Black Litterman and Robust Portfolio Optimization

11112012 p kolm 15 calculating the gls estimator4 we

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Unformatted text preview: we note that this is just a standard linear model for the expected returns m = E (R ) that can be solved using generalized least squares (GLS) RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 11/11/2012. © P. KOLM. 15 Calculating the GLS estimator4 we obtain the Black-Litterman expected return mBL = (X ¢V -1X)-1 X ¢V -1y -1 æ çé = ç êI ç çë ç è -1 ö é(tS)-1 ù é I ù÷ é ù ép ù ê ú ê ú ÷ éI P ¢ù ê(tS) úê ú P ¢ùú ê ÷ê úû ê ÷ ûê W-1 úú êêP úú ø ë W-1 úú êêq úú ÷ êë ë ûë û ûë û -1 æ é(tS)-1 ù ö é(tS)-1 p ù ÷é çé = ç êI P ¢ùú êê -1 úú ÷ êI P ¢ùú êê -1 úú ÷ çë ÷ û ê W P ú÷ ë ûê W q ú ç ç è ø ë û ë û -1 = éê(tS)-1 + P ¢W-1P ùú éê(tS)-1 p + P ¢W-1q ùú ë ûë û -1 = p + tSP ¢ éêëP tSP ¢ + Wùúû éêëq - P p ùúû with covariance (i.e. uncertainty) -1 é ù M º var (mBL ) = ê(tS) + P ¢W-1P ú êë úû RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 11/11/2012. © P. KOLM. -1...
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