## Asset Allocation Process Summary

I want to review the series of posts I wrote about Asset Allocation and Portfolio Construction and show how all of them fit into portfolio management framework.

**The first step of the Asset Allocation process** is to create the Input Assumptions: Expected Return, Risk, and Covariance. This is more art than science because we are trying to forecast future join realization for all asset classes. There are a number of approaches to create input assumptions, for example:

- Historical – estimate historical return, risk, covariance and assume that history will repeat itself.
- Ibbotson’s Building Blocks – estimate expected returns based on the risk premium. Please read Input Methodologies article by Morningstar for a detailed summary.
- The Black-Litterman model – estimate expected return using reverse optimization from current asset class market capitalizations.
- Probability Weighted Input Assumptions

The robust estimation of covariance matrix is usually preferred. For example, the Covariance Shrinkage Estimator is nicely explained in Honey, I Shrunk the Sample Covariance matrix by Olivier Ledoit and Michael Wolf (2003).

Introduction of new asset classes with short historical information is problematic when using historical input assumptions. For example, Treasury Inflation-Protected Securities (TIPS) were introduced by the U.S. Treasury Department in 1997. This is an attractive asset class that helps fight inflation. To incorporate TIPS, I suggest following methods outlined in Analyzing investments whose histories differ in length by R. Stambaugh (1997).

**The next step of the Asset Allocation process** to create efficient frontier and select target portfolio. I recommend looking at different risk measures in addition to the traditional standard deviation of the portfolio’s return. For example, Maximum Loss, Mean-Absolute Deviation, and Expected shortfall (CVaR) and Conditional Drawdown at Risk (CDaR) risk measures. To select a target portfolio look at the portfolios on the efficient frontier and select one that satisfies both your quantitative and qualitative requirements. For example, a quantitative requirement can be a low historic drawdown, and a qualitative requirement can be a sensible weights. For example, if model suggest 13.2343% allocation to Fixed Income, round it down to 13%.

I also recommend looking at your target portfolio in reference to the geometric efficient frontier to make sure your are properly compensated for the risk of your target portfolio. If you have a view on the possible future economic or market scenarios, please stress test your target portfolio to see how it will behave during these scenarios. For example read A scenarios approach to asset allocation article.

Sometimes, we want to combine short-term tactical models with long-term strategic target portfolio. I think the best way to introduce tactical information into the strategic asset mix is to use Black-Litterman model. Please read my post The Black-Litterman model for a numerical example.

**The next step of the Asset Allocation process** is to implement the target portfolio. If you follow a fund of funds approach and implement the target asset mix using external managers, please perform a style analysis to determine the style mix of each manager and visually study if manager’s style was consistent over time. We want to invest into the managers that follow their investment mandate, so we can correctly map them into our target asset portfolio.

We can use the information from style analysis to create managers input assumptions. Let’s combine alpha and covariance of tracking error from the style analysis with asset input assumptions to determine managers input assumptions.

Managers Input Assumptions:

Note, we simply add up mean and covariance because Managers Tracking Error and Assets Returns are independent by construction.

Next we can create managers efficient frontier, such that all portfolios on this frontier will have target asset allocation, as implied from each manager’s style analysis.

**The last step of the Asset Allocation process** is to decide how and when to rebalance: update the portfolio to the target mix. You can potentially rebalance daily, but it is very costly. A good alternative is to rebalance every time period, i.e. quarterly, annually, or set boundaries, i.e. if asset class weight is more than 3% from it’s target then rebalance.

In Conclusion, **the Asset Allocation process** consists of four decision steps:

- create Input Assumptions
- create Efficient Frontier
- implement Target Portfolio
- create Rebalancing Plan

All these steps include some quantitative and qualitative iterations. I highly recommend experimenting as much as possible before committing your hard earned savings to an asset allocation portfolio.

Hi – A couple of questions re: that process.

Have you considered using technical analysis indicators as the source of investor views for Black-Litterman?

What about leverage as the last step in the process (e.g. leverage space trading model)?

Emmanuel

Hi Emmanuel,

It is easy to introduce new information into input assumptions using Black-Litterman model. For example, let’s follow the timing model outlined in A Quantitative Approach to Tactical Asset Allocation by M. Faber (2006). I can add following relative views: all assets that are above their 10 month moving average will outperform all assets that are below their 10 month moving average.

I have not yet read the The Leverage Space Trading Model by Ralph Vince. It is on my todo list. I will answer once I have better understanding of the leverage space trading model.

Thank you for your questions.

Hello Systematic investor, thank you for a very nice post again. I was just wondering whether one could use macroeconomic/fundamental factor models as part of the ‘first step in the asset allocation process’, especially when one is dealing with individual securities(AMZN,GOOG,etc) as oppopsed to asset classes??

Thank you and have a nice Christmas!

Absolutely and thank you for a very good question.

The expected returns can be modeled by a factor model, for example please read

Commonality In The Determinants Of Expected Stock Returns by R. Haugen, N. Baker (1996). The up to date model performance is presented at Haugen Custom Financial Systems.

The covariance matrix can be modeled by a factor model, for example please read an excellent post Factor models of variance in finance by Pat Burns at Portfolio Probe. MSCI Barra Equity Multi-Factor Models is one example of commercial implementation of factor model of covariance.

It seems that Black Litterman model (since it requires market capitalization) cannot be used for say taking positions in asset classes other than equities. Is this correct ?

Also, covariance shrinkage is great for making sure that weights do not change dramitically as risk increases. However, it seems that resampling per Michaud leads to yet better (smoother) transition maps (as shown in your posts).

What are the requirements to use this patented algorithms ? This may be a question for a lawyer but was just wondering if you would know.

The market capitalizations are readily available for equities and fixed income markets. If you want to model other asset classes please read following papers for discussion: