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Quantitative Finance · Glosarium

Apa itu Implied equilibrium returns, Black–Litterman model?

Dikenal juga sebagai: implied equilibrium returns · Black--Litterman model

Definition 26.2 Research Craft: Predictors, Backtests, Measurement, Portfolios · Bab 26 — Portfolio Construction II

The implied equilibrium returns of a market portfolio wmw_m are Π=γΣwm\Pi = \gamma\Sigma w_m: the expected returns for which wmw_m is the mean–variance optimum. The Black–Litterman model (Black and Litterman, 1992) treats Π\Pi as a prior with covariance τΣ\tau\Sigma and views Pr=qPr = q with uncertainty Ω\Omega as observations, and optimises on the posterior mean μ=[(τΣ)−1+P⊤Ω−1P]−1[(τΣ)−1Π+P⊤Ω−1q]\mu = [(\tau\Sigma)^{-1} + P^\top\Omega^{-1}P]^{-1}[(\tau\Sigma)^{-1}\Pi + P^\top\Omega^{-1}q] with covariance Σ+[(τΣ)−1+P⊤Ω−1P]−1\Sigma + [(\tau\Sigma)^{-1} + P^\top\Omega^{-1}P]^{-1}.

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