Statistical arbitrage
Encyclopedia
In the world of finance and investments, statistical arbitrage is used in two related but distinct ways:
. 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 MSCI Barra/APT/Northfield/Risk Infotech/Axioma to constrain or eliminate various risk factors.
Broadly speaking, StatArb 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 designed using such factors as lead/lag effects, corporate activity, short-term momentum
, etc. 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 often 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.
and the liquidity, or size of an allowable bet, approaches infinity. To put it another way, it suffers from the same problems as the martingale betting system
. Over any finite period of time, a series of low probability events may occur that impose heavy short-term losses. If those short-term losses are greater than the liquidity available to the trader, default
may occur, as in the case of Long-Term Capital Management.
Statistical arbitrage is also subject to model weakness as well as stock- or security-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. The existence of the investment based upon model itself may change the underlying relationship, particularly if enough entrants invest with similar principles. The exploitation of arbitrage opportunities themselves increases the efficiency of the market, thereby reducing the scope for arbitrage, so continual updating of models is necessary.
On a stock-specific level, there is risk of M&A activity or even default for an individual name. Such an event would immediately invalidate the significance of any historical relationship assumed from empirical statistical analysis of the past data.
s 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 capital withdrawals or margin call
s. 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. One of the versions of the events describes how Morgan Stanley
's highly successful StatArb fund, PDT, decided to reduce its positions in response to stresses in other parts of the firm, and how this contributed to several days of hectic trading.
In a sense, the fact of a stock being heavily involved in StatArb is itself a risk factor, one that is relatively 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 Khandani and Lo show that the returns to such strategies have been reduced considerably from 1998 to 2007, presumably because of competition.
It has also been argued that the events during August 2007 were linked to reduction of liquidity, possibly due to risk reduction by high-frequency market-makers during that time.
- In academic literature, "statistical arbitrage" is opposed to (deterministic) arbitrageArbitrageIn economics and finance, arbitrage is the practice of taking advantage of a price difference between two or more markets: striking a combination of matching deals that capitalize upon the imbalance, the profit being the difference between the market prices...
. 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. In other words, statistical arbitrage conjectures statistical mispricings of price relationships that are true in expectation, in the long run when repeating a trading strategy.
- Among those who follow the hedge fundHedge fundA hedge fund is a private pool of capital actively managed by an investment adviser. Hedge funds are only open for investment to a limited number of accredited or qualified investors who meet criteria set by regulators. These investors can be institutions, such as pension funds, university...
industry, "statistical arbitrage" refers to a particular category of hedge funds (other categories include global macroGlobal macroGlobal Macro is defined as the strategy of investing, on a large scale, around the world using economic theory to justify the decision making process...
, convertible arbitrageConvertible arbitrageConvertible arbitrage is a market-neutral investment strategy often employed by hedge funds. It involves the simultaneous purchase of convertible securities and the short sale of the same issuer's common stock....
, and so on). In this narrower sense, statistical arbitrage is often abbreviated as Stat Arb or StatArb. According to Andrew LoAndrew LoAndrew W. Lo is the Harris & Harris Group Professor of Finance at the MIT Sloan School of Management. He is a leading authority on hedge funds and financial engineering; he proposed the Adaptive market hypothesis...
, 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 information technology (IT) infrastructure".
Trading strategy
As a trading strategy, statistical arbitrage is a heavily quantitative and computational approach to equity tradingEquity trading
In finance, equity trading is the buying and selling of company stock shares. Shares in large publicly-traded companies are bought and sold through one of the major stock exchanges, such as the New York Stock Exchange, London Stock Exchange or Tokyo Stock Exchange, which serve as managed auctions...
. It involves data mining
Data mining
Data mining , a relatively young and interdisciplinary field of computer science is the process of discovering new patterns from large data sets involving methods at the intersection of artificial intelligence, machine learning, statistics and database systems...
and statistical methods, as well as automated trading systems.
Historically, StatArb evolved out of the simpler pairs trade
Pairs trade
The pairs trade or pair trading is a market neutral trading strategy enabling traders to profit from virtually any market conditions: uptrend, downtrend, or sideways movement. This strategy is categorized as a statistical arbitrage and convergence trading strategy...
strategy, in which stocks
Stocks
Stocks are devices used in the medieval and colonial American times as a form of physical punishment involving public humiliation. The stocks partially immobilized its victims and they were often exposed in a public place such as the site of a market to the scorn of those who passed by...
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
Long (finance)
In finance, a long position in a security, such as a stock or a bond, or equivalently to be long in a security, means the holder of the position owns the security and will profit if the price of the security goes up. Going long is the more conventional practice of investing and is contrasted with...
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
Beta coefficient
In finance, the Beta of a stock or portfolio is a number describing the relation of its returns with those of the financial market as a whole.An asset has a Beta of zero if its returns change independently of changes in the market's returns...
