Portfolio Choice Methods


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

Portfolio choice is the final piece of an asset allocation activity, it is here where the risk and return estimates are used by a model to generate asset weights.

In 1991 when the Black-Litterman model was developed there was not a large number of portfolio choice options. Now in 2014 there are many methods, some of which are naturaly compatible with the outputs of the Black-Litterman model, for example robust optimization and resampling.

The output of the Black-Litterman model is a set of estimates of the mean returns to the assets, expressed as a distribution with an estimated mean and a precision of the estimate. Many portfolio choice models take as inputs point estimates of the mean and the estimated mean from the Black-Litterman model can be used as that point estimate. In this case we lose the information embodied in the precison. Robust optimization and resampling can both use an estimate of the mean which is a distribution. Robust optimization with an elliptical uncertainty set for the mean and no uncertainty for the covariance is the case which would most naturally be driven by the Black-Litterman outputs. In resampling techniques, statistcal means are often used to estimate the uncertainty region, but taking a Bayesian approach the precision of the estimated mean could be used instead

Because the Black-Litterman model estimates the means and the uncertainty region, the posterior uncertainty region can be significantly different from the prior uncertainty region because of the mixing of the prior and the investor's views.


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