In order to rationally develop an investment plan you need to estimate long-term returns for the asset classes in which to invest - without doing so you cannot determine how much to allocate to risky stocks and how much to safer bonds.

When estimating returns we know that current valuations provide valuable information. As good as any methodology we have is to use the earnings yield derived from the Shiller CAPE 10. The research shows that valuation metrics such as this explain about 40 percent of real (after inflation) 10-year returns. However, it's also important to note a Vanguard study found that the estimated historical correlations of the various valuation metrics they looked at with the 1-year-ahead return were close to zero. In other words, short-term forecasts aren't worth anything.

Before going into current estimates of returns, it's important to understand that when constructing the estimates, which assume that valuations will not change, we do live in a world of time-varying risk premiums - meaning valuations do change as perceptions of risk change. Consider that the Vanguard study found that for the period 1926-2011, on a rolling 10-year basis real U.S. stock returns have ranged from approximately -5 percent to 20 percent! Thus, any estimate made should be considered only as the mean of a very wide potential distribution of returns.

To estimate returns we will use the earnings yield on the Shiller CAPE 10. Thanks to AQR Capital Management, I was able to obtain the CAPE 10 (Cyclically-Adjusted Price-to-Earnings) earnings yields for the MSCI EAFE and MSCI Emerging Markets Indices as of January 2014. Because the CAPE 10 is based on the last 10 years of earnings, we'll adjust the earnings yields take into account the five-year average lag. Using an estimated real earnings growth of 1.5 percent a year we multiply the current earnings yield by 1.075 (1.5 percent x 5). As of January 31, 2014 the current earnings yields were 5.94 for the MSCI EAFE Index and 6.64 for the MSCI Emerging Markets Index. Accounting for the lag adjustment increases those yields to 6.39 percent for the EAFE Index and 7.14 percent for the Emerging Markets Index. As of February 24, 2014, the CAPE 10 for the S&P 500 Index was 25.69. That results in an earnings yield of 3.89 percent, and an adjusted earnings yield of 4.2 percent.

One takeaway from the above estimates is that investors needing/wanting a higher return should consider increasing their allocation to international equities - and avoid the home country bias to which many are subject. The higher your allocation to international stocks, the lower your overall equity allocation can be.

Given the above estimates, an equity portfolio that was 60 percent U.S. stocks, 30 percent developed market stocks, and 10 percent emerging market stocks would have an expected real return of just 5.15 percent, well below historical levels. If we add to that figure the current inflation estimate from the Philadelphia Federal Reserve's Survey of professional forecasters of 2.3 percent, we have a nominal return estimate of about 7.5 percent. And with the current yield on 10-year Treasury bonds at about 2.8 percent, the expected nominal return on a typical 60 percent stock/40 bond portfolio is just 5.6 percent - and a real return of just 3.4 percent.

Those estimates are well below the historical returns. And if you are concerned by those figures, consider the results if we had used the other common tool to estimate returns - the dividend discount model (DDM). The DDM uses current valuations, not cyclically-adjusted ones. Given the current low dividend yields and their estimates for future growth in earnings, AQR estimates real returns to U.S. stocks at about 3.6 percent, for developed markets at about 4.5 percent, and about 5.5 percent for the emerging markets. With the same 60/30/10 weighting used earlier, the real expected return for a stock portfolio would be about 4.2 percent, or about 1 percent less than the estimate using the CAPE 10.

Another way to use the above information is to average the two estimates, the roughly 5.2 percent estimate using the CAPE 10 and the 4.2 percent estimate using the DDM. That produces a real return estimate of 4.7 percent and a nominal estimate of 7 percent. However, whatever method you use, it's seems likely that investors who develop investment plans based on historical returns are going fall far short of their goals. Forewarned is forearmed.

**Addressing the Uncertainty of Forecasts**

We know that forecasting returns involves much uncertainty. Which raises the question: How best to address the issue of the difficulty in forecasting returns? I think the best way to address the issue of a probabilistic forecast is to use a Monte Carlo (MC) simulator.

MC simulations require a set of assumptions regarding time horizon; initial investment; asset allocation; withdrawals; savings; retirement income; rate of inflation; correlation among the different asset classes, and - very importantly - return distributions of the portfolio.

In MC simulation programs the growth of an investment portfolio is determined by two important inputs: portfolio average expected return and portfolio volatility, represented by the standard deviation measure. Based on these two inputs, the MC simulation program generates a sequence of random returns from which one return is applied in each year of the simulation. This process is repeated thousands of times to calculate the likelihood of possible outcomes and their potential distributions. This allows you to look at alternative scenarios, including ones where returns will be well below expectations. Being forewarned about the potential for such events allows you to prepare for the various possible outcomes. That includes putting in place a contingency plan (a Plan B) - a plan of action to be implemented if a "black swan" (a major unexpected event) appears. The plan should detail what actions should be taken if financial assets fall to such a degree the investor runs an unacceptably high level of risk of failure. Those actions might include remaining in or returning to the work force, reducing current spending, reducing the financial goal, selling a home and/or moving to a location with a lower cost of living.

MC simulations also provide another important benefit: They allow investors to view the outcomes of various strategies and how marginal changes in asset allocations, savings rates and withdrawal rates change the odds of these outcomes. Looking at various alternatives will help you determine the right asset allocation for your unique situation.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.