Executive Summary
Portfolio123 Equity Strategies are based on a uniform approach that attempts to profit from security mispricing in the equity market. It reflects our assumption that opportunities exist because the equity market is not perfectly efficient.
Our approach is inspired by the nowiconic Gordon Dividend Discount Model^{1}, the Treynor^{2}, Sharpe^{3} and Lintner^{4} Capital Asset Pricing Model, a Robert Shiller 1984 Brookings Institution paper^{5} and the work of Stanford’s Dr. Charles M.C. Lee.^{6}
We aim to buy stocks we believe are (i) valued too low relative to how they should be priced given relevant fundamentals, and/or (ii) likely to benefit from an increase in market “noise.”

We define “Value” not strictly in terms of low PE, low PB, etc. but also in relation to relevant fundamentals as assessed in ways inspired by the Dividend Discount and Capital Asset Pricing Models).

Based on the work of Shiller and Lee, we see “Noise” not as a dysfunctional aberration but as a normal and inevitable aspect of the market than can be analyzed.
Our models stand apart from many other “quant” and “factor” strategies recently and still being launched as of this writing (many using the label “smart beta,” sometimes correctly but often incorrectly) that derive one way or another from what is known as a Fama French factororiented framework.^{7} While aspects of that work are incorporated into portions of our models (for example, through our use of ranking systems), we reject the overall framework which, we believe, is (i) impacted by misspecified samples and (ii) built on the basis of empirical statistical techniques that do not support inferences that would give investors reasonable grounds to infer that characteristics observed in the past are likely to recur in the future.^{8} Further, we do not attempt to build a model that aims to explain the entire market subject to “residual error”^{9} that is ideally zero and in practice, as close thereto as the researcher can achieve. Instead of seeking to describe the performance of the stock market as a whole, we attempt to define small portions thereof that we believe have the potential to outperform the whole and choose among stocks from the limited subsets we create.^{10}
The details of our approach will be elaborated upon in the Appendix A to this document and are expressed in further detail in written material created for and made available in Portfolio123 RESEARCH for subscribers who expressed a desire for comprehensive instruction in strategy design (a linked index is provided in Appendix B).
Summary of Investment Principles
We start with the notion that P (price in the stock market) is equal to V (a reasonable estimate of fair value) plus the impact of N (noise). In other words:
P = V+N
This is an important departure from much conventional thinking, which presumes P = V and dismisses N as a dysfunction one hopes will be corrected by more enlightened analysis and behavior on the part of the investment community. Drawing on the work of Shiller and Lee, we consider N an inevitable and even important aspect of the market’s natural dynamic state.^{11} As a result of this assumption, we don’t ignore N but build models based on an understanding that it’s present and on consideration of how it can impact stock prices.
We define V in terms of the Gordon Dividend Growth Model, not the pure version but in terms of an adaptation that uses Earnings (E) in lieu of dividends. Details of the process through which we do this and relevant citations are contained in Appendix A. For summary purposes, we now define the ideal P/E ratio as follows:
P/E = 1/(RG)
Where,
P = Price
E = Earnings
R = Required Rate of Return
G = Expected rate of Earnings Growth
For reasons that will be explained further in Appendix A, this equation reveals three important strategic considerations:
 We cannot say that lower P/E ratios are better than higher P/E ratios (as presumed by Fama French and other factorbased approaches). Depending on 1/(RG), it is entirely possible that low P/E stocks can turn out to be overpriced, and that high P/E stocks might be bargains.
 All else being equal, the higher the expected rate of earnings growth, the higher the ideal or “fair” P/E. This is familiar to many through the popular PEG (PEtoGrowth) ratio, which is based on the notion of a direct relationship between earnings growth and a reasonable P/E. But PEG is incomplete. It fails to consider R.
 All else being equal, the lower the R term (the required rate of return), the higher the ideal P/E.

The general level of interest rates is an important component of R. This is why we see stocks rallying when the market expects rates to fall and why stocks tend to decline when rates are expected to rise. Adjustments to R cause P/E ratios marketwide to expand or compress.

NOTE: Do not assume from this that stocks must always fall when interest rates rise. The headwind presented by higher rates may be offset, or even more than offset by increases in Growth (as per a stronger economy that causes interest rates to rise) and/or by diminished risk.

