# Projecting Real Portfolio Accumulations, Proceedings of the Association for Financial Counseling and Planning Education, 1997

Proceedings
of the Association for Financial Counseling and Planning Education, 1998

PROJECTING REAL PORTFOLIO ACCUMULATIONS

Sherman Hanna, Ohio State University(1)

How should portfolio accumulations
be projected? A typical method would be to use the mean rate of return
of the portfolio, e.g., the mean rate of return for a particular mutual
fund, or perhaps for large stocks. However, for both stock and bond portfolios,
there is a considerable range of outcomes based on any particular length
of time. This paper illustrates with tables and graphs for the Ibbotson
large and small stock categories and bond categories the mean and minimum
accumulations, and describe use of the tables for projecting portfolio
values and accumulations of contributions. A portion of the tables (created
by the author) is provided below.

Mean and Minimum Real Accumulations
(per initial \$1) for consecutive periods, 1926-97.

 # of years Small Large Stocks Stocks mean minimum mean minimum 20 8.62 2.17 4.50 1.18 25 14.11 3.36 6.26 1.98 26 16.13 4.00 6.68 2.06 27 18.15 5.20 7.13 2.40 28 19.98 5.50 7.59 2.80 29 22.05 4.11 8.18 2.90 30 24.36 5.88 8.73 3.59 31 26.24 8.82 9.20 4.01 32 28.27 9.68 9.76 4.36 33 31.56 11.73 10.48 4.50 34 35.31 11.06 11.14 5.40 35 39.95 13.44 11.79 5.59 36 45.77 16.41 12.58 6.20 37 49.64 15.56 13.25 7.42 38 52.75 11.10 14.24 6.08 39 56.50 15.85 15.16 7.79 40 60.63 23.80 15.94 9.20 41 65.41 27.95 16.86 8.00 42 70.88 26.26 17.96 7.82 43 76.76 29.60 18.99 8.17 44 83.70 29.89 19.93 9.63 45 93.74 18.98 21.34 8.41

Mean and Minimum Real Accumulations
(per \$1/year) for consecutive periods, 1926-97.

 # Small Large of years Stocks Stocks mean minimum mean minimum 20 79.08 21.95 51.01 18.64 25 136.47 42.57 80.86 28.45 26 152.44 48.80 88.02 30.50 27 170.70 54.75 95.55 33.20 28 191.11 60.25 103.41 37.33 29 214.30 64.36 112.07 41.40 30 238.28 71.35 120.40 46.17 31 263.56 81.86 128.38 51.77 32 291.36 101.07 136.91 58.73 33 324.35 126.46 146.94 67.15 34 358.13 147.52 156.18 75.80 35 395.86 167.30 165.63 84.19 36 440.95 187.25 176.10 90.72 37 487.39 214.50 185.64 99.43 38 540.30 225.60 197.20 109.64 39 595.38 243.67 208.18 122.11 40 652.18 268.27 218.53 135.83 41 706.36 298.22 228.63 146.89 42 770.77 370.59 241.76 156.77 43 818.71 419.33 253.55 166.66 44 857.11 458.19 265.43 180.00 45 927.97 487.21 281.26 188.41

The results are very relevant to retirement
planning, as a projection based on the mean rate of return may be much
higher than the minimum projection. For instance, for 20 years of periodic
investing with a large stock index fund, the record of the worst 20 year
period would imply contributing 2.7 times as much per year as the average
record would imply to accumulate a particular amount.

1. 1 Contact
author: Sherman Hanna, 1787 Neil Avenue, Columbus, OH 43210. Phone: (614)
292-4584, Fax: (614) 292-7536. Email: hanna.1@osu.edu.