1. Poincaré (1913, p. 10).
2. If it fails to eventually outperform, it’s not undervalued!
3. See the Asset Allocation site.
4. Although measuring the R2 of our models is possible, the result is not very useful because samples overlap over long-term horizons. Take U.S. equities for which data are readily available since the late 1800s, roughly 150 years. We analyze 10-year returns, calculated monthly. As a result, we have only 15 unique samples. Any regression using monthly data points for 10-year returns will show misrepresented R2 values, because each data point shares 119 of its 120 months with the next data point. Going to non-overlapping returns means we don’t have enough samples for robust results. For example, imagine the same test for the Barclays U.S. Aggregate Bond Index, which started in 1976—four samples anyone?"
5. Indices were added as data became available: 8/1971, Russell 2000; 12/1988, MSCI EAFE; 1/1990, Barclays Corporate High Yield; 1/1992, Barclays U.S. Treasury Long; 5/1992, Barclays U.S. Aggregate; 5/1992, JPMorgan EMBI+ (Hard Currency); 4/1994, Barclays U.S. Treasury 1–3yr; 1/1997, Bloomberg Commodity Index; 3/1997, JPMorgan ELMI+; 1/2001, Barclays U.S. Treasury TIPS; 7/2003, FTSE NAREIT. Analysis is monthly and ends in 2005, the most recent date for which 10-year subsequent returns can be calculated.
6. The range for each of the bars in the chart should be interpreted as including the lower bound but not the upper bound of the range. For example, the range −2% to 0% includes returns from, and including, −2% up to, but not including, 0%. This standard also applies to the charts in Figures 3–5.
7. These forecasted returns represent return expectations that our methodology would have delivered in past decades. The core elements of the methodology were first described by Arnott and Von Germeten (1983); thus, the methodology is not a data-mining exercise of fitting past market returns.
8. Marks (2013, p. 45).
9. The 4% to 6% bucket is an outlier here; however, this result only occurred in 13 months of the entire 34-year period.
10. See "Asset Class and Portfolio Risk and Return Methdology Overview."
11. Graham (2006, p. 477).
Arnott, Robert, and James Von Germeten. 1983. “Systematic Asset Allocation.” Financial Analysts Journal, vol. 39, no. 6 (November/December):31–38.
Graham, Benjamin. 2006 (1973). The Intelligent Investor—Fourth Revised Edition, with new commentary by Jason Zweig. New York: HarperCollins Publisher.
Marks, Howard. 2013. The Most Important Thing Illuminated. New York: Columbia University Press.
Poincaré, Henri. 1913. The Foundations of Science. New York City and Garrison, NY: The Science Press.