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I

N T E R N A T I O N E L L A

H

A N D E L S H Ö G S K O L A N HÖGSKOLAN I JÖNKÖPING

Value vs. Growth

A study of portfolio returns on the Stockholm Stock Exchange

based on the P/B- and P/E ratios

Bachelor’s thesis within Business Administration

Authors: Carlström, Anders

Karlström, Rikard

Sellgren, Jakob

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J

Ö N K Ö P I N G

I

N T E R N A T I O N A L

B

U S I N E S S

S

C H O O L

Jönköping University

Värde kontra Tillväxt

En studie av portföljavkastning på Stockholmsbörsen baserad på P/B-

och P/E talen

Kandidatuppsats inom Företagsekonomi Författare: Carlström, Anders

Karlström, Rikard

Sellgren, Jakob

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Bachelor’s Thesis in Finance

Title: Value vs. Growth - A study of portfolio returns on the Stockholm Stock Ex-change based on the P/B- and P/E ratios

Authors: Carlström Anders, Karlström Rikard, Sellgren Jakob

Tutor: Österlund Urban

Date: 2005-12-20

Subject terms: Finance, P/B, P/E, Portfolio theory, Efficient market hypothesis, Anomali-ties.

Abstract

Research Questions:

• Will a portfolio based on value stocks, on a risk-adjusted basis, outperform a portfolio based on

growth stocks on the Stockholm Stock Exchange?

• Is the superior strategy able to generate abnormal risk adjusted returns by beating the OMXS

in-dex?

Purpose: The purpose is to investigate if an investor by purchasing a portfolio based on

value stocks will outperform a portfolio based on growth stocks. Furthermore the authors aim to examine if the superior portfolio can beat the OMXS index and create abnormal re-turns on the Stockholm Stock Exchange.

Method: The quantitative research method is used when gathering information. To

deter-mine which stocks to include each year between 1993 to 2005 the price-to-book ratio (P/B) is used. Based on this multiple the sample is divided into two extreme groups of low and high P/B companies. These two groups are further divided according to their price-to-earning ratios (P/E). This creates four portfolios, which symbolizes value and growth stocks. Each portfolio’s return is recorded annually during the 12 year period. The returns are risk-adjusted in order to find the superior portfolio. This portfolio is then compared with the OMXS index for the same period to find out whether it has created an abnormal return.

Conclusion: The superior and most extreme value portfolio, consisting of stocks with low

P/B and low P/E ratios generated a cumulative risk-adjusted return of 1908% between 1993-2005 and beat the most extreme growth portfolio consisting of high P/Bs and high P/Es which generated a negative cumulative return. The superior portfolio was also able to beat the OMXS index during the years of 1993-2005, generating an abnormal risk-adjusted return of 7.77 times that of the OMXS index.

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Kandidatuppsats inom Finansiering

Titel: Värde kontra Tillväxt - En studie av portföljavkastning på Stockholmsbörsen ba-serad på P/B- och P/E talen

Författare: Carlström Anders, Karlström Rikard, Sellgren Jakob

Handledare: Österlund Urban

Datum: 2005-12-20

Ämnesord: Finansiering, P/B, P/E, Portföljteori, Effektiva marknads hypotesen, Abnor-maliteter

Sammanfattning

Frågeställningar:

• Kommer en portfölj baserad på värdeaktier, på en riskjusterad basis att slå en portfölj baserad på

tillväxtaktier på Stockholmsbörsen?

• Kan den vinnande strategin skapa en riskjusterad överavkastning över OMXS index?

Syfte: Syftet är att undersöka om en investerare, genom att köpa en portfölj baserad på

vär-deaktier, kan slå en portfölj baserad på tillväxtaktier. Vidare har författarna som mål att un-dersöka om den vinnande portföljen kan slå OMXS-index och skapa överavkastning på den svenska aktiemarknaden.

Metod: Informationsinsamlingen till uppsatsen har en kvantitativ ansatts som grund. För

att avgöra vilka aktier som ska inkluderas i undersökningen mellan åren 1993 till 2005 har författarna använt sig av nyckeltalet aktiekurs över eget kapital (P/B-tal). Med det här ny-ckeltalet till grund har urvalet delats upp i två extremgrupper, lågt och högt P/B. Dessa två grupper delades upp ytterligare efter dess aktiekurs över vinst (P/E-tal). Detta skapar fyra portföljer som symboliserar värde- och tillväxtaktier. Avkastning på portföljerna mäts årli-gen under 12 år och sedan riskjusteras för att hitta den mest lönsamma portföljen. Denna portfölj jämförs sedan med OMXS-index för samma period för att se om portföljen har skapat överavkastning.

Slutsats: Den bästa och mest extrema värdeaktieportföljen som bestod av lågt P/B och

lågt P/E skapade en kumulativ riskjusterad avkastning på 1908% och slog den mest extre-ma tillväxtportföljen som genererade en negativ kumulativ avkastning. Den bästa portföljen slog också OMXS-index under åren 1993 till 2005 och skapade en riskjusterad överavkast-ning på 7.77 gånger OMXS.

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Table of Content

1

Introduction... 1

1.1 Background ... 1 1.2 Problem Discussion... 3 1.3 Purpose... 4 1.4 Perspective ... 4 1.5 Delimitations... 4 1.6 Definitions ... 4 1.7 Methodological Approach... 5 1.8 Methodological Overview ... 5 1.9 Literature Study... 7 1.10 Disposition... 8

