2.7.2 PEAD (Post-earnings-announcement-drift).

Post-earnings-announcement-drift is another factor influencing abnormal return. In its essence, PEAD is characterized by on-going abnormal returns during the period from several weeks to several months (60 days on average). As the starting point for PEAD scientists say it be the so-called earnings surprise, which is, effectively, the difference between reported earnings and expected earnings. Announced earnings are becoming a somewhat of surprise for investors, that were expecting lower or even subnormal returns. Therefore, this interest is very much likely to be supported by increased investing activity. So that stock prices and earnings curves go the same direction as earnings surprise. PEAD might be a hidden variable for some enterprise success during given periods of time and is considered as a robust finding, firstly proposed by Ray. J. Brown and P. Brown (1968). Bernard and Thomas (1989) and (1990) explained PEAD in much more detail, showing up that PEAD is largely depends on positive autocorrelation amongst seasonal difference between 3 out 4 quarters of the financial year (PEAD usually reveals itself after quarterly published financial statements); and negative autocorrelation between seasonal differences that are 4 quarters apart (Bernard & Thomas, 1990). As an important note, Reed (2007) showed the same effect as the firms, which have their stock price increases in a short run do have their long-term prices less effected by announcement of earnings. Such result connects post-earnings-announcement-drift with one of stocks market friction (form of transaction costs).



Statement of research question

We shall start our discussion on the sufficiency of methods used in this paper by stating research question and developing ideas over its skeleton:

We reckon our research question to be: To extent does NCAV (Net Current Asset Value) model show the return on portfolio among companies arranged by using different fundamental valuation models in varying industries?

Precisely, the question we pose aims to answer another question: Is NCAV is better than other valuation models on finding undervalued shares? The fair question in this regard is how we measure the terms “better than others”. While answering this particular question it is vital to recall the core idea of any equity finance in form of stocks investing. We either seek maximization of utility for our own, or for our company. Such a wide notion has been the basis of numerous works both on agency theory and financial analysis theory. As developed by Jensen & Meckling (1976), Fama & Jensen (1983) and as finalized in Gibbons & Roberts (2013), when talking of the internal structure of the firm, we have to remember of two antagonistic sides of agents and principals. Both sides have their own incentives, such as principals are seeking to maximize their utility by increasing shareholders' wealth (stock price), whilst agents are keen on maximizing their utility in form of compensation. By compensation, as was developed by named authors and Ross (1973), we mean different incentives to agents (e.g. base salary or non-equity compensation bonuses). The most efficient method of increasing loyalty to the company and decreasing aberrant activities toward the company is proven to be stocks and options pays. And once again we touch upon stocks' uniqueness and enormous efficiency in use.

If we assume that public companies are considered to be built out of agents and principals as well as private firms, we clearly see that share price becomes the cornerstone of all activities both internal and external to company, performing on stock exchanges. We then connect this comprehensive meaning of stocks utility to increasing of stocks utility. Particularly, we would like to show that increasing returns on stocks does increase utility of all stakeholders gathered around equity trading. Specifically, investors' behaviour and the multiplicity if equity trading strategies us what we aim to elaborate on.

We would like to, first of all, remind that we divide investors in two groups: 1) professional - which we assume are consisted of two subgroups: institutional and non-institutional investors and (2) non-professional investors. In these terms, we had said that we suppose that our results would be presumably to be applied by non-institutional and non-professional investors. In terms of their natural economic interest, we believe that non-institutional investors, in the face of individual enterprise, would be feasibly attracted by increasing shareholders value when investing in undervalued stocks. To put it another way, we believe that non-professional investors as individual actors are seeking to maximize their utility in the form of individual wealth, such as agents are seeking to, as they stay contrariwise the principals.

Developing this logic sequence, we are apt to consider that stocks return, as stocks being central issue for all target audience groups, and their increase will be able to be seen as an instrument of increasing utility of these groups. In other word, the instruments of increasing value of both non-institutional investors and non-professional.

In the review literature as well as in this paper undervalued stocks are seen as primarily the source of abnormal returns. So that are the returns which are if compounded can give return to the investor which will be higher than if investor was to invest in companies provided by returns of the benchmark. Indeed, portfolio investments, as numerously cited method of equity trade, is one of those types income for investor, in which risk of different commodities is flattened by the diversified range of shares with each return and risk. In other words, as clearly as it has been showed in CAPM, portfolio, if used correctly, can give investor a lever to increase returns higher than the benchmark. What is special about portfolio of undervalued shares, is the fact that as long as they provide the abnormal returns, the portfolio of such shares can provide the investor with even higher return, compared to ordinary portfolio investments. However, undervalued stocks are to be chosen with specific criteria, which we will cover in the latter sections of this report. To build the presupposition for future discussion we ought to link the notion of undervalued stocks with models we are going to apply to range of financial data of different companies.

To begin with, highest return on undervalued stock can be reached if the investor considers features described by Fama & Jensen in number of their publications. Compensating CAPM's gap in terms of explaining the nature of return of different stocks, Fama & French key conclusion was formulated as three factors model (FF three factor model). As a recollection, the novelty of the newly proposed model was that no FF could explain higher percent of stocks returns. In comparison to Capital Asset Pricing model, FF introduced Book-to-market ratio variable and Small-to-Big ratio of difference of market capitalisation between small and big market cap companies. The outcome - small companies (in market cap) with big book-to-market ratio tend to outrun opposite companies in terms of stock return. Such an idea completely corresponds with so-called small firm effect, which had been producing much interest among investors all over the globe.

