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Lecture 15 Factor Models - MIT OpenCourseWare

Factor ModelsFactor ModelsMIT KempthorneFall 2013 MIT 15: Factor Models1 Factor ModelsLinear Factor ModelMacroeconomic Factor ModelsFundamental Factor ModelsStatistical Factor Models : Factor AnalysisPrincipal Components AnalysisStatistical Factor Models : Principal Factor MethodOutline1 Factor ModelsLinear Factor ModelMacroeconomic Factor ModelsFundamental Factor ModelsStatistical Factor Models : Factor AnalysisPrincipal Components AnalysisStatistical Factor Models : Principal Factor MethodMIT Models2 Factor ModelsLinear Factor ModelMacroeconomic Factor ModelsFundamental Factor ModelsStatistical Factor Models : Factor AnalysisPrincipal Components AnalysisStatistical Factor Models : Principal Factor MethodLinear Factor ModelData:massets/instruments/indexes:i= 1,2,..,mntime periods:t= 1,2,..,nm-variate random vector for each time period:xt= (x1,t,x2,t,..,xm,t) ,returns onmstocks/futures/currencies;interest-ra te yields onmUSTreasury Modelxi,t= i+ 1,if1,t+ 2,if2,t+ + k,ifk,t+ i,t= i+ ift+ i,twhere i: intercept of assetift= (f1,t,f2,t.)

Statistical Factor Models: Factor Analysis ... Multifactor model satis es the Generalized Gauss-Markov assumptions so the least-squares estimates ^ i. and ^ (K 1) ... BARRA Approach (Barr Rosenberg) Treat observable asset-speci c attributes as factor betas. Factor realizations ff.

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