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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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  • Universal Elements Of Smart Stock Investing

    I have read more than 300 books on investing (mostly stocks) with different points of view. As a physicist I know that good theory base on very few postulates (Occam's razor principle), so I think it should be quite few universal elements of smart stock investing regardless of the investment style. From these 300 books, numerous SA & scholar papers, and from my brain I'd select only 5 elements:

    a) Buy the bests low.

    b) Keep you milky cows (firms which pay and will pay reasonable dividends).

    c) Look forward but remember history.

    d) Sell a former "best" if even distant future for it is negative.

    e) Ignore noise.


    22 July 2015

    Jul 22 10:29 AM | Link | Comment!

    DGI goal

    The prime goal of dividend growth (NYSE:DG) investing is to have reliable adequate cash stream from dividends which rising more than real inflation during the distribution phase in the country a person expect to live.

    Let assume for the moment that DG portfolio produced adequate cash stream in the first year just after the person retirement. The cash needed in the following years of retirement is growing with time because of inflation, and DG stocks provide such outcome. Unfortunately, sometimes companies stop DG (dividend freezes) or even cut or omit dividends. If such "non DG investor friendly" companies represent a significant part of portfolio, such portfolio cannot satisfy the major goal of DG investing.

    In order to achieve the above mentioned goal the person should have a portfolio of DG stocks. Because DG portfolio prime focus is income from dividends and capital gains are less important price volatility isn't so essential. Hence, traditional "zig-zag" approach for estimation of the portfolio size doesn't work. This "zig-zag" approach presumes that when prices for some stock rise (zig), prices of other stocks in portfolio decrease (zag). Investors whose prime goal is total return defined mostly by realized capital gains should understand its components and their dynamics, which is are not obvious and still debating by economist - see Also while prices are usually change gradually and they can be modeled by lognormal distribution, dividends changes "suddenly" on several percents (with lower limit -100% for a dividend omission). Time dependence of dividends reminds rather a telegraph noise than smoth distribution (see e.g. the figure 3B below). Hence estimation of reliable DG portfolio size should be based on another principle than price volatility. This article outline such attempt.

    The major risk for a DG investor is loss of required cash stream, e.g. due to dividend cuts, hyperinflation or errors in DG portfolio assembly. In order to address this risk, I propose a new method for estimation of DG portfolio size. I'll calculate also number of stocks in DG portfolio for different investor's habits and skills.

    Main Equation

    Let me start from empirical equation and then explain and provide numerical estimation for each term of this equation.

    DG portfolio size = (K1+K2)/K3*(DCR-RI) (1)

    Here Ki (i=1,2,3) are positive coefficients which reflect the investor's habits and skills, DCR is investor's portfolio dividend change rate (changes can be negative, zero or positive, in the last case we usually talk about DG rate or DGR), and RI is real inflation the investor faces.

    Real Inflation

    I expect that during the person retirement RI is positive because "good small inflation" ( is almost official policy in many developed countries with relatively big debt distributed inside the country and abroad. Ideally DG portfolio should beat inflation each year, but probably it is impossible if most of dividends are withdrawing by the investor.

    I use Prof. Robert Shiller data for post-WW2 period (when economists sold US politicians idea of "good small inflation") to make the figure 1A, where annual DCR and annual changes in inflation (represented by Consumer Price Index or CPI) are plotted. Negative DCRs in the figure 1A reflect peaks in number of dividend cutters shown in the figure 1B.

    Figure 1A. Annual changes in dividends and CPI in USA.

    Figure 1B. Time dependence of dividend cuts in USA

    For the period shown in the figure 1A the average / medium DCR were about 5.45% and 5.02% during this period with sigma about 5.66%, while average / medium CPI changes were about 3.65% and 2.99%. In about 40% of years DCR was smaller than CPI changes, hence the prime DG goal is not so easy to achieve.

