This is Part 3 of 3 on the general subject of merging withdrawal methods for retirement portfolios. Part 1 is a general description of the proposed withdrawal scheme. Part 2 covers one application of this technique. Part 3, here, provides a measure of how results of using the withdrawal method might play out using both historic data and Monte Carlo type simulations.
Distribution Simulation
It is helpful (and entertaining) to see potential results based on historical data and even some dreamedup bad cases. For starters, I took DJIA historical data and split it into 3 overlapping 40year spans; 19421981, 19551994, 19672006. This put the 1970s bear market at different places in the time span; beginning, midsection, and end, so bear market conditions could be tested in relative time slots. Here one is not totally interested in exact results, only relative outcomes. The portfolio is lower beta than DJIA so price values would have less volatility. The dividend portion would have a higher payout during up markets and a corresponding lower payout during down markets. In part these two counteract, making this proxy reasonable.
As I developed this scheme over time: 1) definition, size and number of the segments were developed; 2) the concept of determining an Initial Z tying segment parameters together was established; and 3) the use of the IRS Uniform Lifetime values was incorporated. The utility of the initial payout goal (G), increased yearly by an assumed inflation rate, gives us a guideline to evaluate performance. Payouts should be higher on essentially a parallel path. Payouts that significantly penetrated this guideline (testing all three time frames) were rejected and either portfolio metrics or distribution scheme were revised. During this time, changes to my portfolio were made, both in rearranging stocks between segments and some selling/buying. The traditional pass/fail test, running out of money before the time period is finished, cannot be used. Using the approach discussed here, the portfolio never depletes.
Some results using the above metrics for each segment: Results are in thousand dollars
DJIA Normalized 
Inflation Guide 
Portfolio Payout 

Period 
Start/End 
Start/End/Total K$ 
Start/End/Total K$ 
19421981 
84.75/668 
22.71/90.21/1965 
27.49/131.96/2904 
19551994 
84.75/804 
22.71/90.21/1965 
27.49/134.86/2454 
19672006 
84.75/1326 
22.71/90.21/1965 
27.49/153.80/2713 
Start/End in DJIA Normalized are in $/share, other data in K$.
Reminder about dividend growth: Core segment, average between exponential and linear; High Income segment, linear; Dividend Growth segment, exponential with gradual decrease  final value half initial value.
Remaining shares: Core  55.7%; High Income  15.2%, Dividend Growth  79.77%.
Using the 19551995 time period with decreasing dividend growth and yield: payouts in thousand $
Initial Z 
Core 
High Income 
Dividend Growth 
Inflation Guide 
Portfolio Payout 
Yield/dg 
Yield/dg 
Yield/dg 
Start/End/ Total K$ 
Start/End/ Total K$ 

