In an article by Robert Allan Schwartz entitled * How Bumpy Are Your Dividends?* published on June 7, the author presented an example of two companies with the same initial dividend and ten years later the same final dividend. Because the initial and final dividends are identical, both have the same Dividend Compounded Annual Growth Rate (also known as a Dividend Growth Rate, or DGR) of about 17%.

Mr. Schwartz makes the point that selecting the company with the “smoother” history of dividend increases provides a planning advantage for those who depend on dividends for meeting their retirement expenses. That seems logical.

However, as a retiree with fixed expenses (or in some cases, expenses with an expected rate of increase), I want to know “will I have the funds to cover those expenses?” Or, from an investment perspective, “**which dividend growth companies should I buy (or avoid) to maximize my yield while minimizing the likelihood of erratic dividends, so I can reasonably plan for my future expenses?**”

How to best maximize yield with dividend growth companies is, I believe a personal decision - one that depends on individual biases and perceptions of risk. For example, all else being equal, my “ultra-conservative” biases direct me away from companies with negative net cash (i.e. more debt than cash). To me, those companies represent a risk I am unwilling to accept for initial entry into my dividend growth portfolio. Other investors, with a better understanding of the circumstances, may find those companies acceptable.

If maximizing yield is subject to personal biases, is there a general rule for minimizing the likelihood of erratic dividend payments? Will minimizing bumpiness minimize dividends? How much bumpiness must I accept for an acceptable dividend yield?

I don't have a clairvoyant crystal ball. And I don't get next week's Wall Street Journal today. However, I do have access to David Fish's Dividend Champions spreadsheet of 449 companies that have a meaningful history of dividend increases. But I have to ask, “is the Champion spreadsheet a representative sample” and can we use it to better understand dividend bumpiness? If so, how? The spreadsheet is available here.

**Is the Champion spreadsheet a representative sample?**

Various sources show about 17,000 publicly traded US companies. A stock screener typically provides access to a smaller subset of companies. For example, the Scottrade stock screener found here lists 10,879 companies with a current stock price above zero, while the Zacks BETA screener found here lists only 7,764 such companies. On the other hand, the Yahoo Java stock screener found here lists 4,294 companies with a current stock price above zero. Of those, 2,042 are companies with a current price at or above $5.00 that also pay a dividend of at least a penny.

In the spreadsheet, the lowest price is for United Community Bank (NASDAQ:UCBA) $6.57. The lowest current annual dividend is for Aaron's Inc. (NYSE:AAN) $0.05. Searching the Yahoo stock screener for companies at or above those values of price and dividend lists 1,935 companies.

The Champion's spreadsheet of 449 companies thus represents about 23% of Yahoo's universe of companies with similar or better values of price and dividend. However, as dividend growth investors we want not just companies that pay dividends, but companies that pay increasing annual dividends. And for that subset of dividend paying companies, I am aware of no other source of readily available free data.

To summarize, the spreadsheet represents:

- 23% of Yahoo screener listed companies with a similar
**minimum**price and dividend. - 100% (barring errors) of the companies that have consistently increased annual dividends for at least five years.

Thus, using the spreadsheet for further analysis seems reasonable.

**What factors predict dividend bumpiness?**

Prediction is not causation. For example, observation shows that when my watch shows noon, the local church bells ring. Thus, my watch is a predictor but, in this reality, my watch does not cause the ringing. I cannot reset my watch and bewilder the local pastor by the unexpected ringing of his church's bells.

So, what factors might predict dividend bumpiness? In discussions with Mr. Schwartz and Mr. Fish, Dividend Growth Rate (DGR), years of available data, average dividend and Average Annual Dividend Growth Rate (AADGR) were identified as potential predictive factors.

DGR is the smoothed annualized gain in dividends over a given time period. DGR is based on the generalized formula for CAGR found here with the caveat that the starting and ending values are the actual dividends paid for t_{o} and t_{n}.

The AADGR is the average of the all the single year dividend growth rates over a given time period.

