# Black-Litterman proof with P=I and Omega=tau*Sigma

Elsewhere on this site (link), Richard notes that $$$$\Pi_{BL} = \frac{1}{2} \Pi + \frac{1}{2}Q,$$$$ so long as we set $$P = I$$ (where $$I$$ is the identity matrix) and $$\Omega = \tau\Sigma$$. This result seems relatively straightforward and intuitively obvious, but in trying to derive it I tend to end up with $$\Pi_{BL} = \Pi + Q$$.

Can someone provide a derivation? Or, at least, maybe sketch a proof so I can see what I might be missing? Thanks,