Approach to Equity Modelling - Rules-Based Strategies Inspired by Classic Stock-Pricing Theory

Executive Summary

 

Portfolio123 Securities White Paper #1 explained our investment philosophy, the ideas we pursue as we select stocks for inclusion in out portfolios. But ideas are just that, ideas. To benefit from them, we need to apply them to the real-world challenge of saying Buy this stock; don’t buy that one, etc.” We do this through modeling. We must translate our ideas into specific instructions that can be understood and implemented by computers that access databases.

 

We believe such modeling is the most effective way to invest given the way it neutralizes the primary obstacle to active investment, the tendency to allow emotion, bias, habit, hype, etc. to infiltrate and damage the selection process. That said, we are by no means the first or only organization to build and use investment models. We believe, however, that we are distinct in two important respects.

 

1. Our models are idea driven, not empirically driven. While we do test and simulate to analyze how our models would have performed had they been used in the past, they are not constructed on the basis of statistical or empirical study. Instead, they are built with the idea of implementing the theoretical foundations explained in White Paper #1. This allows our testing to be much more meaningful. Because past performance cannot assure future outcomes, no model, no matter how well it tests, can be reasonably used unless one can justify, in financial-economic terms, why it should be expected to be productive in the future. even though conditions may vary and possibly to a substantial degree, from what was experienced in the past. The ideas explained in White Paper #1 are what allow us to do this. We use our models because we believe they are justified by sound financial-economic logic, not merely because they tested well.

 

1. Our models are a flexible combination of universe definition, buy (screening rules), ranking systems and sell rules, as opposed the kinds of rigid models offered elsewhere that are based on strict multiple least-squares regression. The latter is fine for purely empirical study (where both testing and implantation are to be done in the same setting, as with, for example, medical research). We believe such techniques are not suitable to the tasks at hand, projecting into the future (i.e. where the implementation is expected to be done in a setting (the future) that is not the same as that in which testing was conducted (the past).

 

In this paper, we’ll explain the structure of our models and the characteristics they all share. Portfolio123 Securities White Paper #3 will then explain the unique features of models used to implement the various strategies we pursue in the portfolios we offer.

Translating the Investment Philosophy into Specific Models

 

Our models are designed on the basis of what we believe it will take to outperform the U.S. equity market and to do so without taking undue risk. We do not attempt to time the market, nor do we issue numeric forecasts of “expected return” or “volatility.” Instead, we qualify and select stocks based on factors that in our view suggest price inefficiencies, differences between what a stock trades for and where it should trade if the market were efficiently assessing the pricing-theory factors discussed in White Paper #1.

 

There are seven matters we address to translate such ideas into Portfolio123 Securities models:

 

 

• Style(s): While everything we do derives from the core DDM (Dividend Discount Model) based concepts explained in White Paper #1, the number of different ways such ideas may conceivably driven be expressed is limitless. So for the sake of convenience, we think in terms of well recognized relevant investment “styles.”

• Universe: We use a first-level eligibility determination to weed out certain stocks that will not be considered under any circumstances. All of our subsequent work is done with regard to those that remain, those that are within the “universe” we define.

• Buy (Screening) Rules: This is a set of objective binary (i.e., pass-fail) tests we impose on all universe stocks to determine which ones are candidates for inclusion in the portfolio. There is nothing necessarily wrong with a stock eliminated by these rules; in fact, the pass-lists are small meaning most stocks are eliminated. It’s just that eliminated stocks are incompatible with the model in question. Many may, however, pass muster and be included in a set of Buy Rules we create for a different model.

• Ranking: Stocks that pass all of the model’s Buy rules are then sorted from highest (best) to lowest (worst) under a ranking system we chose for use this particular model. For a portfolio of N stocks, we select those with the N highest rank scores (e.g., for a 20-stock portfolio, we would select the 20 highest ranking stocks).

• Sell Rules: This is a set of objective binary screen-like rules that determines when an existing position should be sold.

• Position Weighting: This is a protocol through which we determine how much of a portfolio’s assets should be invested in each stock.