Less discussed but also important is the risk component of R. Riskier assets command higher expectations of return. This is conspicuously visible in the fixedincome markets, where it’s widely understood that socalled “junk” corporate bonds must offer yields above those available on higherquality corporate debt, and that yields on both must be above those available from creditriskfree Treasuries. It’s less visible in the equity markets (and hence seldom discussed) because expected equity return is a fuzzier hardtonail down concept. But it’s no less important.
This conceptual framework derives directly from logic, the exact same logic that would make it impossible to justify paying $5.00 to purchase a $1.00 bill. We can use it with complete confidence.
Implementation Challenges
With a theory as powerful as the one with which the investment community can work, why is stock selection so difficult? Why doesn’t everybody succeed 100% of the time?
The challenge lies in implementation. The framework, however compelling, cannot be treated as a formula into which we can simply plug numbers.
One serious problem involves valuation of stocks for which there is no dividend. Although the formula presented above used E, earnings, this is a workaround. The original theory specified use of the dividend, since this is actual cash received by shareholders and since stock valuation, in its purest sense, should refer to what shareholders actually get as a result of their ownership. But earnings is not a perfect workaround, for reasons that will be discussed in Appendix A, nor is it the only possible workaround.
Moreover, use of any workaround, besides being potentially cumbersome, can magnify the already substantial forecast burdens we face when we try to estimate G (growth).^{12} How do we decide what assumptions to make? We know we have to assume a future growth rate because we buy stocks in anticipation of a future return, rather than as a gesture of celebration of a company’s past. But the future cannot be known, especially the infinite future,^{13} which is the time horizon contemplated by the classic form of the Gordon Dividend Discount Model.^{14}
Given that the stock market is an aspect of finance, and given the numbersoriented nature of finance, it seems natural to presume that the solution to the implementation dilemma lies in more and better math. This is why academic papers in finance tend to look like expressionistic exercises in the use of Greek calligraphy^{15} and often seem incomprehensible to all except a select few who know the difference between a Taylor series, an inverted matrix and a second derivative. The typical approach to ramping up the math while toning down the Newtonian extremes involves abandoning consideration of how stocks should be priced and look instead to what can be seen with the naked eye (aided by speedy computer processors). These researchers do “empirical” studies to document what they see, this being the Fama French family of factor studies.
Do these nouvelle approaches work? Time and much more future documentation will tell us for sure. But for now, think of successful investors known to you, the Warren Buffets of the world. How do they speak, and do they use mathematical jargon or commonsense human language?
Our Solution
Stocks perform well or poorly based on what happens in the unpredictable future. Mathematics, quantitative analysis, is necessarily limited by the known and measurable past which may or may not bear any resemblance to the future. Hence the endeavors are inherently incompatible. Because of this, we believe the financial community has erred in doubling down on the math.
This may seem odd coming from Portfolio123, a company dedicated to use of objective models that rely on numbers (not just any numbers but topoftheline pointintime data^{16}). The issue is not actually about whether numbers should or can be used. We have no choice. Numbers must be used. The past is all we have and the data is necessary to describe it. The issue, however, is very much about how numbers are used.
We use numbers, not the way a mathematician would but in a way that’s more in line with what a police detective might do when seeking clues that illuminate an event for which there are no eyewitnesses. We analyze numbers for the clues that can be used to point us in the direction of the future outcomes we seek. While we cannot and do not attempt to actually calculate 1/(RG), we can and do work with clues and “proxies” that make it more or less probable that a stock is or is not priced reasonably, excessively, or meagerly relative to 1/(RG).
What we refer to as clues and proxies are those ratios, indicators, etc. that the investment community at large refers to as fundamental analysis or even technical analysis. For example:
 Much of what has been presented to the investment public as “Buffettology” is, in fact, a process in which Buffett studies considerations relating to the risk components of R and takes advantage of inefficiencies in the market that cause investors to undervalue low levels of risk (or put another way, high levels of company quality).^{17}
 Joel Greenblatt and his Magic Formula use different proxies and clues to pursue the same goal. He doesn’t simply seek stocks that sell for good prices. He combines good prices with good companies.^{18}
 Joseph Piotroski likewise pursues this same theme. His original research recognized that low valuation alone was an unsatisfactory way to choose stocks. The FScores he developed are built on the basis of items that suggest low levels of R; so like Buffett, he seeks stocks that are priced too low given the market’s failure to appreciate low levels of company R.^{19}
 Fama Frenchtype factor strategies falter not only because they fail to account (in the example of value) for the full 1/(RG) metric but also because they amplify this error through research frameworks designed to eliminate such considerations from their work; they would see 1/(RG) as an extraneous variable that must be cleansed from the analysis.
