Alternatives to Mean Variance Optimization

There are a number of different approaches available that improve on both MVO's methodology, and the traditional approach of using unadjusted historical data for asset allocation inputs.

On the methodology side, if one believes that a complex adaptive system makes it impossible to forecast asset class returns, risks, and correlations, one can simply default to the so-called "1/N" or equally weighted approach. More specifically, this approach first identifies broadly defined asset classes that provide exposure to different underlying sources of risk and return. It then allocates equal amounts to index products (mutual funds or exchange traded funds) that provide low cost, passive exposure to these asset classes.

In contrast to equal weighting, if an investor or advisor believes that different asset classes perform better or worse under different economic scenarios, they could determine their allocation weights based on the expected probability of different scenarios developing.

Alternatively, if they assume that the relative ranking of asset class risks is more predictable than the ranking of asset class returns, then equal risk weighting would be an option (though this would also depend on the degree of uncertainty regarding underlying assumptions about future standard deviations and correlations).

The most sophisticated approaches to long-term asset allocation problems (such as the methodology we used in the past to construct our model portfolios) start with a candidate asset allocation, and then simulate a large number of possible portfolio returns that could result under combinations of different regimes (e.g., periods of high uncertainty, high inflation, and relatively normal times). These approaches employ evolutionary algorithms to identify additional candidate asset allocations, and test them in the same way.

Evolutionary algorithms and other so-called heuristic search techniques are used because these asset allocation models typically contain not only a number of portfolio constraints (e.g., the amount invested in commodities and timber cannot, in total, exceed 20% of the portfolio), but also a number of different goals (e.g., at least 95% probability of accumulating a certain amount by a certain date, with a maximum shortfall of no more than 20% under the target goal).

This complicated model structure makes it computationally impossible to either identify a single "optimum" solution, or to exhaustively search the space that contains every possible solution (technically, they are NP-hard problems). The only way to approach such problems is via evolutionary algorithms that search for solutions that have a high probability of achieving the specified goals under a wide range of possible future scenarios. While these solutions can be said to be robust (i.e., they have a reasonable chance of achieving a given set of goals in the face of irreducible uncertainty), one cannot say they are optimal in the MVO sense of being sure there are no better solutions available.

Similarly, there are a number of methodologies available for improving the quality of the asset class inputs used by different asset allocation methodologies. For example, standard deviation estimates can be adjusted to reflect the impact of autocorrelation. It is also possible to use distributions other than the normal (Gaussian or "Bell Curve") distribution to describe asset class returns.

Another approach is to reduce the size of the forecasting problem by making returns, standard deviations and correlations a function of a smaller number of factors (e.g., economic variables or statistically derived "principal components"). However, this still leaves one with the challenge of forecasting the future values of these factors, future returns for being exposed to them, and uncertainty about whether relationships between the factors and the asset class variables will remain stable in the future (which is unlikely in a continuously evolving complex adaptive system).

Yet another approach, known as the Black-Litterman model, assumes that markets are in equilibrium, and uses market capitalization weights to infer the market's assumptions about future asset class returns, standard deviations and correlations (BL then combines this prior assumption with an investor’s own views to generate the final set of assumptions). The major criticism of Black-Litterman is that it is invalid if markets are not in equilibrium. And we are definitely in the camp that believes that while markets are attracted to equilibrium, they are rarely in this state.

An alternative approach attempts to limit parameter estimation errors (e.g., future asset class returns, risks, and correlations) by adjusting (or "shrinking") these estimates derived from historical data or a forecasting model towards a central average, with the more extreme estimates (which are assumed to be most subject to error) being shrunk by the largest amounts (note that mathematically, the common asset allocation practice of setting multiple constraints on maximum asset class weights has a similar impact).

A final approach to improving asset allocation parameter estimates is model averaging, which combines estimates derived from multiple approaches, including historical data, shrinkage estimators, and factor or other econometric models. While there are many different methods for combining estimates that have been made using different methodologies, it has been shown that taking either the median estimate or a simple average often substantially improves forecast accuracy.

These asset allocation/portfolio construction methodologies and new developments in this area are something we wrote about frequently in both Retired Investor and Index Investor (as you can see from our back issues). We believe that it is critical that investors understand the strengths and weaknesses of the methodology that underlies any asset allocation recommendation that they receive.

Having discussed the theory behind portfolio construction, let's move on to a real example: how our model Retired Investor portfolios actually performed between December 2003 and December 2019.

Or you can first take a geeky detour to learn more about the simulation optimization methodology we used to construct our model Retired Investor Portfolios back in 2003.