The table below attempts to summarize some of the differences between the various authors on several dimensions where the author's tend to disagree.
| Author(s) | τ | View Uncertainty | Posterior Variance |
|---|---|---|---|
| Fuasi and Meucci | Ignores (1) | αPΣP, α ≥ 1 | Use prior variance |
| He and Litterman | Close to 0 | diag(τPΣP) | Updated |
| Idzorek | Close to 0 | Specified as % | Use prior variance |
| Satchell and Scowcroft | Usually 1 | ? | Use prior variance |
Description of the various attributes in the table
τ - The authors either expect that τ = 1, or else it is a small number. In general an investor will have τ << 1 if they are going to update the variamce, and will use τ = 1 if they are not going to update the variance. Some authors (not included in the references on this site) also discuss using values of τ > 1. Given what τ&SIGMA; represents (uncertainty in our estimate of the mean) and the fact that τ greater than 1 does not make sense in this context, I've not added those views to the table. See or my paper for further information
View Uncertainty - The authors use various expressions to specify the uncertainty of the views. Fusasi and Meucci specify that the uncertainty of the views will be a multiple of the uncertainty of the prior distribution. He and Litterman specify the view uncertainty as a diagonal matrix, with on-diagonal elements equal to the uncertainty of the prior distribution.
Posterior Variance - The authors either update the variance based on the variance of the posterior distribution, or else they just use the prior variance of returns.
For a more thorough discussion see my paper on the Black-Litterman model.