• Testing/Simulation:

 

Principals of Model Design

Stylistic Considerations

 

Generally, all of our models are based on consideration of Value, Quality and Sentiment. Factors relating to each will be explicitly present, or present by implication (i.e. where a pre-qualified portion of a universe is such as to support a belief that the market is reasonably efficient in assessing that factor to the extent necessary – as will be explained in connection with each model).

 

• Value: In a classic sense, this includes P/E. It also includes relationships between other measures of market value (relationships between price, market capitalization, enterprise value) and corporate wealth (sales, book value, cash flow, etc.).
• Sentiment: As discussed in White Paper #1, potential future growth is a vital consideration in deciding how a company should be valued. The challenge lies in the fact that growth data from the past may, but often does not, indicate the potential for growth in the future. Use of Sentiment measures (including price momentum) allows us to benefit from important clues to hard-to-quantify investment community expectations relating to future growth.
• Quality: This is a very important stylistic consideration in our modelling for three reasons.
• First, as discussed in White Paper #1, it’s a crucial but often overlooked and under-discussed consideration in determining a stock’s fair price and hence, a frequent source of the sort of market mispricing we seek to identify and exploit.
• Second, high quality (the return on capital measures) is an indicator of a company’s potential to generate growth in the future and, hence, provides another clue regarding the important but hard to quantify future-growth factor.
• Also, Quality is important as a means to control portfolio turnover, which we seek to moderate in order to prevent transaction costs from becoming troublesome. It’s dangerous to hold a stock for which the data signals “Sell.” Therefore, the only effective way to minimize turnover is to emphasize stocks for which the data is least likely to have occasion to call for the stock to be sold. Quality metrics tend to be the most stable over time. Hence a portfolio with a quality tilt is best able to deliver low turnover without unduly sacrificing performance.

 

Universe

 

Each Model specification starts with a Universe, a subset of the core (default) Portfolio123 “All Fundamentals U.S.” universe. Each Universe used by Portfolio123 Securities eliminates from the default universe stocks having any of the following characteristics:

 

• Stocks that are, in fact, a Master Limited Partnership units
• We express no opinion as to the pure investment merits of such situations (concentrated as of this writing mainly in the Energy sector). Instead, we take note of the reality that taxation of these securities differs markedly from those of equities and in ways many investors find cumbersome and objectionable.
• The stock is, in fact, an ADR or ADS
• These American Depositary Receipts or American Depositary Shares are devices created to facilitate trading of foreign equities in U.S. markets. We express no opinion on the pure investment merits of such issues. Instead, we note that accounting methods outside the U.S. often mesh uncomfortably – from a database point of view – with those in the U.S. While some or perhaps many in the investment community accept this, the importance of data to our model design and implementation is such that it would pose special obstacles for our models that enhance the potential for unreasonable investment decisions to be made on the basis of data-oddities.
• There is no meaningful figure reported for trailing-12-month Sales
• This is a very small group of companies typically consisting of those for which Sales are offset, at the top of the income statement, by amounts that exceed or equal reported sales. We express no opinion on the pure investment merits of any such situation, but we note that these firms present atypical financial profiles that could lead to investment decisions inconsistent with what our data-driven models seek to accomplish.
• The stock must meet a set of basic trading liquidity rules
• These are
• Stock may not trade in the OTC market
• Average daily dollar volume of shares traded must exceed $10 million over the course of the past 20 trading days
• Average daily dollar volume of shares traded must also exceed $10 million over the course of the 20 trading day period that preceded the past 20 trading days.
• The purposes of these liquidity rules is to facilitate execution of trades at prices that are reasonably representative of normal market levels as of the time the trades are placed.
• The stock must meet a set of share-price rules
• The purposes of these are to avoid trading difficulties in allocating stocks with very high dollar prices to smaller accounts and address the unwillingness of many institutions to trade stocks priced very low (which often signal threats to future trading liquidity).
• We eliminate stocks priced above $200 per share.
• Stocks priced below $5 per share are eligible only if average daily dollar volume of shares traded exceed $50 million over the course of the past 20 trading days, and also over the course of the immediately preceding 20 trading day period (such exceptions that suggest institutional willingness to trade despite the low dollar prices).