 The G (growth) factor is extremely challenging given that historical data often points us in the wrong direction when it comes to formulating assumptions about the future, and that the future defies precise numerical estimation. Technical analysis, sentiment analysis, and momentum are, however, often invaluable in assisting us by focusing us on situations where growth expectations, however unquantifiable they may be, are more likely than not to be favorable, or at least better than what is implicitly presumed by the stock price. William O’Neill (Investor’s Business Daily) is very attentive to factors relating to R but is, perhaps better known for his utilization of such Growth proxies. Much the same can be said of former hedgefund and now CNBC superstar Jim Cramer.
 One of the least discussed aspects of growth is its relationship to Quality, particularly return on equity, return on investment, etc. Such ratios, as well as trends in the ratios (Are they improving or deteriorating?) tell us much about a company’s capacity to grow in the future. (See Appendix C.) Capacity for growth does not assure actual future growth. But considering our inability to know the future, knowledge of capacitytogrow can be well worthwhile.
 N (stockmarket Noise) may be seen by many as unquantifiable. This is not necessarily so (see Appendix D). But even if one were to assume it is true, we can still look to proxies for noise (sentiment indicators such as estimate, ratings and target price revision, changes in short interest, technical analysis, etc.) and combine them with fundamental measures that suggest whether such expectations become irrational.
The Risks We Face
All of our equity models are inevitably subject to market and marketrelated risks such as economic trends. In addition, modelspecific risk comes from three sources, or challenges:
 The "language translation" challenge of translating unquestionably sound concepts (good growth, strong finances, stable earnings, etc.) into algorithms that can be understood and processed using computers and databases.
 The “specification” challenge; the potential for companies to meet the letter of the law of the model while violating the spirit of the law.
 The “expectations shortfall” challenge; the potential for a company to perform, in the future, in a manner that falls shy of what was suggested by the analytic clues and proxies upon which we relied. One basic example of this phenomenon might be a that of a wellmanaged company that becomes poorly managed in the future, or a situation where a wellmanagedfirm is impacted by technological change, increasingly intense competition, etc. Also, this phenomenon is regularly seen in the markets when stocks fall in response to earnings disappointments and/or reduced guidance. The earnings surprise occurred in the past and does not really matter. Guidance is typically too shortterm in nature to matter from the standpoint of intrinsic valuation. What does matter, however, is the feedback the event provides to the market regarding the growth expectations it had held.
Our equity models do not address market risk. They presume that you are willing to accept all such risks with whatever portion of your funds you chose to invest using these models, as would be the case if you were fully bullish in equities. It might also be the case if the portion of assets allocated to equity models is less than the entire amount at your disposal. In this latter case, our models assume you have managed your exposure to market risk through investment of other funds in other vehicles (possibly including Portfolio123 ADVISOR Income and/or Asset Allocation models).
We aim to address translation and specification challenges through the way we develop our models and through use of extensive testing to provide feedback on the efficacy of our solutions. We can never assure that we will be completely successful in avoiding such pitfalls, however we believe we have controlled them as to a reasonable extent.
Expectation shortfall is the stockspecific risk most feared by investors and rightfully so given that it is the hardest concern to address.
 Diversification is one commonplace and often effective solution particularly here, where we seek to mitigate risk that is “unsystematic,” “idiosyncratic” or justplain company specific. Simply put, this is the safetyinnumbers line of reasoning.
 Also, our models on the whole feature what might be described as a quality tilt. Reliance on factors thus classified is important because qualityrelated items tend to be more likely than others to remain relatively stable over time, or at least more stable than others, leading to stocks that are likely, we believe to be less vulnerable to wide swings based on idiosyncratic issues.^{20}
See Also . . .
In addition to Appendixes A through D attached to this paper, it is recommended that readers refer also to four additional Portfolio123 ADVISOR White Papers.
 White Paper #2 describes the structure of a Portfolio123 Equity model, an especially important topic for those whose background in modeling comes from conventional quantitative or factor approaches.
 White Paper #3 details the considerations and criteria used in the specific Equity strategies we offer.
 White Paper #4 describes our Income strategies.
 White Paper #5 describes our Core AssetAllocation strategies.
APPENDIX A
Theoretical Underpinnings of Price Setting in the Stock Market
We start with an assumption that a stock is worth the present value of all cash the investor expects to receive as a result of owning the shares. This consists of dividends plus proceeds from eventual resale.
The logic is impeccable. To argue against it would be equivalent to arguing that it’s reasonable be to pay $5.00 for a $1.00 bill. The challenges – the reasons why everybody does not select winning stocks 100% of the time –result from our inability to precisely implement this concept.
One of the implementation challenges involves uncertainty as to when the stock will be sold and the proceeds expected to be generated. This has been addressed by the recasting of the presentvalue truism in terms of a mathematical infinite series (i.e. reflecting an assumption the investor will own the shares through infinity). Thus we use, as a starting point for stock valuation, the Gordon Dividend Discount Model (DDM):
P = D/(R – G)
Where,
P = Stock Price
D = Dividend
R = Required Rate of Return
G = Expected (Infinite) rate of dividend Growth
This is a big improvement over the presentvalue truism, but it does not fully solve our implementation problems:
The future, even a quarter ahead, is difficult to predict; predictions through infinity are, essentially, impossible to make.

