1 / 30

# Pairs Trading Ch6 - PowerPoint PPT Presentation

Pairs Trading Ch6. Pairs Selection in Equity Markets 郭孟鑫. Stationary and Nonstationary. Stationary. For all t-s, and t-s-j. Stationary and Nonstationary. Spurious regression. Downward bias Using unit root test to verify. Introduction. In chapter 5, we need three steps

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

StationaryandNonstationary
• Stationary

Forallt-s,andt-s-j

StationaryandNonstationary
• Spuriousregression.
• Downwardbias
• Usingunitroottesttoverify.
Introduction

Inchapter5,weneedthreesteps

• Identificationofthestockpairs
• Cointegrationtesting

Thischapterwillfocusoncointegrationtestingandfurtheranalysis.

Introduction
• WedrawparallelsbetweenthecommontrendsmodelforcointegrationandtheideaofAPT.
CommonTrendsCointegrationModel
• Inference1:Inacointegrationsystemwithtwotimeseries,theinnovationssequencesderivedfromthecommontrendcomponentsmustperfectlycorrelated.(correlationmustbe+1or-1)
CommonTrendsCointegrationModel
• Inference2: Thecointegrationcoefficientmaybeobtainedbyaregressionoftheinnovationsequencesofthecommontrendsagainsteachother.
Discussion
• First,theinnovationsequencesderivedfromthecommontrendsofthetwoseriesmustbeidenticaluptoascalar.
• Next,thespecificcomponentsofthetwoseriesmustbestationary.
CommonTrendsmodelandAPT

Isthereturnduetothenonstationarytrendcomponent.

Isthereturnduetothestationarycomponent.

CommonTrendsmodelandAPT
• RecallingtheAPT,thestockreturnsmaybeseparatedintocommonfactorreturnsandspecificreturns.
• Ifthetwostockssharethesameriskfactorexposureprofile,thenthecommonfactorreturnsforboththestocksmustbethesame.
CommonTrendsmodelandAPT
• Observation1: A pairs of stocks with the same risk factor exposure profile satisfies the necessary conditions for cointegration.
• Condition 1: The factor exposure vectors in this case are identical up to scalar.

Stock A:

Stock B:

CommonTrendsmodelandAPT
• If is the factor returns vector, and and are the specific returns for the stocks A and B.

then,

and,

CommonTrendsmodelandAPT
• Condition 2: Consider the linear combination of the returns.

Where,

If A and B are cointegrated, then the common factor return becomes zero.

CommonTrendsmodelandAPT
• Summary
• The common factor return of a long-short portfolio of the two stocks is zero and the integration of the specific returns of the stocks is stationary, then the two stocks are cointegration.
The Distance Measure
• The closer the absolute value of this measure to unity, the greater will be the degree of co-movement.
Interpreting The Distance Measure
• Calculating the Cosine of the Angle between Two Vectors.
Interpreting The Distance Measure
• Appendix:EigenvalueDecomposition

Let

Uisamatrixwitheachcolumncorrespondingto

aneigenvectors.

Interpreting The Distance Measure
• Geometric interpretation
• Key to doing the geometric interpretation is the idea of eigenvalue decomposition.
Reconciling Theory And Practice
• Deviations from Ideal Conditions
• When two stocks are not have their factor exposures perfectly aligned.

Signal-to-Noise(weneedbigSNR)

Example
• ConsiderthreestocksA,B,andCwithfactorexposuresinatwofactorasfollows:
Example
• Step1:Calculatethecommonfactorvarianceandcovariance.
Example
• Step2:Calculatethecorrelation(absolutevalueofcorrelationisthedistancemeasure)