Referring to the models we came across during theoretical foundation, there are some comments concerning the choice of the incoming methods for methodology.

Discount Dividend Model as our basic model, which by the way is seen in the majority, if not in every publication, which touches upon fundamental analysis and accounting anomaly, is considered as the simplest instrument to find undervalued shares. DDM stresses abnormal dividends, which are the direct consequence of remunerative and lucrative capabilities of a company, as dividends are paid from positive profits.

Free Cash Flow (FCF) model can be seen as derivative of DDM. Particularly, we can say so, because it operates with cash flow received by firm's capability to produce cash flow from operations (operational efficiency). From the point of view of corporate finance, the net income which is used to pay dividends is substituted with cash flow that is to be used in investing activities. In this regard, FCF is another possible way to find undervalued stocks.

Residual Income model (RI) is third alternation or inversion of Discounted Cash Flow (DCF) model. Again, the sum of money that will have been used to pay dividends is switched with residual cash flow, which remains within the company.

Speaking of NCAV, the usefulness of the model is not questioned any more, as long as Benjamin Graham's and Warren Buffet's equity trading strategies continue to outperform not only various benchmarks, but CAPM as well. In the core of NCAV there is a very picturesque example of terminal value of the company. Terminal value itself represents the amount of net assets remained on “the ruins” of a company. In other words, when company experiences default on obligations, after paying liabilities, there is bounded list of assets still being possessed by the company as a legal entity. Measuring the value of these assets, we come to the point of understanding net current assets value; or the real cash equivalent that will has been producing profits for the company if it situation of intense economical fluctuations. The intrinsic value found by NCAV is a very power tool for undervalued investors, as even major stocks exchanges platform regard this ratio as one of indicators of company's undervalued characteristic.

The last commentary that is to be done, is about the role of P/E and PEG ratio. Reviewing publications on the topic of fundamentals and anomalies, we can clearly see, that the mentioned ratios are too simplified, and, as was discussed in deep details within second section of this paper, can be used properly on any type of financials. Effectively, out of such presupposition of inconsistent usage of PEG and P/E ratio, as the simplest and straightforward metrics, there are constant attempts to find the most effective model, which would fulfil investors' expectations to the highest possible extent. According to Richardson, Tuna & Wysoski (2010) on the frequency of application of enterprise valuation models, earnings multiples related models are used by investments practitioners (as compared to academics - who teach financial analysis course in academia) around as frequently as 74% amongst all valuations, and 23% infrequently. Book value multiples have been used almost in 83% of all valuations performed by academics in the last 5 years and the number of 100% have been used is for accounting anomaly equity trading strategies. Earnings growth show 30% of frequent use by academics and 53% by practitioners.

The ending result of application of the different models on data has no sense if the criterion of higher return will not have been seen. To finalise the conclusions of the paper we ought to estimate the return of particular portfolio, e.g. calculated with companies chosen by NCAV or the same but using DDM. Estimation of return will be done using CAPM. Most importantly, after this procedure we will compare differences in return of various portfolio, give sufficient discussion on the results and limitations.

By this moment we received an opportunity to build our hypotheses.

1. Based on distinctions between DDM and NCAV we suppose that:

2. NCAV outperforms DDM in multi-industry portfolio

3. Based on distinctions between FCF and NCAV (by operational efficiency parameter)

4. NCAV outperforms FCF in controlled single industry portfolio

5. Based on difference between RI and NCAV

6. NCAV outperforms RI in multi-industry portfolio

7. Graham's Number fails to NCAV in multi-industry portfolio

8. Undervalued stocks investment strategy outruns the market (as S&P500)

NCAV outperforms the Market

DDM outperforms the Market

RI outperforms the market

FCF outperforms the market

Graham Number outperforms the market

Regarding the objective of this paper, we focus on identifying the model which anticipate the highest returns on investments among the particular pool of models: NCAV, DCF, FCF. As the above objective requires comparison of fundamental valuation models, we set up the following tasks that should be solved:

1. Break down the fundamental models in order to figure out their relevance to our objective;

As the companies have different stakeholders which pursue their own goals, the usage of NCAV, DCF and FCF models also varies. As the field of this paper is investments in undervalued stocks in order to increase enterprise value, the authors will put into practice the essence which solely tackles this field. For instance, as it was mentioned, the authors will not look at the free cash flow model from the perspective of increasing shareholders' value by paying the excess of money to them. On the contrary, the authors relate the FCF model with investments;

2. Choose the pool of companies for profound analysis;

For transparent analysis, all the companies should be chosen at random. Moreover, the authors stick to their own guide for companies' selection:

- The medium-sized United States companies which are publically listed on the stock exchange. High capitalisation companies are not considered in this paper because of their popularity (not included in market indices), significant attention from analytical agencies and traders, hence with low share turnover - all of these features are Benjamin Graham's requirements for the companies with undervalues stocks;

- Companies have limited access to most “informal” information dissemination channels (Piotroski, 2000). Without any proof, market price of any company might show fluctuations during a short period of time (hour, day) only because a trading agency or a well-known representative of that company publicly announced some preliminary news without any weight, or even gossip. Therefore, only financial statements represent the most reliable source of information about a company's performance;

- The authors do not include in the pool of companies IT and high-tech SME businesses. The only reason for that is high fluctuations inherent in IT industry. As the paper predominantly takes into account Graham's fundamental principles of value investing, high-risk companies are excluded (the risk is explained as continuous fluctuations of share price);

3. Extract all needed information for calculating the fundamental valuation models (NCAV, FCF, DDM);

The information is extracted from companies' annual reports, official analytical agencies which consolidate financial data (Bloomberg, The United Stated Securities and Exchange Commission).

4. Make all needed computation related to the fundamental valuation models in time-series;

The information which is considered for computations: dividends paid to shareholders, capital expenditures the company has made in every year (or investments to property, plant and equipment), working capital (the difference between current assets and total liabilities), total liabilities, number of shares outstanding, preferred stocks, cash flow, earnings before interest, taxes, depreciation and amortization, changes in working capital, weighted average cost of capital, earnings per share, book to value per share, total shareholders' equity, expected return on the capital asset, risk-free rate of interest.

5. Make a portfolio of the so-called “perfect” shares;

The authors quite agree with the Warren Buffett's main point concerning right interpretation of the results, and the portfolio of shares assembled after NCAV, DDM and FCF computations is compared with a portfolio of shares which are included in Standard and Poor's 500 Index. The main idea is that the profitability of a portfolio can be analysed only with a comparison with another portfolio which is identified as the “standard” and the most productive.

6. Explain outcomes & give comments

The authors will analyse the results in a profound way with precise interpretation of the results generated by fundamental valuation models;

7. Discuss limitations & future development

The authors will enumerate the most significant limitations which have been considered throughout the research, and also suggest some development to cover more periods, companies and valuation techniques.



Methodology

The way we conduct research is primarily the exploratory design, as we formulate problems, clarify concepts and form hypotheses to test, however, since the hypotheses are formulated we tend to demonstrate explanatory and partially descriptive characteristics of the research type. We describe and explain the probable reasons for the outcomes, spending the majority of time saying the nature of choosing of each model. Repeating ourselves, the mentioned actions are to be done after exploratory part finished.

With the research question which is stated in this paper we will also touch a demarcation line between fundamental analysis and other types of investment analysis, such as quantitative and technical. As it has not been identified the most effective way of analysis of undervalued stocks because all types of valuation have both pros and cons, we will try to set up a near step of this comparison. Thus, the research will tackle the thoughts of famous founders and followers of the above types of analysis. On the one hand, Benjamin Graham and Warren Buffet were the founders of fundamental principles, who successfully applied the techniques and achieved extremely significant results. On the other hand, such economists as Harry Max Markowitz (the Nobel and John von Neumann Prizes recipient), Jack Treynor, William F. Sharpe, John Linther and Jan Mossin, who independently introduced the CAPM, and other famous economists who created modern technical tools of valuation based on market trends, head and shoulders pattern, moving averages, pennants, and so on.

Moreover, it is very important to discuss the authors' opinion and thoughts about the types of analysis before the research. The authors are exclusively impartial to the types of analysis and do not have any personal preferences about either fundamental or technical approaches. Contrariwise, the main aim of the research is to find out the most effective and reliable methods, identify its peculiarities based on the data.

The premise of choosing the model of valuation analysis was a deep cover of the most important models, their creator and followers. As the investment might be either short-term or long-term, fundamental or technical, the authors' attention was attributed towards each of them. Taking into account technical analysis, the most applicable and multipurpose is Capital Asset Pricing Model (CAPM) described above. This model meets the research purpose for comparing fundamental valuation models in a proper way.

Regarding fundamental analysis, the authors have reviewed a great number of articles and figured out that the most result-driven fundamental valuation models in terms of returns on investments are models elaborated by Benjamin Graham, later improved and popularized by Benjamin Graham.

4.1 Description of data collected on each stage of the research

4.1.1 First Stage: Raw data sampling

The data that was used for successful fulfilment of data analysis procedures initially has been gathered in the form of raw data. For each valuation technique, the data should have been adapted, based on its syntax. The majority of the models that were used (CAPM, NCAV, DDM, FCF, RI) had derivative figures that could be calculated only by outlining necessary figures out of data bases, that were in hand during the major part of the data analysis. The core data base, that was in use throughout all preparation stage of the data analysis is US Government Securities & Exchange Commission (SEC) official web-site, company fillings section. We touched upon this aspect previously in the paper. So, the primary data that had been collected out of SEC Company Fillings sections is financial statements of the companies from sample. SEC website allows users to analyse, copy and use interactive form of the company particular financial statement.

Basically, in order to calculate all necessary variables that will have been used in the later stages of the analysis, we needed to work with, approximately, all the most important consolidated accounting information under IFRS:

· Balance Sheet of the company

· Statement of Operations

· Statement of Equity

· Statement of Cash Flow

· Statement of comprehensive income/loss (also P&L)

· Statement of Equity (Parenthetical)

These official documents, if allowed for particular company, are downloaded to SEC under code 10-K and 10A-K, which stand for annual financial statements and amendments to financial statements respectfully. Starting from the first valuation framework, next, we will cover used financial variables in the first stage of the data analysis.

