Karlstad Business School
Karlstad University SE-651 88 Karlstad
Ludwig Brindelid Tobias Nilsson
Portfolio performance in Nordic countries
- A quantitative comparison study of investment strategies in Denmark, Finland, Norway and Sweden
Portföljprestationer i nordiska länder
- En kvantitativ jämförelsestudie av investeringsstrategier i Danmark, Finland, Norge och Sverige
Nationalekonomi
Examensarbete - Civilekonomprogrammet
Term: Spring-term 2021
Supervisor: Karl-Markus Modén
Acknowledgment
We would like to express a sincere thanks of gratitude to our supervisor, Karl-Markus Modén for his guidance and assistance throughout this thesis. We also want to thank the participants at the seminars for their valuable inputs and feedback.
June 9th, 2021.
Ludwig Brindelid and Tobias Nilsson.
Abstract
The interest in the stock market has increased in the last couple of years whereas those who invest use all kinds of different strategies, or none at all. Some strategies are quite complicated and time consuming, while others are easier to replicate. The Magic Formula and Piotroski’s F- Score are two of the more well-known investment strategies which have been developed during the 2000s and are relatively easy to follow. The purpose of this study is to compare the
performance of the two investment strategies and if they can create excess return in Denmark, Finland and Norway. In addition, the results will be compared to an earlier study made on the Swedish market, for the sake of discovering any differences between the Nordic countries when investing according to these strategies. The results displayed that both strategies outperformed the market indexes most years and that their accumulated returns were far greater than the market indexes between 2012-2021. Out of the Nordic countries, the portfolios in accordance with The Magic Formula and Piotroski’s F-Score both performed best in Norway. In all the three countries, Piotroski’s F-Score was the better-performing strategy over these nine years regarding accumulated return. However, the results only showed statistical differences between the
strategies in Norway and Denmark. Regarding differences between the countries, including Sweden, the results indicate that there are only statistical differences in accumulated return between Norway and Sweden concerning The Magic Formula portfolios during 2012-2020. On the other hand, the results for the F-Score portfolios showed statistical differences in
accumulated return between all countries except between Denmark and Finland.
Keywords: Investment strategies, The Magic Formula, Piotroski’s F-Score, The Stock Market, Nordic countries.
Sammanfattning
Under senare år har intresset för aktiemarknaden ökat allt mer, där aktörerna använder sig av en mängd olika sorters strategier, eller ingen alls. Vissa strategier kan anses vara mer komplicerade och tidskrävande medan andra är enklare att följa och förstå. Den Magiska Formeln och Piotroskis F-Score är två av de mer välkända investeringsstrategierna som båda har blivit utvecklade under 2000-talet och är relativt enkla att replikera. Syftet med denna studie är att jämföra prestationen för dessa två investeringsstrategier samt om de kan generera någon överavkastning i Danmark, Finland och Norge. Resultaten kommer dessutom jämföras med en tidigare studie gjord på den svenska marknaden, för att hitta eventuella skillnader mellan de nordiska länderna när investeringar skett enligt dessa strategier. Studiens resultat visade på att båda strategierna överträffar marknadens index flera gånger under tidsperioden samt att dess ackumulerade avkastning var högre än marknadens index mellan 2012–2021. Utav alla nordiska länder presterade portföljerna baserade på Den Magiska Formeln och Piotroskis F-Score bäst i Norge, och för samtliga tre länder presterade Piotroskis F-Score bäst av strategierna gällande ackumulerad avkastning under dessa nio år. Resultaten visade dock enbart statistiska skillnader mellan strategierna i Danmark och Norge. Samtidigt visar resultatet på statistiska skillnader för ackumulerad avkastning mellan länderna Norge och Sverige gällande portföljerna enligt Den Magiska Formeln under 2012–2020. Samma period visar även på statistiska skillnader mellan alla länder förutom Danmark och Finland gällande portföljerna enligt Piotroskis F-Score.
Nyckelord: Investeringsstrategier, Den Magiska Formeln, Piotroskis F-Score, Aktiemarknaden, Nordiska länder.
Table of Contents
1. Introduction ... 1
1.1 Background ... 1
1.2 Problem discussion ... 2
1.3 Purpose ... 3
1.4 Method ... 3
1.5 Delimitations ... 3
1.6 Disposition ... 4
2. Economic theory ... 6
2.1 Efficient Market Hypothesis ... 6
2.1.1 Criticism Against the Efficient Market Hypothesis ... 8
2.1.2 Adaptive Market Hypothesis ... 9
2.2 Portfolio Theory ... 10
2.3 Investment Strategies ... 11
2.3.1 The Magic Formula ... 12
2.3.2 Criticism Against The Magic Formula ... 13
2.3.3 Piotroski’s F-Score ... 14
2.3.4 Criticism Against Piotroski’s F-Score ... 15
3. Earlier Studies ... 16
3.1 The Magic Formula ... 16
3.2 Piotroski’s F-Score ... 18
4. Method ... 20
4.1 Research Approach ... 20
4.2 Pilot Study ... 20
4.3 Credibility ... 21
4.4 Reliability ... 21
4.5 Validity ... 22
4.6 Data Collection ... 22
4.7 Investment Strategies ... 22
4.7.1 Portfolio composition with The Magic Formula ... 23
4.7.2 Portfolio composition with Piotroski’s F-Score ... 25
4.8 Hypotheses ... 27
5. Results ... 28
5.1 The Magic Formula portfolios ... 28
5.1.1 The Magic Formulas Performance in Denmark ... 28
5.1.2 The Magic Formulas Performance in Finland ... 29
5.1.3 The Magic Formulas Performance in Norway ... 31
5.2 Piotroski’s F-Score portfolios ... 32
5.2.1 Piotroski’s F-Score Performance in Denmark ... 32
5.2.2 Piotroski’s F-Score Performance in Finland ... 34
5.2.3 Piotroski’s F-Score Performance in Norway ... 35
5.3 Comparisons Between Countries with The Magic Formula ... 36
5.4 Comparisons Between Countries with Piotroski’s F-Score ... 37
5.5 Hypotheses ... 38
5.6 Comparisons between the investment strategies ... 40
6. Analysis ... 41
6.1 Performance analysis of The Magic Formula ... 41
6.2 Performance analysis of Piotroski’s F-Score ... 44
6.3 Comparison between the investment strategies ... 47
7. Conclusion ... 49
8. Further research ... 50
References ... 51
Appendix ... 54
1. Introduction
In this first section of the paper, the reader will be introduced to the specific problem that this study wishes to investigate. It will include some background and problems to the study, which will explain why this topic is interesting and important to discuss. Furthermore, a more solidified description of this study will be presented in the purpose section, followed by the methodology, delimitations and disposition of the paper.
