Interpreting a Negative Coefficient of Variation for Daily Returns
Summary
The document explains that the coefficient of variation, when defined as standard deviation divided by the mean, can become negative if a sample of daily returns has a negative estimated mean. That sign reflects the return sample's estimated drift; it does not give the usual useful interpretation of relative variability.
The answer cautions that the coefficient of variation is intended for ratio-scale data, generally data that cannot take negative values, making it a poor fit for returns. It suggests examining standard deviation directly, or considering a measure that relates return and volatility, such as the Sharpe ratio. The discussion is conceptual and brief: it does not provide a worked calculation, address estimation uncertainty, or establish that either alternative is appropriate for every research question.
Key ideas
- A negative coefficient of variation can result from a negative estimated mean return.
- The coefficient of variation is difficult to interpret when applied to return series that may be negative.
- Standard deviation may be more interpretable when the goal is to describe return dispersion.
- The Sharpe ratio is mentioned as a possible way to relate returns to volatility.
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# What does a negative coefficient of variation mean when calculated from daily returns during a period?
# What does a negative coefficient of variation mean when calculated from daily returns during a period?
I was wondering what a negative coefficient of variation means when calculated from a set of daily returns for an index?
## Answer by Stefan Voigt (score 2, accepted)
https://quant.stackexchange.com/a/32300
With coefficient of variation you refer to the relative standard deviation $\frac{\sigma}{\mu}$ I suppose? In this case, negative values occur, as your historical data exhibits a negative drift, which means your estimate of $\mu$ is negative. In my understanding, the coefficient of variation should only be used for data in a ratio scale, or, more general, for data which does not exhibit negative values - this is not really appropriate for return time series.
In terms of standard interpretation of the coefficient of variation, at least in my understanding, you cannot give any statements as soon as you apply this measure to data in a non-ratio scale (see also Wikipedia).
Why don't you consider the standard deviation itself? Or, if you are interested in relating standard deviation and returns, you can still interpret the magnitude of this value (although I am not sure what it tells you). In general, the coefficient of variation is closely related to the Sharpe-ratio, maybe this helps to find an appropriate measure for you.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.