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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 dreamed-up bad cases. For starters, I took DJIA historical data and split it into 3 overlapping 40-year spans; 1942-1981, 1955-1994, 1967-2006. 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 re-arranging 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$

1942-1981

84.75/668

22.71/90.21/1965

27.49/131.96/2904

1955-1994

84.75/804

22.71/90.21/1965

27.49/134.86/2454

1967-2006

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 1955-1995 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 Mélange and Bond segments were also reduced one percentage point. Setting initial Z at zero and zeroing all Z mid-point 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 year-to-year 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 year-to-year 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

1941-1981

176

0

196

57

1955-1994

142

0

192

68

1967-2006

162

0.16

215

112

Case II

1942-1981

165

0

137

32

1955-1994

118

0.26

143

39

1967-2006

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 sub-par 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 Random-hard, had a characteristic of having long strings of up and down years, often 7 or 8 years in duration and present in nearly every 40-year 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 Random-hard! 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 40-year runs were conducted with these simulations with the following results:

Random-hard

Random-hard

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 Random-hard

80/100

19/100

1/100

Case I Random

60/100

40/100

0/100

Case II Random-hard

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, Random-hard 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 re-run 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.

Source: Life Cycle Of Retirement Portfolios, Part 3