Black Litterman and Robust Portfolio Optimization

n risk and portfolio management with econometrics ver

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Unformatted text preview: 2012. © P. KOLM. 21 A Simple Case: Individual Asset Uncertainty ˆ Consider a point estimate mi and its confidence interval ˆ ˆ mi - ei £ mi £ mi + ei where, for example, ei = 1.96si T Solve the M-V problem for the worst-case realization of the uncertain expected return, i.e. max min w ¢m - lw ¢S w w m s.t. w ¢i = 1 ˆ (mi - mi ) £ ei2, 2 i = 1,..., N The worst-case expected returns are a function of the portfolio weights and the estimation error ˆ mi* = mi - sign (wi ) ei , i = 1,..., N RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 11/11/2012. © P. KOLM. 22 Two Interpretations Interpretation 1: ( ) ˆ max w ¢ m - me, w - lw ¢Sw w s.t. w ¢i = 1 where me, w é sign w e ù ( 1) 1 ú ê ú = êê ú ê ú sign (wN ) eN ú êë û → Shrinkage adjustment of the expected return RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 11/11/2012. © P. KOLM. 23 Interpretation 2: ˆ ˆˆ max w ¢m - lw ¢Sw - w ¢Ew w s.t . w ¢i = 1 where é w1 ù êwú ê 1ú ˆ w = ê ú, ê ú wN ú ê ê wN ú ë û ée ù ê1 ú ê ú E=ê ú ê eN úú êë û → Estimatio...
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This document was uploaded on 02/17/2014 for the course COURANT G63.2751.0 at NYU.

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