Selection of a portfolio of pairs based on cointegration: a statistical arbitrage strategy/Selecao de uma carteira de pares de acoes usando cointegracao: uma estrategia de arbitragem estatistica.
| Autor | Caldeira, Joao Frois |
| Cargo | Artículo en inglés |
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Introduction
The motivation for statistical arbitrage techniques has its roots in works that preach predictability of stock prices and existence of long term relations in the stock markets. In recent years, the notion of mean reversion has received a considerable amount of attention in the financial literature. Since future observations of a mean-reverting time series can potentially be forecasted using historical data, this literature challenges the stylized fact in financial economics which says that the stock prices shall be decribed by independent random walk processes; what would automatically imply no predictability in the stock prices (see, for example Lo & MacKinlay, 1988, 1997, Guidolin et al., 2009). A number of studies have also examined the implications of mean reversion on portfolio allocation and asset management; see Barberis (2000), Carcano et al. (2005), Serban (2010) and Triantafyllopoulos & Montana (2011) for recent works. Active asset allocation strategies based on mean-reverting portfolios, which generally fall under the umbrella of statistical arbitrage, have been used by investment banks and hedge funds for several years. Possibly the simplest of such strategies consists of a portfolio of only two assets, as in pairs trading. This trading approach consists in going long on a certain asset while shorting another asset in such a way that the resulting portfolio has no net exposure to broad market moves. In this sense, the strategy is often described as market neutral. For further discussions on statistical arbitrage approaches based on mean-reverting spreads and many illustrative numerical examples the reader is referred to Pole (2007) and Vidyamurthy (2004).
Pairs trading is a statistical arbitrage strategy designed to exploit short-term deviations from a long-run equilibrium between two stocks. Traditional methods of pairs trading have sought to identify trading pairs based on correlation and other non-parametric decision rules. This study selects trading pairs based on the presence of a cointegrating relationship between two stocks. Cointegration enables us to combine the two stocks in a certain linear combination so that the combined portfolio is a stationary process. If two stocks share a long-run equilibrium relationship, then deviations from this equilibrium are only short-term and are expected to die out in future periods. To profit from this relative misspricing, the trade is opened by buying the stock which is bellow the long-run equilibrium, and selling (short) the equity which is above it. The pair trade is then closed by reversing the opening transactions once the pair reverts to its expected value. The long-short transactions are constructed to yield a net position of zero.
In order to reduce risk in pairs-trading strategies, it is interesting to open many trades all with a very short holding time, hoping to diversify the risk of each trade. According to Avellaneda & Lee (2010), the pairs trading strategy is the "ancestor" of statistical arbitrage. The term "statistical arbitrage" encompasses a variety of investment strategies whose principal characteristic is the use of statistical tools to generate excess returns. Desired characteristics of this class of strategies is market neutrality (low market correlations), and signal generation based on rules rather than fundamentals.
It is well known that pairs trading is a common strategy among many hedge funds. However, there is not a significant amount of academic literature devoted to it due to its proprietary nature. For a review of some of the existing academic models, see Poterba & Summers (1988), Lo & MacKinlay (1990), Gatev et al. (2006), Elliott et al. (2005), Perlin (2009) and Broussard & Vaihekoski (2012). In a recent paper, Khandani & Lo (2007) discuss the performance of the Lo-MacKinlay contrarian strategies in the context of the liquidity crisis of 2007. These strategies have several common features with the ones developed in this paper. Khandani & Lo (2007) market-neutrality is enforced by ranking stock returns by quantiles and trading "winners-versus-losers", in a dollar-neutral fashion. On the parametric side, Poterba & Summers (1988) study mean-reversion using auto-regressive models in the context of international equity markets. Zebedee & Kasch-Haroutounian (2009) analyzes the impact of pairstrading at the microstructure level within the airline industry. Avellaneda & Lee (2010) use Principal Component Analysis or sector ETFs in their statistical arbitrage strategy. In all these cases, they model the residuals or idiosyncratic components of a portfolio of pairs, as mean-reverting processes.
