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
- Assets within an Asset Class should be homogenous.
- Asset Classes should be mutually exclusive.
- Asset Classes should be diversifying.
- All Asset Classes as a group should make up a significant fraction of all investor's wealth.
- The Asset Class should have the capacity to absorb a significant fraction of the investor's wealth.
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.
- Domestic Equity (can be further sub-divided by value vs growth, or large cap vs small cap).
- International Equity (can be further divided by developed, emerging, or frontier, or large cap vs small cap, or value vs growth).
- Domestic Fixed Income (can be further divided by sovereign vs corporate, nominal vs inflation protected, short vs long term, furher sub-divided by issuer or credit rating).
- International Fixed Income (can be further divided by sovereign vs corporate, nominal vs inflation protected, developed vs emerging, or other distinctions.
- Real Estate (can be further divided by public vs private, type of real estate holding, loans vs properties, domestic vs international).
- Commodities (can be further divided by public vs private, by type, e.g. energy vs crops vs metals).
- Private Equity (can be divided by domestic vs international)
- Cash or cash equivalents
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