Dividend Discount Model

The authors were enthusiastic to analyse the dividends paid for shareholders. As this kind of remuneration indicates the distribution of profits, they can be taken into account as an indicator of undervalues stocks. As written in its basic form above for applying framework the following information needed. 1) dividends per share (DPS) - meaning dividends paid in year t divided by number of shares outstanding. Sometimes, when publishing financial statements, companies reflect in the statements of equity (parenthetical) the figure of dividends per share. It depends on the year, and accounting policy of the company and does not obligatory. As proposed by Ohlson (1995) and Kothari (2001), the price of stock (P) is expressed as function of earnings (E) and expected return (r) on stocks. So, the major difference between conventional approach to DDM formula and the mentioned above is the fact that alternation above does not consider growth of the stock, but considers growth of returns per stock:

Such growth per stock is calculated as expected return on stock. However, in order to fix the model for earnings surprise effect and post-earnings-announcement-drift (discussed previously), we decided to use rate of return with adjustment to previous year. In this way, we create situation of perfect denominator in the formula, so that the forecast for the next for stocks price is perfect. Otherwise, we seek for expected return that investors are keen to receive. So, that the expectations could be a bias factor, as long as the stock price in the future period does not contains return expectation, because DDM in its mechanism was created to express intrinsic value, rather than market valued added price.

What is important to admit is that in order to calculate dividend discount model correctly we need to assume next year's dividends accounted for this year's rate of return. Stock prices are to be found on the specialized web-services, containing historical prices, such as Yahoo Finance, Bloomberg, Thompson Reuters and similar professionally oriented web resources.

Last, but not least about dividend discount model, the research assumes that a company may not pay dividends because of its peculiarities related to overall strategy, the authors took net income which could be potentially distributed to shareholder in form of dividends.

Residual Income model

The formula is much similar to DDM, however, as was pointed out with important adjustments. It the syntax of residual income ( we use Net income less Equity charge (Equity capital multiplied by Cost of Equity). Basically, as with DDM the meaning of RI stands behind calculating value of company's stock as the sum of BV (book-value) and the present value of its expected future residual income.

In order to calculate the book value in its conventional form we need to take Total Assets Less Total Liabilities less intangible assets. The segment of the raw data book-value calculation you can find below, as an example:

Example of book value calculation

$'000	2012	2013	2014	2015	2016	2017
Total Assets	4847000000	3872000000	4100000000	4246000000	4334000000	4975000000
Total Liabilities	1802000000	1585000000	1840000000	2178000000	2253000000	2721000000
Intangibles	200000000	153000000	194000000	237000000	330000000	507000000
Book Value	3045000000	2287000000	2260000000	2068000000	2081000000	2254000000
Expected Return, %	10,97	106,81	-26,55	-5,40	-1,83	-15,56

In the syntax of residual income valuation framework, we have expected return on stocks, again, in the form of rate of return, calculated perfectly with completely known information. Total Assets and Total Liabilities, as well as Intangibles could be find within balance sheet of the company accounting documents. Stock prices were to be found on the specialized web-services as well. These web-sites contain historical prices, examples of such resources include Yahoo Finance, Bloomberg, Thompson Reuters and others.

Net Current Asset Value model

Net Current Assets Value, which was firstly introduced in the book “The Intelligent Investor”, made an professional impression on the authors. The authors chose NCAV because of several reasons:

- Both professional and non-professional investors can easily calculate NCAV model because of its transparent syntax;

- The model has understandable explanation and applicability to the real situation;

- Repeating again, if the difference per share between current assets, total liabilities and preferred stocks (which are considered as liabilities as well) is greater than a stock price of a company, then the company's stock is undervalued, and vice versa.

- The existing articles which mentioned or were dedicated to the NCAV analysis, identified that among all other fundamental model and even comparing with Standard and Poor' 500, NCAV demonstrated the highest return:

- According to "Ben Graham's NCAV (Net Current Asset Value) Technique in the 21st Century" the strategy produced an annualized geometric return of 24.7% from 2003 to 2010 that was unexplainable by either the capital asset pricing model (CAPM) or the Fama-French model;

- "Ben Graham's Net Current Asset Values: A Performance Update" also found that the strategy outperformed the benchmark. This study determined that this strategy produced a return of 33.7% compared to 12.1% for the benchmark between 1971-1983.

- The model NCAV takes into account the most liquid asset - cash, cash equivalents which can generate money and scale business;

The investor uses NCAV per share to estimate company's liquidation value because this technique shows “net” current asset. In other words, if an investor buys a company (with a reliable perspective of growth), traded by its liquidity value, undoubtedly, the investment will profitable because the investor will receive more than he/she paid for. Breaking down NCAV per share, it is highly imported to regard all the part of formulae: Current Asset is any asset of a company which can be easily sold or consumed. The main feature of this type of asset is high liquidity. According to the format of Balance sheet, Current Assets are comprised of:

· Cash and cash equivalents (the most liquid asset of a company)

· Marketable securities (equity and debt securities)

· Accounts receivable (the amount of money which customers owe the company)

· Inventory (goods which are available for sale, they are valued at the lower of the cost or market price)

· Prepaid expenses (value that has already been paid for any service)

Total Liabilities regard both current and non-current debt the company has at the moment of valuation.

