Panel 1. Assuming ROI = r (1 + g)/(1 + r) (declining-balance expense for 1 − C = q) | ||||||
Estimate of | Sample | Percentiles: | ||||
10 | 25 | 50 | 75 | 90 | ||
1 − C (steady) | Part 1 | 0.06103 | 0.14648 | 0.33635 | 0.69659 | 1.04849 |
Part 2 | 0.05851 | 0.18256 | 0.34367 | 0.55962 | 0.79686 | |
q | Part 1 | 0.03175 | 0.11841 | 0.23300 | 0.35103 | 0.61049 |
Part 2 | −0.00520 | 0.08901 | 0.20449 | 0.34512 | 0.67673 | |
(1 − C) − q | Part 1 | −0.12330 | −0.02266 | 0.03807 | 0.29137 | 0.87987 |
Part 2 | −0.21477 | −0.04396 | 0.09092 | 0.31696 | 0.66594 | |
Panel 2. Assuming ROI = r (the compound interest (annuity) expense) | ||||||
Estimate of | Sample | Percentiles: | ||||
10 | 25 | 50 | 75 | 90 | ||
1 − C (steady) | Part 1 | 0.06103 | 0.14648 | 0.33635 | 0.69659 | 1.04849 |
Part 2 | 0.05851 | 0.18256 | 0.34367 | 0.55962 | 0.79686 | |
q | Part 1 | 0.02720 | 0.12279 | 0.24787 | 0.38842 | 0.61820 |
Part 2 | −0.00543 | 0.12552 | 0.24853 | 0.40325 | 0.70845 | |
(1 − C) − q | Part 1 | −0.13130 | −0.03792 | 0.02849 | 0.28337 | 0.85969 |
Part 2 | −0.28984 | −0.11683 | 0.04448 | 0.29725 | 0.64846 | |
Panel 3. Assuming ROI = r R/M (rate-of-return (realization) expense) | ||||||
Estimate of | Sample | Percentiles: | ||||
10 | 25 | 50 | 75 | 90 | ||
1 − C (steady) | Part 1 | 0.06103 | 0.14648 | 0.33635 | 0.69659 | 1.04849 |
Part 2 | 0.05851 | 0.18256 | 0.34367 | 0.55962 | 0.79686 | |
q | Part 1 | 0.02730 | 0.12276 | 0.24390 | 0.36898 | 0.62189 |
Part 2 | −0.00544 | 0.12339 | 0.24156 | 0.38466 | 0.69081 | |
(1 − C) − q | Part 1 | −0.13113 | −0.03189 | 0.03419 | 0.30576 | 0.86623 |
Part 2 | −0.26210 | −0.10157 | 0.05089 | 0.30284 | 0.65036 |