0.459 
0.039/0.09 
0.056/0.07 
0.032/0/11 
22.71/90.21/ 1965 
27.49/134.86/ 2454 
0.370 
0.039/0.08 
0.056/0.06 
0.032/0.10 
22.09/87.75/ 1912 
26.23/124.50/ 2264 
0.283 
0.039/0.07 
0.056/0.05 
0.032/0.09 
21.48/85.34/ 1859 
25.00/118.48/ 2133 
0.198 
0.039/0.06 
0.056/0.04 
0.032/0.08 
20.89/82.97/ 1807 
23.79/114.11/ 2039 
0.198 
0.029/0.06 
0.046/0.04 
0.022/0.08 
16.60/65.95/ 1437 
19.84/107.51/ 1767 
In the last data set, yields for MÃ©lange and Bond segments were also reduced one percentage point. Setting initial Z at zero and zeroing all Z midpoint and final values except the Bond segment:
0.000 
0.039/0.09 
0.056/0.07 
0.032/0.11 
22.71/90.21/ 1965 
20.98/148.22/ 2568 
It is obvious from these data that it is important to keep initial yields and dividend growth up. It is also apparent that even with robust D&I, which supply copious income in later years, it is difficult to generate early year income. Again, shares sold cannot pay future D&I.
To provide a more realistic scenario, dividend growth was varied in sync with market volatility by modulating it in the Core, Dividend Growth and High Income segments with yeartoyear changes in DJIA. Dividend growth in each segment was modified in the year after market variations, the same year as corresponding share sales. The first year payout was not varied so that the first year's payout would remain the same. For the Core segment, dividends were modulated with yeartoyear variations, simulating negative DG. For the High Income segment, linear gain times market variations was used for up markets and zero dividend growth used for down markets. For the Dividend Growth segment, for up markets, normal dividend growth was multiplied by 1.5 and by 0.5 for down markets. These changes more closely track actual experience. Payouts were higher simply because there were more ups than downs in the market. This does give us a model for the next simulation, where down markets are more severe.
Two cases were used to illustrate results using these modified values of dividend growth. Case I uses the metrics stated above with dividend growth for Core (0.09), High Income (0.07), Dividend Growth (0.11). For this case, Shares Remaining equals 35.3% and Total Inflation Guide Output/ Initial Portfolio equals 4.91. Initial Payout is $27.49K, Initial Inflation Guide is $22.71K. Case II lowers dividend growth to Core (0.06), High Income (0.04), Dividend Growth (0.08). Note that this case has a dividend growth in High Income segment just above the assumed inflation rate, a marginal portfolio to start with. For this case: Shares Remaining is 18.3%, Total Inflation Guide Output/ Initial Portfolio is 4.52, Initial Payout $23.79K and Initial Inflation Guide $20.89K.
Results are: where % Coverage = Total Payout/Total Inflation Guide; % Penetration = Total Penetration/Total Inflation Guide; % Last Coverage = Last Payout/Last Inflation Guide; % Residual Portfolio = Remaining Portfolio/Total Inflation Guide. Penetration is the event where yearly payout drops below the Inflation Guide line.
Case I 
% Coverage 
% Penetration 
% Last Coverage 
% Residual Portfolio 
19411981 
176 
0 
196 
57 
19551994 
142 
0 
192 
68 
19672006 
162 
0.16 
215 
112 
Case II 

19421981 
165 
0 
137 
32 
19551994 
118 
0.26 
143 
39 
19672006 
158 
0.40 
193 
64 
One concern about this approach is the variability in payout, particularly reductions in down markets. Payout will be a strong function of how D&I holds up, but variations in payout will always be less than market fluctuations.
Recipients will understand that in down markets, less is available for distribution. Some strategy for saving a portion of the fallout in good years will feel good when needed. If you took a portion of the difference between the calculated payout and the inflation guide and 'put it in another pocket' for use during down markets, it would help solve this problem. This subject and portfolio turnover issues deserve more space than can be addressed here.
Monte Carlo simulations are a good extension (to using historical stock market data) for providing fictitious, but plausible, market returns to test the worthiness of portfolio distribution schemes. It is not appropriate to find the absolute worst case, we already know that: you retire on Friday and the next Monday, stock and bond markets crash wiping out all portfolio value. What is important is to find 40 year stretches of stock prices that 'could happen' and stress test the viability of distribution schemes under investigation.
The current scheme, presented here, cannot fail in the traditional sense, i.e., the portfolio runs out of funds before the time period ends. With final values of Z that are less than one (1), some shares remain. Also, using the Uniform Life data insures some shares are unsold at the end of the time period. Thus, the final portfolio has some value, depending on per share market price at the time. A simulation run can be performed using rules and portfolio metrics under scrutiny and results examined. In real life, when subpar results are obvious, changes would be made to correct the situation. Under the scheme discussed here, funds/shares would be available to do this. Keeping this in mind, simulation results will be shown without such changes to show how bad it 'could' be.
Two separate Monte Carlo simulations were performed. The first, called Randomhard, had a characteristic of having long strings of up and down years, often 7 or 8 years in duration and present in nearly every 40year run. The second, called Random, had more realistic variations in the sequence of up and down years, but had a lower end price average compared with the historic data. It turned out that Random was more severe than Randomhard! These Monte Carlos (Carlitos) are not intended to cover the entire universe of market deviations, merely that population just below current market variation levels, the most likely to be encountered.
One hundred 40year runs were conducted with these simulations with the following results:
Randomhard 
Randomhard 
Random 

