In finance, statistical arbitrage (often abbreviated as Stat Arb or StatArb) is a class of short-term financial trading strategies that employ mean reversion models involving broadly diversified portfolios of securities (hundreds to thousands) held for short periods of time (generally seconds to days). These strategies are supported by substantial mathematical, computational, and trading platforms.[1]
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-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[by whom?] 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. [2]
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[3] strategy, in which stocks 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 and the outperforming stock is sold 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, 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 concepts.[4]
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.[5] 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, and Axioma to constrain or eliminate various risk factors.[6]
Risks
Over a finite period of time, a low probability market movement may impose heavy short-term losses. If such short-term losses are greater than the investor's funding to meet interim margin calls, its positions may need to be liquidated at a loss even when its strategy's modeled forecasts ultimately turn out to be correct. The 1998 default of Long-Term Capital Management was a widely publicized example of a fund that failed due to its inability to post collateral to cover adverse market fluctuations.[7]
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.
StatArb and systemic risk: events of summer 2007
During July and August 2007, a number of StatArb (and other Quant type) hedge funds experienced significant losses at the same time, which is difficult to explain unless there was a common risk factor.[8] While the reasons are not yet fully understood, several published accounts blame the emergency liquidation of a fund that experienced capital withdrawals or margin calls. By closing out its positions quickly, the fund put pressure on the prices of the stocks it was long and 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.[9] 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.[10]
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.[9]
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.[11]
It is a noteworthy point of contention, that the common reduction in portfolio value could also be attributed to a causal mechanism. The 2007-2008 financial crisis also occurred at this time. Many, if not the vast majority, of investors of any form, booked losses during this one year time frame. The association of observed losses at hedge funds using statistical arbitrage is not necessarily indicative of dependence. As more competitors enter the market, and funds diversify their trades across more platforms than StatArb, a point can be made that there should be no reason to expect the platform models to behave anything like each other. Their statistical models could be entirely independent.
Worldwide practice
Statistical arbitrage faces different regulatory situations in different countries or markets. In many countries where the trading security or derivatives are not fully developed, investors find it infeasible or unprofitable to implement statistical arbitrage in local markets.
China
In China, quantitative investment including statistical arbitrage is not the mainstream approach to investment. A set of market conditions restricts the trading behavior of funds and other financial institutions. The restriction on short selling as well as the market stabilization mechanisms (e.g. daily limit) set heavy obstacles when either individual investors or institutional investors try to implement the trading strategy implied by statistical arbitrage theory.
↑ Mahdavi Damghani, Babak (2013). "The Non-Misleading Value of Inferred Correlation: An Introduction to the Cointelation Model". Wilmott. 2013 (1): 50–61. doi:10.1002/wilm.10252.
↑ Rad, Hossein; Low, Rand Kwong Yew; Faff, Robert (2016-04-27). "The profitability of pairs trading strategies: distance, cointegration and copula methods". Quantitative Finance. 16 (10): 1541–1558. doi:10.1080/14697688.2016.1164337. ISSN1469-7688. S2CID219717488.
↑ 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"
Bertram, W.K., 2009, Optimal Trading Strategies for Ito Diffusion Processes, Physica A, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1371903. Presents a robust theoretical framework for statistical arbitrage trading.
Richard Bookstaber: A Demon Of Our Own Design, Wiley (2006). Describes: the birth of Stat Arb at Morgan Stanley in the mid-1980s, out of the pairs trading ideas of Gerry Bamberger. The eclipse of the concept after the departure of Bamberger for Newport/Princeton Partners and of D.E. Shaw to start his own StatArb firm. And finally the revival of StatArb at Morgan Stanley under Peter Muller in 1992. Includes this comment (p.194): “Statistical arbitrage is now past its prime. In mid-2002 the performance of stat arb strategies began to wane, and the standard methods have not recovered.”
Jegadeesh, N., 1990, 'Evidence of Predictable Behavior of Security Returns', Journal of Finance 45, p.881–898. An important early article (along with Lehmann’s) about short term return predictability, the source of StatArb returns
Kolman, Joe (1998). "Inside D. E. Shaw". Derivatives Strategy. Retrieved 23 June 2013.
Lehmann, B., 1990, 'Fads, Martingales, and Market Efficiency', Quarterly Journal of Economics 105, pp.1–28. First article in the open literature to document the short term return-reversal effect that early StatArb funds exploited.
Ed Thorp: Statistical Arbitrage, Wilmott Magazine, June 2008 (Part1Part2Part3Part4Part5Part6). More reminiscences from the early days of StatArb from one of its pioneers.
In economics and finance, arbitrage is the practice of taking advantage of a difference in prices in two or more markets – striking a combination of matching deals to capitalise on the difference, the profit being the difference between the market prices at which the unit is traded. When used by academics, an arbitrage is a transaction that involves no negative cash flow at any probabilistic or temporal state and a positive cash flow in at least one state; in simple terms, it is the possibility of a risk-free profit after transaction costs. For example, an arbitrage opportunity is present when there is the possibility to instantaneously buy something for a low price and sell it for a higher price.
Passive management is an investing strategy that tracks a market-weighted index or portfolio. Passive management is most common on the equity market, where index funds track a stock market index, but it is becoming more common in other investment types, including bonds, commodities and hedge funds.