    Unfortunately, an investor cannot often rely on official inflation numbers. My non-systematic observations of reported inflation in various countries with different governments from communist to socialist and to almost pure capitalist show the same picture - any government understated inflation because it has incentives to do this. ( Probably absolutely pure capitalist government would not cheat but at least in USA with quite big groups of people live communism-like life (e.g. welfare recipients in N-generation whose themselves as well whose grand-parent and parents had never work) this is not the case.

    On another hand, independent calculations of inflation are sometimes a little bit too pessimistic ( Also life style during retirement is not uniform (in average we travel more in 65 and need more medical help in 85) as well as inflation is different in various sectors of economy as the figure 2A shows.

    Figure 2A. Recent inflation in USA. Note that in average retiree spend less for housing and education while more for medical care than average population.

    As expected, the inflation rates were different in various countries, as the figure 2B shows. Hence investor needs to know the history of inflation in her country.

    (click to enlarge)
    Figure 2B. Recent and historic inflation in some developed countries.

    In my mid-fifties I'm heading retirement at the end of 2015 in USA. I'd assume to face average real inflation at 5% during my hopefully 45 years of retirement. Recent fiscal policies (QE, ZIRP) in US, European Union and some other developed countries created a possibility of huge inflation in next decade, but it seems (from Treasuries like official bonds yield) that market assume that economists in the majority of developed countries will handle excess fiat money problem smoothly.

    Dividend Change Rate

    Historically US companies delivered positive average DCR or DGR equal to 6.55% during last 100+ years, while stocks included in S&P500 index had average DGR = 5.57% during years 1995-2010 (( This so-called magic number is almost identical to inverse P/E ratio for US stocks during the same period. A Stanford economist, I discussed this finding with, thinks that this is not coincident. I consider that such mean DCR=6.55% probably reflect that average stock market is efficient at the scale above one century. It is also worth to note that 2X expansion of US index from S&P500 to small caps (C&A Market 1000 index in the link just mentioned) produced ~ 1% higher DGR especially in most recent analyzed period, although both indexes contain non-dividend stocks.
    Prof. Shiller's dataset for US stocks as well as many popular indexes like S&P500 or Dow Jones U.S. Broad Stock Market Index do not aimed to represent any DG portfolio, so DCR should be obtained from adequate data set. Fortunately, David Fish created and maintained list of US Dividend Champions (so called CCC list) and some of his followers recently started similar lists for some other countries ( ).
    Unfortunately very useful CCC list cannot be used for estimation of average DCR because of survivorship bias and as the result elevated DGR. Calculation of 10-year DGR for almost survivorship-free reconstructed CCC list ( lead to average DGR about 6.4% which is close to the abovementioned magic number, but lower than it because selected period contains 2008-2010 great recession.
    DCR depends on many factors, e.g. on firm size as shown in the figure 3A or on geographic location as shown in the figures 3B and 3C. Probably higher DGR for small firms than for blue-chips can be explained by life-cycle business model (see e.g. and

    Figure 3A. Recent nominal DCR in USA for different firm sizes.

    Figure 3B. Recent nominal DCR in European Union. Just compare with USA.

    Although I used to have literally perfect crystal balls made from monocrystalline Silicon (used for infrared optics of advanced weapons), I cannot predict future DCR and RI. I expect that during long run average DGR delivered by US companies will be about 6.55% in XXI century i.e. the same as it was more than 100 years ago.
    Any investor can increase personal DGR due to full and partial reinvestment of dividends, and I will count this factor as one of the habits coefficients soon.

    As the result the value of (DCR-RI) in the equation (1) is 1.55% for US stocks which close to numbers (1.2% - 1.6%) of leading economist (see the figure 3C and

    (click to enlarge)

    Figure 3C. (DCR-RI) in academic studies.

    Unfortunately, an investor practically cannot control (DCR-RI) value, except (if possible) to live in the country with low inflation and stable currency ratio to compare of currencies dividend are paid in countries with expected high DGRs. I'm not sure that such combination (stable low inflation, long-term average DCR above this inflation and non-volatile currency ratio) exist. Also there is no DG culture in emerging countries where economists expect to see high growth rates well above local inflation in XXI century.