The formula of NCAV usually is accompanied with Graham's Number formula as well. The latter is often used to check either NCAV shows adequate results. As could be seen from the syntax of the former, Current Assets is a documented number, which can be found in the Balance Sheet of the company, same goes for Total Liabilities. Preferred stocks can be found within Income statement, as well as the number of Shares Outstanding. The example of calculation of NCAV as a table segment please find below:

Calculation of KPIs of a company

Company X	$'000	2012	2013	2014	2015	2016	2017
	Current assets	31054903	43033188	38168583	42234609	51428881	57577778
	Total Liabilities	29825098	46502256	49212265	45912794	43051595	52943043
	Preferred stocks	0	0	0	0	0	0
	Number of shares, #	25451354	25451354	25451354	25451354	25451354	25411623
	NCAV, $	0,05	-0,14	-0,44	-0,14	0,33	0,58

The company in the example above, unfortunately, does not have preferred stocks, however, as it appears to be, the company anyway has negative sum, so the result has been obviously disregarded. Particularly, analysing a great number of companies, the authors noticed not some many companies which reflected their preferred stocks. Running ahead, considered companies usually did not have listed preferred stock.

The models which were described by Benjamin Graham, are not so popular because of their easy calculations, but effective. Throughout the whole research, the author cites eminent and worlds' acknowledged investors (such as Warren Buffett, Peter Lynch), well-known authors (Dudzinski, Kunkel, Bildersee, Cheh, Ajay) because they found practical usage of Graham's principles, and some of them apply them for these days. That is why the process of analysis was also composed of deep and profound analysis of biographies.

For the Benjamin Graham's model the authors have to take into account the following ratios for intrinsic value: Total Current Assets, Total Liabilities, Preferred Stocks, Cash Flow - Net Profit, Discount Rate (depends on industry), Market Capitalization, Book-to-market ratio, Risk free & Risk premium, B (Market risk or systematic risk), EPS; Dependent - Enterprise Value; other variables may be obtained in later study.

Going further, the authors continued analysing Benjamin Graham and Warren Buffett's practice and took into account Free Cash Flow model.

As was described in detail in the previous sections of this paper, the first three consecutive indices are calculated on the Statement of Cash flows, downloaded from SEC data base. Abbreviation of D&A means depreciation and amortization reported by a company, change in working capital shows a deficit or a surplus between current assets and current liabilities. CAPEX, or capital expenditures, counts for all the expenses attributed to a company's property, plant and equipment. The model is used in this paper because of several reasons:

- Both professional and non-professional investors can easily calculate the FCF model because of its transparent syntax (all the data can be retrieved from the financial statements);

- The model has understandable explanation and applicability to the real situation;

- The model Free Cash Flow takes into account the most liquid asset - cash, cash equivalents which can generate money and scale business.

4.1.2 Second Stage: Model Application.

The next stage of the research development has the goal to detect either particular stock is undervalued or not. Generally speaking, this procedure is based on the ratio V/P

where V is intrinsic value calculated, and P is market price taken from the historical stock prices web-service.

Basically, if intrinsic value is more than 1, it is considered undervalued, if they are equal, the company is valuated perfectly. This is assumption can be made, almost in the very only situation of company doing initial public offering. In order for company to have V/P=1, we need to have utopian market efficiency, which goes inconsistent with another assumption, of market efficiency, but with existence of anomalies, subnormal and abnormal returns, transaction costs. The criteria of pure undervalued property we can undoubtedly consider that the company was undervalued this year. It corresponds with a presupposition that companies are tended to vary their book-to-market, or V/P characteristic. What is even more important is that out of this kind of tables we can understand why specific ratio has so big or small ratio. Next page you can find the example of comparison between RI, DDM and NCAV:

Comparison of RI, DDM, NCAV valuation models

	2011	2012	2013	2014	2015	2016	2017
Company Y	NCAV, $	0,17	0,05	-0,016	-0,01	0,02	0,01
	RI, $	2450261	476256	87890	-139903	-194114	188452
	DDM, $	0,02	0,01	0,01	-0,18	-0,02	0,23
	V/P (NCAV)	0,01	0,03	-0,02	-0,01	0,02	0,01
	V/P (RI)	1353735	292182	144082	-208810	-209400	266552
	V/P (DDM)	0,0004	0,0002	7,66	-0,002	-0,00037	0, 04
	Market price, $	1,81	1,63	0,61	0,67	0,927	0,707

Numbers in this table translate questionable conclusions in terms of applicability of particular framework for various industries. In this table, red cells represent negative NCAV, when total liabilities, e.g. are more than current assets; or red cells lined RI represent negative expected return, the same goes DDM. These occasions show correspondence with theory of high sensitivity of DDM and its derivative RI to changes in growth. Purple cells, subsequently, demonstrate V/P>1.

Using V/P reference to each company in each year we may understand which companies shall we include in portfolio for this period or not.