Any forecast for an infinite dividend growth rate will have to be contrived such that it must be lower than the required rate of return, lest the model wind up forecasting a negative stock price (theoreticians accomplish this by noting that an infinite growth rate necessarily encompasses extreme levels of company maturity and, hence, translates to a sufficiently low infinite growth rate).

Many companies pay no dividends at all. We could still use the DDM (multistage versions that compute DDM valuations as of a future date when a dividend policy will be initiated and then discount the resulting P back to today via the presentvalue calculation), but this amplifies an alreadyimpossible forecasting burden.
So rather than using DDM as a specific formula that can be applied exactly as is, we use it as a roadmap to guide the sort of analytic judgments we must inevitably make anyway (i.e., because we are dealing with the unknown future). Doing so is especially important when working with historic data through a process that involves backtesting. Successful tests do not and cannot justify use of any investing model with live money because as we know, past performance does not assure future outcomes. Building models on the basis of a DDMinspired roadmap is what enables us to rationally project research of the known past into the unknowable future; i.e. this theory serves as a logical bridge that connects the known past with the potential future.
Adapting the DDM for such purposes starts by refocusing from D, dividends, to broader measures of wealth created by the corporation all of which relate, one way or another, to a company’s ability to pay dividends now and/or in the future. This is recognizable in the popular contemporary view of corporate wealth as the stream of earnings from which dividends are paid. In fact, we’ve gone so far in this regard that earnings are seen today as having primacy over dividends. We observe this in the way the investment community accepts and at times encourages companies to pay little or no dividends and to reinvest all or a substantial portion of earnings back into the company to pursue future growth opportunities. (Whether this is wise or not is an interesting topic in its own right and specialsituations investors do like to see large amounts of cash returned to shareholders.)
Given the tendency to focus on Earnings, we can restate DDM as an Earnings Discount Model (EDM):
P = E/(R – G)^{21}
Where,
P = Stock Price
E = Earnings
R = Required Rate of Return
G = Expected (Infinite) rate of earnings Growth
Algebraic reshuffling of this equation gives us the formulation presented in the main text for an ideal P/E ratio:
P/E = 1/(R – G)
Because G is a negative term in the denominator of a fraction, we understand that as G rises, so, too, does ideal P/E. This is the basis for the popular PEG (P/EtoGrowth) ratio, as incomplete as it is (due to its failure to consider R).
Because R is a positive term in the denominator of a fraction, we understand that as R rises, ideal P/E falls; conversely, as R falls, ideal P/E rises. As we’ll see below, interest rates are an important component of R. This is why stocks fall when interest rates rise (P/Es shrink across the market), and why they rally when rates fall (marketwide P/Es expand). The equity risk premium (the extra return investors demand as compensation for assuming the risk of owning equities as opposed to riskfree investments) is another important component of R. This is why stocks fall or rise as investors become increasingly fearful or comfortable with overall business prospects.
Interest rates and equity risk premium influence the stock market as a whole. Hence we do not address them in our stock strategies, which take desire for equity exposure as a given and work to achieve above average results from equity investments. There is, however, one important component of R that is stock specific and which is addressed in our stock strategies, B (Beta).
R as a whole can be defined in terms of the Capital Asset Pricing Model:
R = RF + (B*RP) + e
Where,
R = Required Rate of Return
RF = Rate of Return available for riskfree assets (i.e. U.S. Treasury securities)
RP = Risk Premium required by investors to induce them to bypass riskfree securities and take on equitymarket risk
B = a measure of the risk of an individual equity relative to the market as a whole
e = an residual error term that is presumed to be random and to average to zero
This is by no means the only possible formulation of R, but it is sufficient for our purposes. It shows that B, like R, is a positive number in the denominator of the EDM fraction. That means that as B falls (i.e., as risk falls, or put another way, as company quality rises), ideal P/E rises. Conversely, as B rises (i.e., as quality declines), ideal P/E falls.
This insight is an important example of why we consider an EDM foundation to be vital to the development of stock strategies. Many investors assume low P/E stocks are safer. Actually, the opposite is true. All else being equal, low P/E is associated with lower company quality and greater company risk. Conversely, many conservative investors are fearful of the very companies whose shares they should be owning because they fail to appreciate the relationship between higher quality and higher valuation.
Note, too, that theory extends even beyond P/E. This is important because in many cases, we won’t have a usable earnings number. This would be so where the company is losing money, or where profits are barely above zero. It’s also true any time a company’s current earnings is influenced by nonrecurring events.
One useful substitute for earnings is sales, which is earnings is sales multiplied by margin. Substituting that into the equation for ideal P/E allows us to compute an ideal Price/Sales (P/S) ratio:
P/S = M/(R – G)
Where,