2

Theoretical Framework ... 9

2.1 Efficient Market Hypothesis (EMH)... 9

2.2 Portfolio Theory... 10

2.2.1 Return... 10

2.2.2 Portfolio risk and the relation to portfolio performance ... 11

2.2.3 Risk definition ... 11

2.2.4 Risk-free rate ... 12

2.2.5 Portfolio performance in relation to the market benchmark ... 12

2.2.6 Market Index... 12

2.2.7 Risk-adjusted measures ... 12

2.3 Previous Research of Valuation Multiples ... 14

2.4 Value and Growth Definitions... 15

2.5 Examples of value and growth companies ... 17

3

Methodology ... 19

3.1 Quantitative research approach ... 19

3.2 Secondary data ... 19

3.3 Data collection and portfolio creation ... 20

3.3.1 Sample size ... 22

3.3.2 Break points for P/B... 22

3.3.3 Systematic sampling ... 24

3.4 Portfolio Calculations... 24

3.5 Portfolio Analysis... 26

3.6 Reliability and Validity ... 27

4

Empirical Findings and Analysis ... 28

4.1 Empirical findings of the four portfolios... 28

4.2 Portfolio comparison and analysis... 30

4.2.1 Geometric average comparisons ... 30

4.2.2 Cumulative return comparisons ... 30

4.2.3 Reasons for return differences... 31

4.3 Low-Low vs. OMXS index ... 33

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5.1 Conclusion ... 35

5.2 The authors’ reflections ... 36

5.2.1 Reasons for over- and under valuation... 36

5.2.2 Reasons for abnormal return ... 36

5.2.3 Implications for the EMH... 36

5.2.4 Side remarks on β, P/E and the time period used ... 37

5.3 Critique of method used ... 37

5.4 Suggestions for further studies... 39

References... 40

Appendix I... 44

Appendix II... 47

Appendix III... 48

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Figures

Figure 1 Barra Value & Growth Index – a cumulative comparison ... 2

Figure 2 Methodological Overview ... 6

Figure 3 Portfolio creation and composition ... 21

Figure 4 The standard normal distribution... 23

Figure 5 Risk-adjusted portfolio performances each year 1993- 2004 ... 29

Figure 6 Cumulative return... 31

Figure 7 Actual returns, not risk-adjusted... 33

Tables

Table 1 Wilshire Style Index... 17

Table 2 Portfolio performance per year 1993-2004... 29

Table 3 Average geometric risk-adjusted return 1993-2005 ... 30

Table 4 Average portfolio beta and dividend payout 1993-2004 ... 31

Table 5 Low-Low portfolio vs. OMXS ... 34

Formulas

Formula 1 Holding-period return ... 10

Formula 2 Geometric average... 10

Formula 3 Treynor ratio... 13

Formula 4 Jensen’s Measure ... 13

Formula 5 Tail area ... 23

Formula 6 Table area... 23

Formula 7 Break points for P/B ... 24

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Introduction

1 Introduction

“To invest successfully over a lifetime does not require a stratospheric IQ, unusual business insights, or in-side information. What is needed is a sound intellectual framework for making decisions and the ability to keep emotions from corroding that framework”.

- Warren Buffet, 1986

(Cited in Graham, 1973, revised 1986, p vii)

1.1 Background

Humans are by nature value and profit maximizers. In all we do, we implicitly calculate and compare the expected gains with the risks involved. That is, we try to maximize our profit with as low risk as possible.

A number of papers have dealt with methods showing evidence that markets are inefficient and investors are able to achieve abnormal returns1, i.e. finding portfolios of companies

that will beat the market, by conducting different kinds of stock picking techniques. Some of the common market irregularities are the January effect - that stocks generate abnor-mally high returns in the month of January, the Monday effect - that Mondays are the worst day of holding shares, the size effect - that small-cap firms outperform large-cap firms, insider transactions - that insider transactions reveal a concealed message about the company’s true market valuation, and lastly that value stocks outperform growth stocks. (Damodaran, 2002; Ross, Westerfield & Jaffe 2005) The focus in this thesis will be on the value versus growth perspective, since it is a common way for individuals and mutual funds to classify and base their investment decisions on.

An example of a great value investor is Warren Buffett. According to Forbes Magazine (Kroll & Goldman, 2005) Buffett is currently the second wealthiest person in the world with a net worth of more than $44 billion. He has been able to create his fortune by using the techniques of fundamental analysis in order to find value stocks, typically mature com-panies found in the Manufacturing, Real-estate and Timber & Pulp industries, worth $1 selling for $0.5. His skills as an investor are evident when looking at the US holding com-pany Berkshire Hathaway, where he is the chairman and CEO, increasing in value over 30 years from $290/share to more than $84 000/share. (Miles, 2004)

On the other hand, investing in growth companies, typically younger companies found in the Healthcare and Technology-industries (Börsguide, 1993- 2005), can also create high re-turns. An example of this is the Swedish IT-firm Framfab, increasing in share price by 1515% within nine months from its initial public offering in June of 1999. However six years later Framfab’s stock price has dropped 90% compared to the introduction price. (OMX Group - Stockholmsbörsen, 2005) This shows that an investor can make great prof-its on both types of investments but returns might differ remarkably in the long-run. Another support in favor of value stocks is the comparison of the Barra Value & Growth Indexes2, based in the US. Figure 1 shows that value investors have beaten growth

1 The excess return of a portfolio given the return of a market portfolio (Ross, Westerfield & Jaffe 2005) 2 Stock indexes categorized by the P/B ratio. Value implies low P/B ratios and Growth implies high P/B

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tors by about the double, generating a cumulative return of more than 6 000%. (Barra, 2005) 0% 1000% 2000% 3000% 4000% 5000% 6000% 7000% 19 75 19 77 19 79 19 81 19 83 19 85 19 87 19 89 19 91 19 93 19 95 19 97 19 99 20 01 20 03 20 05 Year % Value Growth

Figure 1 Barra Value & Growth Index – a cumulative comparison

These examples show interesting signs that value investing in the long-run, i.e. using fun-damental analysis to find value stocks, is generating higher returns compared to a strategy based on buying growth stocks. The technique of finding undervalued3 companies can be

traced back to 1934 and Benjamin Graham, the father of valuation and author of the book

Security Analysis (Graham & Dodd, 1934). He developed a majority of the ideas which

fun-damental analysts base their investment methods on. The underlying theme in funfun-damental analysis is that the true value of the firm is not always reflected in its price and thus can in-stead be related to its financial characteristics such as growth prospects, cash flows and valuation multiples. This means that a stock should be picked depending on the company’s financial situation. (Graham & Dodd, 1934; Graham, 1973; Damodaran, 2002)

The evidence above, that value stocks are outperforming growth stocks, are of interest to all market participants since value maximization and creating abnormal returns are the ul-timate goals when investing. Creating sustained abnormal returns is however inconsistent with the well known Efficient Market Hypothesis which states that in a truly efficient mar-ket at any point in time, the stock price is fully reflected by all available information. This means that it should be impossible to find undervalued companies unless the market is in-efficient. (Sharpe, Alexander & Baily, 1999) This thesis will nevertheless try to examine the possibility to generate abnormal returns on the Stockholm Stock Exchange using strategies focusing on either buying value or growth stocks.

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Introduction

1.2 Problem

Discussion

There has been a long ongoing discussion among market participants whether growth stocks are constantly being overvalued and hence generating less return on a risk-adjusted basis4, than the more stable value stocks. Value stocks are usually defined as companies

with low valuation multiples (P/B5, P/E6 ratios) and high dividend yield7 while growth

stocks are defined as companies with high valuation multiples (P/B, P/E) and low divi-dend yield. (Sharpe et al. 1999)

Most previous research, by for example Fama and French (1992), Chan, Hamao and La-konishok (1991) and Basu (1977), shows that value stocks outperforms growth stocks. A majority of these studies have been performed on the US stock market, the world’s largest market for listed securities, and the authors have not found any studies that specifically fo-cus on the Swedish stock market, which is relatively small – the eighth largest in Europe based on equity trading. (Federation of European Securities Exchanges, 2005)

According to an article by Fuhrman in Wall Street Journal (2000) European investors are not as fond of value stocks as US investors, meaning that Europeans tend to prefer growth stocks. The author of the article argues this is because of the perception that growth stock’s have seemingly limitless potential gains. With European’s dislike of value stocks in mind, together with the fact that Swedes are very active investors, either directly or through mu-tual funds, it is in their and the authors interest to answer the following questions:

• Will a portfolio based on value stocks, on a risk-adjusted basis; outperform a portfolio based on

growth stocks on the Stockholm Stock Exchange?

Most interestingly, since investing is about value creation and preferably creating abnormal returns:

• Is the superior strategy able to generate abnormal risk adjusted returns by beating the OMXS

in-dex?