4.1.3 Stage three: CAPM application.

If we shall recall the premise of utility maximization in the form of wealth, we may trace such an idea to practical purpose and apply it to calculations. In this section of the paper, we focus on how companies can produce return, when chosen with different methods. We are encouraged to consider this approach, because the number of companies in the portfolio cannot make significant change, as initially our sample consists of specially organized units. In the comparison of pair NCAV versus DDM, for example models start with the same environment. When talking of RI versus NCAV pair, we intentionally choose random pool of companies from the same industry, and apply models for the same companies to find either NCAV is more flexible than RI in this particular environment. By the positivity of the year's overall performance we choose companies in portfolio.

The key moment in this subsection is comparing returns of portfolios, built on different: either (1) number of firms but economically different, so that lesser number of firms still demonstrate better return that bigger number of them, either (2) we have the same number of companies within the portfolio, but the return they produce differs significantly/non-significantly.

The idea of high importance is that, in general, return on undervalued shares have to at least be the same as the most popular benchmarks, such as Russell 1000, S&P 500, Dow Jones, Nasdaq or Merrill Lynch. If return on undervalued shares outruns these benchmarks, then we can strongly correlate such an event with Fama & French (1993) explanation, and recommend such equity trading investment strategy as an efficient one for increasing of enterprise value. The opposite solution is to show that, if, for instance, Dow Jones falls around 10% yearly, and we can see smaller fall on undervalued shares, we still can recommend what we tell about above. The main goal of investing is to choose alternatives, which can give more utility. Outperforming the entire market would be considered as a very good decision anyway.

In order to collect all the data to calculate Net Current Assets Value, Free Cash Flow, Dividend Discount Model, Residual Income, the authors used the following strategy:

1. Identify the resources where it is more convenient to extract data

Most of the numbers are located in the annual reports and financial statements, however, we used a database called “The United States Securities of Exchange Commission”. The form is extremely convenient to select the companies from the particular industries, choose appropriate forms. For example, if we need to find statements of Golden Minerals Corporation, we can just put its name, and then find all available fillings. For this research, we applied for one of the most important and frequently used filling Form 10-K, an annual report which is published solely for the United Stated Securities and Exchange Commission (SEC). This form gives a comprehensive summary of a company's financial performance. 10-K covers company's history, highlights the organizational structure, executive compensation (but this information is limited because the Form DEF 14A (Proxy Statement) officially publish overall remuneration system and real base salary, bonuses for overcoming the target, stocks and options, and other payments), equity, and audited financial statements (Balance Sheet, Income Statement, Statement of Changes in Equity, Cash flow statement). The SEC also gives an opportunity to use interactive data for more convenient analysis and data extraction.

2. Analyse the information on the official web-sites and annual reports published in a free access

The authors faced some obstacles during data analysis and extraction, hence some of the data was taken from annual reports and proxy statements.

3. Analyse information about the stocks on the official analytical web-sites

As the research assumes a broad range of data extraction from different official resources, some information is not reflected in the Form 10-K, annual reports and separate financial statements, and in such cases the authors extract information from Bloomberg L.P., Thomson Reuters, Google Finance, Yahoo Finance, FactSet, S&P Global, Morningstar, Dow Jones, and so on. For example, Table 4 shows the data the authors used.

Overall	Financials
Beta:	0.30		GORO.A	Industry
Market Cap (Mil.):	$219.9	P/E (TTM)	67.02	17.19
Shares Outstanding (Mil.):	56.84	EPS (TTM)	0.06	-
Dividend:	0.00	ROI:	3.02	5,75
Yield (%):	0.52	ROE:	3.10	10.00

Example of extracted information about Gold Resource Corporation*

*Source: Reuters, international news corporation

The main attention should be focused on Beta because there are no precise sources with calculated Beta. It was mentioned above about Beta; hence, the only point here is a difficulty to count it and the solution to take ready Beta.

4. Build the portfolio from the companies according to the returns gained after the fundamental valuation analyses.

Presumably, some of the models will show different outcomes, hence the authors are interested to find and choose the highest ones in order to compare formed portfolio with the above-mentioned indices (S&P 500 and Dow Jones). Again, the main point in comparison is the absolute value difference between S&P returns with calculated ones. If an investor, enthusiastically and naively assuming that the returns will always be positive and high, the nature of the investor might be misinterpreted. Warren Buffett's advice is to compare portfolio return with the most popular and relevant alternative investment instrument - S&P 500, for instance. And if the return has been plummeting for 3 years down to 15%, however the overall portfolio return has been declining down to 10%, that means that undervalued stocks which form a portfolio decisively outperform the index - and this is an evidence of the fundamental valuation model analysis.

Talking about the sample of the study, the research focuses on the company from a particular industry. Taking into account the guide for companies' selection which is mentioned before, the authors decided to analyse companies from Metal and Mining Industry (at the list of SEC codes the industry is marked with 1000 SEC code). The reasons for the analysis are the following:

1. Metal and Mining is a stable industry which has a significant contribution to GDP;

2. The industry is comprised of more than 100 companies which might indicate high competitive conditions;

3. Companies pay dividends to its shareholders;

4. Companies generate significant cash flow and have liquid assets;

5. The overall companies' performance satisfies the pool of requirements suggested by Benjamin Graham and Warren Buffett;

6. The industry does not have fluctuations which can be interpreted as risky;

7. All the financial statements are publically located on the SEC with up to the year updates (the final year is 2018);

8. The industry does not have any anticipated global problems which can significantly influence on companies' performance

The second part of the pool is identified as a part of S&P 500 index. The companies are chosen at random, the only condition is different industries in order to make the returns more transparent for interpretation. This part of the sample is identified as a perfect because such indices as S&P 500, Dow Jones Industrial Average are acknowledged as the best for investments. That is why an investor is more inclined to purchase the index and wait for quite attractive returns in comparison with deposits, bonds and so on.