P = Stock Price
S = Sales
M = Margin
R = Required Rate of Return
G = Expected (Infinite) rate of sales Growth
Higher margins and/or stronger expected sales growth warrant higher ideal P/S ratios.
This formulation would still be problematic if earnings were unusable, due to losses, nonrecurring items and so forth (the net margin, the one the formulation ideally presumes, would be unusable). But we have gained an important strategic element. Given that we’re not naively crunching mathematical formulas but looking for clues about the future, we can look at gross margin, operating margin, etc. and trends therein to get a sense of where a company seems to be heading. We could, therefore, search for companies whose current P/S ratios seem low relative to risk, prospects for sales growth and prospects from growth in operating margins (which would, over time, probably spur growth in net margins and earnings).
Along similar lines, earnings can be expressed as book value multiplied by return on equity. This allows us to express the ideal P/B ratio as follows:
P/B = ROE/(R – G)
Where,
P = Stock Price
B = Book Value
ROE = Return on Equity
R = Required Rate of Return
G = Expected (Infinite) rate of ROE
As ROE or growth of (improvement in) ROE rises, so, too, does the ideal P/B ratio.
Other valuation metrics involving enterprise value (in lieu of price or market capitalization), cash flow, free cash flow, etc. can be similarly expressed.
The key to our approach is recognition that whatever style a strategy is said to pursue, all derive from our view of value, growth, financial strength, and all other aspects of fundamental analysis as a part of a single unified theory of pricesetting in the equity market. All investors who do not passively index, regardless of socalled style, pursue the same goal: to profit from instances of mispricing that arise when a stock is valued lower or higher than in should be based on the valuation that is warranted by fundamentals. Differences among the strategies reflect different approaches to seeking cues to the notreadilycalculable ideals, and the kinds of risks an investor wishes to assume (e.g., expected growth is much harder to articulate so investors wishing to focus on that aspect of the investment case typically are willing to assume greater risks), and, of course, different ways of explaining the approaches.
APPENDIX B
Portfolio123 Strategy Design OnLine Class
Topics
Introduction – We Can Get A Handle On Stock Pricing
https://www.portfolio123.com/doc/side_help_item.jsp?id=201
Topic 1 – The Dynamics of Stock Pricing
Topic 1A  Why Stock Prices Are What They Are – The Core Theory
https://www.portfolio123.com/doc/side_help_item.jsp?id=202
Topic 1B – Valuation Theory, Moving from Dividends To EPS
https://www.portfolio123.com/doc/side_help_item.jsp?id=203
Topic 1C – From EPS to Workaday RealWorld Analytic Ideas
https://www.portfolio123.com/doc/side_help_item.jsp?id=204
Topic 1D – Beyond Value, the Other Noisy Component of Price
https://www.portfolio123.com/doc/side_help_item.jsp?id=205
Topic 2 – A Noise/Value Strategy
Topic 2A – Laying The Groundwork For A Portfolio123 NoiseValue Strategy
https://www.portfolio123.com/doc/side_help_item.jsp?id=206
Topic 2B – Details Of A NoiseValue Strategy
https://www.portfolio123.com/doc/side_help_item.jsp?id=207
Topic 2C – Testing The NoiseValue Strategy
https://www.portfolio123.com/doc/side_help_item.jsp?id=208
Topic 3 – Value
Topic 3A  Designing A PEBased Strategy
https://www.portfolio123.com/doc/side_help_item.jsp?id=209
Topic 3B – Designing A SalesBased Valuation Strategy
https://www.portfolio123.com/doc/side_help_item.jsp?id=210
Topic 3C – Value Based On Cash Flow
https://www.portfolio123.com/doc/side_help_item.jsp?id=211
Topic 3D – Using Price/Book
https://www.portfolio123.com/doc/side_help_item.jsp?id=212
Topic 3E – Special Topics In Valuation
https://www.portfolio123.com/doc/side_help_item.jsp?id=213
Topic 4 – Quality
Topic 4A – Overview Of Quality
https://www.portfolio123.com/doc/side_help_item.jsp?id=214
Topic 4B – The DuPont Framework
https://www.portfolio123.com/doc/side_help_item.jsp?id=215
Topic 4C – The Components Of Quality
https://www.portfolio123.com/doc/side_help_item.jsp?id=216
Topic 4D Using Quality Factors In Your Strategies
https://www.portfolio123.com/doc/side_help_item.jsp?id=217
Topic 4E – Earnings Quality
https://www.portfolio123.com/doc/side_help_item.jsp?id=218
Topic 5 – Working with AnalystRelated Data
https://www.portfolio123.com/doc/side_help_item.jsp?id=219
Topic 6 – Momentum
https://www.portfolio123.com/doc/side_help_item.jsp?id=220
Topic 7 – Special “Graduate” Items
(i) Growth and (ii) Valuation Ratios Based on Q vs. TTM
https://www.portfolio123.com/doc/side_help_item.jsp?id=221
Topic 8 – Hedging and Market Timing
https://www.portfolio123.com/doc/side_help_item.jsp?id=222
Topic 9  Position Sizing (Weighting)
https://www.portfolio123.com/doc/side_help_item.jsp?id=223
Supplemental Material
Supplement 1  Cost of Capital; (1) Intro and Challenges
https://www.portfolio123.com/doc/side_help_item.jsp?id=223
Supplement 2  Cost of Capital; (2) A Usable Approach
https://www.portfolio123.com/doc/side_help_item.jsp?id=224
Supplement 3  Cost of Capital; (3) Keeping It Simple
https://www.portfolio123.com/doc/side_help_item.jsp?id=225
Supplement 4  Cost of Capital; (4) Thinking Outside the Box
https://www.portfolio123.com/doc/side_help_item.jsp?id=226
Supplement 5  Effective Testing on Portfolio123
https://www.portfolio123.com/doc/side_help_item.jsp?id=227
APPENDIX C
The Relationship Between Quality (Return on Assets) and Growth
Table 1 demonstrates the link between Return on Assets (ROA) and earnings growth. It traces the earnings path of two companies, both of which pay no dividends. Company A has an ROA of 12%. Company B has an ROA of 16%.
Table 1 Illustration of Relationship between ROA and Growth

