Any good book on Statistical Arbitrage?

Quote from matador04:

Most of the stuff I'm reading on stat arb (super late to the game haha) talks about the importance of cointegration...seems to be more important than =correl
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Great quote from Wilmott forum's on Correlation vs Cointegration:

You see a man and a woman walking down the street next to each other and going in the same direction. That is correlation.

A dog crosses the street, causing the woman to slow down. She is now several steps behind the man. You notice that the man slows down, while the woman takes several big steps until she is again even with the man. That is cointegration.
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I purchased the book and haven't read it yet. Stat arbing seems a bit overwhelming to me right now because I'm just learning EasyLanguage with Tradestation and even if I was completely fluent in the language, I'd think it would be very tough to find an edge just coming up with my own ideas. That being said, is there any point in reading this book if I am just going to look for isolated setups with individual stocks and not pairs trading?



Quote from Matt1234au:

Hi again

Aug 2007 – intra-day strategies were profitable virtually every day – certainly net profitable at 31 Aug. For the whole month – arb strategies held overnight, minor profit at month end but there was a nasty drawdown mid month.

Returns – for your standard ETF versus basket your return will be about 2-5% per trade (when profitable!). At Chan’s website he has a fully disclosed ETF versus basket strategy using XLE and his real world example gets 3%. Stat arb is for grinding out regular profits; you don’t get massive wins, or massive losses – though you can get a fright like Aug 2007. That’s why you need to see all your trades in the context of a holistic risk management strategy. What is your capital allocation per pair, can you hedge the whole portfolio, what’s the correlations between those trades etc. It’s at these points you can add a real value to your complete strategy.

Sharpes – I won’t enter a trade unless it has a back tested theoretical Sharpe of at least 2.5, but actual realised Sharpe tends to be 1.7 – 2.1. The real world is never as good as your back tests! But having said that I have stuck with some pairs that were in the low 1s.

I see an ad in efinancialcareers.com today where they say - Minimum Sharpe ratio of 4, Sharpe 10-15+ preferred.

I have never met anyone with a consistent Sharpe of over 4.5 but I am confident they exist. However, 10+ seems impossible for a price taking retail trader paying the spread. Maybe a market maker can substantially reduce their standard deviation of return and therefore they have a higher implied Sharpe. I understand theoretically how you could do it in a high frequency low latency situation and I know some good algo boys but they are nowhere near 10+. I also see that the ad says equities, so I’m as keen as you to know how they do it.

Performance degradation: Statistical relationships break down. Management can stuff a company up, FDA approval can be delayed, investors lose interest in companies and suddenly things don’t track the way they used to. That’s why over night I am running combinations of virtually every stock, ETF and option against basket regressions and then keeping a track of their theoretical past performance.

I guess my approach is more dynamic stat arb, you may need to make basket changes more regularly than you think.

Average holding period is about 17 days for the over-night basket trades.

Why hasn’t all the edge been sucked out by the hedge funds? Because I am not entering or unwinding million dollar positions, I (and you) can be more nimble due to our size of transaction so we can get a good entry/exit price; we don’t have to scale in over say a 5 cent range.

Secondly I can trade what I like, I don’t need to run my ideas past a manager.

Also I have got hedging on some baskets plus I’ve got pairs running across (on the surface) stocks that seem to have nothing in common (hint: look deeper – maybe same supplier, maybe the stock price has a high regression to a particular economic factor, there’s always an reason).

Stat arb isn’t very sexy. You don’t needs screen full of indicators, in fact most of the work is actually pretty boring. The computers just grind over data for hours on end punching out averages, correlations and probabilities. Even when the trades are placed you don’t have to watch your trades tick by tick. However, it’s this procedural approach - a bit like being in a job, combined with the (in my case) regular grinding out of profits that I find appealing. It insulates me from the massive emotional highs, lows and frustrations that I used to experience as an options trader.

Stat arb isn’t for everyone but Ezbentley – your time spent investigating stat arb will be well worth it. Enjoy the journey.
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Hello,

and thank you very much for your post on your experience on stat arb for small investors.

I have done some research and I found that looking for example at xfn, a canadian financial ETF. the spread is about 1/20 of the total size of the position to trade (this is due to the prize of the smallest weight component being about 30 $, and the weigh being about 2%).

This means that an average 0.1% percent component bid/ask spread +commissions correspond to 20* 0.1=2%, i.e. 4% on a two ways trade on the ETF- components spread ( ETFCS from now).

From my empirical research this spread can have some intraday oscillation of about 5% but very rarely and it would be a quite risky trade which would only earn 1% of ETFCS , i.e.about 1/(20/3)% of the capital invested considering a 30% margin account such asIB.

I have not regressed the components against the ETF but simply used the weight in the ETF description.

Does the regression gives much bigger oscillation of the ETFCS?

How many intraday opportunities do you have on a given ETF?What are the profits?

Have you checked cointegration on long multiday intervals?I read the links you provide, and one guy correctly observed that out of sample data may not cointegrate as well as the in sample used to estimate the cointegration vectors, but of course you real life experience would be the best proof.

In the end this strategy is equivalent to assume a mean reverting behavior of the stocks you neglect in reproducing the ETf,but why should their weighted sum should mean revert if they are unit roots individually?