1.1 Background
What would you do if you got 100 dollars, with no strings attached? Depending on age, gender and socio-economic background, your decision in this situation might differ. Sure, you might spend it all on Big Macs and nuggets, enjoying your snack while you consume it, but eventually end up feeling a bit queasy if you consume too much, which you probably will regret afterwards.
You might donate everything to a charity that you cherish or give it away to a homeless man walking down the street which are both wonderful choices. Perhaps you want to treat yourself with a nice hotel room during a weekend after a long and exhausting work week. But what if you did not spend it nor gave it away? What if you instead saved your extra income? What would your options be?
You can of course put everything in that little piggy bank your grandpa gave you, but even years later, your initial value will still be the same. Matter of fact, your money will not grow at all, no matter when you come back to collect it. If the price level continues to rise, that Big Mac you wanted to buy will cost more, and therefore prevents you from buying an equal number of Big Macs than you would be able to at first. In real terms, that money will decrease in value and be worth less than it was when you decided to put it there. Although the piggy bank plan has almost no risk, you will not gain any money, but not lose any either (Greenblatt 2010).
Another option would be to bring the money to a bank. The bank will actually pay you interest for holding your money which is also often increased the longer you agree to let them hold it (Greenblatt 2010). Of course, you could also invest in different bonds, which is denoted as a security sold by a corporation or a government to obtain money from investors today, in exchange for a future yield when time reaches maturity (Berk & DeMarzo 2016). If you were to buy a bond for your 100 dollars, it would yield a small yearly return and when the time reaches maturity, your initial money will be paid back (Greenblatt 2010). Although, this option is riskier depending on which bond you choose to invest in, because if you were to invest in a riskier
business and it performs badly, the interest you expect might never get paid and the same goes for your initial investment. Though, you have a lower probability of getting in this situation if you buy bonds in a more established business (Greenblatt 2010).
Excluding earlier options, you could choose to invest in stocks and build your own portfolio. In fact, the enthusiasm for investing in stocks has increased more and more. During 2020 alone, the number of users on the Swedish investment platform Avanza increased by approximately
300000, which is an increase of roughly 30% than the year before (Avanza 2021). But which stocks would you choose? There are thousands of different options on various markets, with the opportunity to select any stocks to your portfolio, however “choosing individual stocks without any idea of what you are looking for is like running through a dynamite factory with a burning match. You may live, but you are still an idiot” (Greenblatt 2010, pp. 73).
Moreover, the lower risk you take, the lower the expected return is, but there is also a lower chance of losing your initial investment. Therefore, it is crucial to construct a well-diversified portfolio, i.e. spreading your investments over several sectors to minimize your exposure to risk (Bodie et al. 2014). As a result, one could presume that the interest in investment strategies will increase since investors pursue the highest possible return on their investment, given a certain risk of course. The intention with investment strategies is to facilitate investors to invest their money in certain stocks, where some strategies are more time-consuming and complicated than others, but many can easily be found and replicated. Of course, the results from investment strategies could differ a lot, but are there any differences by administering a certain strategy in your own homeland, compared with a neighboring country?
1.2 Problem discussion
The vast majority of Nordic investors choose to invest in stocks from their home country. For example, Swedes invest 90 percent of their money in Swedish stocks and 10 percent in foreign stocks (Avanza 2020). Likewise, Finns invest 89 percent of their money in Finnish stocks and 11 percent in foreign (The Bank of Finland 2021). Considering that The Magic Formula and
Piotroski’s F-Score have been studied many times across the world with different results (Piotroski 2000; Greenblatt 2010; Davydov et al. 2016; Turtle & Wang 2017), based on which stock market, could it be that some investment strategies are more applicable in some markets compared to others? In other words, would it matter in which of the Nordic countries you invest in if you use these investment strategies?
1.3 Purpose
The purpose of this study is to investigate whether two different investment strategies, Piotroski’s F-Score and The Magic Formula, can create excess return on an investment compared to a chosen index on the Danish, Finnish and Norwegian market as well as to analyze their
performance. We will henceforth compare our results with an earlier study1 made on the Swedish market, to analyze whether there exist any differences in accumulated return among the Nordic countries when conducting these investment strategies. Furthermore, this leads us to our questions for the study:
• How do the investment strategies perform and differ in result between the Nordic markets, and do they beat their respective market index?
• Are there any differences between the countries’ accumulated return when investing according to The Magic Formula and Piotroski’s F-Score?
1.4 Method
This paper is a quantitative study in which the essential data for our analysis has been gathered as secondary data from Yahoo Finance and Börsdata, where all financial information for listed companies in the Nordic countries can be found. The data has then been analyzed to test if the hypotheses mentioned in Section 4.8 could be rejected or not, which were estimated in order to help the study solve the problem by answering the questions of this paper.
1.5 Delimitations
This study will be delimited to the Nordic countries Norway, Denmark and Finland, and more specifically, their stock exchanges. Iceland is not included due to the low number of stocks on their market which might not give a fair result. The underlying reason for the chosen countries is due to the economical similarities amongst the markets (Nordics 2019), but also since the Nordic countries are often viewed as one combined country, due to their common history and culture (Thelocal 2020). The Norwegian stocks that will be included are listed on the Oslo Stock Exchange, including OBX, OB Match, OB Standard and Oslo Axcess. As for the Danish and Finnish stocks, which are listed on the Copenhagen and Helsinki stock exchanges, will include stocks on their respective Large-, Mid-, and Small Cap as well as First North. Something to take into account is that no brokerage fees will be included and that the portfolios will be equally
1 Lilleng & Karlsson, “Become a winner with fundamental analysis – but ignore what model you use”, 2020.
weighted, which further means that parts of a share can be bought. In total, the three markets consist of 531 companies, more specifically, 167 Danish companies, 168 Finnish companies and 196 Norwegian companies. These specific stock exchanges are included since they are equivalent to the Swedish stock markets used by Lilleng and Karlsson (2020), which will further enable a fair comparison between the reports.
Furthermore, in each of these countries, one portfolio of stocks will be created from their respective stock exchange. The portfolios will be assembled according to the two investment strategies, starting in April and thereafter reassembled once a year in the same month. The choice of April is influenced by Lilleng and Karlsson (2020) since they used that month to rearrange their portfolios. In addition, the study will only be able to include stocks where the financial information is complete enough for the criteria required by each investment strategy.
Moreover, this report will be time delimited to the years 2011-2021, whereas the time period 2012-2021, as well as 2012-2020, will be analyzed. The reason for these time periods is partly based on which years Börsdata had data available, and partly since Piotroski’s F-Score criteria which require a comparison of a company’s key figures from a previous year and also due to Lilleng and Karlsson’s (2020) evaluated time period. In other words, the financial information from 2011 is needed in order to create the portfolios for 2012. Since the comparison between both papers will be determined on an accumulated and excess return during the time period, their results have been adjusted to only cover the period 2012-2020. Thus, this paper’s results can be compared to theirs without any differences in time delimitations.