Company A 
Company B 

ROA 
12.0% 
16.0% 

Div. Payout 
  
  


Assets 
Earnings 
Dividends 
Assets 
Earnings 
Dividends 

Start 
100.00 
  
  
100.00 
  
  

End Year 1 
112.00 
12.00 
0.00 
116.00 
16.00 
0.00 

End Year 2 
125.44 
13.44 
0.00 
134.56 
18.56 
0.00 

End Year 3 
140.49 
15.05 
0.00 
156.09 
21.53 
0.00 

End Year 4 
157.35 
16.86 
0.00 
181.06 
24.97 
0.00 

3 Year Growth Rate 

12.0% 
  

16.0% 
  
In Year 1, Company A earned 12% on its assets, which amounted to $12.00. All of that was added to the original capital base, which at the start of Year 2 is $112. In the second year, it earns 12% of 112, or $13.44—all of which is added to the base of capital available for next year. We follow this path on form one year to another.
Company B charts a parallel path but one that reflects a 16% ROA (each year it earns 16% on its capital) and all of that is added to the capital base.
All else being equal, Company B must grow more quickly than Company A because it in each year, it earns a higher percent relative to a capital base that expands more quickly through reinvestment of profits.
Table 2 varies the scenario. Now, each company pays out 20% of annual profits as dividends. That reduces the earnings growth rates in both cases because now, each company is expanding its capital base by less than the full amount of profit. Even so, all else being equal, Company B must still outgrow Company A.
As simplistic as all this sounds (and is), it does not resemble the way we usually talk about stocks, companies, and growth. With all our focus on stories and predictions, we often lose sight of a core truism; a company is represented by a pool of capital and earnings are the return earned by investment (use) of that capital. We expect to earn returns by investing financial capital in the financial markets. Companies expect to earn returns by investing other kinds of capital in the business markets. Either way, the faster one is able to increase one’s pool of capital, the more growth is likely in the amounts the capital returns.
Table 2 Another Illustration of Relationship between ROA and Growth

Company A 
Company B 

ROA 
12.0% 
16.0% 

Div. Payout 
20.0% 
20.0% 


Assets 
Earnings 
Dividends 
Assets 
Earnings 
Dividends 

Start 
100.00 
  
  
100.00 
  
  

