## Background

I discovered Dividend Growth Investing last July and used that discovery as impetus for taking a more active role in managing my investments. Up until then, my investment philosophy had been simple: if the news is bad enough that i actually hear about it, put some more money into a small number of index and managed funds; otherwise, continue with regular monthly contributions.

I am particularly interested in building an income stream that grows at a faster rate than inflation over time. With that goal stated, one of the first questions that I ran into was "How many positions should my DG portfolio hold?" I've read recommendations anywhere from 15 up to 50 or more. As I haven't seen anything beyond personal experience (from people with long, distinguished track records), I put together a model using Google Spreadsheets to try to answer this question for myself. Ideally a reasonable number of holdings will be small enough that I can be confident in my ability to really understand and monitor each holding but large enough to provide safety against adverse events.

## Model Construction

Before describing the model I built, a disclaimer: Models represent idealized situations that are not always reflective of reality. They can help to think through decisions, but we should be careful to understand what goes into them and what they can and cannot tell us. Most importantly, in this particular case, each holding in a model portfolio acts independently of the other holdings.

That said, here's what I did. I created theoretical portfolios of 10, 15, 20, up to 75 holdings. Each holding was given an initial dividend yield, which was randomly chosen according to a normal distribution (bell curve) with mean 2.86% and standard deviation 1.47%. The mean and standard deviation were computed from the Dividend Champions on David Fish's current spreadsheet. I cut off the ends of the bell curve in selecting the initial yields to only select from the portion of numbers between 5% and 95% on the bell curve. I set a mean dividend growth rate of 8.4% with a standard deviation of 5.6%, numbers again computed from the most current list of Dividend Champions (using the 5 year CAGRs of the dividend growth rates).

Life would be good if dividends always grew, but sadly we have to make provision for a cut in the dividend or a dividend freeze. I had a lot more trouble finding historical data in this area, so I used rough estimates. In the first case, I gave a 5% probability of a dividend cut (by a percentage selected randomly from a uniform distribution) and a 18% probability of a dividend freeze, for a total 23% probability that a non-growth event happens. In the second case, I wanted to test a far more pessimistic scenario given by 10% probability of a dividend cut and a 25% probability of a freeze, for a total 35% probability of a non-growth event.

## Model Results

With these parameters established, I ran 40 simulations of yearly dividend growth for each of my portfolio sizes. Below, I list the overall results. For each portfolio size, I recorded the mean and median growth rates for the 40 events, the standard deviation of the growth rates, the minimal growth rate, and the maximal growth rate. Finally, out of curiosity, I assumed the growth percentages actually reflected yearly dividend growth and projected the growth in income stream from the starting point to year 40. To put the 40 year dividend income stream growth rate in perspective, 40 years at 3% inflation is 326.2%, and 40 years at 3.5% inflation is 395.93%.

With assumptions of a 5% probability of a dividend cut and 18% probability of dividend freeze, the results were:

Positions | Median | Mean | StDev | Min | Max | 40 Yrs |
---|---|---|---|---|---|---|

10 | 5.92% | 4.04% | 5.59% | -12.52% | 10.14% | 458.78% |

15 | 5.52% | 3.89% | 4.86% | -9.72% | 9.33% | 440.86% |

20 | 5.01% | 3.74% | 3.63% | -5.89% | 9.26% | 423.92% |

25 | 4.97% | 3.71% | 3.63% | -3.06% | 9.07% | 421.06% |

30 | 4.43% | 3.80% | 3.19% | -2.82% | 9.31% | 436.83% |

35 | 4.49% | 3.94% | 2.87% | -1.11% | 9.82% | 461.45% |

40 | 4.87% | 4.05% | 2.53% | -1.04% | 7.52% | 484.39% |

45 | 4.51% | 4.11% | 2.26% | -.29% | 7.41% | 496.81% |

50 | 4.41% | 4.17% | 2.23% | -.69% | 7.34% | 507.52% |

55 | 4.29% | 3.99% | 2.08% | -.02% | 7.53% | 474.67% |

60 | 4.21% | 4% | 1.92% | .18% | 6.9% | 476.3% |

65 | 4.30% | 4% | 1.84% | .18% | 6.72% | 478.04% |

70 | 4.27% | 4.05% | 1.83% | -.83% | 6.5% | 485.75% |

75 | 4.25% | 3.98% | 1.79% | -.29% | 7.09% | 473.3% |

I broke out portfolios of sizes 15, 45, and 75 for a closer look. Below are three scatterplots showing the simulated dividend growth rate for each trial.

With assumptions of a 10% probability of a cut and 25% probability of a freeze, the results were:

Positions | Median | Mean | StDev | Min | Max | 40 Yrs |
---|---|---|---|---|---|---|

10 | .7% | -.71% | 7.01% | -24.13% | -18.71% | 67.8% |

15 | 1.08% | -.52% | 6.36% | -18.71% | 7.18% | 74.74% |

20 | .63% | -.72% | 6.01% | -16.10% | 7.47% | 69.49% |

25 | .94% | -.9% | 5.52% | -14.96% | 6.91% | 65.5% |

30 | .19% | -.76% | 4.87% | -12.36% | 6.52% | 70.23% |

35 | .26% | -.41% | 4.35% | -11.84% | 6.32% | 81.69% |

40 | .24% | -.27% | 3.75% | -9.72% | 5.71% | 87.13% |

45 | -.49% | -.59% | 3.72% | -9.05% | 5.44% | 76.90% |

50 | -.5% | -.58% | 3.59% | -8.42% | 5.63% | 77.11% |

55 | -.11% | -.57% | 3.16% | -6.94% | 5.13% | 77.96% |

60 | -.46% | -.74% | 3.23% | -7.07% | 5.02% | 72.70% |

65 | -.43% | -.58% | 2.81% | -6.36% | 4.18% | 78.06% |

70 | -.14% | -.39% | 2.71% | -6.37% | 4.2% | 84.43% |

75 | .13% | -.34% | 2.53% | -5.9% | 4.2% | 86.15% |

## Observations and Conclusions

Thinking about the results of these two simulations, several thoughts occur to me:

- In the first scenario, it looks like about 40 - 50 holdings is a good number if one is able to play darts with a stock market that behaves according to the model.
- In the second scenario, the range is around 35 - 50 stocks and then more than 70. In a much more adverse market, the larger number of holdings provides more opportunities to offset income declines.
- The 40 year dividend growth numbers are a bit silly since a single holding's dividend growth rate year after year is highly unlikely to be randomly determined each year as in this model, but I suspect it's not a bad worst case scenario estimate.
- Adverse dividend events are going to happen, and there may even be some really rocky years, but the overall strategy appears sound over a long time horizon. Unless of course the basket of dividend growth stocks decides to behave like scenario #2.
- Smaller numbers of holdings can perform remarkably well, particularly if careful stock picking can reduce the likelihood of a dividend cut or freeze. My current reaction is that limiting downside is more important than going for dividend growth rate home runs.

As I continue to build my dividend growth portfolio, I will probably aim for 30 - 40 holdings, up from the 20 - 30 holdings I had been considering before this thought experiment. This is as large as I think I can realistically monitor, and I feel that careful monitoring to protect against adverse dividend actions will have a more powerful effect than using more diversification and less monitoring (or longer nights spent doing research instead of other things) to offset losses. In several years after I am more comfortable with my investment process, I may look to decrease the number of holdings. I also think this thought experiment will help me to stay the course should I experience a "bad" year or two early in the portfolio's life.

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