    Investor's Habits/Skills Coefficients

    It is quite difficult to assign numbers to a person habits and skills, especially than we have "chicken and egg" type of problem when we need to know a number to estimate portfolio size and the same portfolio gather the same number. Fortunately both K1 and K2 discussed soon are mostly weak functions, so errors in the following assumptions should not affect result strongly.

    Reinvestment coefficient K1

    Safety or reliability is well known principle in design of artificial objects, such as bridges, cars, semiconductor chips, and… investment portfolios. The margin on safety concept application to the stated above DG portfolio goal means that not all cash stream produced by the portfolio is consumed i.e. a part of the cash stream can be re-invested. I model the reinvestment as

    LN(100 - CS)/e

    for adequate cash stream produced by dividends (when the investor doesn't touch principal capital), and as

    LN(100 + A*W)/e

    for cash stream which is lower than investor needs. Here LN is the natural logarithm, e is constant with value about 2.72 (calculated as EXP(1) in MS-Excel), CS is average percentage of cash stream due to dividends spend, W is average percentage of principle capital withdraw from portfolio (e.g. using infamous 4% rule) during the distribution phase, A is "punishment" factor which is probably in the range 10-20.

    Calculation of K1 for reinvested dividends / portfolio withdraw is presented in the figure 4A. I choose A=15 for the calculation below. I must admit that I'm not going to spend my principle and hence not very familiar with nuances of such approach, so my guesstimation of A value might be incorrect. On another hand, intuitively a person in such situation is more sensible to any losses in dividends, hence her DG portfolio should be more diversified and curve should has larger slope than a portfolio of DG investor who can reinvest some dividends.

    (click to enlarge)
    Figure 4A. Dependence of K1 coefficient from portfolio cash flow.

    In my opinion a DG investor should create portfolio which will allow to reinvest back in average 10%-25% of dividends during retirement. In this case K1 is about 1.6. Assuming for a moment that K2 is zero. In this case the DG portfolio size is a little bit more than 100 different equities.
    If an investor needs to withdraw a part of her portfolio she should use K1 between 1.75 and 2 depending on withdraw rate. If this rate exceeds 7% the investor should seriously think about her life-style during the accumulation phase and safe more money for retirement. Coefficient K1 is about 1 for investor who spends in average only 15% of dividend cash stream during retirement. In this case reliable DG portfolio should consist of about 65 different securities for zero K2 coefficient. If an investor can re-invest above 85% dividends during the distribution phases she probably doesn't need to worry about her retirement and portfolio at all.

    Although it is difficult to know K1 value in several years before retirement, a DG investor might adjust her portfolio just prior retirement to expected CS usage.

    Coefficient of portfolio clustering K2

    The assumption that K2 is zero is valid only in the case if all stocks in DG portfolio are uniformly dispersed between different industries and countries. Unfortunately, dividend growth culture is rare and exists mostly in Great Britain and some countries which were Great Britain colonies (USA, Australia, Canada, and to less extend Hong-Kong). Fortunately, several DG companies from these countries operate as multinational or even global (e.g. Coca-Cola, Johnson & Johnson). Therefore a DG investor might reduce geographical clustering and behavioral home base bias at least partially. Also few companies in David Fish's CCC list are non-US based (with stocks traded in USA) but these companies are often less sustainable for the list selection criteria because of currency fluctuations. In my opinion DG culture should be evaluated in native company currency because DG investor should have long term horizon (even at the beginning of retirement because average life span is now 85 years and hopefully will grow with progress in medicine). Hence the DG investor may ignore the currency fluctuations especially if she has room in cash stream and can reinvest some dividends.

    Unfortunately, DG companies are also cluster in some industries: from currently 726 companies in CCC list about 80 are regional US banks (including very small ones), about 50 are utilities and about 30 work as diversified industrials and midstream oil & gas companies. In average each of industry in CCC list is represented by 6 companies. Fortunately, there are more than 100 different industries in David Fish's list of stocks traded in USA and the CCC-like lists for non-US stocks (not as well developed yet) also give a DG investor valuable choices in industries selection.

