Asset Allocation: An Alternative View

In a recent article, I analyzed a model portfolio designed by Money magazine, in conjunction with analysts at Morningstar.  The focus of my piece was whether I could reconcile the projections of risk and return for this portfolio with my own calculations.  I was pleasantly surprised that the results seemed very consistent.

As a follow-up to that piece, I wanted to see whether I could improve this portfolio in terms of the projected performance. The original portfolio has 40% of its assets in large domestic stocks.  The second-largest allocation is to U.S. bonds.  The third-largest allocation is to international developed economy stocks.  Only 5% of the portfolio is allocated to the emerging economies. In the original portfolio published in Money, the authors specified asset classes but not actual funds, so I selected ETFs that closely matched each asset class selection:

Money Magazine Moderate Strategy for 45-54 Year-Olds.

When I first saw this portfolio, what struck me was that the asset allocation approach was very traditional, with a heavy emphasis on domestic stocks, very little allocation to emerging markets and only nominal exposure to asset classes other than major market indexes. 

As an experiment, similar to others that I have conducted in the past, I used a portfolio optimizer connected to the Monte Carlo Simulation tool that I developed (Quantext Portfolio Planner) to seek out the asset allocation with the highest projected average return that would have the same risk level as the Money magazine portfolio.

Here’s how the process works. The Monte Carlo simulation (a.k.a. MCS) generates asset class projections for risk and return.  These are based on the assumption of a positive risk premium (e.g. that you will get more return for riskier asset classes). The MCS then searches for the portfolio with the highest expected return at each risk level. 

I included all of the asset classes in the original Money portfolio, as well as a few others.  In particular, I added infrastructure stocks such as utilities and energy companies. I also included an index fund that focuses on consistent dividend paying stocks (SDY) and I included a number of bond funds representing different classes of bonds (corporate, short-term Treasury bonds, intermediate Treasury bonds, etc). I then  ran the optimizer, which knows nothing about fundamentals, country of origin, or which asset class is which.  This is purely an automated asset allocation, although I did add a constraint that no single fund could comprise more than 20% of the portfolio. The asset allocation for the final optimized portfolio is quite different than the original, as shown in the table below:

Optimized Portfolio vs. Original Portfolio.

The optimized model portfolio has no allocation to the S&P 500 Index and twice the allocation to small-cap domestic stocks as the Money portfolio. There is a much higher allocation to emerging market stocks in the optimized portfolio, as well. The optimized portfolio also has a substantial 15% allocation to IGE, an ETF that invests in companies that produce and refine energy and basic materials. Bear in mind that these portfolios are purely the result of a mathematical optimization and this is not being held out as an ideal portfolio. 

The table below shows that the projected average annual return for the optimized portfolio is 1.5% per year higher than the projected average annual return for the original Money portfolio, and both portfolios have the same total risk level (as measured by volatility).

Monte Carlo Projected Performance Statistics.

What is perhaps most striking to me about the optimized portfolio, is that it more closely resembles the kinds of asset allocations used by many institutional investors. A 2011 survey of institutional investors found that the average total allocation to domestic equities and domestic fixed income in their portfolios totals 51.5% of the total portfolio.  A global survey of pension plans by Towers Watson found that the average allocation to equities in U.S. pension plans had declined from 64% in 2000 to 49% in 2010.

The largest university endowments have moved away from more traditional allocations that are dominated by domestic equity and bond indexes and have invested more heavily overseas and, particularly, in emerging markets. In addition, there is an emphasis on ‘real assets’—those that produce earnings that should increase with inflation. These firms include energy firms and other natural resource firms, as represented in the optimized portfolio by IGE.  Mohamed El-Erian’s excellent book, When Markets Collide, lays out the narrative for this new approach to asset allocation. It is fairly easy to explain why we might expect emerging economy stocks to provide considerably higher long-term returns than the developed economies and El-Erian explains the fundamental evidence.  It is interesting, however, that a portfolio optimizer which has no information about fundamentals would also point towards a portfolio with substantially higher allocations to emerging markets. 

So, what is the take-away from all this? 

