We tend to take ideas beyond where they ought to go.  That’s especially true if it is convenient to do so — and if we get reinforcement from others.

In the investment world, a metric or theory or meme or fad or guru can be pumped up to the point that it is blown out of proportion to its inherent worth.  As you might infer from the title, today we are in the “metric division” of misapplication, staring at a statistical construct that draws admirers from afar.

William Sharpe wrote about the “reward-to-variability ratio” in 1966 and occasionally thereafter.  After a time, it became known simply as “the Sharpe ratio,” the title of Sharpe’s own article in the Journal of Portfolio Management in 1994.Stanford University | This is the reprint, available via Stanford.  By then, the definition of the Sharpe ratio was often different in practice than was Sharpe’s intent.

So, he took pains to lay it all out:  “Whether measured ex ante or ex post, it is essential that the Sharpe Ratio be computed using the mean and standard deviation of a differential return (or, more broadly, the return on what will be termed a zero investment strategy).  Otherwise it loses its raison d’etre.”  (His italics.)

Sharpe also wrote, “Implicitly or explicitly, it is assumed that historic results have at least some predictive ability.”  In addition, he pointed out that decision errors can be made because of correlation issues and that the Markowitz “mean-variance paradigm” underlying the Sharpe ratio relies on assumptions of normality in the distribution of returns.

In 2002, Andrew Lo published “The Statistics of Sharpe Ratios” in the Financial Analysts Journal.CFA Institute | The FAJ is published by the CFA Institute.  As he noted, “Given the Sharpe ratio's widespread use and the myriad interpretations that it has acquired over the years, it is surprising that so little attention has been paid to its statistical properties.”  Lo wrote that monthly values should not be annualized in the common fashion, the differences in investment strategies mean that Sharpe ratio comparisons “cannot be performed naively,” and that if not adjusted for the impact of serial correlations in returns, rankings of asset managers based upon Sharpe ratios can be very misleading.

Fast forward a decade to when David Bailey and Marcos López de Prado published an updated version of their paper, “The Sharpe Ratio Efficient Frontier,” in the Journal of Risk.SSRN | The paper is available on SSRN.  See also López de Prado’s PDF called “The Sharp Razor.”  One paragraph in the introduction began, “Renowned academics (Sharpe among them) have attempted to persuade the investment community not to use the Sharpe ratio in breach of its underlying assumptions.  Notwithstanding its many deficiencies, the Sharpe ratio has become the ‘gold standard’ of performance evaluation.”  They reviewed those deficiencies, despite noting the apparent futility of doing so, given that most investors had avoided that evidence to date.

The authors stated three goals:  1) To introduce a new metric, the Probabilistic Sharpe Ratio (PSR), that adjusts for the uncertainties inherent in the standard ratio; 2) to show that a “Sharpe ratio can still evidence skill if we learn to require the proper length for a track record” (see the tables on pages 37-38 of the paper for exhibits in that regard); and 3) to introduce a Sharpe ratio “efficient frontier” for portfolio selection.  Cutting to the chase, the PSR increases as the standard Sharpe ratio increases, but also due to a longer track record or a positively skewed distribution.  However, it decreases with fatter tails.Quant Research | López de Prado’s site includes a Deutsche Bank report that has a nice one-page summary of the paper that includes a summary paragraph from which this sentence is derived.

There is other research that could be cited, but just reading the introductions and conclusions of those three papers — you don’t even need to wrestle with the formulas within them — should give you a sense of the risk (so to speak) in using Sharpe ratios without care.  Then take a look around you:  Using Sharpe ratios without care is the industry practice.  Investment managers, consultants, fund firms,Putnam Investments | In a recent speech, Robert Reynolds “suggested that investment providers and advisors could offer tremendous value to their clients by” (among other things) “applying Sharpe-ratio, or ‘high efficiency’ metrics to judge securities and strategies.” advisors, commentators, and journalists toss around this supposed “gold standard” of a metric, without the proper context or disclaimers, ignoring its weaknesses and the decision errors that come with its use.

There is a great edifice of confidence and faith in a statistic whose flaws have been documented over time.  One is tempted to call this impressive façade — this gold standard — a Potemkin village, but it wasn’t necessarily constructed with an intent to deceive (although some managers who should know better in effect use it that way).  Nonetheless, it is like a Hollywood set, impressive and realistic on one side, but remarkably flimsy on the other.  Which side do you see?