One of the most important variables in creating an investment strategy to meet a specific goal (such as retirement) is what you assume about the future returns from stocks, bonds, and other available investment opportunities. Another highly important input to planning is your estimate of the risk associated with each investment alternative. These estimates of future risk and return will determine how much you need to save, when you can expect to retire, and how much income you can expect in retirement. Where do these estimates come from?

By way of example, let’s consider a recent article from the October 2011 print issue of *Money* magazine. In the article, titled “Build Your Future,” *Money* worked with Morningstar analysts to create a series of model asset allocations for people at different stages in life. There are three basic categories of model portfolios:

**Early / Mid Career (ages 35-44)****Peak Earning Years (ages 45-54)****The Wind Down (age 55-retirement)**

Let’s have a look at the *Moderate Strategy* portfolio for people in the 45-54 age group (shown below):

The Morningstar article uses the set of asset classes above for all of its model portfolios, but does not provide any examples of mutual funds or ETFs that represent the asset classes. I have selected the series of ETFs in the table above that matches each asset class. The Percentage of Funds column shows the allocations to each asset class in the *Moderate* *Strategy* portfolio for people in the 45-55 age bracket.

This portfolio has 70% in stocks, 25% in bonds, and 5% in commodities. The *Money* article states that the ‘expected annual return’ for this portfolio is 6.6% and that the worst 1-year return is -34.7%. There is little detail given about these assumptions except in the following footnote:

*Expected returns are based on Monte Carlo simulations over 20 years, with a 70% probability of at least earning these gains.*

This means that the writer at *Money* and/or the aforementioned Morningstar analysts have run a quantitative simulation tool and have calculated the 30^{th} percentile annualized return for this portfolio over a 20 year period—and this is the ‘Expected Annual Return.’ This is interesting because the term ‘expected annual return’ has a specific mathematical meaning—it is the average of the expected returns and not the 30^{th} percentile.

What this means for the less mathematically inclined reader, is that the authors have handicapped their results to provide a more conservative projection of annual return than the average produced by their models. They are projecting that if you buy this portfolio and hold it for 20 years, you have a **70%** or better chance of receiving an average annualized return of **6.6%**. They also note, however, that the worst 10-year annualized returns they have in the historical record for this portfolio is **+1.5%** per year (although they don’t say how far back in history they looked).

One question that always arises with the kind of example above, is exactly what reduction in returns occurs when you apply an actual investment fund and its expense ratio to the math? For simplicity, I have selected a series of well-known ETFs that match each asset class as the basis for examining the expected returns for the model portfolio allocations developed by *Money* and Morningstar.

Another question that comes up is: Where did the assumptions come from for the future returns of stocks and bonds, and especially for the relative returns of foreign vs. domestic stocks or small cap vs. large cap stocks? There are numerous ways to come up with assessments of the future risks and returns of these various asset classes.

To explore these issues, I ran the portfolio above (using the selection of ETFs) through the Monte Carloportfolio management tool that I developed (Quantext Portfolio Planner). This model starts with an assumption for the future average risk and return of the S&P 500 Index and everything else is automated.

The baseline settings are for the S&P 500 to return 8.3% per year, with 15% annual volatility. I am not going to get into where these come from, but they are based on a range of research by me and others (if you really want more details, you’ll have to read my book or some of my articles).

The projections for the future risk and return of every other asset class are calculated automatically by the tool, as are the expected risks and returns of individual funds. The mathematical techniques that I used in developing this model are consistent with results from a range of institutional analyses that I have compared the portfolio management tool’s results to.

When I run the portfolio above, using my selection of ETFs, through the Monte Carlo simulation, I come up with an equivalent annualized return of 5.9% (using a 20-year investment period and looking at the 30^{th} percentile outcome). When I look at the 40^{th} percentile return, I get 6.4% per year (it is projected that you will earn at least this return in 60% of outcomes rather than 70% of outcomes).