In this paper, we investigate the risk and return of a portfolio consisting of many pairs trades all selected based on cointegration. Different from other authors who used the methodology proposed by Gatev et al. (2006) (for example Nath, 2006, Perlin, 2009) and market professionals who have used bollinger bands, in this paper we employ the methodology of cointegration to develop a pairs trading strategy.
The sample period used starts in January 2005 and ends in October 2012, summing up to 1.992 observations. Daily equity closing prices are obtained from Bloomberg. The analysis covers all stocks in the Bovespa index (Ibovespa) from the Sao Paulo stock exchange. An analysis based on Brazilian data is important not only because Bovespa is the largest stock exchange in South America and one of the largest among all emerging economies, but also because the cointegration approach to select pairs have not yet been studied in detail in Brazil. The proposed statistical arbitrage strategy generates average excess return of 16. 38% per year in out-of-sample simulations, Sharpe Ratio of 1.34, low exposure to the equity markets and relatively low volatility. The results show the pairs trading strategy based on cointegration is persistently profitable even in the period of global crises, reinforcing the usefulness of cointegration in quantitative strategies.
The remainder of this paper is organized as follows. In section 2, the concepts of statistical arbitrage and pairs trading strategies are presented in greater detail. Section 3 explain the use of cointegration within this class of strategies. In section 4, we describe the strategy proposed. In section 5 the data are discussed and the results obtained from the out-of-sample simulations are empirically verified. In section 6, a conclusion based on the empirical results is presented, along with suggestions of future research.
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Statistical Arbitrage and Pairs Trading
Statistical arbitrage is a trading or investment strategy used to exploit financial markets that are out of equilibrium. Litterman (2003) explains the philosophy of Goldman Sachs Asset Management as one of assuming that while markets may not be in equilibrium, over time they move to an equilibrium, and the trader has an interest to take maximum advantage from deviations from equilibrium.
Pairs-trading, which is a statistical arbitrage strategy, was pioneered by Nunzio Tartaglias quant group at Morgan Stanley in the 1980's, and it remains an important statistical arbitrage technique used by hedge funds. Tartaglias' group found that certain securities were correlated in their day-to-day price movements, (see Vidyamurthy, 2004). Based on these empirical investigations, trading strategies might be formed to explore the inefficiencies of stock markets. The key references in this area are Lo & MacKinlay (1988), Khandani & Lo (2007), Lo & MacKinlay (1997), Gatev et al. (2006) and Guidolin et al (2009). One of the many possible statistical arbitrage strategies is the pairs trading. In pairs trading we do not deal with trends established for particular assets but with common long-run equilibrium trends among pairs of stocks.
The idea behind pairs trading is to first identify a pair of stocks with similar historical price movement. Then, whenever there is sufficient divergence between the prices in the pair, a long-short position is simultaneously established to bet that the pair's divergence is temporary and that it will converge over time.
Tartaglia and his group used the pairs trading strategy with great success throughout 1987. However, the group was dismantled in 1989, after two years of bad results. Nevertheless, the pairs trading strategy became increasingly popular among individual traders, institutional investors and hedge-funds.
Recently, due to the financial market crisis, it was widely reported in the specialized media that the year 2007 was especially challenging for quantitative hedge funds (see Khandani & Lo, 2007, Avellaneda & Lee, 2010), in particular for the statistical arbitrage strategies. The strategy proposed here is analyzed in the period in question and the results found corroborate those of other authors.
Jacobs & Levy (1993) argues that long-short stock strategy can be implemented in three different ways: as market neutral, as equitizing, or as hedge strategies. Market neutral long-short strategies, as the one proposed here, maintain even exposure to market risks using long and short positions at all times. This approach eliminates exposure to directional risk from the market, such that the obtained return should not be correlated with the market reference index, which is the equivalent to a beta-zero portfolio. The portfolio returns are generated by the isolation of the alfa, adjusted by risk. According to Fung & Hsieh (1999), a strategy is said to be market neutral if its return are independent from the market's relative return. Market neutral funds actively seek to avoid systematic risk factors, betting on relative price movements.
The process of asset pricing can be seen in absolute or relative terms. In absolute terms, asset pricing is made by way of fundamentals, such as discounted future cash flow, for example. Relative pricing means that prices from assets that are close substitutes...
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