The problem in the equation lies solely on its denominator, Standard Deviation. Standard Deviation measures a distribution's dispersion. Dispersion (or variability) does not equal risk. We know that Standard Deviation increases with the square root of the unit of time (Brownian Motion). The effects of a proportional increase in volatility as time increases has been lost on all of the historical risk measures.  While not meant to be an exact forecast (nobody can predict future volatility with certainty, the best one can do is assign probabilities to a stochastic process), the Brownian assumption serves as a long term mean reverting ballast to volatility's stochastic nature (see graphic below).  This greater dispersion will have a lowering effect on the Sharpe Ratio.

   We compared the Sharpe Ratios to the best mutual funds according to 10 year annualized returns by Morningstar. After the funds' first 48 months of results, not one had a Sharpe Ratio greater than 1. This measure is then implying that these funds are indeed riskier than their peers with greater Sharpe Ratios ( >1). So the riskier funds performed the best over the next 6 years? Or is the Sharpe Ratio not adequately quantifying risk, let alone predicting future risks?

   Madoff, LTCM, Amaranth, Matador Funds all had significantly higher Sharpe Ratios after their first few years of existence. According to their Sharpe Ratio, these would be wonderfully safe investments compared to their peers.

   This interesting observation then led to the thesis, do successful funds' distributions take on a more asymmetrical shape over time? The answer is yes. According to 3 different Goodness of Fit tests performed at increasing intervals, the funds from the Morningstar group all passed these tests at increasing confidence levels for positively biased continuous distribution characteristics. Examples of these types of distributions include but are not limited to : Weibull, Gamma, Log-normal, Log-logistic. And yes, the higher Sharpe Ratio funds listed immediately above all failed. When we went further out of sample, we found the same held true regardless of asset class or assets under management.

   Sharpe Ratio's fatal flaw is that it is quite ineffective at measuring non-normal distributions.  We counter that the actual dispersion as measured by Standard Deviation is not nearly as important as the direction of that dispersion. From this insight we have developed a quick measure to determine the likelihood of a distribution passing the Goodness of Fit tests for positively biased continuous distributions (No, it's not just a measure of skewness, we wish it were that easy). The one great aspect to the Sharpe Ratio was its ease of calculation, but is the sacrifice of predictive ability of future risk worth it?

   In a video entitled "Identifying Superior Managers" Ken French explains how he and Eugene Fama cannot spot superior active managers from all of their data.  Their findings do indeed then refute the Sharpe Ratio as a means of accomplishing this. We could not have asked for a better endorsement of this notion (outside of Sharpe himself), thank you.

http://www.dimensional.com/famafrench/2009/06/identifying-superior-managers.html#more