Research On Optimal Statistical Arbitrage Strategy Under Spread Fluctuation Constraints

Statistical arbitrage(usually referred to as StatArb)is a short-term spread trading strategy,which makes a profit by tracking two groups of spread of fully diversified portfolios with stable equilibrium relationship and utilizing the mispricing and mean-reversion characteristics of securities.Constructing portfolio and making transaction rules is the core problem of statistical arbitrage.The traditional Markowitz portfolio theory adopts mean-variance method and portfolio efficient boundary to construct portfolio.That is seek a balance between the expected returns and the risk of the portfolio,given a set of financial assets,by means of mean-variance method.Different from the design requirements of mean-variance portfolio,there are two main factors that must be taken into account in designing a mean-reversion portfolio.(1)The designed mean-reversion portfolio should show a strong mean reversion,frequently traversing the mean value,so as to bring investment opportunities.(2)The designed portfolio should show sufficient but controlled variance so that each trade can provide enough profit,while controlling the probability of imbalance of mean reversion.In pairs trading,it is easy to identify whether there is a mean reversion between the two stocks.But it is much more complicated to separate out a portfolio with significant mean-reversion characteristics.The traditional statistical arbitrage methods of mean reversion include co-integration method and canonical correlation analysis method.The main drawback of these methods is that the portfolio spread varies little and do not create meaningful statistical arbitrage opportunities.How to construct a portfolio with strong spreadreversionandbringprofitopportunitiestoinvestorsthrough frequentlytraversingthe mean is a problem that must be considered to enhance the profit opportunities of statistical arbitrage.How to expand the range of the portfolio spread and form meaningful statistical arbitrage opportunities is of great theoretical and practical significance to improve the effectiveness of statistical arbitrage.In this paper,by minimizing the mixed test statistics given by Box and Pierce,an approximate white-noise spread process is constructed by using the multiple co-integration relations contained in the portfolio,and the variance of the portfolio spread is limited to a fixed level.The constructed portfolio spread sequence not only guarantees the stability of the mean reversion,but also controls the volatility of the spread at an adjustable level.In this paper,the fluctuation level of the spread is set to the highest attainable level(maximum eigenvalue level),which improves the opportunity of statistical arbitrage.In addition,this paper also analyzes the influencing factors of the statistical arbitrage trading returns,providing a theoretical basis for stock screening and risk prevention in the trading of statistical arbitrage strategy.The main conclusions are as follows:1.This paper adopts the optimization method and gives the optimal weight of the spread combination by minimizing the mixed test statistics given by Box and Pierce under the condition of variance constraint of the spread.And then a sequence~?ss t~?that can track the portfolio spread is generated.The sequence?s _t?is a stationary random process whose mean is?and variance is?~2.The random process essentially reflects the difference in the value of the two portfolios.Therefore the systematic risk in the random process?s _t?is eliminated to include only the non-systematic risk of the underlying asset.It is a market neutral process.Once the non-systematic risk of the assets in which the spread portfolio is awarded makes the spread sequence?s _t?deviate from its long-term equilibrium level?,a statistical arbitrage opportunity is formed.2.On the basis of the completion of the portfolio spread sequence?s _t?,the trading rules 1 and 2 of statistical arbitrage strategy are formulated.Rule 1 is the statistical arbitrage rulefor building a position while rule 2 is the statistical arbitrage rule for closing a positon.Rules 1 and 2 give the statistical arbitrage conditions for building and closing position.Rules 1 and 2 include a constant k set by the investors by subjective judgment.This constant k is equivalent to the standard deviation multiple in the principle 3?and is used to control the size of the arbitrage range.The larger k is,the larger the arbitrage rangeis,and the greater the profit is once the position is built.But the cost is that the chance of building a position is smaller,and many profit opportunities will be lost.On the other hand,the smaller k is,the greater the chances of building a position are,but the smaller the profit range is,with limited profit each time.Because the arbitrage trading range is too small,when the spread sequence?s _t?breaks through the upper and lower trading trigger point,it will continue the original trend with a higher probability,which will bring the risk of arbitrage to investors.In order to guard against this risk,we have set up the arbitrage stop loss principle,in which the investor can stop the loss in time when faced with this kind of risk in order to guard against further expansion of investment risks.3.Finally,the influencing factors of portfolio spread's arbitrage are analyzed.This paper mainly discusses the influencing factors which are closely related to the arbitrage of spread,mainly including:turnover rate,trading volume,the length of time for holding position,heterogeneity information and common information.When the time for holding position is short and stocks with small market capitalization,the profit of statistical arbitrage trading strategy is significantly influenced by turnover rate,the change of turnover rate and trading volume.The time for holding position and heterogeneity information have a negative effect on the profit of statistical arbitrage;The greater the difference of diffusion in the portfolio of spread,the greater the profit of statistical arbitrage.