# Comparing standard deviation with coefficient of variation

I have series A that is daily levels of a stock index, from which I calculate daily returns, then calculate the std dev of the daily returns, and multiply by (250)^0.5 to get annual std dev of returns for the series = sd(A).

I have a separate series B that shows daily values of yields for a bond index. If I want to compare the volatility between both series, is it correct to compare the coefficient of variation of B = cv(B) with sd(A) and make a statement of the form 'series A is sd(A)/cv(B) more volatile than series B'?

Or, are std dev and coefficient of variation inconsistent measures that cannot be compared?

The population coefficient of variation (CV) is $$\sigma/\mu,$$ where $$\sigma$$ is the population standard deviation and $$\mu$$ is the population mean. [Perhaps see Wikipedia for definition and examples of useful and improper applications.]
One commonly used estimate of the population CV uses the sample standard deviation and mean $$S/\bar X$$ and, for small sample sizes $$n.$$ the adjusted value $$(1 + \frac 4 n)S/\bar X.$$ Appropriate uses are for positive interval data (height, weight, etc.).