Finally, this report will be delimited to the investment strategies Piotroski's F-Score and The Magic Formula. These strategies were chosen since they performed best out of Lilleng and Karlsson’s (2020) selected strategies, but also since they can be seen as a modern investment strategy that have shown popularity among investors (Novy-Marx 2014). Furthermore, the chosen strategies are well known and can easily be found on the internet for replication.
1.6 Disposition
In the next chapter, the reader will be introduced to the relevant economic theory behind the subject, but also be thoroughly informed of the approach of the two different investment strategies. In Chapter 5, the original studies behind the investment strategies are brought up.
Moreover, some earlier studies made on different markets will also be mentioned, as well as their findings within the area. Our data collection and portfolio construction will be accounted for in the paper’s fourth chapter together with the stated hypotheses. Chapter 5 will include the results
made from the investment strategies amongst the markets and the hypotheses will be answered.
The following chapter will analyze the results that have been made, including a comparison between our findings with results from the Swedish market. Chapter 7 will present the conclusion that has been made from this paper, by answering the questions that have been stated in the introduction. The paper is finished by a brief discussion of further research that can be made within the area, alongside references and the Appendix.
2. Economic theory
In this section of the paper, various economic theories will be introduced which are all related to the paper’s subject. These theories will be thoroughly explained alongside some potential
criticism against it. Additionally, the theory behind each investment strategy is also brought up, together with some weaknesses that have been mentioned against them.
2.1 Efficient Market Hypothesis
The concept of the efficient market hypothesis was first stated in Eugene F. Fama’s article from 1970, in which he ultimately won the Nobel Prize for, together with others (Berk & DeMarzo 2016). In his article, Fama (1970) claims that the capital market’s main role is to allocate the ownership of the economy’s capital stock. The optimal market is a market whose prices presents accurate indications for resource allocation. A market is called efficient when a price is fully incorporated by all accessible information, which later became to be known as the Efficient Market Hypothesis, or EMH (Fama 1970).
Further, Fama (1970) presented three different theories of efficient markets. First, the expected return or fair game model implies that prices in an efficient market should be fully reflected by all new accessible information (Fama 1970). The theory further claims that all accessible information should be reflected into the current price and investors should obtain a return that is consistent with the amount of risk taken. Prices will be swiftly adjusted by competition among profit- maximizing investors when new information arrives, so none of the investors are able to predict new information or market patterns (Bin Tariq & Naseer 2015). The second theory brought up by Fama (1970) is the submartingale model, which states that a price for a security follows a submartingale in relation to new information. That is, the price for a security during a future period, related to future information, is greater or equal to the current period’s price. Thus, old information cannot work as a trading tool for investors to predict future prices and therefore take advantage of this opportunity to gain a greater expected profit. Finally, the random walk model claims that consecutive price changes are independent of each other, their distribution is identical, and that past information and returns are not able to assess investors to predict future movements and returns (Fama 1970).
Moreover, the EMH is divided into three different forms, weak-form market efficiency, semi- strong form market efficiency, and strong form market efficiency (Fama 1970). The weak form of market efficiency proclaims that stock prices are already incorporated by all available
information which can be derived from evaluating trading data, such as past prices, volume, and
short interest. In the weak form of market efficiency, trend analysis is considered pointless, since stock prices in the past are publicly available and costless to procure. In fact, if that kind of data conveyed credible signals of future returns, all investors would utilize these signals (Bodie et al.
2014). As a result, it is not possible to profit from trading on information about past prices (Berk
& DeMarzo 2016). Out of Fama’s tests, the weak form of the efficient market was the most comprehensive, and his results were strongly in support of the EMH (Fama 1970).
The semi-strong form of market efficiency states that all publicly accessible information that regards the prospect of a company, must already be represented in its stock price. Excluding past prices, the accessible information also includes the essential data for a company's product line, earning forecasts, quality of management, and accounting practices, among others (Bodie et al.
2014). It is further stated that it should be impossible to frequently make profits by trading on any public information, recommendations from analysts, and news announcements for instance (Berk & DeMarzo 2016). Tests made on the semi-strong form of market efficiency, which should fully reflect all publicly accessible information, prove that it supports the EMH (Fama 1970).
Lastly, the strong form of market efficiency states that the price of a stock is fully incorporated by all available and relevant information of a firm, this also includes information that is only accessible for company insiders. Although, this form of market efficiency could be seen as quite extreme, and only a minority of people would argue along with the suggestion that company insiders have access to the necessary information long enough to make profits by trading on such information before it is released to the public. Nonetheless, these company insiders and their related parties who make trades on such information are considered to violate the law (Bodie et al. 2014). Ultimately, even trading with such private information, the strong form of market efficiency states that it should be impossible to make profits regularly (Berk & DeMarzo 2016).
In the strong form of the EMH model, the prices are supposed to completely reflect all existing information and are perhaps the easiest way to judge deviations from market efficiency. The tests for the strong form showed limited evidence against the EMH. Of course, this kind of model cannot be expected to provide an accurate portrayal of reality (Fama 1970).
Previous studies have noticed two deviations from market efficiency. Firstly, company insiders usually have monopolistic information about their company, which is not unexpected. Secondly, professionals on major security exchanges are making profits on trade since they are using their monopolistic access to essential information on limit orders that have not been executed. Overall, the evidence that supports the EMH is indeed comprehensive, and the conflicting evidence towards it is rather thin (Fama 1970).
2.1.1 Criticism Against the Efficient Market Hypothesis
The EMH is often related to the idea of a random walk, which is denoted as a time series where the change to a new observation illustrates a random shift from the previous observation. The idea with a random walk is that the flow of new information and news, which are unpredictable, stochastic, and instantly incorporated into stock prices. Additionally, future price changes will only be reflected by future news and therefore be independent of previous price changes and information. Considering that new information is indeed unpredictable, it also implies that price changes are random and unpredictable. Therefore, experts are not expected to obtain a higher rate of return than an uninformed investor, considering that the uninformed investor maintains a well-diversified portfolio. Consequently, neither fundamental analysis nor technical analysis will be able to increase one’s rate of return (Malkiel 2003).
