## Executive summary:

- Both simple models and Monte Carlo models show that initial dividend yields matter more than dividend growth yields.
- Investors should incorporate Monte Carlo models tailored with their own data to anticipate potential shortages in retirement.
- Investors should avoid complacency and sell stock, or not reinvest where necessary, to keep their portfolio earning target dividend yield.

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"Is there a possible scenario that forces all companies to stop paying a dividend? Almost like how real estate prices never go down. That's the biggest possible risk of only owning dividend stocks in your portfolio, if counting on that income. But who knows." … StevePTI

A recent article, "Warren Buffett is wrong about dividends," linked above, got me thinking about the challenges that dividend investors face. More specifically, the quoted statement which opens this article got me thinking about what market trends could derail a perfectly good long-term retirement strategy. Investors who intend to live off cash flows often state that they do not worry about day to day fluctuations in market prices. Is it possible that market prices matter more than we think? Our primary concern should be developing a portfolio that can produce enough cash flow to live off of. But, are there any events or trends that might impact end results? If so, they should be anticipated and mitigated if possible.

Over an investment life cycle, what are some concerns that need to be addressed besides a total cessation of dividends? I decided to model a mock dividend growth (NYSE:DG) portfolio and see if there was anything I could learn from 35 years of "investing" compounded each quarter. To do so, I built two models, one with static inputs, and one, a Monte Carlo simulation that varies the stock price growth rate, the dividend rate at purchase, and the dividend growth rate.

These two models are compared to two corresponding models for equities growing at the same rate per year, without dividend reinvestment. The results, as you can well imagine, were neither earth shattering nor particularly spectacular. Despite the models not turning out quite as robust as I had hoped, I feel that the results can still teach us valuable lessons.

## The First Study

I built a simple excel model to give me a baseline for comparisons between two "competing" portfolios. Furthermore, it served as both the skeleton of, and a bug checker for, the Monte Carlo simulation. The first, the DG portfolio, contained the following assumptions:

- An investor would start out investing $11,000 a year. I chose this amount based on the maximum IRA contribution for a couple. I chose a long time frame (35 years).
- The starting share price for generic stocks in the portfolio was $25.00.
- Equity growth rates, yearly dividend rates and the yearly dividend growth rate were variable in the model, but for this article I will use 8%, 4%, and 9% respectively. Later, I will vary the dividend growth rate to show the magnitude of its impact since I held it close to constant in the Monte Carlo Simulation.
- Each quarter the share price grows by 2% (8%/4), and each quarter the dividend the portfolio receives per share grows by 2.5% (10%/4).
- All transaction costs are ignored.
- Each variable does not represent one particular holding but the holding in aggregate. This is important when we assume new shares can be bought at 4%, even while total portfolio values grow at 8%, and dividends paid by each position grows an average of 10% a year.

The second portfolio, the "value investment" portfolio, assumes the same contributions, no transaction costs, and compounds quarterly. The big difference is the value investment portfolio has no dividend reinvestment, and assumes a constant total return of 12% a year.

Here are the results:

In this ideal model, the Dividend Growth portfolio yields tremendous results. The growth portfolio only produces 27% of the income of the DG version. This shouldn't be a surprise, as we start both with the same total growth rate, but the DG version has additional growth inherent in the numbers with the dividend growing quarterly.

Of course, the weakness of this model is obvious. Every variable involved will fluctuate, sometimes wildly. Our real world results are likely to be vastly different then that presented.

Still, this model is instructive. We can use it to see how changes in various areas will affect our end results. My next experiment is to lower the portfolio dividend rate (dividend rate for each new share purchased) one percent, and separately lower the dividend growth rate by 1%. I can now compare the two results to get a basic idea of which rate has a larger overall impact.

If we compare these two situations, we can see that the dividend rate that new shares earn has somewhat of a larger impact on end results than the dividend growth rate. Of course, this is nominal, not proportional. If I reduce the dividend growth rate proportionally (by 25%, or 2.5% a year), the drop is enormous, with a final income of $182,497.44. We can conclude from this comparison that it is more important to pick companies based on price and earn as close to the 4% dividend yield when purchasing shares than it is to pick companies that maintain the 10% dividend growth rate… to a point. Large deviations from the 10% rule will have oversized impacts, and should be avoided.

## The Monte Carlo Model

Since the market is dynamic, we should try to build a more dynamic model. My method is to build a Monte Carlo simulation which will run the same calculations I ran in the simple model, but will do it 10,000 times. I prefer more than 25,000 iterations, but excel did not respond well. Ten thousand iterations should suffice for our purposes.

Our assumptions for the new model are very similar to the simple models. However, instead of stable growth rates, dividend rates and dividend growth rates, we now have vary our inputs with random numbers within reasonable parameters. We also add the additional assumptions that the value investment portfolio will be more volatile than the DG portfolio, and that the DG investor will try to ensure his new purchases earn dividend rates as close to the 4% and 10% dividend growth rule established in the simple model. Consequently, those two values vary less.

The numbers essentially work out so that the value investment portfolio has a mean return of 12%, and one standard deviation of 8%. The dividend growth portfolio has a mean of 8% and a standard deviation of 5%. The new share dividend rate has a mean of 4% and a standard deviation just over ½%, and the dividend growth rate has a mean of 10%, with a standard deviation of just under 1%. I had to monkey with the numbers somewhat to ensure that we would not get less than 0% for dividend rates, and that under 1% would be a very rare event as well.

