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Choosing the Tau Parameter in the Black-Litterman Model

Article Quant Q&A · Author: Ryan
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Summary

The document addresses the meaning and selection of the tau parameter in the Black-Litterman portfolio model. Although tau is often described as controlling the weight assigned to investor views, the responses indicate that its interpretation and calibration are not settled by one generally accepted method. The parameter is discussed through references to several reviews and papers on the model and its extensions.

One cited treatment suggests setting tau to the inverse of the sample length, while acknowledging more elaborate approaches. Another proposal makes tau stochastic, which introduces additional parameters that must be calibrated. The document offers references for further study rather than deriving a single definition or providing comparative empirical evidence. It therefore leaves the appropriate choice dependent on model specification and the analyst’s calibration approach.

Key ideas

  • There is no universally accepted method for defining or choosing tau in Black-Litterman.
  • Tau is commonly described as controlling the influence of views, but that description alone is imprecise.
  • One cited approach sets tau to the inverse of the sample length.
  • A stochastic specification is another option, but requires additional parameters to be calibrated.
  • The document points to literature rather than establishing one preferred calibration.

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# What is the tau parameter in the Black-Litterman model?


# What is the tau parameter in the Black-Litterman model?












Could someone please provide me with a clear and concise definition of the $\tau$ parameter in the Black-Litterman model? It seems one is rather hard to come by. I understand it to be the 'weight on views', but this is a little vague.

## Answer by Bob Jansen (score 2, accepted)

https://quant.stackexchange.com/a/12652

I don't believe there is one generally accepted method and a number of papers are written on this issue.

The Black-Litterman Approach: Original Model and Extensions (2008) by Meucci has an overview and I believe is generally useful to learn more. It suggests using $\tau = \frac{1}{T}$ but notes more complicated approaches exist. A demystification of the Black–Litterman model: Managing quantitative and traditional portfolio construction (2000) by Satchell Scowcroft "propose an ingenious model where $\tau$ is stochastic, but extra parameters need to be calibrated." (Meucci). The Black Litterman Model: A Detailed Exploration (2008) by Walters gives another overview. Of course, you can't miss Idzoreks A step-by-step guide to the Black-Litterman model (2004). This blog might also be of interest.

## Answer by Raja Pasupuleti (score 3)

https://quant.stackexchange.com/a/12659

Jay Walter's Paper on "The Factor Tau in the Black-Litterman Model" http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1701467 is also useful to review

## Answer by Naoufal EL JAOUHARI (score 1)

https://quant.stackexchange.com/a/15486

There is also http://www.blacklitterman.org/ Where you can find an implementation under Excel and Matlab of the Model.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.