First, critics have indicated the fact that stock prices do not always have the characteristics needed for being a true random walk (Malkiel 2003). Lo and MacKinlay (1999) showed that the serial correlation for stock prices is different from zero in the short run and found evidence that stock prices make too many consecutive moves in the same direction to be considered as a random walk (Lo & MacKinlay 1999). Based on these findings, there seems to exist some momentum for stock prices in the short run. Although the stock market does not appear to be a perfect random walk mathematically, these statistical dependencies that create momentum
tendencies will most unlikely generate an excess return for investors since the opportunity to take advantage of this pattern will probably disappear when the public has this information (Malkiel 2003).
Further criticism against the EMH is the seasonality effect. Studies have proved that Mondays in each week and the month of January appear to create a higher rate of return. There are also reports suggesting a higher return at the turn of a month. Unfortunately, these predictable patterns are not dependable from period to period, because if all investors took advantage of this pattern, the so-called January effect would eventually be moved to December, since one would eventually have to buy and sell before everyone else in order to exploit this pattern. However, if these events would continue, the seasonality effect would ultimately be disturbed. Moreover, it is further argued that these non-random patterns are too small in relation to the transaction costs needed to exploit this effect (Malkiel 2003).
Another criticism towards the EMH is the size effect, where studies have proved that stocks in smaller firms generate a higher return than larger firms. Some studies have also shown that value stocks have a higher rate of return than growth stocks, one can identify a value stock by
evaluating a firm’s price-to-book value ratio as well as their price-earnings ratio. The persistence of a vast historical equity risk premium, which is contradictory to the real riskiness of common stocks, is another conundrum that is frequently used to conclude that markets are not entirely rational. Nonetheless, these patterns are not consistent and reliable over time. Some of them, which are based on basic valuation measures of stocks, might just represent risk even better.
Moreover, as some of them already have done, the majority of these patterns could end up self- destructing in the near future, which is a fair argument that one should not exaggerate and have high expectations with these predictable patterns and anomalies (Malkiel 2003).
2.1.2 Adaptive Market Hypothesis
Roughly 30 years after Eugene F. Fama’s (1970) article about the EMH, MIT professor Andrew Lo (2004) established an alternative theory which he called The Adaptive Market Hypothesis or AMH. Considering that the EMH had been questioned by the new field of behavioral economics and finance, which claimed that fear and greed were the primary factors driving the market and that it was not entirely rational, Lo (2004) combined the EMH with behavioral finance. The combination of the AMH were constructed around an evolutionary approach along with
cognitive neurosciences studies. Furthermore, Lo (2004) mentioned a couple of justifications and concrete implications of the AMH. The first implication in which the degree that a risk-reward relationship exists, is doubtful to be constant over time. Factors such as the relative sizes and preferences of various populations in the market environment, together with legislations, tax laws, and similar aspects, all influence that relationship. Since these variables change over time, it will affect the risk-reward relationship. Thus, the equity risk premium will also fluctuate over time and be subject to a path (Lo 2004).
Additionally, Lo states another implication in which arbitrage opportunities do occur according to the AMH, which is contrary to the EMH (Lo 2004). Grossman and Stiglitz (1980) observed that without arbitrage opportunities, there is no reason to collect information that will ruin the element of price-discovery in financial markets. On top of that, Lo (2004) states that in liquid financial markets, there must occur possibilities to gain a profit, from an evolutionary standpoint.
These will then eventually vanish once they are utilized (Lo 2004).
The next implication being brought up by Lo (2004) is that the performances of investment strategies will have their highs and lows and that they will have scenarios where they will do great while underperforming in others. In other words, the AMH implies that the time and
surrounding conditions will determine how gainful the strategy is at a certain time. However, this is also contradictory to the EMH, where arbitrage opportunities rapidly fade away and ultimately
abolish the possibility to take advantage of the arbitrage. The second to last implication Lo (2004) brings up focuses on innovation. According to the EMH, expected returns can be reached to some degree merely by taking risks to some extent. The AMH however, states that the relationship between risk and reward changes over time, and to adapt to the shifting business environment is a safer way to achieve a stable degree of expected returns. Ultimately, the last implication alludes that survival is the most important goal for everybody operating on the financial market. Though there are other important objectives as well, such as utility
maximization and profit maximization, survival is the final principle that decides the evolution of the market and its technology (Lo 2004).
2.2 Portfolio Theory
In his article, Markowitz (1952) displays a rule which suggests that investors shall maximize their return as well as diversify their portfolio. In other words, the rule states that in order to achieve maximum expected return, one should diversify the stocks among all chosen securities. However, if one would neglect the fact that the market is imperfect, the aforementioned rule never suggests that one diversified portfolio is superior to all portfolios that are not diversified. The underlying assumption for the rule is the existence of a portfolio that has minimum variance and yields a maximum expected return. Nonetheless, all variances cannot be eliminated by diversification and a portfolio with the least variance does not necessarily have the highest expected return. Also, investors are able to obtain expected returns by acquiring more variance or to give up expected returns in order to decrease variance (Markowitz 1952).
Presuming that the series of every attainable combination of minimum variance and maximum expected return is illustrated in Figure 1. The previously mentioned rule claimed that investors should choose among portfolios that have the most efficient combinations, which is denoted by the curve illustrated in the figure, i.e. portfolios with the least variance for a certain expected return or more and portfolios with the highest expected return for a certain amount of variance or less. This curve is more known as the efficient frontier (Markowitz 1952). Furthermore, to optimize the portfolio, a line called the Capital Allocation Line (CAL) is used. This line has a positive slope with the risk-free rate as an intercept. Thus, the optimal risky portfolio is when the Capital Allocation Line is as steep as possible and tangent to the efficient frontier since that point is better than all other viable points (Bodie et al. 2014).
Figure 1. The optimal portfolio which is where the efficient frontier is tangent with the Capital Allocation Line.
Additionally, diversification is not the only feature that the minimum variance - maximum expected return concept emphasizes. It also emphasizes the right type of diversification and for the right purpose. Investors should not believe that the functionality of diversification depends entirely on the number of stocks held in a portfolio. Portfolios with 40 different stocks within the tech industry would not be especially diversified compared with portfolios of the same size, but with some tech, mining, real estate, and different kinds of manufacturing stocks. The underlying assumption here is that companies within the same industry are more likely to perform badly simultaneously, compared with companies in various industries. Hence, one should not only take the variance aspect into consideration, but also prevent investing in stocks that have a large covariance among them. Conclusively, since companies in the same industry have a higher covariance than companies in various industries, one should diversify among numerous industries instead of just one (Markowitz 1952).
When holding a portfolio of stocks, there are two types of risks one is exposed to, firm-specific or non-systematic risk and market risk, also known as systematic risk. The former applies to news about an individual company and the latter applies to news about the market as a whole or the economy which is a risk that cannot be diversified away. Therefore, as a portfolio grows with more stocks, the non-systematic risk fades away since some firms get good news and some get bad news. However, the systematic risk will always remain, no matter how well diversified a portfolio is (Berk & DeMarzo 2016).
