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Single Factor Dividend Income Model. Part 1.

I want to expand famous Gordon (1962) model (a.k.a dividend discount model - see Wikipadia ) to make it a bit more realistic.

Assumptions, definitions and symbols

D - dividends in $, P - price in $

Yo - initial yield in % = Dividends in first year /purchase price = D1/P - see footnote 1.

N - number of years, N≥1, a.u.

<Value>N means average of Value during N years

Dn, Dn+1 - dividends during years n and n+1 in $

DCR - dividend change rate = (Dn+1-Dn)/Dn. I assume that dividends change ones per year. DCR unit is %. DCRm is dividend change rate during year M.

For Dn+1>Dn we can speak about dividend growth rate (DGR), for Dn+1=Dn we label dividends as flat, dividend cut is the case then 0<Dn+1<Dn, and dividend omission corresponds to Dn+1=0. Usually Y and DCR are counted in per-cents and D are counted on annual basis.

Dividends income during N years without reinvestment is


Yo*(1+ [SUMMA from 1 to N of DCRm]) = Yo*(1+ N*<DCR>).

The only single factor - negative <DCR> - reflects risk of income reduction for zero inflation case. Actually average inflation can be included into <DCR>.

Based on academic studies for companies with steady or positive DC history for at least 5 years (see I estimated probabilities of dividend changes (DC) for N>5 (fig. 1 and 2) for regular dividends

Fig. 1

Fig. 2

Here X=-100% corresponds to dividend omission, X=+100% corresponds to dividend doubling and in 1 case regular (not special) dividends were increased in 5 times.

David Fish's so called CCC list for ~ 500 companies with steady positive DCR is a prime source for most dividend growth (NYSE:DG) investors (see To the best of my knowledge not so many US companies have steady negative DCR, an example is Tennessee Valley Authority (NYSE:TVE) in 2000-2012 (footnote 3).

DC probability curve (fig. 1) is highly asymmetric because probability of positive DC is in ~ 4.5 times larger than probability of negative DC. Because many companies did cut dividends from almost any D2007 value to exactly 1 cent (per quater or per year) during 2008-201? recession and there is probably no practical sense to have dividend between 0 and 1 cent many company just omitted dividends at all. As the result, the probability curve bends up near left tail.

The cumulative plot (fig. 2) is restricted to DCR =100% where probability is ~ 99.69.

Selection N>5 in figs. 1 and 2 related to area of relative dividend cuts stability shown in fig. 3 again from plotted from academic papers.

Fig. 3.

One practical conclusion from fig. 3 that it makes more sense to invest in ""new born dividends had a longer life expectancy than 25 year old dividends" as Counterpoint mentioned in comments to On another hand, David Fish is correct that "companies that have reasonable prospects for growing earnings over the long term" (ibid.) have better chances to continue DG strike regardless of their CCC status. So for blind index-like investing Contenders seems more promising than Champions and for stock-picking investing status in CCC list probably not important.

I calculated annual dividends and DCR for S&P500 (fig.4) and found similar info for Euro50 index (fig. 5).

Fig. 4

Fig. 5

It seems interesting to compare actual DCR for US and non-US stocks with scholar papers I used. Because academics are not interested in some practical aspects of dividend investing I hope that real data and the comparison might shed light on proper function for DC probability because it is clear from figs. 1 and 2 that distribution is not normal. I'm collecting data about div cuts - if you have some in addition to please send me email via SA. See footnote 2.

Another point I'm going to investigate is relation between yield (NYSE:Y) and DCR. Some SA authors already compared Y with dividend growth rate (DGR) but I hope to apply better (NYSEMKT:IMO) methodology. Nevertheless from practical point of view a negative correlation between Y and DGR should exist and I'd expect to see a light positive correlation between Y and DGR stability (or might be bumpiness - see and stronger positive correlation between Y and negative DC. On another hand, recent 2008-201? crisis and high inflation ~ 1982 might screw up statistics.

IMO this model is better for dividend stocks (and only for these stocks!) than John C. Bogle's model (see his paper "Investing in the 1990s" in that rely on earnings growth. My model fits Occam's razor principle (see continuation of John C. Bogle paper titled "Investing in the 1990s - Occam's razor revisited" in Journal of Portfolio Management (Fall 1991): 88-91) very well with only tangible fundamental variable that is objective, transparent, and independent of accounting principle. Moreover, for many DG companies periodicity and pattern of dividends change are quite stable (see David Fish papers in SA on dividend increase expectations in and my blog on patterns). Even for companies without established pattern long-term DCR is quite predictable - it cannot be less than -100% and rarely exceed 100%. DGR is usually lower than 8% for time span above 25 years (see Robert Allan Schwartz's masterpiece at and his SA articles) and DCR average was about 6.65% for last 100+ years in US (see /footnote 3/.

Therefore, non-speculative return might be modeled by Yo and set of annual DCR. Total return for dividend stocks should also include speculative part that can be presented as change of Y with time.

25 March 2012


1. Addition 24 April 2012:

Yo was assumed equal to dividends in first year /purchase price. This assumption is almost correct when the stock purchase assumed as a single event was between announcement of (annual) dividend and ex-dividend date. The word almost here is reservation for very rare events when company doesn't keep it promises given in dividend announcement such as BP dividend reduction under political pressure caused by disaster of Deepwater Horizon oil spill ( or OTT dividend suspension on April 20, 2011 caused IMO by company short vision.

2. Addition 24 April 2012:

In good SA article "Dividend Growth Rates: Using The Past To Estimate The Future" ( the author compared Dividend Champions (known in 2012) data for 2 decades 1991-2001 and 2001-2001. Although the analysis contains the survivorship bias the author found slow down of dividend grow rate in second decade to compare with the first one. In contrast dividends of S&P500 (and many Dividend Champions are in this index) increased faster in the second decade - about 29% between 1991 and 2001 and about 69% between 2001 and 2011, see fig. 4. The reasons might be popularity of stocks buybacks in the first decade and some special dividends that happens between 1981 and 1991 (when S&P500 dividends increased ~ 84%) and in first decade of this century.

3. Addition 11 April 2013:

I used Yahoo data for TVE dividends, and added info about average DCR in the blog text.

An application of John Bogle approach for investing in modern time is presented in