 

We then identify three specific universes each of which contains the above-specified filters. The three universes differ from one another only in terms of minimum permissible market capitalization.

 

• For the P123 Invest – A Universe, we add a requirement that the stock’s market capitalization fall within the top 10% relative to all stocks.
• For the P123 Invest – B Universe, we add a requirement that the stock’s market capitalization fall within the top 20% relative to all stocks.
• For the P123 Invest – C Universe, we add a requirement that the stock’s market capitalization fall within the top 35% relative to all stocks.

 

All of the models may include stocks from the largest market-capitalization group (Level 1).

 

1. Models that hold 10 positions are restricted to the Level 1 Universe
2. Models that hold 15, 20 or 30 positions draw from the Level 2 Universe
1. The extent, if any, to which Level 1 stocks will be among those in a portfolio depends entirely on application of the rules of the model. In other words, Level 1 stocks could but are not required to be included.
3. Models that hold 40 positions draw from the Level 3 Universe
1. The extent, if any, to which Level 1 or Level 2 stocks will be among those in a portfolio depends entirely on application of the rules of the model. In other words, Level 1 and Level 2 stocks could but are not required to be included.

 

The impact of these protocols is to allow models spread among larger numbers of positions to hold smaller capitalization issues than would be the case with models holding fewer positions.

 

Buy Rules

 

Each model has a set of “buy rules” (also known as screening rules, filters, etc.). The role of a set of Buy Rules is to pre-qualify the universe from which the “best” (i.e. highest ranked) stocks will be drawn.

 

This pre-qualification process is vital. Hypothetically, it may seem appealing to invest the 10 “best” value plays in the market, the ten stock having the ten highest ranks for value (i.e. the lowest PE ratios). In fact, however, such naïve ranking can be unfruitful or even dangerous. It is possible that the stocks with the ten best value rankings may be associated with companies whose growth prospects are very poor, meaning that the stocks are cheap because they deserve to be cheap. It may turn out more productive if we instead chose the 10 best value plays from a group that has already been pre-qualified to eliminate deteriorating companies. What we do, here, is analogous to what a salesperson would do by resisting the easy way (prospecting for customers by calling number from a random list) and instead, taking the trouble to obtain, typically to purchase, a list of pre-qualified leads.

 

This aspect of our approach causes us to differ substantially from conventional regression-oriented factor analysis such as Fama-French approach used by many including style-focused ETFs. Their approach is, statistically speaking, straightforward and is based on the broad samples favored by pure-statistics. But it is inconsistent with the task that faces investors. Our concern is stock selection and that requires, for example, not the lowest valuation ratios available but shares whose ratios are more likely than not to be low relative to where they “should” be based on their relevant 1/(R-G) profiles. Hence we pre-qualify with Buy rules in order to apply our rankings (Value rank for example) to a group of stocks with appropriate 1/(R-G) characteristics.

 

Another real-world example of the weakness of the factor approach involves its attitude toward equity-income investing. Based on factor analysis, notable academicians conclude that this is an undesirable way to invest. Their research was based on their comprehensive approach to sampling and, necessarily included many very high-yielding stocks that performed poorly. Our fundamental approach would recognize very high yield as a danger signal and our Buy Rules eliminate them even before we rank anything.

 

The Buy Rules we use fall into two categories:

 

1. Uniform Buy Rules: These rules are found in all models and are based on Portfolio123 Securities policy.
1. The stock was not sold by the portfolio at any time during the past 120 trading days.
1. This rule is designed to guard against excess turnover and the trading costs associated therewith. It is our “anti-churn” rule and assures that when a stock is sold, it stays sold until there has been a reasonable opportunity for circumstances to change in a manner sufficiently material to warrant making the stock eligible for re-purchase (if it passes all of the rules of the model on a future date).
2. Purchase of the stock would not cause the portfolio to become exorbitantly concentrated in a single sector.
1. This, actually, is a quasi-uniform rule. We always consider adding it, but may refrain from doing so if, for some specific reason, we believe sector concentration would be reasonable for the strategy in question. Any decision to exclude the rule will be noted in connection with a specific model.
2. Where this rule is used, the maximum allowable level of sector concentration will be specified in connection with a particular model.
2. Strategy-specific Buy Rules: These rules are designed for the specific strategy.
1. These are detailed, for each strategy, in Portfolio123 Securities White Paper #3.

