Statistical arbitrage

In the world of finance and investments Statistical arbitrage is used in two related but distinct ways:


 * In the academic literature Statistical arbitrage is opposed to (deterministic) arbitrage.  In deterministic arbitrage a sure profit can be obtained from being long some securities and short others.  In statistical arbitrage there is a statistical mispricing of one or more assets based on the expected value of these assets. (For a simple example, consider a game in which one flips a coin and collects $1 on heads or pays $0.50 on tails.  In any single flip it is uncertain if one will win or lose money.  However, in the statistical sense, there is an expected value of $1&times;50% &minus; $0.50&times;50% = $0.25 for each flip.  According to the law of large numbers, the mean return on actual flips will approach this expected value as the number of flips increases.  This is precisely the way in which a gambling casino makes a profit.) In other words, statistical arbitrage conjectures statistical mispricings or price relationships that are true in expectation, in the long run when repeating a trading strategy.


 * Among those who follow the hedge fund industry Statistical arbitrage refers to a particular category of hedge funds (other categories include Global macro, Convertible Arbitrage, and so on). In this narrower sense Statistical arbitrage is often abbreviated as StatArb. According to Prof. Andrew Lo StatArb "refers to highly technical short-term mean-reversion strategies involving large numbers of securities (hundreds to thousands, depending on the amount of risk capital), very short holding periods (measured in days to seconds), and substantial computational, trading, and IT infrastructure".

StatArb, the trading strategy
As a trading strategy, statistical arbitrage is a heavily quantitative and computational approach to equity trading. It involves data mining and statistical methods, as well as automated trading systems.

Historically StatArb evolved out of the simpler pairs trade strategy, in which stocks are put into pairs by fundamental or market-based similarities. When one stock in a pair outperforms the other, the poorer performing stock is bought long with the expectation that it will climb towards its outperforming partner, the other is sold short. This hedges risk from whole-market movements.

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 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. 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 Barra/APT/EMA/Northfield to constrain or eliminate various risk factors.

Broadly speaking, Stat Arb is actually any strategy that is bottom-up, 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 formed by lead/lag effects, extreme psychological barriers, corporate activity, as well as short-term momentum. This is usually referred to 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 implemented in an automated fashion and great attention is placed on reducing trading costs.

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.

Other forms of statistical arbitrage
Volatility arbitrage is a form of statistical arbitrage in which options, rather than equities, are the primary vehicle of the strategy.

Clearly, statistical arbitrage (in the general sense) only is demonstrably correct as the amount of trading time approaches infinity, or alternately, it does not take into consideration what is typically called "gambler's ruin."

Risks
Statistical arbitrage is subject to model weakness as well as stock-specific risk.

The statistical relationship on which the model is based may be spurious, or may break down due to changes in the distribution of returns on the underlying assets. Factors which the model may not be aware of having exposure to, could become the significant drivers of price action in the markets, and the inverse applies also.

On a stock-specific level, there is risk of M&A activity or even default for an individual name. Such an event would immediately end any historical relationship assumed from empirical statistical analysis.

Events of Summer 2007
During July and August 2007 a number of StatArb (and other Quant type funds) experienced significant losses at the same time (which is difficult to explain unless there was a common risk factor). While the reasons are not yet fully understood, several published accounts blame the emergency liquidation of a fund that experienced customer withdrawals or margin calls. By closing out its positions quickly, the fund put pressure on the prices of the stocks it was long/short. Because other StatArb funds had similar positions (due to the similarity of their alpha models and risk-reduction models) the other funds experienced adverse returns.

In a sense, for a stock "being heavily involved in StatArb" is itself a risk factor. One that is new and thus was not taken into account by the StatArb models.

These events showed that StatArb has developed to a point where it is a significant factor in the marketplace, that existing funds have similar positions and are in effect competing for the same returns. Simulations of simple StatArb strategies by A. Lo show that the returns to such strategies have been reduced considerably from 1998 to 2007 (presumably because of competition).