4 Returns adjusted for the level of risk taken, a longer discussion is found in section 2.2.7

5 Price per share divided by book value per share 6 Price per share divided by earnings per share 7 Annual dividend per share divided by price per share

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1.3 Purpose

The purpose of this thesis is to investigate if an investor by purchasing a portfolio based on value stocks will outperform a portfolio based on growth stocks. Furthermore the authors aim to examine if the superior portfolio can beat the OMXS index and create abnormal re-turns on the Stockholm Stock Exchange.

1.4 Perspective

This thesis is written from an investor perspective, investors being either individuals or lar-ger institutions such as mutual funds. Investors interested in enhancing their portfolio re-turns will have an interest in the result of this thesis.

1.5 Delimitations

The authors have not been able to find earlier studies about the anomality that value beats growth, which specifically have been performed on the Swedish market. It is likely that other studies have taken place, however these might be published in data bases and at uni-versities not available for the authors.

This thesis will take into consideration the vast majority of the Stockholm Stock Exchange, including the following lists: the A-list, O-list, Attract 40, NGM Equity, Nya Marknaden and

Aktietorget. Due to the lack of data from smaller lists such as beQuoted (inoff.) and Göte-borgslistan they will not be included.

The time span for the research is from 1993 until 2005, this since there is no structured data available before 1993 and due to time constraints the authors have not had the ability to process older information.

Tax effects are not taken into consideration when selling stocks or when receiving divi-dends which will cause profits to be higher and losses to be lower relatively to if returns would have been adjusted for taxes.

Transaction costs will not be considered either, since this cost will differ significantly de-pending on the type of investor and volume traded. The reader should be aware that each transaction both buy and sell, will reduce the total profit. The authors have however inten-tionally with the chosen method tried to reduce the number of transactions in order to minimize the transaction costs.

Reasons for companies’ having either high or low valuation multiples are not considered, nor if these extreme multiples only last temporarily. Purchasing decisions are only based on raw data published once a year not taking any other factors into account that might be of importance when evaluating stocks.

1.6 Definitions

The price-to-book ratio, henceforth referred to as P/B is a valuation multiple used to measure the price paid for a share over the book value per share. The lower the ratio for companies in the same industry the lower the valuation and vice versa. (Frykman & Tolleryd 2003)

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Introduction

The price-to-earnings ratio, henceforth referred to as P/E measures the market price per share over earnings per share, in other words it shows how much investors are willing to pay today for one unit of earnings. The lower the ratio for companies in the same industry the lower the valuation and vice versa. (Sharpe et al. 1999)

Both ratios are frequently used in fundamental analysis when comparing companies’ valua-tions within the same industry. In cases where companies have negative P/B and P/E ra-tios they will be considered as being infinite large. For a more thorough discussion of nega-tive valuation multiples and a numerical example, see appendix I.

1.7 Methodological

Approach

What are you interested in as a researcher? Is it to understand how everything fits together or is it a specific target or event? Within these questions lie basic philosophical thoughts which every researcher has to reflect upon before he or she proceeds. The questions be-hind the issue are the deductive method and the inductive method. These are two plat-forms which a researcher can begin the investigation from.

The deductive method works by using statements which you then can deduct new hy-pothesis from, that is, working with an already known formula, assumption or theory and try to apply this to observations made in the real world and thereby explain the world through the pre understood theories. These hypotheses can then be proven right or wrong by using empirical studies. (Holme & Solvang, 1991) This thesis will tilt towards the deduc-tive method since known formulas are being used, P/B and P/E, and then are applied to observations made on the stock market. The empirical findings can then be tested through statistical formulas in order to confirm or reject the previous conclusions on the US market that value beats growth and see if this is applicable on the Swedish market as well.

The inductive method on the other hand works in the opposite way. It focuses on the ob-servations made of the world and a specific occurrence and tries to work out a formula ex-plaining the observations. The specific observation is made into a generalization about the world (Losee, 2001). To some extent this thesis will also use the inductive method since the sample of value- and growth companies and the conclusions drawn from these observa-tions will be accepted as a description of the whole population of companies, i.e. the ran-dom sample of value companies will be used as a description for all value companies and the random sample of growth companies will be used as a description for all growth com-panies.

1.8 Methodological

Overview

This thesis starts out defining value and growth by certain financial multiples. Listed com-panies on the Stockholm Stock Exchange will be divided into two groups: growth and value companies based on their P/B ratios. To get the statistical framework the authors will gather historical stock information based on annual data from the book Börsguide, explained further bellow. From the first two groups four portfolios will be created, based on their P/E ratios. All four portfolios’ return will be measured and compared each year, with re-gards to their risk, in order to determine which portfolio that has created the highest return on a risk-adjusted basis. The superior portfolio out of these four will lastly be compared to the OMXS index to conclude if it has generated abnormal returns as well. A graphical overview of the methodological steps can be seen in figure 2.

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Introduction

1.9 Literature

Study

The authors have used two main sources in order to retrieve the information: research journals and books. Research journals about previous research in the field of “value and growth” investing were found through the database JSTOR. This database is made up of several research magazines where The Journal of Finance was found to have the highest density of relevant articles. Examples of search words used to narrow the amount of in-formation when searching for applicable articles were “Value Investing”, “Growth Stocks”, “Value”, “Growth”, “Value vs. Growth”, “P/B”, “P/E”, “Definition of value/growth” and a combination of these. Besides explaining the results of previous studies these articles also gave valuable help when defining value from growth stocks.

The type of literature most used in this thesis is books within the field of portfolio theory and corporate finance. These books offer insights when laying out the stepping stones of portfolio analysis, such as return on portfolios relative to their risk, which is of high impor-tance in this thesis.

The historical stock information in the empirical study was obtained through the book

Börsguide which is found in the financial department of Jönköping International Business

School’s library. Börsguide is independent data published twice a year by Delphi Econom-ics and it contains unbiased historical data such as stock prices, earnings, margins, valuation multiples and major stock holders for all public companies in Sweden, except from smaller lists such as beQuoted (inoff.) or Göteborgslistan. It is available in printed form on most librar-ies. This book was the only source available where historical stock prices and valuation multiples were grouped in an efficient way.

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1.10 Disposition

An introduction to the value and growth concepts which leads into a detailed background discussion and problem statement of the thesis. The problem state-ment will further be followed by the purpose and de-limitations. It ends with a clarification of the philoso-phical methods used to gather information for the the-sis.

Chapter 1

Introduction

This chapter clarifies the thesis’ theoretical framework such as defining value and growth and explaining key financial definitions. It will assist the authors in the analysis of the proposed research questions.

Chapter 2 Frame of Reference Chapter 3 Methodology Chapter 4 Empirical Findings and Analysis Chapter 5 Conclusion & Discussion

The method used to conduct the empirical study will be presented in this chapter. The process of gathering information together with a detailed method used to categorize and analyze the data will be explained. The chapter ends with a critical overlook of the processes used.

The empirical findings of the data collection are pre-sented and then analyzed with aid of the theoretical framework.

The conclusion of the thesis, a discussion of the analy-sis and the authors’ own reflections. The chapter ends with criticism of the method used and a proposal for further research.

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Theoretical Framework

2 Theoretical

Framework

The following chapter examines and outlines the theoretical framework which will support the thesis. The chapter begins with a classification of the efficient market and the various measures used to classify and ana-lyze portfolio performance. Furthermore, a summary on previous studies made by different financial scholars are presented, and finally the concepts and characteristics of value- and growth companies are discussed.

