blacklitterman.org

Comparison of Author's Methods

Headlines

RSS Reading List

My paper on the Black-Litterman Model (Updated 20 June 2014), Accompanying MATLAB codes also on the site

A new spreadsheet which illustrates the differences between the reference models.

A new paper Reconstructing Black-Litterman is now available at SSRN. This paper offers a critique of Michaud et al's recent paper, Deconstructing the Black-Litterman Model, from the Journal of Investment Management.

The author's methods section has been updated with a new taxonomy of the model, and many papers have been added.

A new implementation of the Black-Litterman model in Excel is available on the implementations page.

An implementation of the Black-Litterman model in python and the worked example from the He and Litterman 1999 paper (Updated Jun 22 2012)

An excel spreadsheet showing the example worked in the He and Litterman paper (Updated Jun 26 2012)

New paper focusing on Tau and if you really need it (Updated 1 November 2010)

MATLAB and SciLAB implementations of the model

An applet which implements the Black-Litterman model

Here we provide a taxonomy of the models used by various authors. This table is not meant to be complete, but to be a summary of important papers on the model. The information is organized historically and by expression of the model.

At the highest level we can separate the expression of the model used into Bayesian and non-Bayesian. The Bayesian expression of the model is the canonical model presented by Black and Litterman (1991, 1992), He and Litterman (1999) and Litterman et al, (2003). Under non-Bayesian we can further separate the models into a hybrid model which is non-Bayesian but continues to use the τ parameter, and the alternative reference model which eliminates τ.

This list is not complete, though I expect to continually add information to it as time is available.

Model/Author Bayes? Tau Comments
Canonical      
Black and Litterman (1991, 1992) Yes Yes Provides descriptions of the model, but does not include all formulas.
Bevan and Winkelmann (1998) Yes Yes  
He and Litterman (1999) Yes Yes Best summary of the mathematics of the Black-Litterman model by original authors.
Drobetz (2001) Yes Yes One of the first papers on the canonical form not by an original author of the model.
Litterman et al (2003) Yes Yes Overview of Goldman Sachs asset allocation process using BL, little detail on the BL model itself.
Blamont and Firoozy (2003) Yes Yes Provide insight into the parameter τ.
Beach and Orlov (2006) Yes Yes Quantitative views from EGARCH models
Cheung (2009) Yes Yes Integrating factor models
Hybrid      
Satchell and Scowcroft (2000) No Yes τ usually set to 1
Qian and Gorman (2001) No Yes Adds views on covariance of returns
Herold (2003) No Yes Applies to Active Management vs a benchmark
Idzorek (2005) No Yes New expression of ω
Braga and Natale (2007) No Yes TEV sensitivity to views
Martellini and Ziemann (2007) No Yes VaR, CVaR as objectives, inclusion of higher moments in identifying neutral portfolio
Bertsimas, et al (2013) No Yes Replace reverse optimization and bayes formula with various optimization models. Allows for arbitrary distributions.
Michaud et al (2013) No Yes Provides arguments against using hybird and alternative variants of the model. Ignores modern econometrics and Bayesian statistics in the process.
Alternative      
Fusai and Meucci (2003) No No Uses α to tune mixing
Meucci (2005) No No  
Krishnan and Mains (2005) No No Introduce unpriced factor
Giacometti et al (2006) No No Student T and alternative portfolio choice, CVAR
Giacometti, et al (2007) No No VaR, CVaR objectives and use of stable distributions rather than normal distributions.

Description of the various attributes in the table

Bayes - the authors use a Bayesian interpretation of the model expressing uncertainty in the prior and in their estimates. No means the author uses a non-Bayesian or frequentist approach to the model.

τ  -  The authors use the variable τ in their formulas.

For a more thorough discussion see my paper on the Black-Litterman model.

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