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Oct 29

Black Litterman Portfolio Allocation

Posted by abiao at 20:57 | Code » Net | Comments(0) | Reads(13979)
The Black Litterman model was first published by Fischer Black and Robert Litterman of Goldman Sachs in an internal Goldman Sachs Fixed Income document in 1990. This paper was then published in the Journal of Fixed Income in 1991. A longer and richer paper was published in 1992 in the Financial Analysts Journal (FAJ). The latter article was then republished by FAJ in the mid 1990's. Copies of the FAJ article are widely available on the Internet. It provides the rationale for the methodology, and some information on the derivation, but does not show all the formulas or a full derivation. It also includes a rather complex worked example, which is difficult to reproduce due to the number of assets and use of currency hedging.

The Black Litterman model makes two significant contributions to the problem of asset allocation. First, it provides an intuitive prior, the CAPM equilibrium market portfolio, as a starting point for estimation of asset returns. Previous similar work started either with the uninformative uniform prior distribution or with the global minimum variance portfolio. The latter method, described by Frost and Savarino (1986) and Jorion (1986), took a shrinkage approach to improve the final asset allocation. Neither of these methods has an intuitive connection back to the market,. The idea that one could use 'reverse optimization' to generate a stable distribution of returns from the CAPM market portfolio as a starting point is a significant improvement to the process of return estimation.

Second, the BlackLitterman model provides a clear way to specify investors views and to blend the investors views with prior information. The investor's views are allowed to be partial or complete, and the views can span arbitrary and overlapping sets of assets. The model estimates expected excessreturns and covariances which can be used as input to an optimizer. Prior to their paper, nothing similar had been published. The mixing process had been studied, but nobody had applied it to the problem of estimating returns. No research linked the process of specifying views to the blending of the prior and the investors views. The BlackLitterman model provides a quantitative framework for specifying the investor's views, and a clear way to combine those investor's views with an intuitive prior to arrive at a new combined distribution.

For a collection of reference paper and an online application please see http://www.blacklitterman.org/blapplet.html

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