End Year 1 
109.60 
12.00 
2.40 
112.80 
16.00 
3.20 

End Year 2 
120.12 
13.15 
2.69 
127.24 
18.05 
3.61 

End Year 3 
131.65 
14.41 
2.88 
143.52 
20.35 
4.07 

End Year 4 
144.29 
15.80 
3.16 
161.89 
22.96 
4.59 

3 Year Growth Rate 

9.60% 
9.60% 

12.78% 
12.78% 
Each company has a growth rate that is less than its ROA. But that makes sense. Each company is now increasing its asset base each year by less than the full amount that is available. Notice, too, that for each company, all else being equal, dividends grow by an amount that matches the earnings growth rate and hence is higher for Company B (16% ROA) than for Company A (12% ROA).
So what about the ubiquitous “all else” that must be equal in order for all this to make sense. That’s easy, at least easy to say: The ROA must remain steady. Company A, despite a dayone 12% ROA, could be a better choice than Company B if the latter’s ROA is expected to deteriorate from 16%. Could either of those scenarios ever materialize? Yes, absolutely. In the real world, the only constant is change. When strategists using ROA (and similar metrics such as return on equity) develop their strategies, it’s up to them to determine out how to use the available data to uncover clues relevant to ROA stability, growth or deterioration. The degree of skill they bring to bear in this will contribute the realworld success or lack thereof of their strategies.
APPENDIX D
Quantifying “N” (Investment/Market Noise)
The impact of Noise on the price of a stock is surprisingly easy to detect. Actually, it’s hiding in plain sight. If we start with the notion that P (price) = V (value) + N (noise), then the following must be true”
N = P  V
That’s all there is. It’s just that simple. If a stock trades at 25, and we value it at 18, then we know noise is contributing $7 per share (28% of the total) to the price of the stock.
The insight, here, is that we are not necessarily suggesting such a stock is a “Sell” simply because it trades above our estimate of fair value. We assume noise is an inevitable aspect of the market and base our view of the stock on whether we believe 28% noise is excessive (in which case we’d say Sell) or the potential for the level of noise to rise, in which case we might say Buy.
The degree of Noise that’s appropriate for a stock is not random. It’s based on a variety of factors which one way or another relate to our ability to develop a confident forecast of V. For this reason, we would expect shares of an established stable company like Walmart to be significantly less noisy than, say Facebook, a pioneer in what is, essentially, a brand new business for which serious forecasting amounts to little more than guesswork.
Standstill Value
In quantifying Noise, we know P. All we have to do is come up with an estimate for V. The potential ways of doing so are limitless, based on the ideas and imaginations of all investors who tackle such tasks. Here, for illustrative purposes, we’ll come up with a fairly conservative approach to estimating value, one that might be referred to as “standstill” value. It assumes (i) that the worth of the company is based on how it has been performing most recently, and (ii) that this recent (trailing 12 month) performance represents the company’s sustainable level of profitability.
The core approach to valuing a security whose income stream is not expected to grow is:
Yield = Income / Amount Invested
This should be familiar. It’s a quick summary of how we value fixedincome securities that trade at face value. Translating this to the valuation of equity in a nogrowth corporation, we could use the following:
CC = NOPAT / V
Where
CC = cost of capital, or yield on capital employed
NOPAT = Net Operating Profit After Tax
V = Value of corporation, or “fair” market capitalization
Now, let’s restate the equation in terms that will be more useful to our current effort.
V = NOPAT/CC
There are many subtleties beyond the scope of this paper.^{22} What’s important for now is to recognize that we have a usable estimate for V, the “fair” market capitalization of a company’s stock. Once we establish that, we can easily articulate a dollar amount of Noise that is reflected in the stock and the percent of the stock that consists of noise.
N = V – P
Where
N = Noise
V = Fair Market Capitalization
P = Price, or actual Market Capitalization
Finally, we have:
%N = (N/V)*100
Where
%N = the percent of market capitalization (or price) attributable to Noise
This is a conservative approach in that it presumes all growth expectations, bona fide or speculative, are part of Noise. In the alternative, one could develop a model for V that includes allowance for reasonable growth expectations (the challenge being to distinguish between reasonable expectations versus hopes, dreams and pure guesswork). Then again, considering popular rhetoric among value investors regarding the need for a margin of safety, using a zerogrowth assumption seems defensible.
For some companies, %N will be near or at 100%. For others that can be valued more plausibly, %N may be in the 20%30% range. For some, where the market is especially pessimistic, %N can even be negative. Expectations regarding future changes in N would be based on expectations regarding changes in the character of a company^{23} or its situation.^{24} Momentum, sentiment, technical analysis, etc., can be invaluable as a gauge of trends in the level of noise in ways beyond what can be seen through calculation and subtract
1 Initially described in 1956 by Myron J. Gordon and Eli Shapiro based on ideas drawn from John Burr Williams, The Theory of Investment Value (Harvard University Press, 1938).
2 Jack L. Treynor, Toward a Theory of Market Value of Risky Assets (an unpublished 1962 manuscript later published in Robert A. Korajczyk (editor), Asset Pricing and Portfolio Performance: Models, Strategy and Performance Metrics,(Risk Books, 1999, pp. 1522).
3 William F. Sharpe, Capital asset prices: A theory of market equilibrium under conditions of risk, 19(3) Journal of Finance 42542, (1965).
4 John Lintner, The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets, 47(1) Review of Economics and Statistics 1337, (1965).
5 Robert J. Shiller, Stock Prices and Social Dynamics, 1984 Brookings Institution Paper, http://www.econ.yale.edu/~shiller/pubs/p0616.pdf
6 Charles M.C. Lee, Market Efficiency and Accounting Research, 31 Journal of Accounting and Economics, 23353 (2001)
7 Eugene F. Fama and Kenneth R. French, The Cross Section of Expected Returns, 47 (2) Journal of Finance, 427 (1992) expanded upon in A fivefactor asset pricing model, 31 Journal of Accounting and Economics 233 (2001).
8 See, e.g., Michael Edesses and Kwok L. Tsui, Why You Shouldn’t Trust Most Financial Research, http://www.advisorperspectives.com/articles/2015/08/18/whyyoushouldnttrustmostfinancialresearch
9 Residual error in this context refers to those aspects of market performance that cannot be explained by the model and which are presumed to be random.
10 See generally, Marc H. Gerstein, Screening The Market (Wiley, 2002) Chapter 4.
11 Fischer Black acknowledges noise trading as an essential aspect of the stock market and insofar as it pertained to the financial markets, he defined it as that which “keeps us from knowing the expected return of a stock or portfolio.” (Noise, Papers and Proceedings of the FortyFourth Annual Meeting of the America Finance Association, New York, New York, December 2030, 1985, Journal of Finance, Vol. 41, Issue 3 (July 1986), p. 529543 at 531 (emphasis supplied) citing JeanJacques Laffont, On Welfare Analysis of Rational Expectations Equilibria with Asymmetric Information, Econometrics, Vol. 53 (January 1985) pp.129.) It’s not identical to our definition, which acknowledges the existence of noise even when we are able to properly value stocks. What’s important is that Black recognizes that deviations between price and value is a normal and, he believes, necessary part of the market landscape. He maintains that if trading occurred only on the basis of relevant information (i.e. in the absence of noise), it would be impossible for transactions to occur since one party would necessarily have to be willing to make a mistake.
