Black Litterman and Robust Portfolio Optimization

w uncertainty in views risk and portfolio management

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Unformatted text preview: estor views (forecasts) description of types of views (asset, spread, ...) W: uncertainty in views RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 11/11/2012. © P. KOLM. 10 Market Equilibrium Basic assumption: unless the investor has a specific view on a security, its expected return should be consistent with market equilibrium No views → Hold market portfolio Our starting point is CAPM E(Ri ) - Rf = bi (E(RM ) - Rf ) where bi = cov(Ri , RM ) 2 sM RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 11/11/2012. © P. KOLM. 11 Denote by wb = (wb1,..., wbN ) the market capitalization (or benchmark) weights, so that the return on the market can be expressed N RM = åwbi Ri i =1 By CAPM, the expected excess return on asset i becomes pi = bi (E(RM ) - Rf ) = = Defining d = E (RM ) - Rf 2 M s cov(Ri , RM ) 2 M s E (RM ) - Rf 2 M s (E(R M ) - Rf ) N å cov(R , R )w i j bj j =1 (market price of risk), we write CAPM as (matrix- vector form) p = dSw RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 11/11/2012. © P. KOLM. 12 Some Remarks Given market capitalization weights, market price of risk and a covariance matrix: Determining p by calculating p = dSw is called “reverse optimization”3 p is referred to as the “market implied expected returns” or “equilibrium implied expected r...
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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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