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Sorry I hide my true identity but I'm a physicist/engineer, native contrarian and idea generator. I am an eclectic dividend investor with motto "In God We Trust, All Others Pay Cash" applied to companies I invest in. I like to read /and read a lot - did you look on my SA photo 8-)? /... More
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  • Single Factor Dividend Income Model. Part 1.  12 comments
    Aug 1, 2012 7:59 PM

    I want to expand famous Gordon (1962) model (a.k.a dividend discount model - see Wikipadia en.wikipedia.org/wiki/Dividend_discount_model ) 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

    or

    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 seekingalpha.com/instablog/725729-sds-se...) 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 (DG) investors (see dripinvesting.org/Tools/Tools.asp). To the best of my knowledge not so many US companies have steady negative DCR, an example is Tennessee Valley Authority (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 seekingalpha.com/article/419801-dividend.... 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 seekingalpha.com/instablog/725729-sds-se... please send me email via SA. See footnote 2.

    Another point I'm going to investigate is relation between yield (Y) and DCR. Some SA authors already compared Y with dividend growth rate (DGR) but I hope to apply better (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 seekingalpha.com/article/273656-how-bump...) 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 iijournals.com/doi/abs/10.3905/jpm.1991....) 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 seekingalpha.com/author/david-fish/articles and my blog seekingalpha.com/instablog/725729-sds-se... 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 www.tessellation.com/dividends and his SA articles) and DCR average was about 6.65% for last 100+ years in US (see seekingalpha.com/instablog/725729-sds-se...) /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

    Footnotes.

    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 (en.wikipedia.org/wiki/Deepwater_Horizon_...) 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" (http://seekingalpha.com/article/516181-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 web.iese.edu/jestrada/PDF/Research/Refer....

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Comments (12)
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  • SDS,

     

    Interesting.

     

    Figure 1 appears similar to a shifted Levy probability density function (scale parameter = 1/2) with the addition of a left hand tail.

     

    Kiisu
    27 Mar 2012, 05:13 AM Reply Like
  • Author’s reply » Kiisu,
    Thank you for stopping by. I try to collect more data points to see that function might fit. Stay tuned....
    SDS
    27 Mar 2012, 11:19 AM Reply Like
  • SDS, interesting and well done. As you know, I suspected the relationship was more complex than some d-g investors assume and this begins to show it quite clearly. I hope this provides some pause for thought for those that rely heavily on this metric.
    2 Apr 2012, 10:02 PM Reply Like
  • Author’s reply » Counterpoint,
    Thanks for comment. Well I think it is still not very complex but let's see if more data change my opinion.
    SDS
    3 Apr 2012, 12:55 AM Reply Like
  • Impressive work. Have you run these numbers ex-financials?

     

    My thinking on this topic is that financials and highly leveraged companies will significantly skew your cut data. It will also skew your portfolio inclusion rules. Reason is that leverage allows you to run up the dividend faster than your underlying economics, and that of course works in reverse on the back end.

     

    A simple filter for levererd non-financials would be to screen them based on credit rating higher than BAA or A and see what pops out.
    28 Apr 2012, 08:18 PM Reply Like
  • Author’s reply » No. I use all companies regardless their business.
    28 Apr 2012, 08:43 PM Reply Like
  • I would be curious. It might reduce your dividend cutter problem to insignificance. Many of the large cap dividend cutters were financial related, and accounted for a major part of the SP500 total dividend yield by 2008.
    29 Apr 2012, 02:29 AM Reply Like
  • Author’s reply » Well, I doubt because:
    (a) There is a kind of herd effect for div. cuts. But who know what is next industry there most cuts will occur?
    (b) I invest (and lost some $) in financials (it seems that it was possible avoid some losses as reported in my SA instablog post on banks).
    SDS
    29 Apr 2012, 08:18 AM Reply Like
  • My understanding is bank dividends are regulated. Banks cannot pay a dividend unless their regulator says they have enough capital, which is a matter of the regulator's opinion. I would look at leverage, and growing leverage rates, as an indicator of a future dividend cut.

     

    The only way financials make money is through leverage. For non-financials, you would have some utilities and telcos also highly leveraged. Cyclical industrie like autos have hidden leverage - their customer's need credit.

     

    It's a big topic.

     

    29 Apr 2012, 04:52 PM Reply Like
  • Author’s reply » Now it is correct at least for US banks. Because banks biz model is few hundred years old they know much more about leverage than I. The XXI century problem IMO - they became too greedy and unprofessional.
    29 Apr 2012, 07:14 PM Reply Like
  • I'm not sure what you mean by correct. The biggest dollar amount financial dividend payers like WFC and JPM are in the process of restoring their dividends after they were ordered to virtually eliminate them. Your data will show unusually high growth rates for the next few years. Others like BAC will take longer to restore. But all the dividends are highly sensitive to a narrowing of the spread between short and long rates. Then you could see sudden cuts or at least the elimination of the growth. It may not be their choice.

     

    I do not think the long term basics of dividend growth have been radically altered by the great recession for other sectors, just financials.

     

    And by the way, although banking has been around since the Medicis in the 1400s. But in its current form, with public insurance (FDIC) and regulations on capital structure, it has only been around since the 1930s. It underwent two major changes, with the Savings and Loan deregulation in the early 80s and again in the 90s with the gradual elimination of Glass Steigal and changes to other regulations and the rise of Basel 1 and 2.
    29 Apr 2012, 09:05 PM Reply Like
  • Author’s reply » "My understanding is bank dividends are regulated." - it is correct at least if bank took money from government. Banks evolve but their main purpose and ability to earn money didn't change.

     

    "I do not think the long term basics of dividend growth have been radically altered by the great recession for other sectors, just financials." - In long-term (10+ years) hopefully yes.
    29 Apr 2012, 10:40 PM Reply Like
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