Below are four models that would pass the "well-established standards of value" test.
GMO 7-Year Asset Class Return Forecasts
GMO's Jeremy Grantham provides one of the best quarterly investment commentary that money cannot buy. His quarterly commentaries often refer to GMO's estimate of the fair value of the S&P 500, which is useful in and of itself. In addition, the firm also provides access to its 7-Year Asset Class Return Forecasts, which are published monthly with about a month lag. This forecast provides the estimated annual real return GMO expects for 12 broad asset classes: US large cap stocks, US small cap stocks, US high quality stocks, international large cap stocks, international small cap stocks, emerging market stocks, US bonds, international bonds, emerging market debt, inflation linked bonds, cash, and timber.
Like any model, there are assumptions and a margin of error to consider. The long-term inflation assumption is currently 2.5% per year. The nominal return is equal to [(1+real rate)*(1+inflation rate)]-1. Most investors think of their investment returns in nominal terms, i.e. not adjusted for inflation. The second item to consider is the estimated margin of error for each 7-year annualized real return. For example, the April 30, 2011 forecast shows a real return of 4.5% for Emerging stocks with an estimated range of +/- 10.5%. The 4.5% is most likely the average of the two annualized return extremes: 15% and -6%. Lastly, this is a black box model that uses GMO's proprietary valuation methodologies. As it notes in the small type at the bottom, "actual results may differ materially from the forecasts above."
Note that the forecasts exclude some asset classes such as commodities, real estate and subsets of asset classes such as high-yield bonds, municipal bonds, and investment grade bonds to name a few. You can't get everything for free. Unfortunately, it takes somewhere in the neighborhood of $1 million or more to get into a private timber investment. Head over to John Hancock Timber Resource Group if that fits your profile (or another similar firm).
In Jeremy Grantham's 2011 First Quarter Investment Letter, he provides a "very crude way" of showing that the asset class forecasts provide value to the price conscious investor. Take for example his cognitive exercise: Starting in 1994 when the forecasts first started, place 100% of a portfolio in the single asset class that GMO estimates will provide the highest return. Rebalance each month, if necessary, when the new asset class forecast comes out. The example assumes zero transaction costs such as trading commissions and other investment fees. The "Max Forecast Portfolio" provided a 16.7% annualized return compared to 8.8% for the S&P 500, however, the enhanced return was also accompanied by an increase in volatility. As Grantham notes, this strategy "would not be tolerable for much more than 5 or 10% of one's money, rebalanced each year.”
Using the 2001 1st Quarter Asset Class Return Forecast, I tested a few asset classes using Morningstar.com's portfolio tool and Yahoo! Finance's historical quotes:
US equities large cap - 2.2% nominal [(1+0.00)*(1.022)]-1. S&P 500 total return index. 2.53%.
Emerging market stock - 13.9% nominal [(1+.114)*(1+.022)]-1. T. Rowe Price Emerging Markets Stock Fund ($10.25 to $36.06 or approx 14.84% per year with reinvested dividends and capital gains)
Small cap stock - 6.5% nominal [(1+.042)*(1+.022)]-1. iShares Russell 2000 Index ($43.75 to $84.17 or approx 6.79% with reinvested dividends).
I didn't try to find the best fit forecast with 10 years of data available, but as one can see, the estimates are accurate in this instance. In the case of the 10 year period ending March 2009, the actual return should be probing the low end of the estimated range. For the 10 year period ending April 2000, one would expect the return to be at the high end of the estimate range. In any event, the forecasts appear to be a useful tool assuming overall market valuations revert to their historical mean over time,
The 7-Year Asset Class Forecasts are available at GMO's website with a free registration.
John Hussman's Forward Operating Earnings S&P 500 Valuation Model
This model is outlined in John Hussman's August 2, 2010 weekly commentary. To gain a thorough understanding of the model, read his piece. He does a great job of explaining how he arrived at the equation, the assumptions embedded in the model, historical accuracy via graphs, and caveats. The model is used to estimate the 7-10 year annualized return of the S&P 500. He notes "the long-term annual total return for the S&P 500 over any horizon T can be written as:
Long term total return = (1+g)(future PE / current PE)^(1/T)-1 + dividend yield (current PE / future PE + 1)/2"
The first term, up to the first "+" sign, represents the annualized capital gain and the second term approximates the average dividend yield. The return is based upon the sum of the capital gains and dividends. As he notes, the two most important things to get right are g, the long-term earnings growth rate, and the future PE (price/earnings multiple). Based upon his work, the best estimate for g over a 10-year horizon is:
g = 1.063 * (0.072 / (FOE/S&P 500 Revenues))^(1/10) - 1
He also notes that over a 7-10 year period, the correct future PE to use is 12.7. Note this is different than the typical 15, which is the ratio of the S&P 500 to trailing 12-month net earnings.
The data to populate the model is available via free registration at Standard and Poor's. Based on my understanding of the inputs, the S&P 500 was set to return approximately 4.06% as of June 3, 2011. This is close to the 3.9% John Hussman provided in his June 6, 2011 weekly commentary (his value may be an average of several models he uses). See spreadsheet below for details.
John Hussman's Price to Sales S&P 500 Valuation Model
This simple revenue-based valuation model is outlined in John Hussman's May 23, 2001 weekly commentary. The model follows the same form as the previous model. The first term represents the estimated annual capital gain and the second term estimates the expected dividend yield. The correlation of the model to subsequent returns is provided in his weekly commentary. Below is a spreadsheet with the model populated with data from Standard and Poor's. The June 3, 2011 expected return for the S&P 500 is 4.04%.
Schiller P/E
Robert Schiller's cyclically adjusted p/e ratio averages profits over a 10-year period in an attempt to smooth out the effects of the economic cycle. The ratio is the real S&P 500 price divided by the 10-year average real earnings of the S&P 500. The Schiller P/E is controversial. Here is a piece from The Economist's Buttonwood's Notebook in defense of the Schiller P/E. In any event, the ratio should be mean reverting around an average over time. John Hussman provides, in his March 14, 2011 weekly commentary, a general framework for using the Schiller P/E to provide expected market returns over a 5 and 10-year horizon. The table of his findings is provided toward the top of the commentary. Clearly, when the Schiller P/E is high, returns tend to be lower in future years and vice versa. This effect is more pronounced over a 10-year total return period than a 5-year total return period. This is due in part to the bubbly 1990's. The really interesting data is the frequency of P/E level. The current P/E levels around 23-24 have not occurred very often in the history of the data set and provide average annual returns over a 10-year period of 3.5%. This jives quite well with the previous valuation methodologies.
Other Models
Two other models that may come in handy are the Tobin Q and Market Cap to GDP ratio. Tobin Q was oulined by Andrew Smithers and Stephen Wright in their book Valuing Wall Street : Protecting Wealth in Turbulent Markets.
The model compares the value of the market with the net replacement cost of corporate assets. The model is used with the same mean reversion assumption of the Shiller P/E. When market prices exceed corporate asset values, investors would be best off buying corporate assets directly instead of equities. An updated Tobin Q graph can be found here. It's best used as a broad view of over and undervaluation. Another broad valuation model is Total Market Cap to GDP. Gurufocus.com provides a nice explanation and anticipated future return calculation based on this model. The green line in the first graph is the total market cap to GDP value. The green, brown, and red lines in the lower graph provide the anticipated annualized return over an 8 year period with green being the lower bound, brown the middle bound, and red the upper valuation bound.
