is especially useful when the scales of the variables being compared are different.
The method to compute the CV is correct. It is calculated by dividing the standard deviation (which measures the dispersion in the data set) by the Mean or Expected Value (which predicts the long-term result of the statistical experiment), and then multiplying the result by 100 to make it a percentage.
However, the final statement is incorrect. Contrarily, a higher CV denotes a greater level of risk, not lower. It indicates that the data points are more dispersed and further from the mean, thereby reflecting a higher risk.