股市为什么会崩盘-Why-Stock-Markets-Crash

WhyStockMarketsCrashWhystockmarketscrash?Sornette’sargumentinhisbook/articleisasfollows:1.Themotionofstockmarketsarenotentirelyrandominthe’normal’sense.2.Crashesinparticularare’abnormal’andhaveacertainstatisticalsignature.3.Aplausiblemodeloftraderbehaviourduringcrashesisbasedon’copying’or’herdmentality’.4.Thestatisticalsignatureproducedbysuchmodelsisclosetothatseeninthemarkets.5.Fittingparametersofcopyingmodelstostockmarketdatagivesareasonablefit.6.Sornetteandhiscolleagueshavepredictedtheoccuranceofparticularcrashes.MathematicsappliedtosocialsciencesSornette’sargumentinhisbookisasfollows:1.Themotionofstockmarketsarenotentirelyrandominthe’normal’sense(observation).2.Crashesinparticularare’abnormal’andhaveacertainstatisticalsignature(observation/statistics).3.Aplausiblemodeloftraderbehaviourduringcrashesisbasedon’copying’or’herdmentality’(model).4.Thestatisticalsignatureproducedbysuchmodelsisclosetothatseeninthemarkets(solution).5.Fittingparametersofcopyingmodelstostockmarketdatagivesareasonablefit(datafitting).6.Sornetteandhiscolleagueshavepredictedtheoccuranceofparticularcrashes(prediction).MathematicsappliedtosocialsciencesSornette’sargumentinhisbookisasfollows:1.Themotionofstockmarketsarenotentirelyrandominthe’normal’sense(observation).2.Crashesinparticularare’abnormal’andhaveacertainstatisticalsignature(observation/statistics).3.Aplausiblemodeloftraderbehaviourduringcrashesisbasedon’copying’or’herdmentality’(model).4.Thestatisticalsignatureproducedbysuchmodelsisclosetothatseeninthemarkets(solution).5.Fittingparametersofcopyingmodelstostockmarketdatagivesareasonablefit(datafitting).6.Sornetteandhiscolleagueshavepredictedtheoccuranceofparticularcrashes(prediction).CourseOutline1.Short,MediumandLongTermFluctuations2.PricingDerivatives(JohanTysk)3.Positivefeedbacks,negativefeedbacksandherdbehaviour.4.Networksandphasetransitions.(AndreasGrönlund)5.Log-periodicityandpredictingcrashes.6.StockMarketCrashDay.TheDowJones1790-2000TheDowJones1980-1987Short,Medium&LongTermFluctuationsinReturnsReturnsareusuallydefinedas(p(t+dt)-p(t))/p(t).ShorttermfluctationsAutocorrelation2))((ttXXERTradingstrategy•Canusecorrelationwithpasttopredicttheexpectedfuture.•Profitisdeterminedbystandarddeviationofreturnfluctuations(sayapprox0.03%).•Invest$10,000,20tradesaday,250daysayear:10000*(1.0003)5000=$44,806(!).•Buttransactioncostmustbelessthan$3per$10,000.MediumtermfluctationsMediumtermfluctationsEfficientmarkethypothesis(Samuelson1965)Example:.020406080050100150200250300350400450500X(1)02468101214161820050100150200250300350400450500Y(3,1)020406080050100150200250300350400450500X(2)02468101214161820050100150200250300350400450500Y(2,2)020406080050100150200250300350400450500X(3)02468101214161820050100150200250300350400450500Y(1,3)020406080050100150200250300350400450500X(4)02468101214161820050100150200250300350400450500Y(0,4)FrequencytttaXX1Efficientmarkethypothesis•Axiomofexpectedpriceformationbasedonrational,all-knowingagents.•Noisegeneratedbyunderlyingnoiseinthevalueoftheworld(similarvariance).•Anyirrational,ill-informedagentswillgeneratemorenoise,butwillovertimebepushedoutthemarketbyrationalagents.•ReliesonagentsnotusingYtintheirpricingoffutures(nocopyingeachother).LongtimescalepatternsHiddenpatterns?•Autocorrelationdoesnotdetectallpatterns.Hiddenpatterns?•Autocorrelationdoesnotdetectallpatterns.•Lookatdrawdownsinstead.DrawdowndistributionDrawdowndistributionLargestdrawdownsConstructingaconfidenceinterval•Takealldaysoftimeseriesandreshufflethem.•Findthedistributionofresultingdrawdowns.ConfidenceintervalStretchedexponentialmodelPowerlaws(Mantegna&Stanley,1995)Powerlaws(Mantegna&Stanley,1995)Summary•Coststoohightogainfromshorttermcorrelations.•Mediumtermfluctationsareusuallyexponentiallydistributed.•Inthelongtermthereareoccasionaldrawdowns(crashes)whichareinconsistentwiththeexponentialmodel.•Otherapparentstructuresinthemarket.