In financial mathematics, the implied volatility (IV) of an option contract is that value of the volatility of the underlying instrument which, when input in an option pricing model, will return a theoretical value equal to the price of said option. A non-option financial instrument that has embedded optionality, such as an interest rate cap, can also have an implied volatility. Implied volatility, a forward-looking and subjective measure, differs from historical volatility because the latter is calculated from known past returns of a security. To understand where implied volatility stands in terms of the underlying, implied volatility rank is used to understand its implied volatility from a one-year high and low IV.
In finance, arbitrage pricing theory (APT) is a multi-factor model for asset pricing which relates various macro-economic (systematic) risk variables to the pricing of financial assets. Proposed by economist Stephen Ross in 1976, it is widely believed to be an improved alternative to its predecessor, the capital asset pricing model (CAPM). APT is founded upon the law of one price, which suggests that within an equilibrium market, rational investors will implement arbitrage such that the equilibrium price is eventually realised. As such, APT argues that when opportunities for arbitrage are exhausted in a given period, then the expected return of an asset is a linear function of various factors or theoretical market indices, where sensitivities of each factor is represented by a factor-specific beta coefficient or factor loading. Consequently, it provides traders with an indication of ‘true’ asset value and enables exploitation of market discrepancies via arbitrage. The linear factor model structure of the APT is used as the basis for evaluating asset allocation, the performance of managed funds as well as the calculation of cost of capital. Furthermore, the newer APT model is more dynamic being utilised in more theoretical application than the preceding CAPM model. A 1986 article written by Gregory Connor and Robert Korajczyk, utilised the APT framework and applied it to portfolio performance measurement suggesting that the Jensen coefficient is an acceptable measurement of portfolio performance.
Long/short equity is an investment strategy generally associated with hedge funds. It involves buying equities that are expected to increase in value and selling short equities that are expected to decrease in value. This is different from the risk reversal strategies where investors will simultaneously buy a call option and sell a put option to simulate being long in a stock.
Convertible 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.
Financial risk is any of various types of risk associated with financing, including financial transactions that include company loans in risk of default. Often it is understood to include only downside risk, meaning the potential for financial loss and uncertainty about its extent.
Algorithmic trading is a method of executing orders using automated pre-programmed trading instructions accounting for variables such as time, price, and volume. This type of trading attempts to leverage the speed and computational resources of computers relative to human traders. In the twenty-first century, algorithmic trading has been gaining traction with both retail and institutional traders. A study in 2019 showed that around 92% of trading in the Forex market was performed by trading algorithms rather than humans.
A 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. Pair trading was pioneered by Gerry Bamberger and later led by Nunzio Tartaglia's quantitative group at Morgan Stanley in the 1980s.
An investment strategy or portfolio is considered market-neutral if it seeks to avoid some form of market risk entirely, typically by hedging. To evaluate market neutrality requires specifying the risk to avoid. For example, convertible arbitrage attempts to fully hedge fluctuations in the price of the underlying common stock. A portfolio is truly market-neutral if it exhibits zero correlation with the unwanted source of risk. Market neutrality is an ideal, which is seldom possible in practice. A portfolio that appears market-neutral may exhibit unexpected correlations as market conditions change. The risk of this occurring is called basis risk.
In finance, volatility arbitrage is a term for financial arbitrage techniques directly dependent and based on volatility.
Alternative beta is the concept of managing volatile "alternative investments", often through the use of hedge funds. Alternative beta is often also referred to as "alternative risk premia".
In finance, the Heston model, named after Steven L. Heston, is a mathematical model that describes the evolution of the volatility of an underlying asset. It is a stochastic volatility model: such a model assumes that the volatility of the asset is not constant, nor even deterministic, but follows a random process.
In finance, volatility is the degree of variation of a trading price series over time, usually measured by the standard deviation of logarithmic returns.
Mean reversion is a financial term for the assumption that an asset's price will tend to converge to the average price over time.
Jonathan Kinlay is a quantitative researcher and hedge fund manager. He is founder and CEO of Systematic Strategies, LLC, a systematic hedge fund that deploys high-frequency trading strategies using news-based algorithms.
Quantitative analysis is the use of mathematical and statistical methods in finance and investment management. Those working in the field are quantitative analysts (quants). Quants tend to specialize in specific areas which may include derivative structuring or pricing, risk management, investment management and other related finance occupations. The occupation is similar to those in industrial mathematics in other industries. The process usually consists of searching vast databases for patterns, such as correlations among liquid assets or price-movement patterns.
Macro risk is financial risk that is associated with macroeconomic or political factors. There are at least three different ways this phrase is applied. It can refer to economic or financial risk found in stocks and funds, to political risk found in different countries, and to the impact of economic or financial variables on political risk. Macro risk can also refer to types of economic factors which influence the volatility over time of investments, assets, portfolios, and the intrinsic value of companies.
Brandywine Asset Management, Inc. is an American investment management firm founded and managed by Michael Dever. The firm is registered as a commodity trading advisor.
Factor investing is an investment approach that involves targeting quantifiable firm characteristics or “factors” that can explain differences in stock returns. Security characteristics that may be included in a factor-based approach include size, low-volatility, value, momentum, asset growth, profitability, leverage, term and carry.
This page is based on this Wikipedia article Text is available under the CC BY-SA 4.0 license; additional terms may apply. Images, videos and audio are available under their respective licenses.