2.1

Efficient Market Hypothesis (EMH)

The Efficient Market Hypothesis (EMH) states that at any point in time asset prices should fully reflect all available information (Damodaran, 2002; Ross et al. 2005). Since the price reflects all available information, investors cannot expect to make abnormal profits. Ab-normal profits also called abAb-normal return, is the excess return of a portfolio given the re-turn of a market portfolio (see section 2.2.6. for a discussion of the market portfolio). It is the part of the return that is not due to systematic impacts, meaning; the difference be-tween actual return and the expected return from market movements. Abnormal returns can be positive, i.e. when the portfolio has beaten the market, or negative, i.e. when the market has beaten the portfolio. (Ross et al. 2005)

The EMH does not state that the market price of an asset or investment must be equal to the true value at any point in time, but merely that the errors in market price are unbiased, i.e. that the stock price can actually be higher or lower than the true price as long as these errors are random. This random error term implies that at any point in time, there is an equal chance that the stock is under- or overvalued. So in an efficient market, stocks with low P/E ratios should have an equal chance of being undervalued as stocks with high P/E ratios. (Damodaran, 2002)

In 1970 Eugene Fama (1970) presented an influential article where he divided the efficient market into three forms; weak, semi-strong and strong.

The weak form of market efficiency states that it is not possible for investors to make ab-normal profits based on knowledge of past stock performance. This due to the fact that the stock price follows a specific random process called a random walk, meaning that new in-formation will affect the price through an error term and future prices cannot be predicted from past prices. (Fama, 1970)

The semi-strong form of market efficiency states that, in addition to the rules of the weak form, it is not possible for investors to make abnormal returns based on information that is publicly known. This due to the fact that a semi-strong market quickly responds to publicly announced information and will therefore adjust the stock price to a correct level. (Fama, 1970)

The strong form of market efficiency states that an investor will not be able to make ab-normal profits based on any information, neither public nor private (such as insider infor-mation). This is due to the fact that the stock price reflects all available information at all times and no investor will have superior information that will not already been taken into account. (Fama, 1070) This implicates that, even though trading on inside information is il-legal in Sweden, this information is somehow leaking and is incorporated into stock prices (Mandell & O’Brien, 1992).

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One important implication of the EMH is that it does not state that no investors will be able to beat the market, in fact, about half of the investors will beat the market at any given time, and half of the investors will not. (Mandell & O’Brien, 1992)

The Swedish stock market is according to Wramsby and Österlund (2001) semi-strong. However, it shows a lower degree of efficiency than larger foreign markets this because the Swedish market is relatively small which makes it easier for large investors in Sweden to ef-fect stock prices in their favor.

2.2 Portfolio

Theory

Depending on the investor’s motive with his/her investments there will always, to some degree, be a payoff between the return of the investment and the risk of that same invest-ment. This means that the more uncertain the future returns of an investment are, the higher should the expected return of that investment be (Bodie, Kane & Marcus, 2004; Strong, 2000) i.e. the higher risk a portfolio has, the higher return it is excepted to generate and vice versa. The factors that an investor has to consider before making a rational in-vestment decision will be discussed in the coming paragraphs.

2.2.1 Return

A measure of a stock investment’s success is the rate at which the funds has grown from one period to another, called the total holding-period return (HPR). The HPR depends on both the capital gain/loss, i.e. the increase/decrease in share price during the period, and any dividends paid. The percentage return the dividends have generated in relation to its price is also called dividend yield. (Bodie et al. 2004)

The HPR formula is as follow:

eld DividendYi price Beginning price Beginning ce Ending pri HPR= − +

Formula 1 Holding-period return (Bodie et al. 2004)

The return to use when dealing with multiple time periods is the cumulative return ap-proach. The underlying assumption in this approach is that the return earned is re-invested in the asset and hence each years return is compounded into a final, cumulative return. (Bodie et al. 2004)

When measuring the average return over several periods of time it is appropriate to use a geometric average, which, as in the case with cumulative return, takes into consideration the compounding effect. (Bodie et al. 2004)

(

) (

) (

) (

)

n n R r ... r * r + + = + + 1 1 1 1 1 2

Formula 2 Geometric average (Bodie et al. 2004)

rn = Return for period n

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Theoretical Framework

2.2.2 Portfolio risk and the relation to portfolio performance

In order to be able to determine which portfolio that is actually the most profitable, one has to compare the returns on a risk-adjusted basis. This since the portfolios all have dif-ferent risks and hence will have difdif-ferent returns. Without risk-adjusting for these differ-ences, a comparison between them would not be objective. An objective comparison there-fore demands that the portfolios are adjusted for the respective risk. In the next section the various aspects to consider when doing this risk-adjusted comparison will be described.

2.2.3 Risk definition

The risk when investing is the likelihood of losing your invested capital and hence generate a negative return. This risk is measured by the variability, the standard deviation8, of

re-turns. A risk-free asset has a standard deviation of zero. The total risk of a stock is made up of unsystematic and systematic risk where the unsystematic risk is firm-specific risk, i.e. fac-tors that only affect the single company and not the market as a whole. Unsystematic risk can be lowered and actually eliminated by diversification. (Suhar, 2003) The reasoning be-hind diversification is that if one asset is having a negative development, there will be other assets in the investor’s portfolio that is doing well and hence will counteract the poor per-forming asset. The classical expression, do not put all your eggs in one basket is a good summary of the logic of diversification. (Bodie et al. 2004)

To tell whether a portfolio is diversified or not one must look at the number of securities in the portfolio, the variance and the covariance of each security. The variance (risk) of a portfolio consisting of only one security is, of course, the same as the variance of that secu-rity. As more securities are added to the portfolio the variance drops, which is called the diversification effect. The risk however cannot be fully reduced; this since the minimum variance of a portfolio is the average covariance9 of the each pair of securities. This means

that the variance of the portfolio becomes smaller and smaller for each security added until it reaches the average covariance of the portfolio. This has implications for an investor who is considering adding an additional security, instead of looking at the total risk of that rity, he will only look at the proportion that cannot be diversified away, i.e. how the secu-rity correlate with the other securities in the portfolio. (Ross et al. 2005) According to Da-modaran (2002), a well diversified portfolio, consists of 20 or more securities.