Noise trading provides the essential missing ingredient . . . . With a lot of noise traders in the market, it now pays for those with information to trade. It even pays for people to seek out costly information which they will then trade on.
So far, so good. But that is not the full quote. Here is the complete version:
Noise trading provides the essential missing ingredient. Noise trading is trading on noise as if it were information. People who trade on noise are willing to trade even though from an objective point of view they would be better off not trading. Perhaps they think the noise they are trading on is information. Or perhaps they just like to trade.
With a lot of noise traders in the market, it now pays for those with information to trade. It even pays for people to seek out costly information which they will then trade on. Most of the time, the noise traders as a group will lose money by trading, while the information traders as a group will make money.
Black does more than acknowledge the existence or even importance of noise trading. He suggests noise trading is a bad thing for those who practice it. Put another way, he suggests that noise traders are important because in order to have market winners, we also need market losers. We adopt the ShillerLee view which sees noise trading in less judgmental terms,
12 Another of a workaround is the twostage version of the Dividend discount model. For example, we might assume Company X will continue to reinvest all of its profits back into the business, but start paying dividends five years hence, when it has progressed to the degree that it no longer needs to retain all of its profits. In this case, we would imagine ourselves as being placed five years into the future, and we would then compute a DDMbased valuation as of that point in time. Next, we would use a standard presentvalue computation to translate that into a hereandnow price. Others might use multistage models, in which they would divide the assumed future into different stages reflecting different, but gradually decelerating, growth periods until eventually, the dividend initiation stage is reached. The penultimate version of the multistage modeling concept is the Discounted Cash Flow model (DCF), in which forecasts are made for each year for a period of time, five years, sometimes ten or more, with a DDMlike final “terminal value” computed at the end. Such approaches inevitably appear impressive when set forth on paper (for this reason, analyst reports often include them), but the forecasting burdens they impose are utterly inhuman; hence the reason why estimates often turn out wrong and need to be continually revised.
13 Observe, for instance, the considerable cottage industry that has grown up around estimate revision and surprise, which shows how hard it is even to forecast one quarter ahead.
14 Use of an infinite growth rate is important. As time stretches, we can comfortably presume that even the most dynamic companies will mature and see growth rates compress – presumably to a level well below the required rate of annual return. If we were to cheat and plug in a higher estimatedgrowth number relating to a current period characterized by strong but not infinitely sustainable growth, we could easily wind up with a situation in which G is greater than R, a scenario that would produce the absurdity of a negative fair P/E. This is an example of the dangers to an investment process that relies primarily on mathematics, and why we use math for strategic guidance instead of as a “spec” for an Excel spreadsheet.
15 Advanced mathematical and statistical terms are often expresses using Greek characters.
16 Pointintime data is data that aims to depict a state of affairs as it actually existed at a particular point in time, as opposed to how it ideally should have existed. Consider for example, a company’s fullyaudited 2013 earnings. Ideally, they would have been available to investors on January 1, 2014, and many databases will presume this to have been the case. As a practical matter, however, they are not disclosed until several weeks into the new year. Our pointintime database does not make use of the 2013 numbers until they were known and actually available to investors. Hence a Portfolio123 simulation that requires a hypothetical portfolio to have been refreshed on 1/6/14 will still be using 2013 numbers because that it what investors had actually been using on that date. Through this approach, we avoid “lookahead bias.” We also avoid “survivorship bias.” Consider, for example, Gillette. Until early 2005, it was a major publicly owned publiclytraded company. It ceased to be so, however, when it was acquired by Procter & Gamble. Many databases today do not include Gillette at all because it no longer exists as an independent entity. However, a Portfolio123 simulation that starts to run on, say, 1/2/04 will include Gillette in the early period (if and when it warrants inclusion in the portfolio based on the models’ rules) and continue to do so until its existence as an independent entity ended.
17 See generally, Andrea Frazzini, David Kabiller and Lasse Heje Pedersen, Buffet’s Alpha http://www.econ.yale.edu/~af227/pdf/Buffett's%20Alpha%20%20Frazzini,%20Kabiller%20and%20Pedersen.pdf (2013) (analyzing returns earned by Berkshire Hathaway in terms of his use of lowcost leverage and, as relevant to our discussion, quality or in academic parlance, qualityminusjunk); Robert G. Hagstrom, The Warren Buffett Way (Wiley, 3^{rd} Ed. 2013) (extensively discussing Buffett’s regarding company character which mesh with the factors we regard as giving rise to highqualitylow risk and hence low R in our EDM formulation; and the many Chairman’s letters penned by Warren Buffett for Berkshire Hathaway annual reports, which can be accessed via http://www.berkshirehathaway.com/letters/letters.html.
18 Joel Greenblatt, The Little Book That Beats the Market (Wiley 2008)
19 Joseph D. Piotroski, Value Investing: The Use of Historical Financial Statement Information to Separate Winners from Losers 38 Journal of Accounting Research Supplement 2000
20 Such stability also plays an important role in controlling portfolio turnover and transaction costs.
21 We could even define D as E*(1PR) where PR is the dividend payout ratio. In this case, the DDM would be (E*(1PR))/(RG). Use of EDM rather than DDM presumes the investment community’s willingness to tolerate payout ratios of zero, or put another way, to act as if all earnings were paid to shareholders as dividends with all shareholders voluntarily choosing to reinvest the proceeds back into the corporation. Under this framework, we’d see realworld dividends as instances of a corporation paying out cash that management believes cannot be productively reinvested in the businesses and recipient shareholders holding onto same and using the proceeds for other purposes.
22 See, e.g. Appendix B, Topic 2
23 For example, as an emerging business ages, it becomes less challenging to create valuation models resulting in potential decreases in the degree of noise that should normally be associated with the stock price.
24 For example, noise might be negative (i.e. might cause a company’s stock to be priced below “standstill value”) if future deterioration is expected. Noise could be expected to rise in the future if a company breaks out of historical patterns in a favorable way.