 

Ranking

 

Quantitatively oriented investors (quants) are most likely to recognize ranking as the most familiar component of our models. The classic quant approach works with the following formulation:

R = a + b1F1 + b2F2 + b3F3 + . . . + bNFN + re

 

Where

 

R is the expected return of a stock

a is a constant calculated via regression

b is a “factor loading” (weight, or degree of importance) associated with a Factor

F is a Factor (size, value, quality, etc., etc., etc.)

re is the “residual error,” that portion of the stock’s expected return that cannot be explained by the rest of the model

 

Typically, factors (Fs) are selected heuristically with b values calculated through a process known as multiple regression. Factors are then retained or eliminated based on whether tests show them to be useful or not useful in the model (through such tests as R-square and measures of statistical significance).

 

While our ranking systems bear a surface resemblance to this basic APT (Arbitrage Pricing Theory) formulation, they differ in some important respects.

 

• We do not use regression to define our models. We believe such statistical analyses are misplaced as applied to real-world stock selection, where we cannot presume the that the future will resemble historic sample periods. We believe regression works best when one is seeking to interpolate (apply findings to the same population as the one that was sampled for research purposes, as is routinely done, for example, in medical research). Investors, on the other hand, must extrapolate; apply finding based on one population (the historic past) to another (the unknown future) that may be different in substantial ways. We believe the investors’ task is best accomplished heuristically with a focus on sound principles that have the potential to logically bridge the gap between past and future, the logic inspired by the concepts explained above. Our “F” and “b” values reflect this.
• We do not calculate values for “a” (the constant). We aim for overall models (ranks combined with rules and universes) that ultimately deliver “a” (alpha), but we do not quantitatively forecast this.
• We do not calculate R as return. We believe such calculations are inherently lacking in credibility. Instead, in this context, we simply we redefine R as, simply, a rank score.
• We do not concern ourselves with residual error and, in fact, recognize that this term is apt to be high. In contrast to academic studies, we are not seeking to describe the factors that influenced a specific historic period (those who conduct such studies seek low “re” terms with zero being the ideal.) We are simply seeking to select 10-40 stocks we deem worthy of investment without necessarily making judgments about the merits of the many others.

 

Most of our ranking systems are multi-factor. In some systems, all of the factors will reflect one style (e.g. our “Classic: Quality” ranking system). In other cases, ranking systems will reflect multiple styles (e.g. our “Classic: Quality - Sentiment” ranking system). As noted, none of them are offered to provide an APT-like explanation of the entire market. They are instead, designed to serve as part of a strategy. The role of the ranking system is to pick the 10, 15, 20, 30 or 40 “best” stocks from among those in the universe that have met the pre-qualification Universe and Buy Rules.

 

Once a stock enters a portfolio through the combination of Universe, Buy Rules, and Rank, it remains there indefinitely – until it “triggers” any one of several Sell Rules that form the final part of the model.

 

NOTE: The classic method of using a ranking system is as a sort key: In other words, sort all stocks from high to low based on Ranking System A and select the 20 highest ranked stocks. Also, however, rank scores can be very valuable when used as thresholds for Buy or Sell rules. Here, for example, a Buy rule might require that stocks be ranked 80 or better for Value. This allows us to identify well-valued stocks without having to articulate separate thresholds for each possible valuation ratio. This can often be more effective than a series of conventional ratio-specific rules given that different ratios may be more or less meaningful for different stocks with different fundamental profiles and that use of too many rules makes it increasingly likely that the number of passing stocks will fall too low, or even to zero.