The systematic risk, also called market risk, can not be eliminated by diversification. This risk is measured by the beta coefficient (β). The higher the beta the larger is the portfolio’s volatility compared to the market, and vice versa. The market portfolio has a beta of 1 since the variability of returns with itself is always 1. A portfolio’s beta is the weighted av-erage of the individual stocks. The more systematic risk someone is willing to take on the higher is the expected return. (Suhar, 2003)

8The standard deviation is the square root of the variance and measures the spread or deviation of a particular

return from the mean return. (Azcel & Sounderpandian, 2002)

9The covariance of a pair of stocks is simply how their movements relate to one another. If both stocks are above or below its average, at a given time, they are positively related and have a positive covariance. If one is above and the other one is below its average, at this time they are negatively related and have a negative co-variance. (Ross et al. 2005)

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2.2.4 Risk-free rate

The definition of the risk-free rate, denoted Rf, is the rate that an investor can earn with

certainty, without taking any risk. A risk-free asset, generating the risk-free rate, has a stan-dard deviation of zero. The rate should match the expected holding period of the invest-ment, i.e. a 10-year holding period should preferably use a 10-year risk-free rate, such as a Treasury bond. The problem with long-term bonds however is that the greater the maturity the more risky they become. (Voitle, 2002) If the inflation is greater than the interest rate, the actual purchasing power will be lower in the future, thus the only true risk-free asset in this case would be a price-indexed government bond. This because interest rates in real terms are adjusted for inflation and government bonds can be assumed default free. In fi-nance theory, the Treasury-bills (maturities less than 1 year) are considered as true risk-free assets. (Bodie et al. 2004)

2.2.5 Portfolio performance in relation to the market benchmark

The return of the portfolio as shown in section 2.2.1 is a good measure of the performance of the portfolio. By using the HPR you can easily see whether your portfolio has generated a loss or a profit. However, the HPR solely might not be enough to conclude if the portfo-lio has been successful or not. In order to determine the actual portfoportfo-lio performance one has to compare the return against a market portfolio, i.e. a market benchmark. The most commonly used benchmarks are stock market indexes. (Damodaran, 2002; Bodie et al. 2004)

2.2.6 Market Index

According to Strong (2000) the theoretical market portfolio is a portfolio consisting of all risky securities in proportion to each share’s market capitalization weight. Since it is impos-sible to include all securities in one index, a simplification is to use a broad listed market index. One frequently used index is the Standard & Poor’s 500 index which contains 500 stocks listed on the U.S. stock market (Friend & Blume, 1970). The broadest index on the Stockholm Stock Exchange is the OMX Stockholm Index (OMXS), previously called SAX. It contains all the listed stocks on the A- and O-list. According to OMX Group, the com-pany behind the index, OMXS is tracking the overall Swedish stock market and its changes. The index date is set to 100 at 1995-12-31. The index is weighted after value, meaning that the individual stocks weights are in proportion to their total stock value. (OMX Group – Stockholmsbörsen, 2005)

2.2.7 Risk-adjusted measures

According to Bodie et al. (2004) and Strong (2000) it is important to conduct portfolio comparisons on a risk-adjusted basis. This since investors are risk-averse, meaning that if facing two investments with the same expected return the one with the lowest risk will be preferred and therefore they expect compensation for the level of risk of the portfolio. (Bodie et al. 2004) That means that the returns on two different portfolios are compared on a fair basis, adjusting for the fact that riskier portfolios should earn higher expected turns than not so risky portfolios. There are a number of ways to calculate risk-adjusted re-turns; all of them require data such as the portfolios’ standard deviation, rate of return, overall market performance and the risk-free rate.

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Theoretical Framework

The three most commonly used methods are the Sharpe ratio, the Treynor ratio and Jen-sen’s measure (Bodie et al. 2004; Strong, 2000). It is important to pick the appropriate risk measure when making risk-adjusted comparisons. It all depends on the composition of the portfolios to compare. This is because the ratios above measures return relative to risk in different ways. The Sharpe ratio10 can always be used since it measures risk by the standard

deviation, i.e. total risk, which all portfolios have. The Treynor- and Jensen measure can however only be used on well diversified portfolios since they only take into account the systematic risk, beta.

The Treynor ratio, seen in formula 3, measures the excess return per unit of systematic risk. The higher the ratio, the better the portfolio has performed. The formula is:

(

RP-Rf

)

Treynor ratio

=

P

β

Formula 3 Treynor ratio (Bodie et al. 2004)

Rp = Portfolio Return Rf = Risk Free Rate βp = Portfolio’s Beta

Jensen measures the average return on a portfolio above the return predicted by the Capital Asset Pricing Model, CAPM11. CAPM is used to predict the expected return based on the

risk, given the portfolio’s beta, average market return (OMXS) and the risk free rate. Given CAPM, Jensen’s measure can be used to rate fund managers’ performance against a market index to check if the risk was worth the reward. A positive Jensen’s measure implicates that the portfolio has generated abnormal returns on a risk-adjusted basis. (Strong, 2000) The formula is:

(

RP-Rf

)

−βP

(

RM-Rf

)

=Jensen'smesure

Formula 4 Jensen’s Measure (Bodie et al. 2004)

Rp = Portfolio Return Rf = Risk Free Rate βp = Portfolio’s Beta

RM = Market Return (Benchmark)

The factors explained in this chapter need to be considered before making an investment decision. However, what is also important is how the investor builds the portfolio, how he/she chooses the stocks to buy. In this thesis, the authors are focusing on value and growth companies, hence it is crucial to first understand the concept of value and growth. The authors will through previous research about these two concepts clarify and define 10 ( ) ratio Sharpe R -RP f = P σ 11 ⎠ ⎞ ⎜ ⎝ ⎛ + = f s m f s R β R R R

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what valuation multiples that best describes the two and henceforth will be used in the the-sis.

2.3

Previous Research of Valuation Multiples

There has been a lot of research done in the field of variables explaining stock returns; most of them have based their samples on the US stock market. Many research papers have included theories about size and calendar effects. These are not of interest in this the-sis since it is only focusing on factors explaining valuation aspects, which in turn can iden-tify growth from value stocks. None of the reports have explicitly focused on the value versus growth aspect, but rather on the different multiples that help define these two. Some examples of previous studies follow bellow.

Fama and French (1992) made a study on the US stock market between 1963 and 1990. They described the relations between, market β, market capitalization, P/E, leverage and P/B with average returns. Their conclusion was, firstly that β does not seem to explain av-erage returns, hence rejecting the Sharpe-Lintner-Black model (that there is a positive rela-tionship between β and average stock returns), secondly the combination of size and P/B absorbs the role of leverage and P/E when describing average returns. Their final and main conclusion was that market capitalization and the P/B multiple best describe average stock-returns, where P/B is the most powerful explanatory variable of the two. A part of the re-sult of their study is found in appendix I. The average returns, grouping companies with regards to their P/B ratio, show a clear trend that the lower the P/B, the higher average re-turns.

Fama and French (1998) also conducted an international study where they evaluated the value premium in 13 countries from 1974 to 1994. They found that value stocks, i.e. shares with low P/B, P/E and P/CF12, experienced higher returns than growth stocks. The

dif-ference in returns between the two groups was 7.68% per year.

Chan, Hamao and Lakonishok (1991) described differences in expected returns on the Japanese stock market between 1971 and 1988. They based their study on four variables: P/E, market capitalization, P/B and P/CF. Their choice of predictor variables was moti-vated by the fact that these variables were shown most applicable on the US stock market and the practice of fundamental security analysts. A theoretical justification for these vari-ables was, as the authors put it: “out of the scope of this paper” (Chan et al. 1991, p. 1740). The size effect was, as earlier studies conclude, dependent on the specific model and time period. Earnings yield did not seem to be related to stock returns in their study, but their research showed a clear relationship between expected stock returns and the P/B multiple and cash flow yield, where the companies with the lowest P/Bs posted the highest returns. They also concluded that their variables are more or less correlated; low P/B companies tend to have low P/CF. The second part of their study was to conduct a regression analysis called Seemingly Unrelated Regressions (SUR) with unadjusted fundamental variables (i.e. variables were not adjusted for change in levels over time) and a SUR with adjusted fun-damental variables. The regression results showed a negative relation between P/B, P/CF and return, meaning that the lower the valuation multiples get, the higher returns were gen-erated. In their regression both variables were significant, especially P/B, which was eco-nomically and statistically most important. This is according to the authors interesting since

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Theoretical Framework

P/B and P/CF had, compared to the P/E ratio, received little attention in the financial lit-erature. They did point out though that the relationship found in their study would not for certain hold in the future.

