How high a Sharpe is considered "good?"

[Rickets]

I was just curious as to what kind of Sharpe for a trading system is considered "good." Two? Three? Five? Eight? This would be for live trading results, not a backtested history, and measured using daily returns.



Since there are many variables involved here, let's say we restrict this to systems that:



1. Do not sell options, or attempt to replicate short option positions



2. Do not engage in market making. I'm most interested in evaluating the quality of a directional strategy, not one that collects the spread and employs only minor directional views.



3. Have at least 3 years of live history.



I realize there are many other variables at work here, such as what asset classes are being traded, etc. But just as a general statement, if you approached a bank and said I have a system with a 0.5 Sharpe, they would probably not be too interested. If the Sharpe were 9, that would be a different story. So what kind of Sharpe is considered "good" in the world of quant trading?

[FDAXHunter]

That depends on a lot more factors, such as scalability, time frame (which are related, but not 1:1), the market (it's easier to make money in an inefficient market) and a bunch of other stuff.



For a single market, you can have long term systems that may hold positions for 12 months or more. For these, a Sharpe Ratio of > 1.0 might already be quite acceptable. For something that flips it's sign 3 times a day a Sharpe Ratio of 2.5 might still not be that great.



As a very rough rule of thumb, single systems with a Sharpe Ratio of above 3 and that [b]scale[/b] reasonably well (note added emphasis) are considered very good. I guess that's the answer you are roughly looking for, without further waffling. Now the only thing to answer is what you consider reasonably scalable... and that depends very much on the house.



Note that some people throw around Sharpe Ratios of way above 10. These are always very constrained in the amount of actual profits they can generate. Sure, you can have a Sharpe Ratio of 25, but if you consider that the most you can do is generate a million dollars a year with it, that's not how you build a scalable business. Scalability is never to be underestimated and indeed, is more important to the business as such than pure risk-adjusted performance.



Having said all that, you can't really pick a single simplistic number to classify what constitutes a good investment. There are lots of grey areas that need to be taken into consideration. In my opinion anyway.

[margarita]

FDax, would you please elaborate a bit more on the time frame relation to Sharpe ratio?  Or refer me to some useful reading material?



Thank you,



margarita

[Bachelier]

I'd ditto FDAX on the inefficient markets and scalability front.



I'm in one, and frankly a Sharpe of 1+ is a yawn, and *no*one* notices. Above 2 and you get attention.



Inefficient and small markets can also, hmmm, "subsidize" Sharpe ratios. I had a Sharpe of 10.4 one month (whoo hoo!), simply because I was away from one ja-mumb-O position in my index that had a big fall out. My portfolio moved not a hair's bredth, the index took the full vol hammer, and I looked like the genius that I am for a brief, shinning month. The portfolio fell to earth and ended the year with a 3.34 Sharpe and 11.37% return, all very very good in my space, but certainly not 10.



As FDAX pointed out, scalability is key. My market is closed and worth about 85 billion Euros. I already feel my own size and could def not scale that Sharpe and return at all. If I was doing that Sharpe and return trading currencies though, you probably would not even begin to see me until I was 82 billlion in exposure.



back to shelling peas.....

[FDAXHunter]

[b]margarita:[/b][i]FDax, would you please elaborate a bit more on the time frame relation to Sharpe ratio[/i]



Sure. For you, anything.



Allright: First thing about the Sharpe Ratio is that it's not independent of the time frame it is calculated on. Why? Because drift (i.e. average return) scales linearly with time whereas volatility of returns scales with the square root of time (assuming the usual: GBM).

So, an annualized Sharpe Ratio is different than a daily Sharpe Ratio (no surprise there to anyone who's ever annualized a volatlity, just wanted to point that out for starters so there's no confusion).



The second thing is the nature of the trading strategy. Take a buy and hold strategy. This will expose you to the natural volatility of the market. There's nothing you can do about it. You're long USD/JPY, you're going to be tracking the volatility of dollar yen over the period.

So, the only way to improve your Sharpe Ratio over the Sharpe Ratio that's inherent in the market is by altering the sign (and/or value) of the position (say in the range from +1 to 0 to -1). The more often you do this, theoretically the higher your Sharpe Ratio can be because you could extract more from the time series without introducing additional volatility (okay there's some shaky assumptions in this, but humor me).