2.3 Investment Strategies
An investment strategy is defined as the strategy that investors use in order to facilitate their decisions regarding the allocation of capital in various options, such as stocks and bonds.
Capital Allocation Line
Efficient frontier Optimal portfolio
rf
σ
E(R)
Investors’ future need for capital and their tolerance for risk should be considered when
choosing a certain strategy (Nasdaq 2018). There exist several investment strategies with various characteristics. In the upcoming sections, the two chosen investment strategies mentioned in the first chapter are introduced and explained, followed by some criticism and weaknesses behind them. A more exact methodology and portfolio composition of the two chosen investment strategies will be thoroughly presented in the method section2.
2.3.1 The Magic Formula
The Magic Formula was originally introduced in Joel Greenblatt’s book in 2006, where the intention is to simply find good companies at bargain prices. The investment strategy pursues building an investment portfolio based on two ranking systems, which is to include companies with a high return on capital and a high earnings yield. A company with a high return on capital is denoted as a company whose factories or stores earn more relative to the cost to build them and a company that has a high earnings yield is denoted as a company that earns a lot relative to the paid price of the stock. This suggests that The Magic Formula helps to systematically discover companies that are above average in which one can buy for a bargain price. However, there exists no specific limitation of what a high return on capital or a high earnings yield is, but the higher it is, the better (Greenblatt 2010).
To break it down, companies that can obtain a high return on capital will also have the opportunity to reinvest their earnings to gain an additional rate of return in the future, these reinvestments might also facilitate a higher rate of earnings growth. Greenblatt (2010) explains further that companies that are able to attain a high return on capital will additionally have a special competitive advantage. This advantage impedes their competition from destroying their opportunity to obtain profits that are above average. Respectively, companies that have a deficiency of this special competitive advantage will presumably gain average or below-average returns on capital. Consequently, this investment strategy sorts out and removes these companies that earn mediocre or poor returns on capital and only retains a group of companies that have a higher return on capital than the other companies. Obviously, both mediocre and poor
companies could be capable of achieving a high return on capital in a particular year over a longer time period. The same goes for a company that is chosen by The Magic Formula, which might not be able to maintain a high return on capital over time since it often attracts competition.
However, since The Magic Formula reallocates its portfolio each year, it will discard the stocks
2 See Section 4.4
that do not maintain a high return of capital, in relation to the comparing stocks. Even so, a high return on capital does not guarantee a considerable return, which is why the strategy performs best with a long investment horizon (Greenblatt 2010).
2.3.2 Criticism Against The Magic Formula
A long investment horizon is seen as an attribute that most of the existing investment strategies have in common. However, it is in the short investment horizon that this strategy falters. The Magic Formula could perform worse than the market for years, which develops into absent earnings for investors during this affected period. Even though the investment strategy persists that it beats the market on average in the long run, most investors will presumably abandon their strategy. On the other hand, if the investment strategy worked constantly, the number of
investors that would exploit this phenomenon would increase the stock demand to the roof, which will result in an increase in the stock price. Ultimately, this contradicts The Magic Formulas basics and might make it dysfunctional (Greenblatt 2010).
Additionally, Greenblatt emphasizes the fact that the returns, if one would invest based on this strategy, could be theoretically extraordinary when a computer system picks stocks, but problems may arise when conducting these results into the real world (Greenblatt 2010). Also, some critics claim that investors are not able to beat the market by following this strategy since the stocks chosen by the formula are too small and illiquid (Carlisle 2014). For example, the strategy might select stocks that only a minority of people are able to buy, which ultimately makes it
problematic. Since smaller companies have fewer shares available than larger companies, they are more sensitive to a change in demand because a small increase in demand might lead to a higher price for those shares. As a result, the strategy might perform better on paper than in the real world (Greenblatt 2010).
Further, critics point out another criticism against The Magic Formula, they argue that the strategy will not work as well as it did in the test period as it is affected by data mining. Data mining is denoted as a repeated evaluation of a data set to detect a correlation which only exists occasionally, and a continuation outside the data set is therefore doubtful. They also suggest that Greenblatt examined several factors and combinations of them before he finally found one that was able to beat the market. Greenblatt then retroactively induced a rather questionable
explanation to the chosen factors, which ultimately became The Magic Formula (Carlisle 2014).
Regarding data mining, Greenblatt claims in his book that the specific factors were in fact the first two factors he investigated and analyzed since these factors were judged as the most important factors when one would analyze a company (Greenblatt 2010).
Moreover, Carlisle and Gray (2012) denote another issue with The Magic Formula in their book.
The formula comprises two parameters, the quality measure return on capital and the price ratio earnings yield, which are both equally weighted. When separating the formula to its constituent parameters and comparing the performance of the entire formula with the performance of the parameters, they found that return on capital deteriorates the performance of the formula during their investigated time period of 1974-2011. Additionally, they replaced Greenblatt’s quality measure with another quality measure, gross profits on total assets or GPA, and ultimately got a better result when conducting the same comparisons. However, both quality measures do not single-handedly match up with the overall contribution that earnings yield adds to the formula.
They argue that one should not pay extra for quality measures because they are more short-lived and will eventually fade back to their mean. After all, the formula is a systematic value strategy that is constructed to pay more for higher quality. However, their findings suggest that The Magic Formula consistently overpays for quality which makes it structurally inaccurate (Carlisle &
Gray 2012).
2.3.3 Piotroski’s F-Score
With the use of historical financial statement information, Joseph Piotroski (2000) developed the F-Score strategy, which sorts out the fundamentally strong and weak companies. Piotroski’s F- Score is built around the book-to-market ratio combined with nine fundamental signals. The more of these signals or criteria that are met, the stronger the company is, fundamentally. The purpose of these criteria is to measure the company’s financial stability based on profitability, financial leverage/liquidity, and operating efficiency. Piotroski (2000) further describes that these signals were found through various experts and academic articles. For each criterion met, one point is awarded and when a criterion is not met, zero point is awarded. The sum of the criteria achieved is intended to evaluate the strength or quality of the financial status for each company.
Notably, Piotroski (2000) concluded that firms with a high F-Score performed better than those with a low F-Score. He defined high F-Score as firms who fulfilled 8-9 criteria, and low F-Score as firms which met 0-2 criteria. Although Piotroski (2000) made that conclusion, he did not specify that exactly 8-9 criteria are optimal, since his result indicated that firms who met 7 criteria achieved almost the same return as those with 8 or 9. This could be the reason why other
researchers such as Walkshäusl (2020) and Turtle and Wang (2017) used 7-9 criteria as the definition of high F-Scores in their studies when they applied Piotroski’s F-Score on different markets. Additionally, in Piotroski’s original work, he short-sold the stocks he saw as poor (Piotroski 2000).