    At any given day it is possible to design DG portfolio with equal income out of each company and industry they invest in. Such equal income portfolio is very fragile because companies have different DCR and DCR of a single company is usually changes with time. At least annual rebalance of portfolio for equal income is needed. If the portfolio value is smaller than 10M$ the rebalance is more profitable to a broker than to investor. Such equal income DG portfolio can be described by simple clustering coefficient


    where LG is decimal logarithm, Ns is mean number of stocks in a representative industry and Ni is number of independent industries.
    Usually DG investors tilt their portfolio to few industries they are familiar with or confident in their long-term future. For example my DG portfolio contains probably more semiconductor stocks than average DG investor has. I usually invest the same amount of money into each company but my initial and following yield on cost are different. The drawback of such clustering is historical evidence that companies in the same industry (country) tend to cut or omit dividends at the same time as the figures 4B and 4C show.

    Figure 4B. Clustering of dividend omissions at the top level of Standard Industrial Classification (SIC) granularity (see is shown in red boxes (values above 2 sigma of symmetrized distribution of the tables numbers).

    Figure 4C. Distribution of Cutters and Non-Cutters across industries over the 40-year period 1965-2004. Red/green boxes are industries with more/less dividend cuts than the average just based on my eye-scrolling.

    Recent examples of dividend cuts clustering within an industry are US banks in 2008-2010, coal producers in 2013-2014 and oil sea-drillers in 2015. Analysis of dividend cuts is out of this article scope and will be discussed elsewhere (see
    When DG portfolio is designed to be non-uniform, clustering coefficient K2 can be expressed through the Fano factor ( as


    Here Ds is dividend from investment in a company S, Do is the minimal dividend from one of the S companies in different industries, and, hence Ds/Do is relative weight of income stream from the company S, M is the mean and V is the variance of (Ds/Do) distribution (or sigma square of it).
    As expected for both DG portfolios considered in this section diversification across different industries is an important factor of portfolio design.

    Analysis of DG portfolios of some UK trusts with long DG histories (see below in the next section) and few diversified portfolios of SA members show that values of K2 are usually in range 0.05-0.25.

    Stock picking ability K3

    We have now numerical values for most terms of the equation (1). Assuming for the moment that K3=1, and using RI = 5% and for US-based DG investors in XXI century with K1=1.6 and K2=0.1 for calculations of DG portfolio size, we obtain 113 different equities {(1.6+0.1)/1*(0.065-0.05)} in a DG portfolio. This number looks like di-worsification rather than diversification at the first glance, hence the assumption that K3 =1 needs to be examined.

