Pairs trading strategy

I. Introduction

In the area of investment quantify, since less rigorous risk-free arbitrage opportunity, meager yields, actual implementation process can not completely eliminate the risk. So if there is a choice, can relax a 100% risk-free requirements, such as allowing a 5% risk, but at the same time was able to make arbitrage opportunities to increase more than 100%, it would be a better choice? Today, we have to introduce such a method - pairs trading .

Second, statistical arbitrage

1. Definitions

Statistical arbitrage that is mainly in the statistical analysis of historical data as a basis for estimating the distribution of the target statistic, combined with stock data to guide its fundamentals arbitrage trading.

2. Evaluation

Statistical arbitrage with respect to the risk-free arbitrage, it adds some risk, but also accompanied by attractive risk premium, ie more arbitrage opportunities. But it is essentially a limitation on the use of historical data from which information can only reflect the past, using them to predict the future is sometimes difficult to make sense.

3. Examples

In fact, statistical arbitrage principle with the image below can explain:

We now apply this scenario to the market to stock as an example:

Stock A, B: price --Random Walk;

A and B share the difference (or other time series Linear combination) - have stability.

Suppose we now find such a sequence of A and B shares, and their price difference, after Cointegration test statistics have proven stability (such as Adfuller test), we calculate the mean and std of the time series, you can set a domain stabilizing valve, when the offset buy / sell, until the return to a stable domain and then open the valve.

For example, the last 6 months, spreads A and B shares sequence is stationary shares sequence, a mean of 10 and standard deviation of 2, we set the valve domain was 1.5 standard deviation, then the stable range is 7-13.

When AB> 13, we buy B, A sell;

When AB <7, we buying A, sell B.

Wait until smooth return to the open range.

Third, stock pairs trading

1. Definitions

Stock pairs trading is one of the main statistical arbitrage, which aims to find the similar historical trend of the stock market pairing, when the price difference is large (higher than the historical average) arbitrage buy low and sell high.

2. The main method

i. distance methods

Definition: The distance method using a retrospective time interval, standardized prices. N is then calculated in the stocks 2-norm distance between any two pairs (SSD). SSD to the minimum value of the subject serving as the first 20, in the subsequent 6 months to 2 times the standard deviation as the threshold value statistical arbitrage, open Back mean distance. Update the subject of six months to continue arbitrage.

Evaluation: the subject of the selection criteria it contains can not maximize profits, because each of its spread income (SSD) is proportional; in addition a high correlation does not mean that co-integration, so that the mean return is not guaranteed.

Improvements: (A) to select only the subject within the same industry;

(B) using the Pearson correlation coefficient measure of the correlation period.

ii. Method cointegration

Premise: a linear combination of an unstable economic time series may be smooth.

Engle-Granger method: logarithmic price OLS regression residuals ADF test, in which the error correction model Johansen method. If the verification of cointegration, the stock can be described A, B relationship between long-term equilibrium, so that the sequence is the mean of the residuals reply.

Rating: model is too simple, only two kinds of underlying stock, the time limit is limited to 2 years, no single revenue maximization to ensure the overall revenue maximization.

Improvements: first distance screening before making a co-integration.

iii. time series

Definition: assume that the spread is a Markov chain with a mean reversion characteristics, along with the Gaussian noise.

Evaluation: This method is advantageous in that captures the core pairing Trade --- Mean recovery; secondly the model is continuous, and thus can be used to predict; Finally, the model tractable, the minimum MSE can be obtained by the Kalman filter method Parameter Estimation.

However, the spread should use the natural logarithm of the price difference to avoid the effects of different dimensions; demanding conditions of earnings parity model, which is actually very difficult to achieve; financial assets does not meet the real data Ornstein-Uhlenbeck process.

Pairs trading strategy

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