Furthermore, Piotroski arranged stocks based on their book-to-market value, whereas earlier studies have shown that portfolios consisting of stocks with high book-to-market value, often called value stocks, have generated higher returns than portfolios with low book-to-market ratios (Fama & French 1992; Lakonishok et al. 1994). However, Piotroski also mentions that
companies with high book-to-market ratios are on average financially troubled, which has earlier been observed by Fama and French (1995) as well as Chen and Zhang (1998). Piotroski (2000) therefore chose nine fundamental signals to measure a company’s general financial situation. Due to the simplicity of F-Score and its previous results, the investment strategy has become widely known by institutional and individual investors (Hyde 2018). The following nine criteria were the ones used by Piotroski (2000):
Profitability
1. Positive return on assets in the current year.
2. Positive cash flow from operations in the current year.
3. Return on assets is higher in the current year compared to the previous year.
4. Operating cash flow is greater than return on assets in the current year.
Leverage, liquidity, and source of funds
5. Lower ratio of long-term debt in the current year, compared to the previous year.
6. Higher current ratio this year compared to the previous year.
7. No new shares were issued in the previous year.
Operating efficiency
8. Higher current gross margin ratio compared to the previous year.
9. A higher asset turnover ratio compared to the previous year.
2.3.4 Criticism Against Piotroski’s F-Score
Piotroski (2000) mentions some weaknesses of his investment strategy. For example, the use of a binary system in the formation process of the portfolios in order to simplify could be
problematic. His response to this was to take a portfolio consisting of companies with a high book-to-market ratio and split them based on the firm’s financial distress which measures firm health as well as profitability changes in past years to measure firm performance. The results from this showed that these two measurements could distinguish firms with higher returns from firms with lower returns, which therefore partly eradicates the previously mentioned weakness.
Furthermore, there is a risk that a data-snooping bias exists from the strategy’s development, though some of the criteria are included due to results from previous research (Piotroski 2000).
3. Earlier Studies
In this section, some previous studies on the chosen investment strategies will be presented and reviewed. More thoroughly, the original study for both strategies will be presented first, followed by several studies made afterward on different markets worldwide. Their respective study’s approach will be presented consecutively, including their market of choice, sample size, results and conclusion.
3.1 The Magic Formula
In Joel Greenblatt’s book from 2010, he presents his results obtained by The Magic Formula which he conducted on the US market by analyzing a sample of the largest 3500 companies between 1988-2004. His results, containing a portfolio of 30 stocks with the best-combined score each year3, showed that The Magic Formula returned on average 30,8% per year compared to the overall market which had an average annual return of approximately 12,3% per year. Despite beating the market from a general standpoint, The Magic Formula was unable to beat the market three years during this 17-year period. Furthermore, Greenblatt wanted to push the stakes by decreasing the sample size to the largest 2500 and 1000 companies over the same time period.
Both these sample sizes were able to yield an average annual return twice as large as the market average (Greenblatt 2010).
Additionally, Greenblatt conducted another investigation including the largest 2500 companies by dividing them into 10 separate groups ranking them from best to worst, based on their combined ranking. Therefore, each group consisted of 250 companies whereas the formula seemed to work in order. Group 1 contained the best 250 companies and achieved an average 17,9% rate of return. The average returns for the following groups were then ranked in descending order i.e., group 2 yielded 15%, group 3 yielded 14,8%, and ultimately group 10 with a 2,5% average annual return. However, by examining every implemented test on a monthly level, the strategy seemed to perform lower than the market in five out of every twelve months tested on average. For whole years, it was unable to beat the market once every four years. On the other hand, the formula has proven that it functions well in the long run since it was able to beat the market in 160 out of 169 three-years periods tested. It was also able to beat the market in 169 out of 169 times when looking at a three-year period or more. Thus, one will on average gain a higher rate of return when investing according to The Magic Formula when holding the portfolio for longer than a three-year period. (Greenblatt 2010).
3 See Section 4.4.1
Another study that was based on The Magic Formula was a study by Davydov et al. (2016) which compared the strategy with other known investment strategies on the Finnish market in 1991- 2013. Their sample consisted of 2234 company-year observations and the size for each portfolio varied between 39-136 companies depending on the observed year. Their results indicated that all evaluated strategies were able to beat the market index frequently where The Magic Formula had an average annual return of 19,26% compared to the markets return of 13,63%. However, their results showed further that the abnormal returns are not compensated for a higher level of risk (Davydov et al. 2016).
In 2020, Aronne et al. conducted a study about The Magic Formula on the Brazilian stock market between 2006-2019 with a sample of 598 stocks. However, they excluded some companies that did not have the necessary data available for the specific period. Their result indicated that the portfolio made by Greenblatt’s strategy was exposed to growth companies with low liquidity, suggesting that it could have lowered the performance of the portfolio. Despite this, the portfolio’s annual rate of return was on average 35,75% compared with the markets return of 9,26%, in which they further concluded that the investment strategy was able to beat the market during the evaluated time period on average (Aronne et al. 2020).
Another study made on The Magic Formula was done by Rani (2019) on the Indian stock market during the time period of 2010-2018. The portfolios were constructed in accordance with
Greenblatt’s (2010) methodology, suggesting that both measurements were ranked and
combined, in which the 30 companies with the lowest scores were selected into the portfolios.
The portfolios exceeded the market return in six out of eight years and yielded an average annual return of 50% compared with the market’s 15% return. This implies that the strategy was able to beat the market on average during the period. During these eight years, The Magic Formula portfolios managed to outperform the Indian market index NSE 500 with 232.6%. Rani (2019) concluded that investors on the Indian market were able to yield a higher rate of return when investing according to The Magic Formula (Rani 2019).
In contradiction to previously mentioned studies, a more worldwide comparable study was made by Blackburn and Cakici (2017) who implemented the Magic Formula on a more global scale between 1991-2016. Their sample consisted of 23 countries divided into four major regions, North America, Europe, Japan, and Asia4. The sample included on average, 11000 companies each year within Large- Mid- and Small Cap over the four regions, with 3499 North American
4 The groups consisted of: North America – United States and Canada, Europe – Austria, Belgium, Denmark,
Finland, France, Germany, Ireland, Israel, Italy, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and the United Kingdom, Japan, Asia – Australia, New Zealand, Hong Kong, and Singapore.
companies, 3462 European companies, 2626 Japanese companies, and 1600 Asian companies.
