Pairs Trading-A Cointegration Approach
一篇关于应用协整的配对交易的paper。

                                              Abstract
      This study uses the Johansen test for cointegration to select trading pairs for use within a
pairs trading framework. A long-run equilibrium price relationship is then estimated for
the identified trading pairs, and the resulting mean-reverting residual spread is modeled
as a Vector-Error-Correction model (VECM). The study uses 5 years of daily stock
prices starting from the beginning of July, 2002. The search for trading pairs is restricted
to 17 financial stocks listed on the ASX200. The results show that two cointegrated
stocks can be combined in a certain linear combination so that the dynamics of the
resulting portfolio are governed by a stationary process. Although a trading rule is not
employed to access the profitability of this trading strategy, plots of the residual series
show a high rate of zero crossings and large deviations around the mean. This would
suggest that this strategy would likely be profitable. It can also be concluded that in the
presence of cointegration, at least one of the speed of adjustment coefficients must be
significantly different from zero.


Table of Contents
1. Introduction ................................................................................................................................ 7
2. Discussion of key issues ............................................................................................................. 8
2.1 Long/Short Equity Investing: Profit from both Winner and Losers ...................................... 8
2.2 Why Long/Short Investing Strategies? ................................................................................ 10
2.3 A role for market neutrality in a pairs trading strategy? ...................................................... 12
2.4 Cointegration and correlation in long/short strategies ......................................................... 13
3. Literature Review ..................................................................................................................... 15
3.1 The distance approach ......................................................................................................... 16
3.2 The stochastic spread approach ........................................................................................... 17
3.3 The stochastic residual spread ............................................................................................. 20
3.4 The Cointegration Approach ............................................................................................... 24
4. Data .......................................................................................................................................... 26
5. Method ...................................................................................................................................... 29
5.1 The process of selecting trading pairs – an introduction to cointegration and the associated
VECM. ...................................................................................................................................... 30
5.1.1 What is stationarity? ..................................................................................................... 31
5.1.2 A definition of cointegration ........................................................................................ 31
5.1.3 Testing for Cointegration: The Engle-Granger Methodology ...................................... 39
5.1.4 An alternative approach: The Johansen test for Cointegration (1988) ......................... 41
5.1.5 Obtaining the residual spread ....................................................................................... 46
5.2 Modeling procedure and variance analysis ......................................................................... 47
5.2.1 Deriving a usable VAR model ..................................................................................... 47
5.2.2 The problem of identification ....................................................................................... 50
5.2.3 Choosing an appropriate lag length: Akaike Information Criterion ............................. 54
5.2.4 Impulse Response functions ......................................................................................... 54
5.2.4 Variance Decomposition .............................................................................................. 57
6. Results ....................................................................................................................................... 60
6.1 Identifying Trading Pairs ..................................................................................................... 60
6.1.1 Cointegration Test Output ............................................................................................ 60
6.1.2 Testing for Granger Causality ...................................................................................... 63
6.1.3 Cointegrating Equation and Residual Spread ............................................................... 66
6.2 Calibrating a Vector Error-Correction model (VECM) ....................................................... 71

6.3 Results of variance analysis ................................................................................................ 75
6.3.1 Impulse response functions ......................................................................................... 75
6.3.2 Variance decomposition ............................................................................................... 81
6.4 Is the assumption of error term normality critical? ............................................................ 82
6.4.1 The issue of normality .................................................................................................. 82
6.4.2 Common trends model and APT .................................................................................. 83
7. Conclusion ................................................................................................................................ 89
Bibliography .................................................................................................................................. 91