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
Mean reversion
Mean reversion is a mathematical concept sometimes used for stock investing, but it can be applied to other assets. In general terms, the essence of the concept is the assumption that both a stock's high and low prices are temporary and that a stock's price will tend to move to the average price...
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 MSCI Barra/APT/Northfield/Risk Infotech/Axioma to constrain or eliminate various risk factors.
Broadly speaking, StatArb 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 designed using such factors as lead/lag effects, corporate activity, short-term momentum
Momentum (finance)
In finance, momentum is the empirically observed tendency for rising asset prices to rise further, and falling prices to keep falling. For instance, it was shown that stocks with strong past performance continue to outperform stocks with poor past performance in the next period with an average...
, etc. 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 often 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.
Risks
In general sense, statistical arbitrage is only demonstrably correct as the amount of trading time approaches infinityInfinity
Infinity is a concept in many fields, most predominantly mathematics and physics, that refers to a quantity without bound or end. People have developed various ideas throughout history about the nature of infinity...
and the liquidity, or size of an allowable bet, approaches infinity. To put it another way, it suffers from the same problems as the martingale betting system
Martingale (betting system)
Originally, martingale referred to a class of betting strategies popular in 18th century France. The simplest of these strategies was designed for a game in which the gambler wins his stake if a coin comes up heads and loses it if the coin comes up tails...
. Over any finite period of time, a series of low probability events may occur that impose heavy short-term losses. If those short-term losses are greater than the liquidity available to the trader, default
Default
Default may refer to:*Default , the failure to do something required by law**Default judgment*Default , failure to satisfy the terms of a loan obligation or to pay back a loan*Default , a preset setting or value...
may occur, as in the case of Long-Term Capital Management.
Statistical arbitrage is also subject to model weakness as well as stock- or security-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. The existence of the investment based upon model itself may change the underlying relationship, particularly if enough entrants invest with similar principles. The exploitation of arbitrage opportunities themselves increases the efficiency of the market, thereby reducing the scope for arbitrage, so continual updating of models is necessary.
On a stock-specific level, there is risk of M&A activity or even default for an individual name. Such an event would immediately invalidate the significance of any historical relationship assumed from empirical statistical analysis of the past data.
Stat-Arb and systemic risk: events of summer 2007
During July and August 2007, a number of StatArb (and other Quant type) hedge fundHedge fund
A hedge fund is a private pool of capital actively managed by an investment adviser. Hedge funds are only open for investment to a limited number of accredited or qualified investors who meet criteria set by regulators. These investors can be institutions, such as pension funds, university...
s 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 capital withdrawals or margin call
Margin Call
Margin Call is a 2011 American independent drama film, written and directed by J.C. Chandor. The film has an ensemble cast that includes Kevin Spacey, Demi Moore, Paul Bettany, Jeremy Irons, Zachary Quinto, Stanley Tucci, Simon Baker, and Penn Badgley...
s. 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. One of the versions of the events describes how Morgan Stanley
Morgan Stanley
Morgan Stanley is a global financial services firm headquartered in New York City serving a diversified group of corporations, governments, financial institutions, and individuals. Morgan Stanley also operates in 36 countries around the world, with over 600 offices and a workforce of over 60,000....
's highly successful StatArb fund, PDT, decided to reduce its positions in response to stresses in other parts of the firm, and how this contributed to several days of hectic trading.
In a sense, the fact of a stock being heavily involved in StatArb is itself a risk factor, one that is relatively 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 Khandani and Lo show that the returns to such strategies have been reduced considerably from 1998 to 2007, presumably because of competition.
It has also been argued that the events during August 2007 were linked to reduction of liquidity, possibly due to risk reduction by high-frequency market-makers during that time.
See also
- CointegrationCointegrationCointegration is a statistical property of time series variables. Two or more time series are cointegrated if they share a common stochastic drift.-Introduction:...
- CorrelationCorrelationIn statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence....
- Covariance matrixCovariance matrixIn probability theory and statistics, a covariance matrix is a matrix whose element in the i, j position is the covariance between the i th and j th elements of a random vector...
- Currency correlation
- Dimension reduction
- Fourier-related transforms
- Machine learningMachine learningMachine learning, a branch of artificial intelligence, is a scientific discipline concerned with the design and development of algorithms that allow computers to evolve behaviors based on empirical data, such as from sensor data or databases...
- Principal component analysis
- Singular value decompositionSingular value decompositionIn linear algebra, the singular value decomposition is a factorization of a real or complex matrix, with many useful applications in signal processing and statistics....
- Volatility arbitrageVolatility arbitrageIn finance, volatility arbitrage is a type of statistical arbitrage that is implemented by trading a delta neutral portfolio of an option and its underlier. The objective is to take advantage of differences between the implied volatility of the option, and a forecast of future realized volatility...