FRM一级培训项目：数量分析（学习笔记）.docx

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I uh' *. bw1M% I "f ' JJ M又无扬叶"B九d川Gi相 伸3 7出个同令 Kurtosis失小LeptokurtNormalDistributionA R口竺kurtjjjtbul2n has mofg frequent PxrtrPmeIY IdrgR deviatiom Qorii411gJI£3ii£KaD)a normal distribution.Q A2re 妨e true CkSVtm Oj retur右 t ItORUrtCC 弓 We %wne nwmtj.v帆We SlMote -the V>R. 7e / ½R. <s Mck/aFNb件 3F >Sf*K<. 但现晞l+令CoskewnessandCokurtosis"急IMeSS罩磁魄SThethirdcrosscennimomentisTef曰TedtoasCeSkeWness.eThefourthcrosscentralmomentisreferredtoascokurtosis.>Riskmodelswithtime-varyingvolatilityortime-varyingcorrelationcandisplayawiderangeofbehaviorsWIthveryfewfreeprmeters4ihi-tail8沱Hi5(庙豳联性)aCopulascanalsobeusedtodescribecomplexinteractionsbetweenvariablesthatgobeyondcovariances,andhavebecomePoPUlarinriskmanagementinrecentyears.3CoskewnessandCokurtosisExampleA«umcfourscriesofhindrclurn5(A.氏&D)whorethemean,standarddcvalin.skew,andku11oisarealltheampjbutonlytheordcfofctussdifferentUmeIAonr.DCDIilliriCA*日COIK3”153%I1<1、53".心3-72%2J3H-，/100%33Hj153%458%S3M,00%38,00%519%19%G77%72%72%67153、1M%153%38%T(1537»I95%Thetwoportfolios(A+BandC«D)havethesamemeanandstandarddeviation,buttheskewsoftheportfoliosaredifferent.令CoskewnessandCokurtosisSCaURfPloISshowthedifferencebetweenBversusAandDversusC:/AandB:theirbestpositivereturnsoccurduringthesametimeperiod,butIheirworstnegativeretf11soccurindifferentperiods.ThiscausesthedistributionOfpointstobeskev/edtowardthetop-rightofthechart.CandD.theirworstnegativereturnsoccurinthesameperiodbuttherbestpositivereturnsoccurindifferentperiods.Inthesecondchart,thepointsareskewedtowardrhebottom-leftof(hechart令CoskewnessandCokurtosisThereasontheabovechartslookdifferentorthe侔独曲t>ereturnsQflhetw。portfoliosaredifferent,isbecausetheCQSkCWne55betweentheportfoliosisdifferent.Notices,毛尸。GandF依andD)«碱,w一0S8”099Qf3ttWQVa11aDieS.)d!U/Forexample力灯=EK胃尸¾说明辞手无处游，9Ja)=EIX-讲IL()yS=日X-EX)，疝ThenontrivialCpkurlgsisCrftwoVanaMes：(and玉，/ForexampleKXXxY二SmWn终=tyj令BestLinearUnbiasedEstimator(BLUE)川口3g""rBLUlnolhrrproprr1yof»»"<v"1p%hr114tr.h11r>1111(jfjlIhliphoui<i"«iHfrhr114tr(*,itc；“itjrus<das.lf"%Mh"Mhcn11ltl11r.a)erlata)Utheestimator«5theh，J.v<(ablrk(1.h%lh<，finrrnuu；WMlnrr>),(xhfl