Basu (1977) conducted a study between 1957 and 1971 where he determined the relation-ship between investment performance of US stocks and their P/E ratios. He grouped secu-rities by their P/E ratios and formed portfolios out of these groups. The portfolios were held for a year and then reinvested with the same criteria as before. This procedure takes into account that stock prices and reported earnings fluctuate during a year, creating differ-ent P/E ratios. He found that low P/E portfolios beat high P/E portfolios by about 4% per annum and this was not due to levels of systematic risk. He concluded that investors are able to profit from strategies based on buying low P/E companies; hence the US capital market is not truly efficient.

Depending on the definition of value and growth stocks, the above studies show that the premium earned by holding value stocks compared to growth stocks is evident during sev-eral time periods on the US market and also internationally. This even though different methods was used to perform the research. All studies confirm that the lower the valuation multiples, the higher returns one can expect. The researchers above also conclude that the most common risk measure beta, cannot explain the better performance of value stocks. It also showed, perhaps to some surprise, that the more commonly used (in the financial press), P/E ratio, even though explaining differences in stock returns, does not seem to do it to the same extend as P/B does.

2.4

Value and Growth Definitions

Even though there is no clear definition of growth and value stocks according to theory (Sharpe et al. 1999), it is seen in section 2.3 which multiples that are most significant and that there are differences in the explanatory power of different valuation tools. By focusing on these, the research done in the past has narrowed the field, especially down to two mul-tiples, P/B and P/E. According to the following authors these two multiples can be used when separating the growth from value stocks, since it is clear that they have the highest explanatory power of all the multiples mentioned in the previous section.

According to Sharpe et al. (1999) a growth stock has high P/B and P/E ratios, the same but inverse relation holds for value stocks13. This classification is also supported by Fama

and French (1998), but they also added the P/CF multiple when separating growth from value.

Wall Street Journal classifies growth stocks as companies, which experience higher-than- average gains in earnings or stock price during the past few years and are expected to con-tinue to do so. It also states that these companies have high P/E ratios and pay little or no dividends. Value stocks have low valuation measures, such as P/E or P/S14 ratios. (Talley,

2003)

13 There are no precise definition of high and low P/B and P/E ratios, and by looking at the Stockholm

Stock Exchange one can see that the average P/B during the time period 1993-2005 has increased from 1,3 to 4,6 and the P/E has increased from 11,9 to 22 (Börsguide, 1993 & 2005)

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According to Ibbotson and Riepe (1997) growth managers invest in companies experienc-ing rapid growth in earnexperienc-ings, sales or return on equity. These stocks tend to have the char-acteristics of high P/B and high P/E ratios. Value oriented managers on the other hand, look for less popular stocks (stocks in industries considered mature, with modest growth prospects) and turn-around companies (stocks of companies experiencing problems but that are expected to recover). These value stocks are, according to the authors, usually as-sociated with low P/B, low P/E, low P/CF ratios and high dividend yields.

Morningstar, a provider of independent investment research in the United States, catego-rize value stocks in the following way: 50% is based on the P/E ratio; the other 50% is based on equally weights of P/S, P/B, P/CF and dividend yield. (David, 2004)

To shed further light on the classification issue, a description of two indexes, often used as a benchmark when classifying growth and value stocks, will follow.

The first one is; Standard & Poor’s Barra Growth and Barra Value indexes created in 1992. The classifications of these two indexes are based on William Sharpe’s, Eugene Fama’s and Kenneth French’s thoughts that a growth stock has a high P/B and a value stock has a low P/B ratio. The creators of Barra argue that even though there are no clear definitions of growth and value stocks, the P/B multiple is most suitable to use since it is easy to under-stand and captures the fundamental differences between value and growth companies. This because the P/B ratio tends to be more stable over time, since the book value is not as volatile compared to alternative ratios such as the P/E ratio, earning growth rates, and re-turn on equity. Shares in the Barra Value index display characteristics, besides low P/B ra-tios, also lower P/E rara-tios, higher dividend yields, and lower historical and predicted earn-ings growth. While shares in the Barra Growth index have characteristics such as high P/B and P/E and lower dividend yields. (Barra, 2005)

The second index; Wilshire, is another frequently used American stock index. It uses both the P/B and the P/E multiples in order to define growth and value stocks. The P/B multi-ple is given three times the weight of the P/E multimulti-ple because the former is believed to be a more accurate identifier of growth and value stocks. As can be seen in table 1 the Wil-shire Growth Index has higher P/B and P/E ratios than the WilWil-shire Value Index counter-part, while the dividend yield for the Wilshire Growth Indexes is lower. (Wilshire Associ-ates Incorporated, 2005)

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Theoretical Framework

Table 1 Wilshire Style Index (Wilshire Associates Incorporated, 2005)

To summarize the above discussion one can see that the P/B and the P/E multiples best describe growth and value stocks, thus these will be used as explanatory variables in this thesis. The most common method used out of these two, is the P/B multiple. It is the ratio that best and easiest separates the two categories. Since the book value of equity is less volatile than for example cash flow, this multiple becomes more stable and will not depend as much on current business cycle or investment decisions.

The P/E ratio is probably the most popular valuation multiple in the financial press since earnings are usually easily available, and from the above discussion it is a common method to identify growth from value stocks.

Other valuation multiples such as P/S and P/CF are used by a few but always together with P/B and P/E, hence they do not seem to be as important explanatory variables. Fac-tors like “higher-than-average growth in earnings and cash flow” appear to be used by a few, but not as frequently, because of the subjectivity in these measures.

2.5

Examples of value and growth companies

Value and growth companies tend to be found in different industries. Value stocks typically come from consumer- and financial services, real estate and utilities industries, while growth stocks have historically come from the healthcare and technology industries (Barra, 2005). Examples of value stocks on the Stockholm Stock Exchange are SKF (manufactur-ing), Öresund (financial services) and Tornet (real estate). Examples of growth companies are Ericsson (telecom), AstraZeneca (pharmaceuticals), and H&M (consumer goods). (Börsguide, 1993-2005)

In this chapter the theories and previous research supporting the thesis was presented. The reader is now familiar with the different concepts such as risk, risk-adjusted return, market index and the two valuation multiples that defines value and growth companies, P/B and P/E. In the following sections, the reader will understand how these concepts are used,

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processed and analyzed in order to determine whether a portfolio based on value stocks will outperform a portfolio based on growth stocks.

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Methodology

3 Methodology

This chapter will in detail describe the procedure used to conduct the empirical research. This includes how the data was collected, assumptions made, determination of the sample used and how the information will be interpreted. The chapter ends with a discussion on the reliability and validity of the chosen methods.