According to their findings, they do not present any support globally for the Magic Formula to hold, since their return compared to their respective markets are insignificant. Europe is the only group that showed significance for an excess return. However, when they replaced earnings before interest and taxes (EBIT) with gross profits, their results were significantly better and more consistent. The results showed significance among all groups concluding that the formula may not hold globally in its original form, but with small adjustments, the Magic formula is actually magical, according to Blackburn and Cakici (2017).
3.2 Piotroski’s F-Score
In the paper Value Investing: The Use of Historical Financial Statement Information to Separate Winners from Losers (Piotroski 2000), Joseph Piotroski examined the difference in returns by sorting out US firms with high book-to-market ratios and then using a fundamental analysis strategy on those firms, based on accounting information. The results displayed that by selecting companies with a high book-to-market ratio, the mean returns are able to improve by no less than 7,5% annually. Piotroski also concluded that an annual return of 23% would have been earned between 1976 and 1996 if one would have purchased the stocks he labels as expected winners and shorted the expected losers. The expected winners are stocks with a high book-to- market ratio together with a high F-Score and the expected losers are the complete opposite.
Additionally, Piotroski tested both one- and two-year returns with a total of 14043 different companies with a high book-to-market ratio. For instance, 333 of these firms had an F-Score of nine while more than 2000 companies had an F-Score of four, five and six separately (Piotroski 2000).
About 20 years after Piotroski (2000) released his article, Walkshäusl (2020) performed a similar study between the years 2000 and 2018, with data from numerous developed and emerging countries around the world. The results displayed strong international evidence for Piotroski’s strategy since firms with high F-Scores achieved significantly higher returns than firms with low F-Scores, which was statistically significant over all explored regions. Additionally, the results showed that these high F-Score firms achieved an average annual premium of 9,9% in developed markets in Europe, Australasia and the Far East, and 12% in emerging markets, compared to low F-Score firms (Walkshäusl 2020). Similarly, Piotroski and So (2012) found that high F-Score firms in the US had an average annual return of 10,03% higher than the return for low F-Score firms.
Furthermore, Tikkanen and Äijö (2018) have done a study on the effect of applying the F-Score screening method together with other strategies, such as earnings before interest and taxes to enterprise value (EBIT/EV) and earnings to market capitalization (E/M). They analyzed firms on the European markets during 1992-2014 by first creating portfolios based on the
aforementioned strategies, and then applying the F-Score screening to select stocks with high F- Scores from the previous portfolios into a new portfolio. The results showed that the returns of the new portfolios exceeded the previous, which means that each portfolio’s return got improved by applying the F-Score screening method (Tikkanen & Äijö 2018).
Another article that has been made following Piotroski’s (2000) article is from a study by Turtle and Wang (2017) that investigates the performance of the F-Score on 11 499 companies in the Asian markets Hong Kong, Japan, Korea, Singapore and Taiwan between the years 2000 and 2016. Turtle and Wang (2007) found that all portfolios with high F-Score achieved positive return and that these portfolios earned a higher return in all markets except in Korea, compared to the portfolios with low F-Scores in the equally weighted category. However, as for the value- weighted portfolios, only the stocks in Singapore displayed the same result. Ultimately, Turtle and Wang (2017) concluded that the F-Score strategy can be used in the Asian markets to distinguish winners from losers, not just in value stocks and that it is related to positive future returns (Turtle
& Wang 2017).
4. Method
In this part of the paper, the underlying methodology for this study will be presented, including the research approach, a pilot study, data collection as well as management and portfolio composition of the two investment strategies. Also, for the paper to be scientifically strengthened, the factors validity, credibility, and reliability will be explained alongside an explanation as to why these are fulfilled. The method section will end with the paper’s hypotheses, which will ultimately facilitate the evaluation of the strategies’ performance.
4.1 Research Approach
According to Denscombe (2018), quantitative research uses numbers in the analysis and is often associated with studies on a larger scale as well as an analysis of more specific variables. The fact that the data analysis occurs after all data has been collected is also related to quantitative
research. Another factor in close connection to this research approach is the authors’ impartiality (Denscombe 2018). Since this study sought to investigate and evaluate the investment strategies return and performance on three different markets, but also by interpreting the aforementioned statements, a quantitative research approach was best suited throughout the paper. The data that has been collected was certain key figures from the publicly available financial information, which came from a total of 531 companies spread over three Nordic countries. It was also impossible to make a fair evaluation and analysis of the investment strategies until all portfolios had been created for the entire time period. Regarding the methodology of this paper, a deductive method was most appropriate to use since a deductive method compiles various hypotheses, or premises, where a deductive conclusion examines whether these hypotheses correspond with reality
according to Thurén (2019). In other words, a deductive method uses a combination of logic and theory (Thurén 2019) which suits this study.
4.2 Pilot Study
In order to evaluate whether this paper’s underlying idea was feasible to manage, a pilot study was made by reading previous financial articles in the area of interest with an unbiased view. It was concluded that there existed several relevant articles that could be used to investigate the problem of the paper even further. In addition, based on the authors’ awareness, there exist several papers that compare different investment strategies on the same market, but none of them compares the strategies over several markets, it was concluded that this subject was
interesting to analyze further. Moreover, to see if the investment strategies were functional within
the chosen countries, a smaller sample of firms was gathered within each country. This sample was later analyzed to conclude if all necessary data were included for each firm, and therefore, portfolios were created for each country. Since the portfolios were able to be assembled as expected for each country, the study could continue in full scale.
4.3 Credibility
Regarding the concept of credibility, studies have defined credibility as a result of a communicator’s expertise and trustworthiness, i.e. one’s ability to make valid and credible
statements based on that person’s skill and knowledge about a specific topic (Cowley et al. 2019).
As one could expect, the study by Copeland et al. (2011) demonstrated that individuals were more likely to accept a certain conclusion made by an expert within a specific subject compared to a person that lacked enough expertise (Copeland et al. 2011). Hence, the writers and authors behind the literary works mentioned throughout this study can be seen as experts in their field of work. In this paper, a critical and unbiased procedure has been attempted in order to improve this study’s credibility. The information throughout this study has been gathered from various economic books and literature which can be found by book publishers or in digital libraries of financial articles, respectively.
4.4 Reliability
Reliability is the concept that the measurements and calculations within a study are correct, and not incomplete or biased. Also, if other individuals would have used the same method, data, and research approach, the results would be the same if the study was recreated, i.e. the study has a high level of reliability (Thurén 2019). This study has consistently pursued the methodology and calculations made by the original studies as well as Lilleng and Karlsson’s (2020) variation, which mitigates any possible misconceptions and inaccurate calculations. Additionally, this paper’s data was collected as historical data which will never be removed or changed and will always be attainable since it is publicly available. The essential data has been gathered from Yahoo Finance and Börsdata, whereas the latter collect their data from Nasdaq, Millistream, and Refinitiv, which all are reliable data bank sources. Nonetheless, the results could somewhat vary if the market, number of companies, or time period differs from this study. However, if all factors are identical, and the same methodology is used, the expected result would be the same.