    Actually it is really hard to quantify K3 (at least for me - I spent significant time thinking how to do it), so I'd start from the upper and lower limits.
    If a DG investor has absolutely perfect stock picking skills she needs only single the best stock with ideal DG pattern (no freezes or cuts) during let say 30 years before and 30 years after her retirement. In this case K3 is at the upper limit which is about 40 (actually for her K2 =LG(2) is about 0.3, and DG is probably above 0.065 but perhaps below 0.1 (see for such long run as few decades).
    If a DG investor has absolutely terrible stock picking skills she needs to have "whole market" according to MPT pundits or all DG stocks. There are about 700 stocks traded in USA in David Fish's CCC list and about 300 DG stocks traded only outside USA in similar lists. Actually such unskilled DG investor does not need to have ~ 1000 various stocks because redundancy is high in some industries there companies do not compete with each other but face the same macro-factors which might lead to dividend cuts (e.g. regional banks in USA, midstream oil pipelines). On another hand, for industries with active competition such unskilled DG investor should adopt the coherent risk approach and spreads bets uniformly within such industries (see to reduce idiosyncratic risk of dividend cuts in weak companies. For example I'd prefer to split my invested capital between Visa and Mastercard that deploy all money into one of these companies. A very initial analysis of companies in various CCC lists shows that probably about 450 stocks represent whole non-redundant DG universe. Hence, the K3 coefficient is about 0.25 for the DG investor unskilled in stocks selection. Probably a cheap diversified DG fund is the best choice for such unskilled DG investor, but unfortunately there is no such fund in US with reliable DG history (see and other David van Knapp SA papers on DG ETFs and funds). There are few closed-end DG funds (trusts) in UK with DG history above 40 years ( Interestingly that the trusts with the oldest DG histories (like Bankers Investment Trust, Alliance Trust and City of London) not being index funds keep from 75 (plus half-dozen of funds) to more than 200 equities in their portfolios. It can be translated to K3 in the range about 0.4 to 3 for these active fund managers with presumably some stock picking skills which are one-two orders of magnitude smaller than the absolutely perfect stock picker has. Each of these fund managers has back-up from several analysts who specialize in only couple of closely related industries but still they are only in about dozen times better in stock selection than unskilled DG investor.
    I expect that very few small self-directed investors know more than half-of-dozen industries deep enough to compete with Wall Street in capital gains game. Fortunately a DG investor she can limit analysis with non-precise long-term (10-20 years) vector of demand from industry and company (like declining, weakly or strongly growing to compare with GDP/inflation, relatively stable, etc.) and forms her DG portfolio accordingly. Such analyses of different industries will definitely have mistakes but if the DG investor can allow modest re-investment even during distribution phase (e.g. has some margin of safety) she will not hurt by these mistakes. On another hand, crowd might solve investment problems better than analysts and Seeking Alpha is good tool to form collective wisdom especially in such aspects as dividend cuts. Also a DG investor can use results of analyses and rating from different WWW sites beyond SA like Morningstar, but in all cases nothing is 100% correct.
    In summary of mussing stock picking ability of a DG investor, I think that reasonable estimate for K3 is in the range from about 0.3 to about 2. Hence our initial assumption K3=1 is in the ballpark and investor with such skills should have about 100 equities from different industries of companies which operates in several countries.
    Of course each DG investor should estimate all numbers for her portfolio and plug them into the equation (1) to figure out the portfolio size. I'd only suggest not to be very optimistic about economy in your country and about your skills and habits.

    There are 2 ways to reduce impact of the dividend cuts - diversification and the cut forecast. The first way (proper diversification of DG portfolio) is discussed here. I'm forming research team to create good cut forecast industry-dependent proprietary models. The work supposes to start this fall. Send me SA email if you want to participate in the team.


    Size of DG portfolio depends on investor financial situation and her habits and skills. Country economy also influence on DG portfolio size. In my opinion most DG investors should have between about 100 and 150 equities of companies from different industries and operating in various countries.

    DGI is a good strategy ONLY if you will spend retirement in the country where expected average RI is smaller that expected DCR from you portfolio.

    Questions to readers:
    What other K coefficients should be count?
    What functional form K3 should have?


    14 July 2015

    Jul 15 2:07 AM | Link | 8 Comments
  • Book Review: "Investment Management: A Science To Teach Or An Art To Learn?"

    CFA Institute Research Foundation published recently the excellent book "Investment Management: A Science to Teach or an Art to Learn?" written by Frank J. Fabozzi, Sergio M. Focardi and Caroline Jonas.
    In this short (~ 120 pages) book contributors from academia and the industry presented their views on what should be change in the education of future investment professionals.
    Most of contributors agree that mainstream financial economics MPT, CAMP, EMH are strongly flawed and practical aspects such as Portfolio Optimization, Risk Measurement in current form cannot paste with reality of financial markets. Outlined proposals to change curriculum are also quite interesting.
    I think this free book is very useful not only for MBA/PhD-finance students and their professors but also for all institutional and individual investors.

    I can email the book (pdf file ~ 1.5Mb) upon a request.


    17 June 2015

    Jun 17 3:32 PM | Link | Comment!
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