Beyond Black Litterman Views on Non Normal Markets资料.pdf

Attilio Meucci Lehman Brothers, Inc., New York personal website: Beyond Black-Litterman: Views on Non-Normal Markets the Copula - Opinion Pooling (COP) approach AGENDA BLACK-LITTERMAN APPROACH - overview COP OBJECTIVES - fixing con’s of BL approach COP IN THEORY - from prior and views to posterior COP IN PRACTICE - a five-step implementation recipe COP EXAMPLE - portfolio management REFERENCES Attilio Meucci – Beyond Black-Litterman: Views on non-Normal Markets, the COP Approach AGENDA BLACK-LITTERMAN APPROACH - overview COP OBJECTIVES - fixing con’s of BL approach COP IN THEORY - from prior and views to posterior COP IN PRACTICE - a five-step implementation recipe COP EXAMPLE - portfolio management REFERENCES Attilio Meucci – Beyond Black-Litterman: Views on non-Normal Markets, the COP Approach BLACK-LITTERMAN APPROACH – motivation Markowitz mean-variance optimization: ⎧ w Cov {R}w ⎫ w : relative portfolio weightsN × 1 wς ≡ argmax ⎨w E {R}− ⎬ R : linear returns N × 1 w 1≡1 ⎩ 2ς ⎭ w ≥0 ς : risk propensity coefficient Efficient allocations wς are extremely sensitive to the inputsE {R } and Cov {R }: minor changes give rise to extreme, nonsensical allocations • Very hard to estimate/model the inputs • Very hard to tweak the inputs according to the practitioner’s views • BL use equilibrium arguments to determine the inputs • BL use Bayesian arguments to tweak the inputs according to the views Attilio Meucci – Beyond Bl