Sharpe Ratio useless: "[...] It is worth noting that the Sharpe ratio tends to infinity as the denominator, the standard deviation, tends to zero. Jump & Dump tried to achieve a large Sharpe ratio by limiting its profits to ensure that they were consistent. This highlights a problem with the Sharpe ratio: Any agent that can guarantee a positive average profit (no matter how small) may be able to engineer an enormous Sharpe ratio, by limiting its profits to ensure a small standard deviation. [...]" (Rahul Savani and Ben Veal, "A Novel Strategy for the 2005 PennâLehman Automated Trading Competition" http://www.cdam.lse.ac.uk/Reports/Files/cdam-2005-12.pdf page 12 ("Conclusions" at the end of Section 6) )
Interesting, but not realistic. This in no way would prove the Sharpe Ratio was useless. There's no one in the world that could buy the whole ask book. It apparently didn't allow short selling or there were too few systems to do short selling. In either case, the ask book could never be completely eliminated by one entity. I'd love to see these guys try it in another market with real stock data.
This does not make the sharpes ratio useless. If you can guarantee small but consistent profits, all you have to do is leverage to the moon and you can be extremely profitable.
Sharpe ratio is indeed too simplistic and outdated... The industry should use my index to select traders and trading system: TRADER PERFORMANCE INDEX, TPI = %R * (1- %MaxDD) * time e.g. for myself, %R = 10% a month = 0.1, %MaxDrawDown = 10% = 0.1, time = 12months = 12 A larger value of time would mean a longer track record so TPI would be larger.
How does that make Sharpe ratio useless? If I am able to deliver a positive return (in excess of the risk-free rate) with very little volatility (a la Madoff), why is a very high Sharpe ratio misrepresenting my performance?
Totally stupid. Limiting profits is not enough. The agent must also limit losses accordingly or proportionaly. That is NOT always possible since by trying to limit losses, he may end up turning profits into losses. I often wonder about these people but...hey...the more stupid traders around, the better it is for us...Let them be...wish them well...
If you can deliver a return over and above the risk free rate w/ 0 volatility - well then that's an arb, isnt it. So it deserves the infinite sharpe ratio 'cos there's no risk you won't outfperform.
Well, you are correct about arb. I didn't read the paper but I know some fund managers used "equity smoothing" to fix their Sharpe ratio for a while and attract institutional funds. At some point though they had to face reality. I know of one who faced the reality of 60% drawdown when he got his margin call. In the meantime however he bought his mansion, sports car, got him a nice girl and lived a lavish lifestyle, OPM of course. Too many idiots and too many scams around. That's a fact
think of it another way; if you had a mechanical system w/ +ve (and stat. significant) expectations, How much would you pay for it, in "sharpes"? what if you waited a year and it still posts the same +ve expectation? what would you pay in sharpes then?? Ceritis paribus the more your sample size goes up the lower your volatility goes - to the point that your sample size is infinite, and you still have +ve expectations - a system that will make money forever. How many sharpes is that worth?
The OP's paper is wrong. Sharpe's problem is not a decreasing denominator rather, an increasing one. Standard Deviation increases with the square root unit of time (Brownian Motion). This will have a lowering effect on Sharpe as N approaches infinity. It is also important to distinguish between upside and downside variance, which Sharpe fails to do. Hence in a positively biased asymmetrical return distribution, the Sharpe will tell a misleading story on associated risks. Academics have been arguing this for decades. This paper dates back to 1979. http://ideas.repec.org/a/cup/jfinqa/v14y1979i02p361-384_00.html Also search Andrew Lo from MIT, he has done considerable work on Sharpe Ratios.