Using standard mathematical techniques one can optimize a portfolio (such as the Money magazine portfolio), and produce an arguably “better” (will achieve greater return for the same risk) investment result. Such a new portfolio has the following differences from the original:

  1. Much lower exposure to market-cap weighted domestic equity indexes
  2. Zero allocation to the S&P 500 Index
  3. Lower allocation to international developed economies
  4. Much higher exposure to emerging market stocks
  5. Targeted exposure to companies that focus on natural resources

These projections, as I have said, are purely based on a quantitative model that projects expected returns and risks and ‘knows’ nothing about geopolitical or economic trends.  As always, model results must be conditioned on the basis of common sense.  In addition, I have just performed the portfolio optimization on a small number of asset classes. The point of showing this analysis, however, is that once we start down the road of using tools to estimate portfolio risk and expected return, it is of considerable interest to then ask whether it is possible to use these tools to design better portfolios.  If the tools suggest new and different asset allocations, we are then faced with the challenge of deciding whether we believe that the model projections have merit. 

Finally, I will note that this portfolio is not being held out as optimal in a global sense.  In addition, this is a risky portfolio in light of current and expected market volatility levels.

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12 thoughts on “Asset Allocation: An Alternative View

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  2. Jane

    what historic time period did you use to create the risk return chracteristics of the asset classes used to generate your optimal portfolio (data from the past 20yrs? longer period? shorter?)
    1. I’m interested to know if money magazine was working off of the same time period.
    2. If the data is only from the past 20 years or less and one was to believe that the same trend in interest rates wasn’t going to occur over the next 20 years then the optimal portfolio wouldn’t be optimal, correct

  3. Geoff Considine Post author

    Hi Jane:

    Thanks for the comment. In a previous companion to this piece, I gave some background on the Monte Carlo. There are several ways to do Monte Carlo simulation. You can simply use historical data–and that seems to be what you are thinking about. Another approach–a better one, I believe–is to generate estimates of future risk and return of various asset classes based on an estimate of the equity risk premium. In fact, given an equity risk premium and a future volatility, the Monte Carlo model generates its own estimates of future returns and volatilities for all asset classes, based on correlations between asset classes and other factors. There was no detailed information on the approach that Money used in their article.

    You are totally correct that if you simply use a single period in history and optimize to match that period, you are likely not to end up with a good portfolio. You just end up over-fitting to history. In fact, William Bernstein provides a good analysis of this problem in The Intelligent Asset Allocator. And I like your example. Using a 20-year period in which interest rates have continuously fallen to record lows as the basis for your asset allocation could easily result in a portfolio that will thrive in an environment of falling interest rates but not rising rates.

    So, while for some models it may be meaningful to ask what period of historical data you have used, there is not a simple answer for forward-looking Monte Carlo simulations. For a great overview of one approach to forward-looking Monte Carlo, I reccomend this paper (which is written by Tom Idzorek who is quoted in the Money article):

  4. Jane

    I appreciate that you took the time to reply.
    I suppose a less ambigious statement would have been:
    It seems possible that assumptions put into the monte carlo simulation, in this case used to estimate the equity risk premium as opposed to the rsk/return characteristics of the assets, may be biased by the past 20 years of historic data due to the recommended portfolio allocating 20% to EEM, and likely a fair amount more if not constrained.

  5. Geoff Considine Post author

    Hi Jane:

    I think that what you are asking is whether the model generates a high allocation to emerging markets simply because emerging markets have out-performed in recent years. The answer is no. The Monte Carlo projections generate an expected risk level for an asset class and then use the equity risk premium to calculate an expected return: higher risk, higher return. The trailing performance may be higher or lower than this projected level and a very high trailing performance does not make an asset class more likely to be selected or to be given a high weight. The equity risk premium is a constant across all asset classes in this approach.

    Quantitative models are just models, of course, and are far from perfect. I tend to put more confidence in the models if they have been tested in a wide range of conditions and are consistent with other research, using different models and thinking. The question that I think we should start from is whether it is rational to simply assume that market-cap weighted developed markets make sense as the core or whether it is reasonable to consider alternative world views: hence the name of this post.

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