Statistics Fundamentals: Coefficient of Variation (“CV”) and the Sharpe Ratio

Relative Dispersion is the amount of dispersion relative to a benchmark. Coefficient of Variation is a scale-free (it has no units of measurement) ratio, of the standard deviation, of a set of observations. It measures volatility, where the lower the ratio, the better risk-return tradeoff.

• Formula: CV = s/Xbar; (i) s is the sample standard deviation and (ii) Xbar is the sample mean

 
Sharpe Ratio is a measure of the average excess return, earned per a unit of standard deviation of return. It is a readily used performance evaluation measure, but it has a couple of drawbacks being:

• If Sharpe Ratios are negative and risk increases, it would result in a higher ratio by the increase in the standard deviation (i.e: -2/1 = -2 where -3/1 = -3). Where in reality, the impact does not necessarily mean better risk-adjusted performance
• The conceptual limitation of the ratio only considering one aspect of risk, being standard deviation.

Note that the formula is: Sh = Mean Excess Return / sp; where (i) Mean Excess Return = (Rp – Rf) where (a) Rp is the mean return to the portfolio and (b) Rf is the risk-free asset; (ii) sp is the standard deviation of returns on the portfolio.