Transcription of (2.1) Markowitz’s mean-variance formulation (2.2) Two …
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(2.1) Markowitz’s mean-variance formulation (2.2) Two …
2. mean-variance portfolio theory( ) markowitz s mean-variance formulation ( ) Two-fund theorem( ) Inclusion of the riskfree markowitz mean-variance formulationSuppose there areNrisky assets, whose rates of returns are given by the randomvariablesR1, , RN, whereRn=Sn(1) Sn(0)Sn(0), n= 1,2, , (w1 wN)T, wndenotes the proportion of wealth invested in assetn,withNXn=1wn= 1. The rate of return of the portfolio isRP=NXn= There does not exist any asset that is a combination of other assets in theportfolio, that is, non-existence of redundant = (R1R2 RN) and1= (1 1 1) are linearly independent, otherwiseRPis a constant irrespective of any choice of portfolio first two moments ofRPare P=E[RP] =NXn=1E[wnRn] =NXn=1wn n,where n=Rn,and 2P= var(RP) =NXi=1 NXj=1wiwjcov(Ri, Rj) =NXi=1 NXj=1wi denote the covariance matrix so that 2P=wT example whenn= 2, we have(w1w2) 11 12 21 22! w1w2!=w21 21+w1w2( 12+ 21) +w22 The portfolio risk of return is quantified by 2P.
folio model. Investment theory prior to Markowitz considered the maximization of µP but without σP. 2. The measure of risk by variance would place equal weight on the upside deviations and downside deviations. 3. In the mean-variance model, it is assumed that µi,σi and σij are all known. 4
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