Editing Statistical arbitrage (section)

==Trading strategy==
[[File:Statistical Arbitrage.png|thumb|Shows a statistical arbitrage strategy on artificial data. The portfolio prices are a result of combining the two stocks.]]
Broadly speaking, StatArb is actually any strategy that is bottom-up, [[Beta (finance)|beta]]-neutral in approach and uses statistical/econometric techniques in order to provide signals for execution. Signals are often generated through a contrarian mean reversion principle but can also be designed using such factors as lead/lag effects, corporate activity, short-term [[momentum (finance)|momentum]], etc. This is usually referred to{{by whom|date=June 2011}} as a multi-factor approach to StatArb.

Because of the large number of stocks involved, the high portfolio turnover and the fairly small size of the effects one is trying to capture, the strategy is often implemented in an automated fashion and great attention is placed on reducing trading costs. <ref>{{cite web|date=28 February 2020|title=Statistical Arbitrage|url=https://www.daytradetheworld.com/trading-blog/maximizing-returns-using-statistical-arbitrage-strategy/|publisher=DayTradeTheWorld}}</ref>

Statistical arbitrage has become a major force at both hedge funds and investment banks. Many bank proprietary operations now center to varying degrees around statistical arbitrage trading.

As a trading strategy, statistical arbitrage is a heavily quantitative and computational approach to securities trading. It involves [[data mining]] and statistical methods, as well as the use of automated trading systems.

Historically, StatArb evolved out of the simpler [[pairs trade]] strategy, in which [[stock]]s are put into pairs by fundamental or market-based similarities. When one stock in a pair outperforms the other, the under performing stock is bought [[long (finance)|long]] and the outperforming stock is sold [[short (finance)|short]] with the expectation that under performing stock will climb towards its outperforming partner. 

Mathematically speaking, the strategy is to find a pair of stocks with high [[Correlation and dependence|correlation]], [[cointegration]], or other common factor characteristics. Various statistical tools have been used in the context of pairs trading ranging from simple distance-based approaches to more complex tools such as [[cointegration]] and [[Copula (probability theory)|copula]] concepts.<ref>{{Cite journal|last1=Rad|first1=Hossein|last2=Low|first2=Rand Kwong Yew|last3=Faff|first3=Robert|date=2016-04-27|title=The profitability of pairs trading strategies: distance, cointegration and copula methods|journal=Quantitative Finance|volume=16|issue=10|pages=1541–1558|doi=10.1080/14697688.2016.1164337|s2cid=219717488|issn=1469-7688}}</ref>

StatArb considers not pairs of stocks but a portfolio of a hundred or more stocks—some long, some short—that are carefully matched by sector and region to eliminate exposure to [[Beta (finance)|beta]] and other risk factors. Portfolio construction is automated and consists of two phases. In the first or "scoring" phase, each stock in the market is assigned a numeric score or rank that reflects its desirability; high scores indicate stocks that should be held long and low scores indicate stocks that are candidates for shorting. The details of the scoring formula vary and are highly proprietary, but, generally (as in pairs trading), they involve a short term mean reversion principle so that, e.g., stocks that have done unusually well in the past week receive low scores and stocks that have underperformed receive high scores.<ref>{{cite web | url=http://www.math.nyu.edu/faculty/avellane/Lecture8Risk2011.pdf |last=Avellaneda |first=Marco | title=Risk and Portfolio Management; Statistical Arbitrage | publisher =[[Courant Institute of Mathematical Sciences]] | date=Spring 2011 | access-date=2015-03-30 }}</ref>  In the second or "risk reduction" phase, the stocks are combined into a portfolio in carefully matched proportions so as to eliminate, or at least greatly reduce, market and factor risk. This phase often uses commercially available risk models like [[MSCI|MSCI/Barra]], APT, Northfield, Risk Infotech, and Axioma to constrain or eliminate various risk factors.<ref>For example, Andrew Lo (op.cit.) states "the widespread use of standardized factor risk models such as those from MSCI/BARRA or North-field Information Systems ... will almost certainly create common exposures among those managers to the risk factors contained in such platforms"</ref>