I was wondering what a negative coefficient of variation means when calculated from a set of daily returns for an index?


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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.


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