Set 1 
Set 2 

Avg. end price 
1092 
1189 
743 
Maximum 
4822 
4725 
2802 
Minimum 
211 
237 
152 
# less than 1000 
61 
63 
77 
# more than 1000 
39 
37 
23 
Note: End prices for the 3 historic data sets were: 669/805/1326 Average: 933
Running the Monte Carlo simulation yielded the following results:
0% Penetration 
Less than/equal to 5%Penetration 
Greater than 5%Penetration 

Case I Randomhard 
80/100 
19/100 
1/100 
Case I Random 
60/100 
40/100 
0/100 
Case II Randomhard 
50/100 
42/100 
8/100 
58/100 
39/100 
3/100 

Case II Random 
33/100 
47/100 
20/100 
36/100 
46/100 
18/100 
Two set of 100 runs were made for Case I, Randomhard and Random with same result.
Of the 49/400 runs with more than 5% penetration, % penetration ran from 6% to 19%, mostly on the low end. At the 6% end, % Last Coverage and % Coverage was about 100%, Residual portfolio/Total Inflation Guide was about 20%. At the high end, corresponding values were 45%, 82% and 10%. In real life, some of the residual portfolio could have been used toward the end of the time period to improve results. This exercise shows that if you let dg sag on you (over the lifetime), you won't run out of funds, but for about 20% of the lifetime experiences you may not be as happy as you had hoped. Case II Random was rerun with one change; final dg for the Div Gr Segment was increased from 50% of start DG to 75%. The number of 'greater than 5%' penetrations decreased from 38/200 to 19/200.
Adjustments to payouts should not be made for reduced amounts due to down markets. Don't eat tomorrow's lunch. An exception would be if there are residual shares and you are well into the latter part of the time period. It is more reasonable to adjust payouts by varying yearly Zs, as suggested earlier, if DG falls off and cannot be corrected by other measures, such as replacing equities with better performance.
Efforts could be made to improve these simulation characteristics. This would not alter the results substantially. These simulations are accurate enough to illustrate that the 'goodness' of your portfolio is paramount. Increasing diversity, selecting solid companies with consistent dividend growth will insure more satisfying results. The simulations clearly show that results improve as initial yield and dividend growth are increased. We may not know precise points where performance is degraded as dividend growth falls off, but if we do the best we can in creating a portfolio, what more is needed? This means you may have to (gasp) work at it (to improve your portfolio). Performing the technical steps outlined here, to help organize the program, is the easy part.
A major value of distribution simulations is to verify that calculations of Init Z and resultant spreads of yearly distributions (from segments) provide the proper mix to balance payouts over the time period . Too small an Init Z leaves too much in later years and the reverse is also true. I cannot answer for all portfolios out there, but this I believe: if your calculation for Init Z is between 0.1 and 0.5 (give or take), Zs are reasonably distributed over the time period, weighed average Z does not exceed unity (1) at any time, somewhere between 0.2 to 0.3 (give or take) of equivalent share are planned to be unsold at the end, you are in good shape. Mid course corrections will fine tune later years. From my research, Eq. #3 and #4 perform surprisingly well in setting initial conditions, even for two segment (Core and Bond) portfolios.
DISCLAIMER
The portfolio discussed here is my own and presented only to illustrate one application of the retirement portfolio distribution scheme described. The stocks and bond funds listed are not recommended without due diligence by intended users. The effort here is a work in progress. I am in the accumulation phase with four years to go, so the distribution scheme (for my portfolio), as described here, is untested in real life. A major issue to be resolved is the portfolio turnover needed to maintain dividend growth. The general distribution scheme, using Eq. #1 and Eq. #3 and #4 (if appropriate) with the other general guidelines, stand independently. Make of it as you can.
Disclosure: I am long MCD. I am long all stocks and bond funds mentioned in part 1, 2 and 3 of this article.