The third part of the pool is defined from the website with intentionally calculated undervalued companies (the fundamental valuation model was Graham's approach).

4.2 Tools used to perform analysis.

In order to perform the abovementioned analysis, we used the power of Microsoft Excel. Excel was used primarily to analyse raw data. To calculate some of the ratios and returns, that were exploited within valuation techniques we referred to valuation tables provided by Aswat Damodaran, professor in NYC Stern University. For example, risk.xls and betas.xls were used to perform calculation of (beta) for each year and each company, and the latter was used to compare industrial beta with portfolio one. The second importance tool we can name as comprehensive search engine of SEC official web-site.

The choice of excel was made, depending on two reasons. First of all, valuation of companies is usually made in specifically excel. Investment banks and private equity companies reckon excel as one of the cornerstones of analysis financial data. Secondly, Aswat Damodaran's models, proposed to professional society in the scope of his publication, including Investment Valuation (2012), which made the entire analysis closer to his unique approach.



Description of findings

5.1 Ratios estimation

5.1.1 DDM & NCAV

As we have discussed in the previous section of our paper, the findings of this work shall start from description of the models' application. The centre idea of this segment is to reveal the ratios V/P (intrinsic Value of the stock divided by its market Price), performed for each company in the observed period from 2012 to 2018, from various industries, and for each intrinsic value calculations (NCAV, DDM, RI, FCF, Graham Number). The ratios V/P for Discounted Dividend Model please find in the table below. We first assess the DDM paired to NCAV. In this pair, we apply both NCAV and DDM for the same companies:

	Year	2012	2013	2014	2015	2016	2017	2018
GameStop Corp.	VP (NCAV)	0,0696	0,0353	0,0349	-0,0436	-0,1292	-0,3081	-0,2271
	VP(DDM)	0,0000	0,0002	-0,0015	-0,0119	-0,0562	-0,0049	-0,0054
Signet Jewellers	VP (NCAV)	0,3876	0,2776	0,1787	0,1070	0,2781	-0,4084	-0,4671
	VP(DDM)	0,0002	0,0001	0,0001	-0,0012	-0,0003	0,0035	-0,0011
Canfor Corp	VP (NCAV)	1,6514	1,2210	1,1604	0,8956	1,4364	-1,3094	-1,4880
	VP(DDM)	0,0003	0,0018	0,0025	-0,0005	-0,0065	0,0017	-0,0152
CNO Financial Group	VP (NCAV)	-3,4000	-7,9000	-8,6000	-9,4000	-7,9000	-10,500	-12,600
	VP(DDM)	0,0015	0,0010	-0,018	0,0027	0,0058	0,0011	-0,0047
Bed Bath & Beyond	VP (NCAV)	0,1773	0,0977	0,0949	0,0073	-0,0174	-0,1639	-0,1182
	VP(DDM)	0,0248	0,0013	-0,2054	-0,0055	-0,0174	-0,0068	-0,0081
Prudential Financial	VP (NCAV)	-6,7000	-5,6000	-4,9000	-3,7000	-6,8000	-4,5000	-4,9000
	VP(DDM)	-0,0009	0,0008	0,0001	-0,0010	0,0002	0,0007	-0,0004
Lincoln National Corp	VP (NCAV)	0,3856	0,3136	0,1669	0,2474	0,0482	-0,0204	0,0192
	VP(DDM)	0,0000	0,0001	0,0029	-0,0013	0,0004	0,0009	-0,0009
Unum Group	VP (NCAV)	-1,6000	-2,6000	-2,1000	-1,9000	-2,0420	-1,7800	-1,6900
	VP(DDM)	0,0034	0,0003	0,0055	0,0043	0,0005	0,0004	-0,0008
Invesco	VP (NCAV)	-16,815	-12,894	-13,074	-12,434	-11,318	-10,084	-9,9952
	VP(DDM)	0,0005	0,0006	0,0012	-0,0033	0,0221	0,0012	-0,0015

Consolidated calculated ratios of 9 companies

As it appears to be, there are companies that demonstrate the interest from the authors. Particularly they are highlights in green colour. These companies reflect undervalued nature of their stocks, at the same time some of them (like those of Lincoln National and Signet Jewellers reflect the number close to the optimal, as explained by Benjamin Graham (2/3 = 0,66). A small pattern that can be seen from 2012 to 2014, as well as in 2016 corresponds with the economy of United States recovering from the Great Recession. Based on these figures, basically we can make a decision on which companies to include in portfolio based on choice method (valuation method).