The difference can be demonstrated with Mr. Schwartz's original example. While the DGR for both company “A” and company “B” is the same at 17.29%, the AADGR is different, as it is the sum of the nine single year DGRs which is then divided by nine. The AADGR for company “A” is 19.02% and unsurprisingly, the AADGR for “B” is the same as its DGR, 17.29%. (For the details see here.)

For the analysis, I discarded data for years with zero dividends and discarded dividends prior to a dividend decrease. Discarding such data is not a problem as I'm dealing with dividend growth companies, which I've interpreted as companies that have a history of non-zero and non-decreasing dividend payments. For example, Alliant Energy Corporation (NYSE:LNT), a dividend Challenger, paid a $2.00 annual dividend for the years 1999 through 2002. In 2003, the company cut the dividend to $1.00. Thereafter, the company consistently raised its dividend. In order to maintain data with non-decreasing dividends, the dividend payments for 2002 and prior years were discarded. Discarded data were not used in any subsequent calculation.

How well does each factor predict dividend bumpiness? A “Linear Correlation and Regression” statistical analysis shows:

- Years of data
**do not**predict dividend bumpiness. - Average annual dividend
**does not**predict dividend bumpiness. - DGR predicts only a small fraction (~30%) of the population's dividend bumpiness.
- AADGR is an excellent predictor, predicting more than 90% of the population's dividend bumpiness.

Better yet, an analysis of the statistical trend line shows a high likelihood of achieving zero dividend bumpiness with a maximum of 8% AADGR. However, once that modest “average annual dividend growth rate” is exceeded, the probability of dividend bumpiness grows rapidly as shown below:

**Table of Bumpiness Coefficient as a function of AADGR**

AADGR | BumpinessCoefficient |
---|---|

8% | 0.0 |

10% | 1.5 |

15% | 5.2 |

20% | 8.9 |

30% | 16.4 |

50% | 31.3 |

A bumpiness coefficient of 100 means “one standard deviation”. Based on the analysis, a generalized rule for zero bumpiness is to look for companies where the maximum “Average Annual Dividend Growth Rate” is about 8%.

How well does such a rule match the reality of the CCC companies?

There is only one company with a zero BC - Tootsie Roll Industries (NYSE:TR).

If we expand the acceptable minimum AADGR to 10%, we find:

67 Champions. However, there are 62 Champions with a BC of 1.5 or less. 58 of those two groups overlap. The 10% AADGR also identifies 9 companies with a BC greater than 1.5 and misses 4 companies with a BC of 1.5 or less.

63 Contenders. However, there are 51 Contenders with a BC of 1.5 or less. 43 of those two groups overlap. The 10% AADGR also identifies 20 companies with a BC greater than 1.5 and misses 8 companies with a BC of 1.5 or less.

54 Challengers. However there are 29 Challengers with a BC of 1.5 or less. 28 of those two groups overlap. The 10% AADGR also identifies 26 companies with a BC greater than 1.5 and misses 1 company with a BC of 1.5 or less.

As a rule of thumb, the AADGR is not perfect (but rules of thumb never are) as it only correctly identifies ~87% of the Champions, ~68% of the Contenders, and ~52% of Challengers with minimum bumpiness.