Thanks Again

LY
 
I read somewhere on ET that big quant shops use up to 19 factors for entering trades. Does anyone know what those consist of besides the obvious:

cointegration, correlation, ratios, RSI?, etc
 
Factors analysis has nothing to do to technical analysis.
Factors can be considered "factor" which are unpredictable and have influence on a given stock for example.
One is the market, other can be gold, oil, inflation etc.

Hedge funds like to neutralize all these factor by taking factor neutral positions, something like beta neutral portofolios , but generalized to all the factors.

In these way they can exploit ( supposedly...) idiosyncratic stock movements without exposure to factor fluctuations risk.

In a way it is done in the paper mentioned in the other forum, using PCA analysis or ETF as factors.
 
Quote from Matt1234au:

Hi

I have taken a fair bit from Elite over the years (just running keyword searches over the old posts throws up heaps of good stuff) so here I am giving something back. I do stat arb every day and make money so I know a thing or two about it.

Many people will most likely recommend: Pairs trading By Ganapathy Vidyamurthy. Its OK, however I found a more recent book titled Quantitative Trading: How to Build Your Own Algorithmic Trading Business by Ernie Chan a more practical read. He has a blog that goes into many stat arb issues.

In addition I know guys getting reasonable results from spearman correlations. You can get a good Excel spreadsheet and explanation by hunting around http://www.gummy-stuff.org/. He has a Google search add in at the site - look for “spearman”. Also try “pairs trading”.

I use IB and my best results are from stat arb between an ETF and say ten of its constituent stocks (hint: select the stocks by regressing against the ETF)

With the basket method you have you outlay a lot more $$ as you are buying around 11 stocks/ETFs so that can be around $60K in a hit (based on 100 share minimums).

I'm mainly using MATLAB and IB, some Excel and IB, but am following up on the openquant idea posted by dareminator on 04-29-08.

I’ve been profitable using derivations of the above from the get go – mainly intra-day and basket construction methods. These mean reversion (MV) strategies have a lot going for them. However, you do need to play around with the models a bit, particularly if you want to try and get arb going across different industry sectors (what links them – if anything – maybe try a factor model…..) or build your own indices to trade against a basket. It’s no coincidence that the big boys play in the stat arb space because it is an area in which an edge can be found.

A lot of people throw pairs trading in after a couple of single pairs trades go bad, that’s why you need to look at baskets and ETFs – they provide a form of diversification. However, you need more cash to play using that strategy hence a few less players and therefore a bit less info on the ground about how to go about it. The Hedge funds are all over it but on a much larger scale.

With stat arb you can go into smaller timeframes including intra-day – I’m sure I once downloaded a recording of Don Bright and Maverick(??) discussing prop trading and Don said they encouraged intra-day pair strategies – I may be wrong – but anyway I have had good success in that space as well.

Throw in options and futures and you have a whole lot more strategies. A lot of people will talk about Aug 2007 and the quant strategy crashes, but you can do hedging with ETF options. Try running cointegrations over spread trades. There are heaps of ideas and plays to look at.

I’ve written a bit and in a way I’m responding to all those people what write “it takes years to be profitable, or what’s a good system, or what indicator to use etc”. Stat arb is where it’s at (for me at least). As for the maths – understand correlation, regression, mean reversion, standard deviation – you can learn it all on the web – you only need a working knowledge - and that gummy reference is a good place to start. He’s going to take that site down soon so have a look now if you are interested. He has heaps of models and spreadsheets that he encourages people to use. I’ve had no difficulty adding the IB TWS API into his stuff.

Once you are in the stat arb space directional plays also can be derived – obviously you’re not hedged so to speak but the logic of MV throws up lots of ideas.

So in summary these should get you going:
http://epchan.blogspot.com/
http://www.gummy-stuff.org
Pairs trading By Ganapathy Vidyamurthy
Quantitative Trading: How to Build Your Own Algorithmic Trading Business by Ernie Chan
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Great post, thank you very much.

One question: your hint at pairing ETFs with 10 underlying and choosing the underlying based on regression. Now, in your experience is it better to choose the ones with a lower correlation to maximize the chance of profitable trading opportunities, but also the chance of divergence or would it be better to choose the ones with the highest correlation, minimizing divergence risk, but also minimizing profitable trading opportunities.

Your insight is much appreciated..
 
You want higher correlation.

Remember you are looking for the unusual variation (2+ standard deviation), because when things deviate they will have a higher probability of snapping back - as the stocks are highly correlated - as per your suggested method

If you chose the lower correlated set then you don't necessarily have a higher probability things will suddenly align (so you can straddle them for the expected break), rather you just have a higher probability things won't align.
 
i attach a note re difference between correlation and cointegration.

he says cointegration is the name of the game in pairs

i don't get it, any ideas?

i also thought it was correlation
 

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Besides MATLAB, is there any other software that can analyze cointegration with reasonable programming effort? Cointegration calculation seems quite involved and MATLAB is not that accessible to average retails traders.

Also, is there any recommended time frame to re-evaluate the cointegration among traded products? Supposedly, cointegration, which exists for whatever reason, may change or get stronger or weaker over time.
 
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