One final assumption I included was that our make believe investment manager needed around $50,000 in today's dollars of earnings to live off of in the future. Averaging 3% inflation a year over the next 35 years, our investor needs to produce $140,700 to call either method a success.

Results for the dividend growth and the value investment portfolio are very similar, with the value investment portfolio achieving slightly higher returns on the outliers:

The results are as follows:

**The dividend growth portfolio**:

Average income after 35 years: $206,881.65

Minimum income generated (10000 runs): $40,916.05

Odds of earning greater than $140,700: 77.48%

**The value investment portfolio**:

Average income after 35 years: $256,767.45

Minimum income generated (10000 runs): $62,720.85 (assuming total reinvested at the end in investments yielding 4%)

Odds of earning greater than $140,700: 87.23%.

By looking at the very best results and the very worst results, I hoped to gain some insight into what brought portfolios down and what led to success. The worst performing dividend portfolios tended to have several things in common.

First, poorly performing dividend portfolios would have consistently low dividend rates for new shares, often hovering around 1%. Obviously, early rates mattered much more than later rates, but even lower rates later on were harmful to overall performance. Dividend growth rates played a secondary role in overall portfolio performance. Many of the poorly performing portfolios had slightly lower dividend growth rates than average, but if the initial dividend rate was low, dividend growth had a hard time compensating. Finally, the worst performing portfolios had high rises in share prices early on, and stagnating growth late in the portfolio's life cycle.

The very best performing portfolios were simply the inverse of the worst. They consisted of very high dividend yields, high dividend growth rates and slow appreciation of share prices.

## Weaknesses/Issues noted:

The problem with any model is that assumptions enable us to work with large amounts of data and tease out patterns, but they do so at the cost of realism. Commenters are likely to point out a number of issues, and they are invited to do so. Here are a few that I have noted as I developed the model.

1: The rate of return is too generous. Excel and just as many pundits and forecasters assume market returns lie on a normal distribution. They do not. Consequently, there are no "100 year events" that tend to happen every twenty years or so. With occasional real sharp drops in equity returns (-30%- -50%), we know that the returns displayed are almost certainly too generous.

2. The variations from year to year are, by necessity, random. In order to keep me from cherry picking results, I let Excel pick return and dividend rates for every year at random, within the loose parameters I assigned. But of course, there is some correlation between each variable. Big drops in the market are often followed by years of higher returns. Not necessarily so in my model. Dividend rates for new shares should go up when portfolio growth rates drop into the negatives. Again, this is not always reflected in my model. High dividend growth rates are likely to prompt higher share prices, but my model did not reflect that. My own limitations with Excel as well as time limitations have prevented me from making a model as robust or as accurate as I would have liked. But I will likely continue to refine this model, or revamp it after brushing up on script writing.

3. Although the inflation adjusted numbers, which drive the probability of success is calculated with yearly inflation, there is no assumption that contributions will increase.

## Lessons Learned

Despite both models' limitations, there are some important takeaways. First, the model indicates that the value investment model provides a little more consistency and a little more likelihood of achieving our investment goals. However, the numbers presented must be taken with a grain of salt. The dividend growth results are more inconsistent because there are more variables that can shake things up. This does provide a window into issues the DG investor must focus on.

First, maintaining a portfolio whose current dividend yield meets or exceeds 4% is very important. This may require an investor to stop automatic dividend reinvestment on positions which are overpriced, or to sell positions that are overpriced when there are better yields to be had. I understand this is uncomfortable for some, but I can think of no other way to encourage one's portfolio to stay within needed parameters.

Next, and somewhat related to the first point, dividend growth rates matter. However, if one is choosing between two positions that meet the investor's DG requirements, the investor should choose the position with a higher current yield, even if its historical dividend growth rate is somewhat smaller. This, of course, is a simplification. An investor can, and should, take into account the cash flow growth prospects for both companies and balance that information with current price and rates accordingly. However, that is up to each individual's skill sets and desires, and I can't account for that.

Finally, my Monte Carlo Simulation, with all its weaknesses, could be a powerful tool for the individual. I would recommend that any investor, DG or otherwise, adopt one adapted to their own investing rules and expectations, and actual purchases. As each year passed, the investor would get a better and better idea of how his/her plan is progressing, and what market conditions, if any, could disrupt the plan. By having established rules, and measuring the effects of those rules over time, an investor could tailor their holdings to meet their specific goals, without chasing yield, or over trading.

## Conclusion

The prospect that companies are forced by law to stop paying dividends may not be a realistic worry, but that doesn't mean there aren't legitimate concerns that could ultimately hurt the performance of a portfolio. Anything that would hurt company's ability to pay dividends resulting in long term lower yields, or lower dividend growth rates, would be deleterious to a DG investor's success.

For instance, increased taxes on dividends could reduce their appeal, resulting in a trend of lower dividend payments across the market. Overall long-term economic malaise impacting growth could produce poor performance, for DG investors and other equity investors alike. Finally, market forces that push equity prices too high early in a DG investor's accumulation, followed by stagnating growth, later could force the investor to fall short of his/her goals. Companies such as The Coca-Cola Company (NYSE:KO) and McDonald's Corp. (NYSE:MCD) may be appealing because of their long-standing performance and dividend history, but unless they offer a significant dividend yield, they can still hurt an investor's prospects in his/her retirement years.

All of these concerns can be mitigated somewhat through vigilance. Picking candidates with somewhat of a "value investor" mindset can improve long-term performance. Being mindful of cost will hopefully prevent complacency, which is probably the biggest risk of all.

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