This is one of the aspects of high(er) frequency trading: It allows you to squeeze the same (or higher) return out of a time series with less risk (assuming that you have an edge in the first place) (The second aspect of high frequency trading is to be able to capture microstructural effects).



Not sure that there is any material out there that goes into this. It's kinda obvious if you think about it.

There might be, I'm just not aware of any of the top of my hat.



I've got to jump here. Bye.

[mib]

actually, many strategies do not have their vol scaling as square root.



although square root scaling holds not just for GBM, it does not hold for non-trivial return autocorrelations. many long-horizon convergence plays have vol scaling slower than square root at under-convergence horizont periods; regime dependent strategies like trend-follwoing and many CTAs scale faster than square root because of regime switches



besides that, scaling power depends a lot on risk-management strategy used by the fund or FoF

[Johnny]

To clarify, the assumption needed for square root scaling of vols (st devs) is the same as that needed for adding variances, which is zero correlation between returns. Hence it holds for GBM or any other framework with zero autocorrelation. It also holds for returns that are not independent but which nonetheless have zero correlation.



Anyway, this wasn't FDAX's main point, which clearly still holds and makes sense etc etc.

[zinmaster]

> I was just curious as to what kind of Sharpe for a trading system is considered "good." Two? Three? Five? Eight? This would be for live trading results, not a backtested history, and measured using daily returns.



Depends a lot on size. If you can run 0.5 at large size and *uncorrelated* to other strategies, you can get a lot of capital from the right sources. There is huge portfolio benefit to uncorrelated strategies. [The real difficulty is because you can't prove your strategy is really 0.5 rather than -0.5...]

Anything over 2 with size is a huge home run. But if you want to trade for, say, Millennium, you probably need a 3 at maybe only $20M capacity. N.B. under your 3 rules, if you think you have a Sharpe of 8, you probably have forward data contamination in your backtest ;-) And if you ran an 8, you are probably doing something equivalent to shorting vol or making markets...

[DeepQuant]

That has been my exact experience, high Sharpe strategies tend to have little capacity, bare in mind with a sharpe of 8, you are either looking forward and or you have not accounted for costs. Even RenTec run something like 1.8 and they are in a totally different class to the rest of us mortals.  Capacity is often overlooked by the system builder who is hunting for hi sharpes, yet  from a biz perspective a high SR system is of little to commercial value if you can't make money out of it. North of 1.25 would make you a serious player, take AHL, they manage 10bln on what is claimed to be SR=1.00, but in reality is more like 0.5. furthemore, thier system is almost noddy, in contrast RenTec were closed at 6 yards running at 1.8 coupled with a super sophisticated ensemble. It really depends what you want, if you start of trading small then the high SR will help you, but as you make more profits you become more limited from a reinvestment perspective. If your strategy has an SR of 8, and it is costed, it maybe a very high frequency beast, which means that a slight miss-calc in the costs could render the strategy useless, if anything, increase the costs and see if you are able to retain the bulk of you SR. Strategies that place orders on either side of spread can often result in an underestimation of costs. If after doing all of this you have an SR of 8, you need to get into the market. Personally, I look to the portfolio to deliver the SR, you will find that some 9 parts in 10 come from diversification, and only 10% is delivered through getting a stong predictor. In this respect it is easier to get two uncorrelated strategies of SR=1, yielding a portfolio SR of 1.4, instead of a single  strategy with SR=1.4. The sqrt(N) argument is a powerful one, and not to be underestimated. Go for robustness as opposed to SR, recall all those horror stories of neural nets which worked fantastically well in sample yet failed dismally in live trading... no robustness, over fitted....

[SirAppleby]

I have found Sharpe ratios to be a starting point but lacking in one key respect. You mentioned that you were looking at directional traders, and most of their strategies are very much path dependent. This is not inherently bad, but the long run profitability of a path dependent strategy is directly correlated to that traders ability to increase and decrease leverage at the appropriate times. The Sharpe does not consider that high volatility in a strong trending market is a desirable characteristic.



In option terms, I want my trader to be a call option with positive gamma and low theta risk. The Sharpe fails to reward the high gamma trader. In fact, I can get an infinitely high Sharpe with a negative gamma strategy (until I blow up).



Does anyone know how to evaluate a trader’s performance with a non-linear benchmarking approach?