4.5 Validity
The concept of a paper’s validity clarifies if the study truly has examined the problem in question and not anything else. Although, even if the calculations are correct and reliable, but lacked the ability to answer the specific problem, i.e. had low validity, the results and the study itself could be seen as irrelevant (Thurén 2019). As this study makes a contribution to research in the problem being studied, the validity of the study is considered to be high. Furthermore, the study has examined what was intended to be done.
4.6 Data Collection
During this study, the necessary financial data for the 531 companies have been collected as secondary data from Börsdata for the 2012-2021 period. Additionally, data for 2011 were also mandatory to obtain since some of the criteria for the investment strategies required the previous years’ key figures in order to construct the portfolios. The reason behind using secondary data is simply because of the amount of time it would have required to single-handedly collect data from each and every one of the companies’ financial reports by hand. However, a smaller sample has been made to investigate whether the financial data collected were correct and reliable, which was made by analyzing some of the companies’ financial reports. Furthermore, the collected data were later processed by using Excel to construct the portfolios. The companies’ stock prices were collected as adjusted closing prices whereas the dividends are reinvested, from the first trading day of April each year from Yahoo Finance. The returns for each portfolio were then calculated on a yearly basis in Excel, as well as the return for the entire time period. Afterward, the
calculated return for each portfolio was compared with a chosen market index for each country.
Throughout this study, the selected market index for Norway was Oslo Börs All Share Index GI (OSEAX), the Danish index was OMX Copenhagen All GI (OMXCGI), and the Finnish market index were OMX Helsinki All GI (OMXHGI). These indexes were chosen since they include all shares that are listed on their respective stock exchange, but also since they include dividends, which makes it a fair comparison with the company’s stock prices.
4.7 Investment Strategies
In the following subsections, two investment strategies are thoroughly presented, including both calculations and explanations. Beforehand, the number of stocks within each portfolio had to be determined. Greenblatt (2010) concluded that an experienced investor with good knowledge about the stock market could aim for approximately ten stocks in his or her portfolio.
Furthermore, an investor with a shorter amount of experience and less knowledge about the stock market should increase his or her number of stocks to roughly 30. Since Lilleng and Karlsson (2020) chose to include 30 stocks in their Magic Formula portfolio, the number of stocks throughout this paper when using the Magic Formula was also chosen to be 30.
Furthermore, Piotroski (2000) did not determine a specific number of stocks that should be included in an investor portfolio. Therefore, the number of stocks included in each portfolio according to Piotroski’s F-Score is undetermined, which means that all firms that fulfilled enough criteria have been included in the portfolios. It was decided that seven criteria were the minimum amount a stock needs in order to be included, considering that Lilleng and Karlsson (2020) used the same limits as well as Turtle and Wang (2017) and Walkshäusl (2020), which simplifies any comparisons.
Moreover, if the number of stocks does not reach the predetermined amount of 30, The Magic Formula portfolio’s will still be created but with the number of stocks that are available. The reason for this is that one does not want to stretch the different rules and criteria enough for the investment strategies to lose their characteristics and capability. Ultimately, this study would lose its ability to make a fair evaluation.
4.7.1 Portfolio composition with The Magic Formula
The investment strategy Magic Formula includes stocks with a combination of a high return on capital and a high earnings yield (Greenblatt 2010). The return on capital is calculated as:
𝑅𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 = 𝐸𝐵𝐼𝑇
(𝑁𝑒𝑡 𝑤𝑜𝑟𝑘𝑖𝑛𝑔 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 + 𝑁𝑒𝑡 𝑓𝑖𝑥𝑒𝑑 𝑎𝑠𝑠𝑒𝑡𝑠)
(Greenblatt 2010).
The return on the capital measure was calculated as the ratio between pretax operating earnings or EBIT and tangible capital employed, which is the sum of net working capital and net fixed assets, where intangible assets such as goodwill were not included in these calculations (Greenblatt 2010). Greenblatt (2010) used this measure for various reasons. Firstly, earnings before interest and taxes (EBIT) were favorable over-reported earnings, since firms are often operating with various debt and tax rate levels. By using EBIT, one is granted to compare and evaluate different companies without the misinterpretations that could arise from the different levels of debt and tax rates. Secondly, the sum of net working capital and net fixed assets was favored over both equity and total assets which are used in the return on assets and return on
equity calculations. Greenblatt’s (2010) goal with this measure was to inspect the required amount of capital in order to manage a company’s business (Greenblatt 2010).
The second part of the Magic formula, earnings yield, were calculated as:
𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑦𝑖𝑒𝑙𝑑 = 𝐸𝐵𝐼𝑇 𝐸𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑠𝑒 𝑣𝑎𝑙𝑢𝑒
(Greenblatt 2010).
The earnings yield is the ratio between EBIT, and enterprise value, which is the sum of the market value of equity and the net interest-bearing debt. Greenblatt (2010) favored this ratio above the frequently used P/E ratio for various reasons. However, the underlying idea behind this measure is figuring out the earnings of a company in relation to the purchase price for it. In addition to the price of equity i.e. total market capitalization, enterprise value was used since it includes both the financed debt which is used to facilitate a company’s operating earnings as well as the price for an equity share in a business. By comparing these measures, one can compute a company’s earnings yield before tax on the purchase price of the whole firm. Therefore, when comparing different company’s earnings yields, one can put firms on a balanced level despite their various levels of debt and tax rates (Greenblatt 2010).
The 30 companies that have been included in the portfolios have been selected through two ranking systems, which were based on return on capital, earnings yield, and two delimitations.
Firstly, all companies have been ranked from the highest to the lowest amount of return on capital where the company with the highest amount achieved a score of one, the second highest got a score of two, and so on. This procedure was then repeated for earnings yield, so each company would achieve a score for both measurements. Secondly, the scores achieved on both rankings were then summarized for each company and the companies with the lowest combined score were placed on top of the ranking system. The first delimitation was the elimination of financial firms, including banks, real estate, investment and insurance companies. The second delimitation was the fact that all companies that had a negative value on return on capital for a certain year, were also eliminated. Consequently, the 30 companies with the lowest combined score within the delimitations were assembled in a portfolio each year (Greenblatt 2010).
A fictitious example of how the stocks are assembled in each portfolio is illustrated in Table 1 in the Appendix. After the previously mentioned delimitations has been made, country X is left with 10 stocks. Out of these ten stocks, the three best available stocks will be included in this year’s portfolio. The return on capital and the earnings yield has been calculated for each firm and sorted into order from highest to lowest in those two categories, separately. The firm with the
