The Hybrid Reference Model
The Hybrid Reference Model presented by Satchell and Scowcroft (2000) sets τ to 1 and then
applies the usual Black-Litterman formulas. In this case the prior and view estimates are point estimates, they are not distributions. As such, the basis of the model is no longer a Bayesian or mixed estimation model, it is now just a shrinkage model where the weights are proportional to the covariance of the assets. The weight on the prior will be Σ and the parameters τ or Ω can be adjusted to regulate the amount of shrinkage realized. Given that τ or Ω can control the
shrinkage, we arrive at the Alternative Reference Model where the shrinkage is controlled by Ω
and we no longer need the parameter τ.