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**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.*

**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)

**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 consisting of stock price returns and trailing 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.

**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 portfolios 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 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.

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 stocks^{15}. 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 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)

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.

**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).

**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 distribution 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)

1 Introduction

1.1 Background

1.2 Problem Discussion

1.3 Purpose

1.4 Perspective

1.5 Delimitations

1.6 Definitions

1.7 Methodological Approach

1.8 Methodological Overview

1.9 Literature Study

1.10 Disposition

2 Theoretical Framework

2.1 Efficient Market Hypothesis (EMH)

2.2 Portfolio Theory

2.3 Previous Research of Valuation Multiples.

2.4 Value and Growth Definitions.

2.5 Examples of value and growth companies

3 Methodology

3.1 Quantitative research approach.

3.2 Secondary data

3.3 Data collection and portfolio creation

3.4 Portfolio Calculations

3.5 Portfolio Analysis

3.6 Reliability and Validity

4 Empirical Findings and Analysis

4.1 Empirical findings of the four portfolios

4.2 Portfolio comparison and analysis

4.3 Low-Low vs. OMXS index

5 Conclusion and Final Remarks

5.1 Conclusion

5.2 The authors’ reflections

5.3 Critique of method used

5.4 Suggestions for further studies

References

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