According to the omega formula in B-L tau is used in the Omega estimation to determine the degree of uncertainty given to views of the investor:
So, if tau is given a low value then the inverse of omega will be large and therefore suppose a lot of uncertainty in the investors view and so giving more importance to implicit returns in contrast to investors. In short, and based on this assumption (don't hesitate in correct it) tau can be used to calibrate the importance I give to investors views in opposition to implicit returns and vice versa.
Supposing the above statement is correct, according to Thomas M. Idzorek paper on B-L model regarding page 15 he comments that
"When the covariance matrix of the error term ( Ω ) is calculated using this method, the actual value of the scalar ( τ ) becomes irrelevant because only the ratio τ ω / enters the model. For example, changing the assumed value of the scalar ( τ ) from 0.025 to 15 dramatically changes the value of the diagonal elements of Ω , but the new Combined Return Vector ( ] [ R E ) is unaffected. "
I have made some calculations assigning tau a 0.025 and a 1 and the new Combined Return Vector is unaffected
Then I understand that there is no way I can assign investors views a degree of uncertainty because it does not matter the value I assign to tau, that the return vector will be the same.
Therefore, my questions are: Are my statements above correct? If so , whats the point of the existence of tau? Are there alternative methods to determine investors uncertainty / weights given to implicit or investor returns ?
Thank you in advance for taking your time reading my post.