What is Implied equilibrium returns, Black–Litterman model?

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