Asset Allocation

What is Asset Allocation?

All investors are asset allocators. If you put your entire investable funds into Treasury bills you have made an asset allocation decision. Asset allocation is how one decides to allocate assets among various asset classes such as stocks, bonds, and cash.

How do you decide how to allocate your assets?

The goal of asset allocation is to create a diversified portfolio with an acceptable level of risk and the highest possible return given that level of risk. A portfolio or asset allocation that maximizes return for the level of risk is called an efficient portfolio.

Asset allocation software helps create such a portfolio using Nobel Laureate Harry Markowitzs’s mean-variance optimization framework. The user selects a set of assets that represent possible investment choices for the portfolio. For each asset class the user forecasts an expected return, a standard deviation, and a correlation to each of the other assets. Given these inputs, the software uses mean-variance optimization to build an efficient frontier. The frontier represents the efficient set of portfolios that can be created using the selected asset classes. Each portfolio on the frontier has the maximum expected return for a given amount of risk.

Figure 1

Figure 1 is an efficient frontier built using Zephyr’s AllocationADVISOR. In this case, the assets are US stocks (S&P 500), US Dow Jones Corporate Bonds, US Treasury Bills, International stocks (MSCI EAFE), and US government bonds (5 and 10 year treasury bonds). For the expected return, standard deviation, and correlation forecasts we used the historical averages from 1926 to 2004. The efficient frontier shows the trade-off between risk and return. The extreme point on the right side of the frontier represents the highest expected return and riskiest portfolio with 100% invested in US stocks. On the other extreme (lower left) we see the lowest risk portfolio with almost 100% in US T-bills, which is called the minimum variance portfolio. As we cruise up or down the efficient frontier we can see the combinations of assets that make up the various portfolios along the frontier (Figure 2). Investors should select a portfolio that strikes an appropriate balance between risk and return.

Figure 2

The most difficult aspect of this procedure is to accurately predict expected returns. In the example above we used long term historical returns, but is it reasonable to expect that history will repeat itself? There are a number of other ways to make such predictions. One of the most promising methods is a model developed by Fischer Black and Robert Litterman while they were at Goldman Sachs. We are in the process of adding this state-of-the-art model to AllocationADVISOR. Our implementation is based on “A Step-By-Step Guide to the Black-Litterman Model: Incorporating User-Specified Confidence Levels,” by Zephyr Associates’ Tom Idzorek, CFA. (For a copy of this research paper please contact Zephyr Support).

A recent criticism of standard mean-variance optimization is that input-sensitivity in mean-variance optimization leads to poorly diversified portfolios. Two relatively new solutions to mean-variance sensitivity are resampling methodologies and Bayesian asset allocation. Our research indicates that the Bayesian Black-Litterman approach results in better diversified portfolios and is superior to resampling.¹

So far we have talked about creating an efficient frontier using indices that represent broad asset classes. Many of our clients also build frontiers using managers or funds in order to find the “optimum” mix of managers. The problem with this approach is that most managers or funds have a limited history of returns. Consequently the frontier may be dominated by the best performing manager over the short-term. Often this is not necessarily the most skillful manager but one whose style happened to be in favor. This approach can lead to poorly diversified portfolios.

A more sophisticated approach is to start by performing the asset allocation with broad asset class indices as in the example. Once a target asset allocation with the desired risk return profile is selected from the frontier, we convert this into a “policy benchmark” by creating a composite (a “fund” in StyleADVISOR) made up of the various indices and their respective weights. For instance, a policy benchmark based on Mix 2 of Graph One is 21% US Corporate Bonds, 31% International Equities (MSCI EAFE), and 48% US Stocks (S&P 500). Next, using StyleADVISOR we search for the most skillful managers in each asset class. After selecting the individual managers or funds we use StyleADVISOR’s powerful “Optimize Managers to Track a Benchmark” feature. This tool finds the optimum mix of managers to track the policy benchmark. This results in a portfolio of managers that have outperformed their specific benchmarks with a very low tracking error to our policy benchmark.

End Notes:

¹Problems with resampling include: it is always suboptimal (see Harvey et. al [2003, p3]); estimation error in the original inputs is reflected in the final asset allocation; it isn’t based on economic theory; it can lead to upward sloping frontier sections (see Scherer [2002]); from Harvey et. al [2003, p. 3], it “…implicitly assumes that the investor has abandoned the maximum expected utility framework;” and, if you have a benchmark, the procedure leads to unwanted active risk.

References:

Harvey, Campbell R., John C. Liechty, Merrill W. Liechty, and Peter Müller. (2003). “Portfolio Selection with Higher Moments.” Working Paper, October 16.
Scherer, Bernd. (2002). “Portfolio Resampling: Review and Critique.” Financial Analysts Journal, November/December , 98-109.