blacklitterman.org

Selecting Asset Classes

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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

One of the first steps in using the Black-Litterman model, or any asset allocation process, is to identify the universe of potential investments. For a strategic asset allocation, we cal investments asset classes.

According to Maginn, Tuttle, McLeavey and Pinto (2007) the criteria for specifying asset classes are

It is important that each investment be unique so that the mean-variance optimizer will work properly. These unique investments typically represent different asset classes, such as domestic equities or domestic bonds. Depending on the investors interests, the asset classes can be very narrow such as small cap value stocks, or broad such as US equities. There is generally good agreement that equities, bonds and inflation protected bonds are unique asset classes. For most investors, these categories can be further sub-divided into domestic and foreign (developed, emerging, frontier) markets.

The next section provides a list of typical Asset Classes along with discussions about each Asset Class. Each investor should select the appropriate universe of investments for their own situation, and what is appropriate for one investor may not be appropriate for another investor.

Finding a time series for the liquid Asset Classes, equities, fixed income, and cash is fairly simple, once the investor identifies the specific Asset Classes of interest, and identifies proxies for the Asset Class returns. Asset Class Resources contains some resources to help find this information. Some portion of Commodities and Real Estate are also publiclly traded (commodity futures, REITS) and so some returns can be gathered from the market.

The modeling of Real Estate and Private Equity is complicated by the fact that they are not traded transparently in liquid markets. This makes access to an accurate time series of returns very difficult. For example, most indices for these types of assets price monthly or quarterly. They may also exhibit a significant lag where transactions settled in one time period are not reported until a later time period. There is a large body of research trying to deduce clean time series of returns for these asset classes.

One way to approach the problems with Real Estate and Private Equity is to proxy them, or include them in related liquid Asset Classes, such as using REITs to model all Real Estate, and using small cap equity to model Private Equity returns.

You will notice I did not include hedge funds, or absolute return funds. There is a significant body of research into how to approach the asset allocation problem for these investments. The research is mixed in how to deal with this class of assets. Some say they are not a separate Asset Class, others say they are. Most investors break them out (within their Asset Allocation) into a separate Asset Class. When using plain mean-variance optimization they can be treated as a separate Asset Class, or as a set of Asset Classes sub-divided by strategy or region. However, within the Black-Litterman model we would need to specify a market capitalization for these assets. We would also not want to count assets from the other Asset Classes multiple times, and we also need to take into account leverage in any analysis of these funds. Given these difficulties and the lack of clear results in the research is it not clear how to treat these funds. Martellini, Vaissié and Ziemann (2005) provides one view of how to deal with these types of funds within the context of the Black-Litterman model.

Maginn, Tuttle, McLeavey and Pinto (2007), Managing Investment Portfolios, A Dynamic Process

Martellini, Vaissié and Ziemann (2005), Investing in Hedge Funds: Adding Value through Active Style Allocation Decisions

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