Mean and Minimum Real Accumulations, Sherman Hanna, 1/98


Paper, “Taking Uncertainty Into Account In Projecting Portfolio Accumulation” by Sherman Hanna. To be presented at the Midwest Finance Association, March, 1998

Mean and Minimum Real Accumulations (per initial $1), Annualized Rates of Return, Ratio of
Mean to Minimum Accumulation, and Number of Periods Real Value Increased, for Small and
Large Stocks, by Holding Periods from 1 to 40 Years.


Small Large
N Mean
Acc.
Mean % Minimum
Acc.
Minimum
%
Mean/
minimum
<1 %<1 Mean
Acc.
Mean
%
Minimum
Acc.
Minimum % Mean/
min
<1 %<1
1 1.141 14.1% 0.407 -59.3% 2.802 21 30.0% 1.092 9.2% 0.626 -37.4% 1.744 23 32.9%
2 1.308 14.4% 0.320 -43.5% 4.094 19 27.5% 1.187 9.0% 0.501 -29.3% 2.372 18 26.1%
3 1.482 14.0% 0.177 -43.8% 8.352 17 25.0% 1.277 8.5% 0.457 -23.0% 2.791 14 20.6%
4 1.670 13.7% 0.187 -34.2% 8.924 16 23.9% 1.366 8.1% 0.468 -17.3% 2.918 16 23.9%
5 1.840 13.0% 0.264 -23.4% 6.970 12 18.2% 1.461 7.9% 0.612 -9.3% 2.386 14 21.2%
6 2.000 12.2% 0.285 -18.9% 7.013 9 13.8% 1.567 7.8% 0.556 -9.3% 2.819 11 16.9%
7 2.207 12.0% 0.335 -14.5% 6.587 11 17.2% 1.707 7.9% 0.590 -7.3% 2.894 9 14.1%
8 2.453 11.9% 0.529 -7.7% 4.640 6 9.5% 1.858 8.1% 0.710 -4.2% 2.619 11 17.5%
9 2.675 11.6% 0.497 -7.5% 5.382 6 9.7% 2.001 8.0% 0.618 -5.2% 3.241 9 14.5%
10 2.971 11.5% 0.679 -3.8% 4.375 6 9.8% 2.178 8.1% 0.681 -3.8% 3.197 7 11.5%
11 3.336 11.6% 0.685 -3.4% 4.873 3 5.0% 2.363 8.1% 0.748 -2.6% 3.159 10 16.7%
12 3.751 11.7% 0.643 -3.6% 5.833 3 5.1% 2.542 8.1% 0.793 -1.9% 3.204 9 15.3%
13 4.275 11.8% 0.533 -4.7% 8.014 2 3.4% 2.753 8.1% 0.769 -2.0% 3.578 8 13.8%
14 4.771 11.8% 0.705 -2.5% 6.764 2 3.5% 2.956 8.1% 0.816 -1.4% 3.623 5 8.8%
15 5.201 11.6% 0.938 -0.4% 5.543 2 3.6% 3.146 7.9% 0.917 -0.6% 3.432 4 7.1%
16 5.656 11.4% 0.955 -0.3% 5.923 1 1.8% 3.361 7.9% 0.854 -1.0% 3.934 1 1.8%
17 6.299 11.4% 1.263 1.4% 4.988 0 0.0% 3.626 7.9% 0.943 -0.4% 3.847 2 3.7%
18 7.050 11.5% 2.054 4.1% 3.432 0 0.0% 3.901 7.9% 1.085 0.5% 3.596 0 0.0%
19 7.857 11.5% 2.083 3.9% 3.773 0 0.0% 4.180 7.8% 1.205 1.0% 3.469 0 0.0%
20 8.598 11.4% 2.173 4.0% 3.958 0 0.0% 4.477 7.8% 1.182 0.8% 3.788 0 0.0%
21 9.298 11.2% 2.649 4.8% 3.510 0 0.0% 4.778 7.7% 1.382 1.6% 3.458 0 0.0%
22 10.062 11.1% 2.013 3.2% 4.998 0 0.0% 5.077 7.7% 1.475 1.8% 3.442 0 0.0%
23 11.237 11.1% 2.614 4.3% 4.299 0 0.0% 5.469 7.7% 1.627 2.1% 3.362 0 0.0%
24 12.709 11.2% 3.387 5.2% 3.753 0 0.0% 5.912 7.7% 1.902 2.7% 3.109 0 0.0%
25 14.205 11.2% 3.358 5.0% 4.230 0 0.0% 6.285 7.6% 1.985 2.8% 3.166 0 0.0%
26 16.243 11.3% 4.004 5.5% 4.057 0 0.0% 6.704 7.6% 2.056 2.8% 3.26 0 0.0%
27 18.373 11.4% 5.199 6.3% 3.534 0 0.0% 7.168 7.6% 2.404 3.3% 2.982 0 0.0%
28 20.301 11.4% 5.501 6.3% 3.690 0 0.0% 7.658 7.5% 2.800 3.7% 2.736 0 0.0%
29 22.385 11.3% 4.114 5.0% 5.441 0 0.0% 8.257 7.6% 2.900 3.7% 2.847 0 0.0%
30 24.622 11.3% 5.876 6.1% 4.190 0 0.0% 8.802 7.5% 3.590 4.4% 2.452 0 0.0%
31 26.590 11.2% 8.823 7.3% 3.014 0 0.0% 9.304 7.5% 4.012 4.6% 2.319 0 0.0%
32 28.553 11.0% 9.683 7.4% 2.949 0 0.0% 9.864 7.4% 4.361 4.7% 2.262 0 0.0%
33 31.830 11.1% 11.732 7.8% 2.713 0 0.0% 10.585 7.4% 4.502 4.7% 2.351 0 0.0%
34 35.569 11.1% 11.058 7.3% 3.217 0 0.0% 11.230 7.4% 5.400 5.1% 2.08 0 0.0%
35 40.439 11.2% 13.442 7.7% 3.008 0 0.0% 11.923 7.3% 5.594 5.0% 2.131 0 0.0%
36 46.235 11.2% 16.409 8.1% 2.818 0 0.0% 12.679 7.3% 6.197 5.2% 2.046 0 0.0%
37 50.281 11.2% 15.555 7.7% 3.233 0 0.0% 13.379 7.3% 7.415 5.6% 1.804 0 0.0%
38 53.374 11.0% 11.099 6.5% 4.809 0 0.0% 14.368 7.3% 6.076 4.9% 2.365 0 0.0%
39 56.646 10.9% 15.850 7.3% 3.574 0 0.0% 15.203 7.2% 7.790 5.4% 1.952 0 0.0%
40 61.198 10.8% 23.800 8.3% 2.571 0 0.0% 16.070 7.2% 9.201 5.7% 1.747 0 0.0%


Calculated by Sherman Hanna based on 1926-1996 rate of return data from:

Ibbotson Associates (1997). Stocks, Bonds, Bill, and Inflation 1997 Yearbook. Chicago: Ibbotson Associates.