3.1

Quantitative research approach

The philosophy of information gathering has concluded two different ways to gather in-formation. The two classifications are named qualitative and quantitative method. The two methods are, since they gather information differently, also used differently in research. The qualitative method uses information where the source has had a great degree of free-dom in forming its own opinion. This way of gathering information will give information about a certain and very specific problem and is normally conducted during normal con-versations or interviews. The information gathered will also be very specific and apply only to that particular research question. (Holme & Solvang, 1991)

The quantitative approach on the other hand, bases information gathering on a more ob-jective base, which means that the researcher should stand far away and observe the infor-mation and not be apart of it, to be as neutral as possible (Holme & Solvang, 1991). This can be done by using a random sample from the whole population, and from that draw a conclusion which can be assumed true for the general population as well. This approach will lead to conclusion of the more general type. Statistics is often used in this method to prove hypothesis about the population sample (Ejvegård, 1993).

The method which best will fit the purpose of this thesis is the quantitative research method. These since the authors are using historical unbiased data retrieved from inde-pendent sources, and the conclusion is supposed to be true for all the following observa-tions, hence a generalization although specific to value and growth companies. (Holme & Solvang, 1991)

3.2 Secondary

data

In the field of methodological research, data is classified into two distinct groups, primary and secondary data. They differ in their closeness to the question being researched. Primary data is collected specifically for the proposed research question, usually through interviews or questionnaires, while secondary data is already existing data that has been collected for other purposes.

The benefit of using primary data is that the researcher can adjust the data based on the specifics of the research question and by that gather the information needed. The major reasons to use secondary data is that it is cheaper and faster to collect than primary data and that it, depending on the research question proposed, might provide the precise data needed (Saunders, Lewis &Thornhill, 2003). As stated before, this thesis will be based on the quantitative method and objective statistical data will be used, meaning that only sec-ondary data will be used.

There are two types of secondary data, raw- and compiled data. Raw data is data where there has been little, if any, processing, while compiled data is data that have received some form of selection and processing (Kervin, 1999). This paper will only use raw data

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consist-ing of stock price returns and trailconsist-ing twelve months P/B and P/E ratios, this in order to avoid the subjectivity that otherwise might be present if using predicted future earnings (see appendix I). This will further strengthen the validity and reliability of the thesis. The secondary data used is evaluated on the basis of relevance to the research question pro-posed.

3.3

Data collection and portfolio creation

In order to compare value and growth portfolios’ returns the authors need to set up port-folios that clearly define them. The aim is to create four portport-folios with appropriately 30 stocks in each, two of these will represent value stocks and the other two will represent growth stocks.

The most important identifier of value from growth stocks, according to previous studies, is the P/B multiple, and the second most important is the P/E ratio. Value stocks have low P/B and P/E ratios and growth stocks have high P/B and P/E ratios (see section 2.3-2.4). Due to the significance of the P/B multiple, each year’s sample is selected entirely on this multiple and two categories, one value and one growth, are created by calculating so called break points for the P/B multiple, explained in section 3.3.2. To only consider stocks be-low the be-low break point and above the high break point ensure the authors that only com-panies with “extreme” P/B multiples are chosen. This method will exclude the average P/B companies leaving the authors with a clear sample of value and growth firms. The method of selecting stocks is done by systematic sampling explained in section 3.3.3

The two categories with value and growth stocks are further split into two portfolios each creating the final four portfolios. This is done by sorting the companies in each category from the lowest to the highest P/E multiples and then put the bottom half and the top half in separate portfolios. This is done in order to create four portfolios with different P/B and P/E characteristics.

The four portfolios symbolize value and growth stocks where the two portfolios within the low P/B group (Low-Low and Low-High) will contain value stocks and the two portfolios within the high P/B group will contain growth stocks (High-Low and High-High). The Low-Low portfolio contains “extreme” value stocks (companies with both low P/B and low P/E ratios) and the High-High portfolio contains “extreme” growth stocks (companies with both high P/B and high P/E ratios). Creating these four portfolios with different characteristics makes it possible to test if for example a portfolio with high P/Bs and low P/Es is generating higher returns than a portfolio invested only in low P/Bs and low P/Es. Figure 3 shows graphically how the portfolio creation is carried out.

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Methodology

Figure 3 Portfolio creation and composition

A numerical example of how the portfolio creation is done the first year in 1993 will fol-low. There are 210 listed companies in 1993 on the lists covered by Börsguide (see appen-dix III for details of included lists and sectors). Out of these 210 companies the aim is to first of all sample 120 stocks (2 categories * 60 stocks in each). Since two extreme catego-ries of value and growth stocks are wanted and no official break points between them exist they need to be calculated. So in 1993, the calculated break points are 1.0 and 1.6 meaning that stocks with P/B ratios below or equal to 1.0 will be considered as being value stocks and stocks with P/B multiples above or equal to 1.6 will be considered as being growth stocks15. Companies with P/Bs between 1.0 and 1.6 are excluded from the sample since

these according to the authors cannot be classified as value- nor growth stocks.

In 1993 the value category was invested in 60 value stocks while the growth category was only invested in 47 stocks, this since there were not 60 growth stocks available with P/B ratios above 1.6, hence all companies with a negative P/B or a P/B above 1.6 was chosen. The 60 and 47 selected stocks in each category are, as mentioned previously, further di-vided based on their P/E ratios. To clarify, the 60 stocks in the value category are split up into a low P/E and a high P/E portfolio with 30 stocks in each (60 divided by 2) and the 47 growth stocks are also split up into a low P/E portfolio with 24 stocks and a high P/E portfolio with 23 stocks (47 divided by 2). So for example the value category is split up in one half that contains the 30 stocks with the lowest P/E ratios and another half that con-tains the 30 shares with the 30 highest P/E ratios.

Due to the fact that the average market P/B ratio has increased from 1.6 in 1993 to 3.7 in 2004 (Börsguide, 1993 & 2005), the break points are adjusted and recalculated each year in order to reflect this increase (see appendix III for calculations). The four portfolios are up-dated each year, due to the changing P/B break points and since some stocks might no

15 Note that the data source Börsguide is using adjusted stockholders’ equity as book value when calculating

the P/B ratio. Adjusted stockholders’ equity is book value increased with 72% of the untaxed reserves, where reserves are profits. (Börsguide, 2004)

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longer qualify to be in a certain category or get de-listed. By only replacing the non-qualifying and de-listed stocks and not the whole portfolio the transaction costs are mini-mized. The same sample process is used when selecting the new stocks, replacing the elimi-nated ones, in order to reach our goal of 30 stocks in each portfolio.

It should be pointed out that reasons for companies’ having either high or low valuation multiples are not considered, nor if these extreme multiples only last temporarily. The aim is to create portfolios only based on raw data published once a year not taking any other factors into account that might be of importance when evaluating stocks.

3.3.1 Sample size

According to Popper (1959), a theory can never be proven true by a finite number of ob-servations because even if every observation that is made confirms the assertion put for-ward by the theory, logically one can never be certain whether some future observation might contradict the theory (Brannick & Roche, 1997). The general opinion is that the lar-ger the sample the greater is the reliability of the statistical analysis. The reason for this is that the sampling error is minimized by increasing the number of observations. (Brooks, 2002; Bryman & Bell, 2003; Cooper & Schindler, 2001).

