Pairs trading ch6
This presentation is the property of its rightful owner.
Sponsored Links
1 / 30

Pairs Trading Ch6 PowerPoint PPT Presentation


  • 153 Views
  • Uploaded on
  • Presentation posted in: General

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

Download Presentation

Pairs Trading Ch6

An Image/Link below is provided (as is) to download presentation

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


Pairs trading ch6

Pairs TradingCh6

PairsSelectioninEquityMarkets

郭孟鑫


Stationary and nonstationary

StationaryandNonstationary

  • Stationary

Forallt-s,andt-s-j


Stationary and nonstationary1

StationaryandNonstationary

  • Spuriousregression.

    • Downwardbias

  • Usingunitroottesttoverify.


Introduction

Introduction

Inchapter5,weneedthreesteps

  • Identificationofthestockpairs

  • Cointegrationtesting

  • Tradingruleformulation

    Thischapterwillfocusoncointegrationtestingandfurtheranalysis.


Introduction1

Introduction

  • WedrawparallelsbetweenthecommontrendsmodelforcointegrationandtheideaofAPT.


Common trends cointegration model

CommonTrendsCointegrationModel

  • Inference1:Inacointegrationsystemwithtwotimeseries,theinnovationssequencesderivedfromthecommontrendcomponentsmustperfectlycorrelated.(correlationmustbe+1or-1)


Common trends cointegration model1

CommonTrendsCointegrationModel


Common trends cointegration model2

CommonTrendsCointegrationModel

  • Inference2: Thecointegrationcoefficientmaybeobtainedbyaregressionoftheinnovationsequencesofthecommontrendsagainsteachother.


Discussion

Discussion

  • First,theinnovationsequencesderivedfromthecommontrendsofthetwoseriesmustbeidenticaluptoascalar.

  • Next,thespecificcomponentsofthetwoseriesmustbestationary.


Common trends model and apt

CommonTrendsmodelandAPT

Isthereturnduetothenonstationarytrendcomponent.

Isthereturnduetothestationarycomponent.


Common trends model and apt1

CommonTrendsmodelandAPT

  • RecallingtheAPT,thestockreturnsmaybeseparatedintocommonfactorreturnsandspecificreturns.

  • Ifthetwostockssharethesameriskfactorexposureprofile,thenthecommonfactorreturnsforboththestocksmustbethesame.


Common trends model and apt2

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:


Common trends model and apt3

CommonTrendsmodelandAPT

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

    then,

    and,


Common trends model and apt4

CommonTrendsmodelandAPT

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

    Where,

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


Common trends model and apt5

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 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

Interpreting The Distance Measure

  • Calculating the Cosine of the Angle between Two Vectors.


Interpreting the distance measure1

Interpreting The Distance Measure

  • Appendix:EigenvalueDecomposition

Let

Disadiagonalmatrixwiththeeigenvalues

Uisamatrixwitheachcolumncorrespondingto

aneigenvectors.


Interpreting the distance measure2

Interpreting The Distance Measure

  • Geometric interpretation

    • Key to doing the geometric interpretation is the idea of eigenvalue decomposition.


Interpreting the distance measure3

Interpreting The Distance Measure


Reconciling theory and practice

Reconciling Theory And Practice

  • Deviations from Ideal Conditions

    • When two stocks are not have their factor exposures perfectly aligned.

      Signal-to-Noise(weneedbigSNR)


Example

Example

  • ConsiderthreestocksA,B,andCwithfactorexposuresinatwofactorasfollows:


Example1

Example

  • Step1:Calculatethecommonfactorvarianceandcovariance.


Example2

Example

  • Step2:Calculatethecorrelation(absolutevalueofcorrelationisthedistancemeasure)

    • Ifwehavetochooseonepairforpurposetrading,ourchoicewouldthereforebethepair(A,B)


Example3

Example

  • Step3:Calculatethecointegrationcoefficient

    • Wewilldiscussonthenextchapter


Example4

Example

  • Step4:Calculatetheresidualcommonfactorexposeinpairedportfolio.Thisistheexposurethatcausesmeandrift.


Example5

Example

  • Step5:Calculatethecommonfactorportfoliovariance/varianceofresidualexposure.


Example6

Example

  • Step6:Calculatethespecificvarianceoftheportfolio.(assumethespecificvarianceforallofthestockstobe0.0016)


Example7

Example

  • Step7:CalculatetheSNRratiowithwhitenoiseassumptionsforresidualstockreturn.


  • Login