 

Sell Rules

 

These are rules against which each stock in the portfolio is tested at each refresh period (e.g. once per week). Any stock that fulfills any of these rules is sold with the proceeds invested in the highest rated stock that is not yet in the portfolio and which satisfies all the Universe and Buy Rules. If there is more cash available (e.g. as a result of the sale of more than one holding) than can be invested in a single stock (i.e. if reinvestment of all cash into one stocks would lead to that stock having a larger-than-targeted weight), then multiple new buys will be made. It is possible that modest amounts of surplus cash (amounts too small to be feasibly invested in a new equity position) will remain in the portfolio.

 

The Sell rules are designed with a view toward controlling portfolio turnover and related trading costs. Stocks may also be sold on the basis of a Sell rule relating to criteria relating to investment merit.

 

As with Buy rules, there are two kinds of Sell rules; uniform and strategy specific.

 

1. Uniform Sell Rules: These rules are found in all models and are based on Portfolio123 Securities policy.
1. Liquidity Deterioration
1. Average daily dollar volume of shares traded was less than $5 million over the course of the past 20 trading days
2. Excess position size
1. Each position has an “ideal” weight based on the goals of the portfolio. For example, in a ten-stock portfolio, the ideal weight of each position is 10%. Under normal conditions, actual weights will vary as stocks move up and down and we control turnover by accepting this so long the weight codes not become excessive, which we define as 50% above ideal. If that occurs, we sell such a portion of the position as to bring its weight back down to ideal.
3. Lagging performance
1. After having been held for at least 60 trading days, a stock will be sold if its 13-week performance trails the market by more than 25 percentage points.
2. After having been held for at least 250 trading days, a stock will be sold if its 52-week performance trails the market by more than 25 percentage points.
2. Strategy-specific Sell Rules: These rules are designed for the specific strategy.
1. These are detailed, for each strategy, in Portfolio123 Securities White Paper #3.

Position Weightings Within Portfolios

 

A stock’s weight within a portfolio (i.e. the percent of assets allocated to it) is based on one of two approaches: It can be liquidity driven, or suitability driven. Market capitalization weighting is an example of a liquidity driven protocol and is useful for very large portfolios, portfolios for which liquidity considerations make it unfeasible to invest equally in a $50 billion company and a $15 million issue. Portfolio123 Securities do not have liquidity-based needs for such an approach to weighting. Accordingly, therefore, we use suitability-based weights.

 

In a suitability-based approach to weighting, the percent of assets allocated to a stock will depend on its degree of suitability according to the characteristics of the chosen approach. One example of such a protocol is volatility weighting, where stocks are weighted on the basis of their scores as per a model that calculates some measure of volatility. So-called “Smart Beta” is another example (e.g., a stock will be weighted on the basis of its score as per a model that measures various fundamental data-points or metrics). It might even be said the Modern Portfolio Theory (MPT) and the “efficient frontiers” on which it relies is a version of this; stocks are weighted (portfolios are “optimized”) based on combinations of expected return and standard deviation of returns.

 

The present Portfolio123 Securities approach to modeling is such that it views all stocks selected for the portfolio (as a result of application of Universe and Buy rules and the Ranking System) as being of equal merit. No stock is deemed more important than any other. The weighting protocol we use reflects this. Ideally, all positions in the portfolio will be equally weighted and that is how the portfolio is comprised at inception.

 

In practice, however, and as time passes, modest variations will occur:

 

• As we allow winning positions to maintain larger weights (in order to manage turnover)
• Uniform sell rules, however, set limits on how large a position may become until it is trimmed back to its ideal weight
• As we allow losing positions for which selling is not warranted to maintain their smaller weightings until they are sold or until they recover
• As proceeds from selling are reinvested in new positions (if more than one stock is purchased, available cash is, to the extent possible, allocated equally among the new positions)

 

Testing/Simulation

 

The process of backtesting or simulating model performance is a crucial aspect of our process as well as a challenging one.