According to Buglear (2005) the previous stated fact that the larger sample the better, does not necessarily has to be true. Buglear argues that the larger the sample you have, the less is the marginal advantage per increase in sample size. Using a sample of 30 observations means that the standard normal distribution can be use in any statistical decision-making and that the sample does not have to come from the normal population. To have 30 ob-servations or stocks in each portfolio also fulfils the assumption that the portfolios are di-versified, making it possible to use beta as a measure of risk (Strong, 2000).

3.3.2 Break points for P/B

Since the number of listed shares on the Stockholm Stock Exchange will exceed 30 in every year from 1993 to 2005 (increases from 210 listed companies in 1993 to 338 in 2004) it can be assumed that the distribution of the P/B ratios is normally distributed. (Aczel & Sounderpandian, 2002) Given that a total of 120 shares, 60 value and 60 growth companies are wanted each year, a new break point that defines these two categories is calculated an-nually. In order to determine the break points the Z-value, found in a standard normal dis-tribution table, must first be found (see appendix II for a standard normal disdis-tribution ta-ble). This is done by first of all calculating the area of each tail in the standard normal dis-tribution (see figure 4) by using formula 5. The left tail area represents the value stocks (the lowest P/B stocks) and the right tail area represents the growth stocks (the highest P/B stocks), and the area in between is the rest of the companies on the Stockholm Stock Ex-change with average P/B multiples. (Aczel & Sounderpandian, 2002)

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Methodology

Figure 4 The standard normal distribution (Aczel & Sounderpandian, 2002)

2 120 / ted shares No. of lis Tail area ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ =

Formula 5 Tail area (Aczel & Sounderpandian, 2002)

120 = Total sample size

No. of listed shares = Varying from 210 (1993) to 338 (2004) 2 = To make it a two-tailed test

When the tail area is calculated, one must, in order to derive the left-or right hand table area, subtract this value from 0.5 (see formula 6). This is done since the table area is meas-ured from the middle and out in the standard normal distribution figure and each side represents 50% of the total area. The table area is the same for both the left and right hand side, the only difference is that the left area is a negative number and the right area is a po-sitive number. (Aczel & Sounderpandian 2002)

Area Tail .

Table Area= 50 −

Formula 6 Table area (Aczel & Sounderpandian, 2002)

0.5 = Total left- or right side area under the standard normal distribution

The calculated table area is used to find the Z-value in a standard normal distribution table, seen in appendix II. Once the Z-value is found along with the market’s average P/B ratio, the break points can be calculated using formula 7 (Aczel & Sounderpandian 2002). The standard deviation16 of P/B is computed using each sector’s average P/B ratio, found in

Börsguide and also in appendix III. The average market P/B is not calculated but taken di-rectly from Börsguide were the ratios are value-weighted. During the IT-boom around the year 2000, a few sectors have abnormally high P/B ratios compared to the other sectors that same year. To adjust for this, sectors with P/B ratios above 10 are temporarily reduced 16 ∑ = − = N i N Xi tion dard devia S 1 2 ) ( tan μ N=Total population µ=Mean of population i=Observation i

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to this number in order not to get the standard deviation too large, causing the lower break point to become a negative number. This correction is only done when calculating the break points, all companies keep their original P/Bs and none are excluded when sampling for shares to include in the portfolios. Having negative and extremely high break points makes it impossible to find any value companies since they must have P/Bs above 0 or to find even five growth companies, hence makes it impossible to construct portfolios these years. The number 10 is chosen because it is a relatively large number compared to the lower valued sectors for the same years, but not large enough to cause the standard devia-tion to be too high. It turned out that consistently correcting down abnormal sectors to 10 made it possible to come close to 30 stocks in each portfolio. It should be mentioned that this correction only is done in three years for seven sectors out of the total number of about 140 (12 years times about 12 sectors).

(

S dard deviation of P/B

) (

* Z-value

)

Market P/B s

Break point = ± tan

Formula 7 Break points for P/B

3.3.3 Systematic sampling

Once the break points are determined for each year the portfolio must be created based on the break points. The method used to select stocks is called systematic sampling. This is an unbiased way to sample when data is arranged in a specific order, for example in alphabeti-cal order as in Börsguide. It is easy to draw a random unbiased sample by using a system-atic approach rather then using a random selection based on specific features within the population (Aczel & Sounderpandian, 2002). The formula for the sampling is the follow-ing;

K n N =

Formula 8 Systematic sampling (Aczel & Sounderpandian, 2002)

N = Total population n = Sample size (120)

K = Equidistant number from each observation

For the first year a number in the interval 1 – 120 is chosen. That number represents the first observation. Onwards, every kth number is selected until the wanted sample size is

achieved. One advantage with this method is that the sample is spread evenly throughout the population (Aczel & Sounderpandian, 2002).

3.4 Portfolio

Calculations

The authors have used Microsoft Excel for all calculations and construction of tables. This since it is a well-known program and it is easy to use. The pre-knowledge of this program was good and results are easily presented, hence the choice of this program.

Once the four portfolios are created each year the following assumptions are made in order to calculate the annual return and the risk-adjusted returns:

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Methodology

• Dividends are assumed to be paid once a year at the end of the holding period prices with a percentage equal to the last know dividend yield.

• Stock prices are adjusted for splits, stock dividends and new stock issues.

• Each company has the same weight in the portfolio when calculating returns and betas. This means that the same amount of money is spent on each company, the actual amount is not important it is the percentage returns that matter. This results in the portfolios having more than one stock of companies with a low stock price and less than one stock of companies with a high stock price. By doing this each company will have the same total weight within each portfolio.

• Companies acquired during the holding period (marked * in appendix) without known acquisition price will be assumed to have a 0% return, i.e. acquired for the latest known stock price. The same holds for de-listed companies and these are marked as *** in the appendix.

• Companies going bankrupt during the holding period are assumed to have a 100% negative return. Bankrupt companies are marked with ** in the appendix.

• The constructed portfolios are, even though divided into different groups with similar characteristics (P/B and P/E), assumed to be well diversified. This since each portfolio consists of more than 20 securities from various industries. (Damo-daran, 2002) Taken this into account, the Treynor ratio and the Jensen’s measure will be used when risk-adjusting the portfolio returns.

• The betas for each stock are given in Börsguide. They are calculated over a 48 month period and compared with “Affärsvärldens General Index”. (Börsguide, 1993) For stocks where betas are not available an average portfolio beta is calculated by aver-aging the accessible betas only. Portfolio betas are calculated by summing the indi-vidual betas in each portfolio and then divide them by the number of stocks.

• For the portfolios’ average P/E the median is used. This in order to level out the extreme values present during some years and make the result more comparable. Again as a reminder, negative P/E ratios are considered as being infinite large (see appendix I).

Total annual returns for each stock are calculated by dividing the capital gain/loss with the initial purchase price and then adding the dividend yield. These returns are summed for all four individual portfolios and then divided by the number of stocks in each portfolio in order to get the total portfolio return.

Figure

Figure 1 Barra Value & Growth Index – a cumulative comparison
Figure 2  Methodological Overview
Table 1 Wilshire Style Index (Wilshire Associates Incorporated, 2005)
Figure 3 Portfolio creation and composition
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References

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