Black Litterman and Robust Portfolio Optimization

11112012 p kolm 13 expressing investor views in b l

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Unformatted text preview: eturns” RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 11/11/2012. © P. KOLM. 13 Expressing Investor Views in B-L Let us assume we have four assets and three views: E(R1)=3%±3.9% with 95% confidence (1.96×2%=3.92%) E(R2)=4%±5.9% with 95% confidence (1.96×3%=5.88%) E(R4)-E(R3)=1%±2% with 95% confidence (1.96×1%=1.96%) We express the views as q = P m + e where e ~ N (0, W) é1 ê P = êê 0 ê0 êë 0 1 0 0 0 -1 0 0 1 é3%ù ù êú ú ú , q = ê 4%ú , êú ú ê1% ú ú úû ëê ûú é2%2 ê W = êê 0 ê êë 0 0 3%2 0 0 ùú 0 úú ú 1%2 ú û Note: It is often assumed (but of course not necessary) that views are uncorrelated RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 11/11/2012. © P. KOLM. 14 Calculating Black-Litterman Expected Returns We have : p = m+n q = Pm + e where where n ~ N (0, tS) e ~ N (0, W) Stacking these two equations in the form () y = X m + e, e ~ N 0,V where ép ù éI ù é tS ù ú y = êê úú , X = êê úú , V = êê Wúú êëq úû êëP úû êë û with I denoting the N ´ N identity matrix,...
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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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