Debate over value of Sharpe Ratio in HF analysis continues in new academic study
Jul 13th, 2009 | Filed under: Performance, Analytics & Metrics, Today's Post
As we learned from Ranjan Bhaduri in a post last week, the non-normal qualities of managed future returns and their low correlation with traditional stock/bond portfolios means that traditional measures such as the Sharpe ratio should be viewed with some suspicion.
While this makes intuitive sense (and certainly seems to be correct when applied to managed futures), other research has suggested that even in cases of non-normality, the old-fashioned Sharpe ratio performs pretty well as a ranking system. Regular readers will remember this post about a research study by Martin Eling of the University of St. Gallen and Frank Schuhmacher of the University of Applied Sciences and Technology Aachen. Eling and Schuhmacher found that:
“Despite significant deviations of hedge fund returns from a normal distribution, our comparison of the Sharpe ratio to the other performance measures results in virtually identical rank ordering across hedge funds.”
So much for the Sharpe ratio then, eh? Well, not so fast…
A study this year by Valeri Zakamouline of the University of Agder in Norway asserts that “the choice of performance measure does influence the evaluation of hedge funds.” (our emphasis)
In fact, contrary to Eling and Schuhmacher, Zakamouline finds that: More…
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270 funds is hardly a representative sample. We have tested more than 8000 hedge funds using 13 different distributions and four different goodness of fit measures and find less than 12% of those funds to have returns that are normally distributed.
Further ETL a.k.a Expected Shortfall (ES) and Conditional Value at Risk (CVaR) stands for Expected Tail Loss and not Extreme Tail Loss which invites spurious comparisons with Extreme Value Theory. For more on this see Kevin Dowd’s ‘Measuring Market Risk’ or any of several other references. The ratio of the right tail measure to the left tail measure is equivalent to an Upside Potential Ratio measure of which there are also several forms including the Gaussian and Forsey and Sortino’s 3-parameter lognormal version.
Empirically given 100 observations of your P&L sorted in descending order your 95th percentile Historical VaR will be the 95th observation and the 95th percentile Historical CVaR will be the average of the 5 losses greater than the 95th loss i.e. the expected / probability weighted VaR conditional on the 95th percentile having been exceeded. This measure meets all of the measures of mathematical coherence as proposed by Artnzer et al most particularly sub-additivity which VaR does not save for the special case of multivariate normality.
A Sharpe Ratio is a sharpe ratio no matter what it is measuring, i.e. equities, commodities, other investments… correct ?
What is, say an industry accepted and desired level of Sharpe Ratio… anything above 0.5 considered attractive ? A super attractive investment is one greater than a Sharpe of 1.0 ? I heard that Goldman targets 0.5 – 1.0, does this sound reasonable ? Thanks
garbage in … garbage out! Regardless of the risk measure statistic, using only month end data, when all is marked to market daily — and sometimes minute to minute if highly leveraged & volatile — ignores the interday risk we all live with, as traders & investors. How many positive, smooth, month end to month end returns really consist of x number of std deviations within the month? Hence, trading system back/acid walk forward test design, on a trade by trade time period basis, yields hypothetical data events far superior for valid statistical analysis than the month end to month end statistical snap shots of legacy track records over a systemically skewed time preference marketplace.
In other words, all else being equal, does an investor give their funding to a trader with a “superior” risk/reward 5 year month end to month end real track record, or a new trader with 10+ years of hypothetical back/acid test walk forward results, trade-by-trade, marked to market, that can be R&D duplicated to measure data & algorithm integrity? I’d go with the new trader every time.
If one ranks a set of hedge funds via Sharpe, and via Omega, then one should (in most cases) expect to see similar rankings for some of the funds (though in comparing a set of rankings, one should take care in selecting the appropriate threshold for the Omega function). Funds that have a high Omega ranking compared to a low Sharpe ranking, will most typically be funds that are being penalized for upside volatility by the Sharpe. Funds that have a high Sharpe and a low Omega score, are those that most typically have some unfavorable characteristics in their higher statistical moments that are being ignored by the Sharpe. The Sharpe Ratio is only good for funds that have a Gaussian (i.e. Normal) Distribution since it only takes the first two statistical moments into consideration (look at its formula). The Omega function encodes all of the higher statistical moments (again, look at its formula – as some mathematicians say “A formula is worth a 1000 pictures”). The fact that some of the rankings via Sharpe will be similar to the Omega, does not in any way justify the use of the Sharpe. One would simply be using inferior statistical analysis via the Sharpe, and making themselves more vulnerable to tail events. The Sharpe ratio is mathematically uncivilized, and it’s rather embarrassing for the industry that some folks still use the Sharpe, and the Sharpe’s cousin – the Information Ratio – which is just as bad, if not worse. I do encourage readers of this blog, to read Dr. Shadwick’s posts.