**References**

- Brinson, G., Hood, R., and Beebower, G. 1986. “Determinants of Portfolio Performance.” Financial Analyst Journal 42(4): 39-44.)
- Brinson, G., Singer, B., and Beebower, G. 1991. “Determinants of Portfolio Performance II: An Update.” Financial Analysts Journal 47(3): 40-48.
- Investment Company Institute. 2013. “2013 Investment Company Fact Book: A Review of Trends and Activities in the U.S. Investment Company Industry.” 53rd edition. http://www.ici.org/pdf/2013_factbook.pdf
- Markowitz, H.M., and Usmen, N. 1996a. “The likelihood of various stock market return distributions, Part 1: Principles of inference.” Journal of Risk and Uncertainty, 13(3), 207-219.
- ibid., 1996b. “The likelihood of various stock market return distributions, Part 2: Empirical results.” Journal of Risk and Uncertainty, 13(3), 221-247.
- Michaud, R. 1981. “Risk Policy and Long Term Investment.” Journal of Financial and Quantitative Analysis. 16(2), 147-167.
- Michaud, R. 2003. “A Practical Framework for Portfolio Choice.” Journal of Investment Management, 1(2), 1-16.
- Michaud, R. and Michaud, R. 2008a. “Efficient Asset Management: A Practical Guide to Stock Portfolio Optimization and Asset Allocation.” Oxford University Press, New York. 1st ed. 1998, originally published by Harvard Business School Press, Boston.
- Michaud, R. and Michaud, R. 2010. “Target Date Funds Aren’t a Panacea.” Investment News, May 2, 2010.
- Silverblatt, R., 2009. “Target Date Funds Go Under the Microscope.” Fund Observer, US News and World Report, Oct. 30, 2009. http://money.usnews.com/money/blogs Fund-Observer/2009/10/30/target-date-funds-go-under-the-microscope

**Endnotes**

- This is partially based on the observation that early investment experiences affect lifetime investment behavior. An early experience of loss can lead to prohibitive risk aversion later in life.
- A typical family of TDFs may have as many as 12 dates in five-year increments and an income fund for investors in retirement.
- Under restricted assumptions, optimal glide paths can be solved for analytically. We believe the illustrations of the Monte Carlo results are more persuasive since the strictest and most unrealistic assumptions can be tested and varied.
- We need not test the impact of varying this assumption too greatly, since the impact of an unexpected outstanding contribution in a particular year is mathematically the same in terms of retirement wealth as the impact of an outstanding portfolio return, and outstanding returns do occur with considerable frequency in the simulations. Because our experiment considers a wide range of outcome scenarios mathematically equivalent to erratic investment patterns, we ignore the pattern of contributions as an experimental variable without loss of generality.
- We tried matching on other risk measures such as value at risk (VaR) and conditional value at risk (CVaR), but standard deviation provided the best comparisons, especially as presented in the graphical analysis of the appendix.
- In the single lump-sum case, it is convenient to note that the wealth distributional properties of any glide-path investment policy are identical to those of a single fixed-risk policy over the investor’s investment horizon. Wealth distributions result from compounding return over time. A constant compounding of return over an investor’s investment horizon generally leads to highly right-skewed wealth distributions. In this case, a terminal wealth risk criterion will necessarily have to deal with the often-misleading character of the mean for describing investor risk. This is because the mean of the income of 99 paupers and one millionaire may often inadequately reflect a summary of a wealth distribution. As a consequence, the median of terminal wealth is often the criterion of choice to describe compound return that long-term investors experience. Michaud (1981, 2003) showed that the median of compound terminal wealth is often well approximated by the nth power of the mean of the geometric mean distribution. This framework is analytically convenient for understanding the distributional properties of the lump-sum glide-path wealth distribution. In the more general case of 401(k) investing, the investor is often encouraged to provide periodic additions to investments resulting in a wealth distribution that is the sum of many lump-sum compounding-return wealth distributions. There is no simple analytical framework for analyzing such wealth distributions, and simulation remains the only solution. We report median wealth results but find that, for our assumptions, the mean of retirement wealth moves nearly parallel to the median and generally provides similar conclusions in comparing the glide paths.
- We simulate returns using Student’s t-distribution with 5 degrees of freedom. We make no claims that this model for returns is a perfect representation of real stock and bond returns, only that this distribution provides suitably fat tails to represent a broad array of realistic market scenarios, including many cases of substantial downside risk.
- The robustness of the results to various stock and bond mixes was of particular concern. We tried several different stock/bond mixes, and found that a 40 percent stock, 60 percent bond mix provided a nice range for comparison because glide paths generally match to a lower stock ratio than their average stock ratio over time, but the analysis is extremely similar for 50/50 or 60/40 stock/bond ratios. We present a 60/40 analysis in Figure 7.
- Ten-year Treasury returns and CPI data are available from the Federal Reserve Economic Data (FRED). Equity returns are available through CRSP.
- The total real investment over 40 years is $604,020.
- Perhaps the strongest criticism of glide-path investing is that few investors follow the steady contribution plan that glide paths assume they will be making.
- E.g., Silverblatt 2009.