So which Champions with minimal BC did the AADGR correctly identify?** **

**Correctly Identified Champions**

Symbol | AADGR | BC | Yield |
---|---|---|---|

CWT | 0.0084 | 0.09 | 3.25 |

ED | 0.0097 | 0.09 | 4.52 |

MGEE | 0.0122 | 0.13 | 3.60 |

CTWS | 0.0150 | 0.16 | 3.69 |

MSEX | 0.0178 | 0.14 | 3.89 |

AWR | 0.0182 | 0.40 | 3.24 |

WGL | 0.0194 | 0.26 | 3.95 |

HCP | 0.0270 | 0.60 | 5.06 |

FUL | 0.0285 | 0.27 | 1.35 |

NWN | 0.0297 | 0.58 | 3.85 |

TR | 0.0300 | 0.00 | 1.09 |

BHK | 0.0301 | 0.26 | 4.71 |

WSC | 0.0304 | 0.10 | 0.43 |

IRET | 0.0310 | 0.86 | 7.08 |

WC | 0.0335 | 0.24 | 4.89 |

PPG | 0.0335 | 0.51 | 2.57 |

PBI | 0.0335 | 0.89 | 6.20 |

SON | 0.0364 | 0.53 | 3.27 |

UBSI | 0.0366 | 0.59 | 4.95 |

NFG | 0.0367 | 0.11 | 1.92 |

WRE | 0.0375 | 0.68 | 5.02 |

FRT | 0.0376 | 0.62 | 3.06 |

SWK | 0.0401 | 0.26 | 2.22 |

TNC | 0.0412 | 0.87 | 1.76 |

UW | 0.0419 | 0.68 | 4.55 |

HP | 0.0422 | 0.64 | 0.38 |

GPC | 0.0428 | 0.66 | 3.28 |

EGN | 0.0438 | 0.60 | 0.87 |

SCL | 0.0440 | 0.76 | 1.55 |

STR | 0.0446 | 0.64 | 3.52 |

NDSN | 0.0454 | 0.66 | 0.81 |

PNY | 0.0456 | 0.27 | 3.69 |

BWL.A | 0.0458 | 0.99 | 4.89 |

SJW | 0.0495 | 0.48 | 2.96 |

RPM | 0.0518 | 0.80 | 3.57 |

T | 0.0523 | 1.08 | 5.45 |

CLC | 0.0529 | 1.09 | 0.99 |

BCR | 0.0549 | 0.69 | 0.64 |

DBD | 0.0552 | 0.82 | 3.39 |

MMM | 0.0596 | 1.24 | 2.33 |

ABM | 0.0618 | 0.68 | 2.46 |

TDS | 0.0619 | 0.43 | 1.44 |

CSL | 0.0626 | 0.91 | 1.40 |

BMS | 0.0658 | 1.19 | 2.90 |

LANC | 0.0663 | 0.94 | 2.18 |

EMR | 0.0674 | 1.50 | 2.53 |

XOM | 0.0695 | 1.01 | 2.25 |

BRC | 0.0734 | 0.96 | 2.09 |

MHP | 0.0742 | 1.00 | 2.35 |

CTBI | 0.0783 | 1.50 | 4.44 |

CB | 0.0797 | 1.47 | 2.38 |

PNR | 0.0828 | 1.44 | 1.98 |

DOV | 0.0847 | 1.08 | 1.64 |

KMB | 0.0878 | 1.18 | 4.10 |

BF.B | 0.0892 | 1.17 | 1.77 |

ABT | 0.0918 | 1.32 | 3.67 |

CINF | 0.0931 | 1.30 | 5.26 |

KO | 0.0966 | 0.72 | 2.81 |

Which minimal BC companies did 10% AADGR not identify?

**Unidentified Champions**

Symbols | AADGR | BC | Yield |
---|---|---|---|

PG | 0.1058 | 0.60 | 3.13 |

FDO | 0.1078 | 0.61 | 1.29 |

MKC | 0.1078 | 1.32 | 2.23 |

JNJ | 0.1314 | 0.93 | 3.39 |

And which companies did 10% AADGR mis-identify?

**Mis-identified Champions**

Symbol | AADGR | BC | Yield |
---|---|---|---|

GRC | 0.0524 | 2.30 | 1.03 |

PH | 0.0833 | 2.03 | 1.67 |

NC | 0.0899 | 3.27 | 2.18 |

HRL | 0.0900 | 1.66 | 1.74 |

ORI | 0.0944 | 2.09 | 5.63 |

OBSH | 0.0963 | 2.30 | 2.15 |

APD | 0.0973 | 1.58 | 2.44 |

VAL | 0.0987 | 1.54 | 1.87 |

CLX | 0.0995 | 2.41 | 3.41 |

The mathematical and logical details for the analysis are here.

An analysis of the computations mathematical complexity are here.

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