 

Unlike the live portfolios, back-tested and simulated performance presents hypothetical results based upon the retroactive application of our investment strategy over a select market period. Hence they do, necessarily, benefit from 20-20 hindsight regarding “what worked” in the past. The challenge is that what worked in one environment may not also succeed in the future, which could turn out to be quite different and in material ways. This is why regulators require – wisely so in our opinion – disclosures cautioning clients that they cannot rely on past performance to be indicative of future results.

 

For many in the field of quantitative finance, this reality poses powerful obstacles. Empirical research, such as that popularized by Fama French and which forms the basis of many strategies offered today, is necessarily dependent on one or more specific past periods and is of no use to investors unless they are able to infer that the model’s output can be projected into the future. Empirical observation alone cannot justify that.

 

As discussed in White Paper #1, our strategies are not based on what we learn through empirical study. They are instead based on financial theory which transcends the peculiarities of any particular market environment. Nothing we do, and nothing we learn from our testing, can assure that the market will favor stocks bearing the “right” traits at all times. We can, however, assure that the ideas that motivate our choices are rationally related to sound financial theory. And we believe that over time, if not day in and day out, the market will recognize and price the stocks as such.

 

This raises the question of why we test at all. What are we seeking to accomplish if we aren’t looking for a numerical forecast of potential future performance? The answer lies in the nature of the strategic tasks as described in White Paper #1. We can never know that which we need to know, future growth prospects, future risk, and all the future factors on which they will depend. What we must do, what all investors must do whether they openly acknowledge it or not, is look the data we have to develop clues that point us in the direction of stocks we believe are more probably than not mis-priced, and do so in language a computer (or borrowing from today’s popular parlance, a “robo” manager) can understand and process by accessing a database (robo food!).

 

The purpose of our testing is to seek feedback as to the efficacy of our efforts to translate our modeling ideas into language that can be understood and followed by our robo manager. For example:

 

• Financial theory makes it clear if two stocks sell for 20 times trailing 12 months EPS, the one that grows more quickly in the future is the one that will perform better all else being equal. We don’t need testing to tell us this: We know it.
• But how do we measure future growth? We know we cannot do it directly because we don’t know the future. We can however consider various clues:
• One widely used set of clues is the historical track record of EPS growth over various time periods. We can also look to the historical track record of Revenue growth rates over various periods (revenues do not reflect essential costs, but they are also less impacted by unusual accounting items); trends in margins that enable companies to generate differing levels of EPS based on a given amount of revenues, etc.
• Such clues, however, are often misleading. Companies do not trend in straight-line manners. The default expectation involves a company lifecycle, which calls for companies of a certain age to start decelerating and eventually deteriorate. We may need to supplement or even replace our historical clues with other factors, such as share price momentum, estimate revision, and so forth which may give us clues to the judgements reached collectively by the investment community which incorporate qualitative factors that cannot be seen in historical fundamental data.
• We can and do use testing to help us choose among the various clues at our disposal. We can judge the historical efficacy of our clues. We can also be aware of changes, over time, in efficacy, as, for example, estimate revision may gain or diminish in stature as changes occur in the structure of Wall Street research departments.

 

To test successfully, under our needs and in the context of investing, we can never naively or “robotically” interpret any result we see. We must always seek to understand why the results were as they were and make judgments about whether we can or cannot use the factors tested.

 

Note, too, that we do not draw any conclusions from the returns generated by our hypothetical test portfolios. Much of a stock’s return depends on uncontrollable market factors. Hence a portfolio that returns 25% may be deemed unsatisfactory if the market returned 40%. Conversely, a portfolio that lost 5% may be judged to have been successful if the market lost 10%. Also, we would not avoid or abandon a strategy that performs poorly and in a manner that seems at odds with what testing suggested if we recognize why the poor performance occurred and have sound reason to believe those conditions will not be permanent.

 

Accordingly, testing is not a process that dictates whether we use or do not use particular factors or models. It’s a process that helps us understand factors and models and which provides feedback on the efficacy of our efforts to make ideas actionable by translating them into robo-speak.

 

Ultimately, your choice to invest in a model should not reflect any set of test results but your judgment as to whether you find the ideas we are pursuing appealing and consistent with your goals and risk tolerances.