5.1.2 RI & NCAV.

In terms of NCAV against Residual Income, the situation is quite intense. Please find the table with segment of comparison and explanations below as well:

	Year	2012	2013	2014	2015	2016	2017	2018
GameStop Corp.	VP (NCAV)	0,1	0,0	0,0	0,0	-0,1	-0,3	-0,2
	VP (RI)	0,5	0,0	0,7	0,8	1,2	1,1	0,75
Signet Jewellers	VP (NCAV)	0,4	0,3	0,2	0,1	0,3	0,6	-0,5
	VP (RI)	0,5	0,4	0,3	0,3	0,7	0,6	1,1
Canfor Corp	VP (NCAV)	1,7	1,2	1,2	0,9	1,4	-1,3	-1,5
	VP (RI)	0,7	0,6	0,5	0,7	1,1	0,8	1,4
CNO Financial Group	VP (NCAV)	-3,4	-7,9	-8,6	-9,4	-7,9	-10,5	-12,6
	VP (RI)	2,5	1,4	1,6	1,3	1,4	1,2	1,3
Bed Bath & Beyond	VP (NCAV)	0,2	0,1	0,1	0,0	0,0	0,7	-0,1
	VP (RI)	0,3	0,2	0,2	0,3	0,4	0,9	1,9
Unum Group	VP (NCAV)	-1,6	-2,6	-2,1	-1,9	-2,0	-1,8	-1,7
	VP (RI)	1,3	0,8	1,0	1,0	0,7	0,6	1,0

Computations of RI and NCAV of considered companies between 2012 and 2018

The model of residual income (RI) shows a very dense frequency of undervalued estimation. As a reminder, all of the V/P ratios were performed through the same stock price information. The segment of the previous table contains only those companies, which are considered to be possibly undervalued with estimated preferable V/P. Effectively, pointed out figures are key for choosing portfolio at this time as well.

Described companies were taken out of different industries and sectors of the US NYSE (10 multi-industry), in order to provide the possible portfolio with diversity in terms of risk variation and to diminish the seasonal effects, as well as cycle effects and industrial particularities. In theory, such portfolio is considered to be mathematically reasonable to invest, if the return for portfolio was to be calculated and the return estimation would be acceptable by an investor.

5.1.3 FCF and NCAV

Speaking about NCAV and FCF (Free Cash Flow), you can find the sample of analysis below:

		2010	2011	2012	2013	2014	2015
BIO-AMD	NCAV	0,1	0,1	0,1	0,1	0,0	0,0
	FCF	101,4	178,6	75,9	-9,0	1,0	0,0
	VP (NCAV)	0,1	1,8	8,5	0,6	0,4	0,2
	VP (FCF)	108,3	3572,0	7594,0	-76,9	9,1	0,0
	Market price	0,9	0,1	0,0	0,1	0,1	0,1

Computations of RI and NCAV of considered companies between 2010 and 2015



Computations of FCF and NCAV of considered companies between 2012 and 2017

		2012	2013	2014	2015	2016	2017
EMX Royalty	NCAV	0,2	0,0	0,0	0,0	0,0	0,1
	FCF	2450261,8	476256,9	87890,4	-139903,2	-194114,5	188452,9
	VP (NCAV)	0,1	0,0	0,0	0,0	0,0	0,1
	VP (FCF)	1353735,8	292182,2	144082,6	-208810,7	-209400,8	266552,9
	Market price	1,8	1,6	0,6	0,7	0,9	0,7

The companies presented above, as well as the companies not included in this report are taken from the single industry - Metal & Mining, US Stock market. 10 random Metal and Mining sector companies were taken to be tested, as we have discussed in the previous sections. All of the companies are being traded on NYSE and have special features, characterised by the sector. First of all, all companies have negative net income, but each year each company issues additional common stocks, and has its cash flow moving actively enough. That is why NCAV and FCF became a good use for testing the FCF/NCAV related hypothesis 2.

FCF would have been used for special type of companies - meaning companies with non-typical or negative net income. However, we faced a couple of major fixations. Nevertheless, companies were weighted by their CAPEX and D&A losses, as the mining sector companies tend to experience high assets turnover in their current form, as well as current liabilities form. Increased tax rate on raw materials for private companies in US market is another way of potential use of FCF approach, however, negative income influenced the results, apart from relatively big numbers. The range of FCF intrinsic value estimation could vary from $101 per share to $18000 per share. Amongst some enterprises, the figures were fluctuating between 2-digits to 5-digits number. Such a preliminary result questions the applicability of the framework on some current-assets intensive sectors of the economy. Nonetheless, the valuation model estimated undervalued stocks, thus made it possible to form a portfolio.

5.1.4 Graham's number computations.

Another important model considered in this paper is Graham's number which was implemented only for the second camp (10 multi industry enterprises). The idea of the ratio is rather transparent - exclude the companies which are less than 22,5 or, repeating Graham's thoughts, “However, a multiplier of earnings below 15 could justify a correspondingly higher multiplier of assets. As a rule of thumb, we suggest that the product of the multiplier times the ratio of price to book value should not exceed 22.5” (Graham & Zweig).

The authors calculated NCAV and Benjamin Graham's number for two camps of companies - 10 single-sector (metal and mining companies) and 10 multi-sector companies. Briefly analysing the companies, the authors received the following results, or a snapshot of the industry:

1. As the industry is characterized by tremendous non-current liabilities and compatible low current assets, it was challenging to select the companies with positive working capital and even positive difference between current assets and total liabilities.

2. Almost all the companies did not publish any preferred stocks for repurchasing and launching, thus the total sum of liabilities did not include them (remembering the concept of Benjamin Graham's value investing philosophy, preferred stock should be considered as a form of liability);