So, my statistical projections into the future are more conservative that *Money* / Morningstar for this portfolio, but not dramatically so. In fact, I was somewhat surprised at how close the numbers are.

Perhaps the strangest thing about the projected returns in the *Money* article is that they are very non-standard. The more standard approach is to present the expected future returns in the form of Compound Annualized Growth Rate (CAGR). This is the return that you will get, on average, if you invest over a number of years. In my projections, the CAGR for this portfolio is 7.0%. This number should, indeed, be higher than the 30^{th} percentile returns provided by *Money* (the average return should be higher than the 30^{th} percentile). The model portfolio that I constructed has an expense ratio of 0.25% which is very low compared to the average mutual fund. The analysis in *Money* makes no reference to assumptions about expense ratios. In real life, this is a very important issue.

If we have a consistent way to calculate future returns and risk, the world looks more reasonable. We can, for example, compare to the portfolios from the *Money *article to the very simple low-cost asset allocations that Vanguard uses in their Target Date Funds, for example. How does the model portfolio above compare to the Vanguard 2025 fund in terms of risk and expected return? This fund, comprised of only three index funds, has 74.3% in equities, quite similar to the portfolio we are analyzing from Money magazine. When I run this fund’s holdings through the Monte Carlo, I find that this fund has slightly lower return and slightly lower risk than the Moderate Strategy model portfolio. The *Moderate Strategy* portfolio (created using ETFs) has 0.33% higherCAGR than the Vanguard 2025 fund in theMonte Carlo projection, principally due to the inclusion of additional asset classes not captured in the Vanguard fund.

While this exploration of the expected future returns in the *Money* article may seem a bit involved, it is a crucially important issue for investors and advisors to understand. The asset allocation that you choose will have a big impact on your financial future, how much you need to save, and how much income you will be able to draw in retirement. The choice of asset allocation will be largely determined by the way that you or your advisor estimates future return and risk for various portfolio choices. My findings suggest that the results shown in this article from *Money* are reasonable, if a bit optimistic. I have seen plenty of ‘expected return’ estimates that do not meet these standards of reasonableness and every reader should be a critical consumer of such numbers.

So what are the take-away points here? The idea for this article started when I read the piece in *Money*’s print edition for October (this article is not online yet). As we look at a world of 2% yield on ten-year Treasury bonds, it is clear that most of us will need to keep a substantial portion of our savings in risky assets with unknown future returns (read: stocks and funds covering other asset classes). When you buy a government bond, you know the yield to maturity. As soon as you add stocks, precious metals, commodities, real estate, and other risky asset classes into the mix, you have to estimate future returns and risks. As I read the article in *Money*, I wanted to see if the estimates of the future portfolio returns were consistent with my own research. The first take-away is that the *Money* portfolio projections for return look reasonable and the asset allocations look pretty good, as long as you invest in low cost funds. The second take-away for the average reader is that coming up with estimates of future risk and return is a pretty involved business. Certainly you can attempt to do this yourself, but it takes time and expertise. Even though it is hard, you need to have a reasonable estimate, whether that comes from a financial advisor, from Morningstar, or elsewhere. For this reason, I applaud *Money* magazine for including estimated returns for a series of diversified model portfolios. If this presentation method became more standard, the world would be a better place for individual investors.

### Related Links:

- Risk Budgeting: A Critical Tool for Portfolio Management
- Social Security and Retirement
- Are Americans Saving Enough for Retirement?

SPONSORED BY Folio Investing *The brokerage with a better way. *Securities products and services offered through FOLIOfn Investments, Inc. Member FINRA/SIPC.

BrianThe following article also provides a scientific look at estimated returns for the next 15 years. It is much more gloomy and downright scary for a 47 year old such as myself. Any comments on this study? http://advisorperspectives.com/dshort/guest/Estimating-Future-Returns-Update-110926.php

rpseawrightWade Pfau has a number of excellent articles related to this subject. His blog, which provides links to his many other works, is here: http://wpfau.blogspot.com/

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