Hello,Could anyone give me advice on materials/books/articles about Statistical Arbitrage? My understanding of it is that you long/short a basket of hundred of stocks, doing high frequent trading to make sure that all the risk factors(which may be very subjective) are close to 0... Is that true?... I reli don't quite understand... Why this is an "arb"?

Try looking up Co-integration in google. 'Time Series Analysis' by Hamilton would be a good book to start with. Although you will need to do a lot of work before you get to the point where you fully understand the concept of statistical arbitrage

Stat arb is not really arbitrage. It is typically a heavily levered bet that deviations from usually observed relative price relationships are temporary. Arbitrage is term that is way overused in the marketplace. Used in this context it is like putting lipstick on a pig - it may look nicer to some, but a pig is still a pig. True arbitrage literally means getting something for nothing, that is a very, very rare thing.Here is my favourite definition of arbitrage (alas, I lost the source and cannot give credit to who wrote it):1. Two portfolios can be created that have identical payoffs in all future states of nature but have different costs;2. Two portfolios can be created with equal costs, but where one portfolio has at least the same payoff in all future states of nature and a higher payoff in at least one future state of nature;3. A portfolio can be created with zero cost that has a non-negative payoff in all future states of nature and a positive payoff in at least one future state of nature.Now ask yourself, what has this to do with "statistical arbitrage"?

I recently search the net for Stat Arb stuff. There are a few interesting papers, but, as a whole, the strategy remains classified. Don't bother looking for books - whatever papers you can find are much better. That includes both the book ofVidyamurthy and the obviously trashy book of Pole.

Grinold and Kahn, "Active Portfolio Management"

Grinold and Kahn, "Active Portfolio Management" +++++++++++++++++++++Is it worth it? I just check the table of contents and there is only one chapter out of 22 called "Long-Short investing".

The definitions you gave are correct but they are termed under "Law of one price". Technically, no arbitrage implies law of one price but law of one price does not necessarily imply no arbitrage. But loosely, they are used synonymously since law of one price could result in negative stochastic discount factor in incomplete markets which is sort of absurd but no arbitrage always means positive stochastic discount factor. No Arbitrage: If the cost of a portfolio with positive expected returns (no negative payoffs with probability one) is zero, there is arbitrage. So getting a free lottery ticket is arbitrage. Finding a dollar bill on street is arbitrage. Finding a front seat in a U2 concert is arbitrage.Statistical arbitrage: If two time series are co-integrated but show deviations in the short term then the prior is they will converge so arbitrage exists. There may or may not be any economic reason behind this pattern. That is why it is called "statistical arbitrage" since it is observed only statistically. So the prior is they will converge if there is any deviation. The problem is speed of convergence - which no one knows. This was the basis of strategies used by LTCM - betting on spreads. It is hard to find a book on this topic but there is paper by Gatev and Goetzmann on pair trading which you might want to check out.

would you please tell me what stochastic discount factor means? I just want to learn something.

That Gatev and Gotzman paper is probably over 10 years old.As I said, there are very few more or less up-to-date results that arepublicly available.

Statistical Arbitrage by Andy Pole, Algorithmic Trading Insights and Techniques. Wiley 2007.

Pole's book is a total trash. Dominic would say that even the lowest Accenture employee could do better.

Actually, in this instance the English Wikipage is a fairly good place to start:http://en.wikipedia.org/wiki/Statistical_arbitrageJust read trough and look up the references on the bottom of the page.

Also, I came across this page:http://www.stat.purdue.edu/~ntuzov/Site ... #StatArbIt discusses some StatArb papers that are more or less up-to-date.