1. Introduction - Lund University Publicationslup.lub.lu.se/.../record/5474068/file/5474070.docx ·...

Department of Business Administration- School of Economics and Management – Lund University

Market Value Approximation Using MultiplesAn Investigation of American Large-, Mid-, and Small-Cap Stocks

Thesis Supervisor: Master Students:

Naciye Sekerci Berglund, Oscar 900115

Zisiadou, Argyro 920706

May, 2015

Master’s Programme in Corporate & Financial Management (EAGCM)

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Berglund Oscar Zisiadou Argyro

Abstract

The aim of this paper is to provide answers to questions related to valuation accuracy and error determinants by investigating the US market over the last 15 years (2000-2014). The first questions are related to the market efficiency in its weak form, while the rest of the paper is focused on valuation accuracy using the multiples approach and the error determinant variables that can influence the valuation accuracy. The main results for the market efficiency are that only the small capitalization index (S&P 600) is efficient in its weak form. Regarding valuation accuracy, it was discovered that the 12-month forward-looking multiples are more accurate at approximating market values than trailing multiples. In addition, the authors were able to conclude that equity multiples performed better than entity multiples. Lastly, through estimations, it is proven that valuation errors are influenced by specific error determinants both from the current period and the past period observations, while the valuation error of the previous year appears to have a significant influence on the new valuation error.

Keywords: Valuation Error, Valuation Accuracy, Error Determinants, Multiples, Market Efficiency, US market, Capitalization


Acknowledgements

We would like to acknowledge our supervisor, Nacyie Sekerci. We would also like to acknowledge and thank Julienne Stewart-Sandgren. Without their help and support we would not have been able to write this thesis. Thank you!

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Table of Contents

1. Introduction 81.1 Background 81.2 Aim and Objectives 91.3 Research Purpose101.4 Research Limitations 111.5 Outline of the Thesis 11

2. Literature and Theoretical Review 132.1 Market Efficiency 132.2 Discounted Cash Flow Model 142.3 Multiples152.4 Mispricing and Error Determinants 19

3. Methodology 213.1 Research Approach 213.2 Research Design 223.3 Data Collection 243.4 Data Analysis 24

3.4.1 Market Efficiency – Time Series Approach 243.4.2 Multiples 303.4.3 Valuation Accuracy – Statistical Approach 333.4.4 Error Determinants – Panel Data Approach 35

4 Analysis and Discussion 464.1 Market Efficiency 46

4.1.1 Descriptive Statistics 464.1.2 Model Approach 474.1.3 Residual Diagnostics 484.1.4 Forecasting 504.1.4.1 Forecasting Large Capitalization 504.1.4.2 Forecasting Mid Capitalization 514.1.4.3Forecasting Small Capitalization 52

4.2 Valuation Accuracy 534.3 Valuations Error Determinants 57

5. Conclusion 645.1 Practical Implications 665.2 Future Research 66

References 67

Appendix A 69

Appendix B 70

Appendix C 94


Table of Figures

4.1.1 DIFFERENCE IN VALUATION ERROR FOR DIFFERENT SIC-LEVELS 56 4.1.2 PERCENTAGE OF SIGNIFICANCE OF ERROR DETERMINANTS (TIME T) 604.1.3 PERCENTAGE OF SIGNIFICANCE OF ERROR DETERMINANTS (TIME T-1) 61 4.1.4 GOODNESS OF FIT 62

List of Tables

4.1.1 DESCRIPTIVE STATISTICS 464.1.2 BEST MODEL APPROACH 484.1.3 LARGE CAPITALIZATION FORECASTING RESULTS514.1.4 MID CAPITALIZATION FORECASTING RESULTS 514.1.5 SMALL CAPITALIZATION FORECASTING RESULTS524.1.6 AVERAGE VALUATION ERRORS – TOTAL SAMPLE 534.1.7 P/E MEDIAN ERROR DETERMINANTS AND DIAGNOSTIC TESTS 58

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Abbreviations

Abbreviation MeaningAbs. AbsoluteAIC Akaike Information CriterionAR AutoregressiveARCH AutoRegressive Conditional HeteroskedasticityARIMA AutoRegressive Integrated Moving AverageARMA AutoRegressive Moving AverageBDS Brock-Dechert-ScheinkmanBPG Breusch-Pagan-GodfreyCap. CapitalizationCAPM Capital Asset Pricing ModelCorr CorrelationCov CovarianceCSU Cross-section UnitsCV Continuing ValueDCF Discounted Cash FlowDDM Dividend Discount ModelDW Durbin - WatsonE-GARCH Exponential Generalized AutoRegressive Conditional HeteroskedasticityEBIT Earnings Before Interests and TaxesEBITDA Earnings Before Interests, Taxes, Depreciation and AmortizationEV Enterprise ValueEV/EBITDA (1) 12-month Forward EV/EBITDAFE Fixed EffectsFFIG Fama and French Industry GroupingsGARCH Generalized AutoRegressive Conditional HeteroskedasticityGICS Global Industry Classification StandardICB Industry Classification BenchmarkIPO Initial Public OfferingIT Information TechnologyIV Instrument VariableJB Jarque - BeraLM Langrange MultiplierM/B Market to Book ratioMA Moving AverageNAICS North America Industry Classification SystemOLS Ordinary Least SquareP/E Price to EarningsP/E (1) 12-month Forward P/E


P/EBITDA (1) 12-month Forward P/EBITDAP/S Price to SalesR&D Research and DevelopmentRE Random EffectsRHS Right Hand SideRIV Residual Income ValuationRW Random WalkSE Standard ErrorsSIC Standard industrial ClassificationT-GARCH Threshold Generalized AutoRegressive Conditional HeteroskedasticityTA Total AssetsWACC Weighted Average Cost of Capital

1. Introduction

1.1 Background

Students of finance, private investors, and finance professionals are all concerned with

valuation of corporate entities. As aid in these efforts, they have different models to choose

from, where the most prominent and commonly used are the DCF-method, the RIV-model,

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the DDM-model, and the Multiples approach (Lie & Lie, 2002). Although, the DCF-method

is widely accepted by economists, a vast majority of finance professionals mainly use the

multiples approach in their daily work (Demirakos, Strong & Walker, 2004; Kaplan &

Ruback, 1995). Reasons for this are many. For example, the multiples approach tends to be

less time consuming to complete, the method is easy to grasp for individuals not well versed

in finance, and ratios are very accessible since they are usually quoted in financial

publications and on trading platforms (Schreiner, 2007). Surprisingly, although a vast

majority of finance professionals, around 65%, favor using the multiples approach, very little

prior research has been conducted on the subject of corporate valuation using multiples

(Schreiner, 2007).

In addition, the research to date, which is scant, seem to only focus on multiple valuation of

large cap companies, mainly in the United States. Furthermore, to the best of our knowledge,

there is only one published article looking at European large cap stocks. Filling the gap, we

believe that our contribution of valuing US mid- and small-cap stocks through the multiples

approach could prove useful both for professional finance practitioners and private investors.

1.2 Aim and Objectives

The main objective of this thesis is to investigate which corporate valuation multiple(s)

provides the closest approximation to market value. In this effort, we will use the valuation

approach outlined in the papers by Lie & Lie (2002), Schreiner (2007), Kaplan & Ruback

(1995), and Ek & Lillhage (2012). The approach is described in detail in the Methodology

chapter of this thesis. A secondary objective, a natural extension, will be to see how the results

of previous studies support our sample of mid- and small-cap stocks. Essentially, we aim to

explore if the previously deemed best multiples for valuing large cap stocks prove to be the


best for our sample as well. Based on our results, we also aim to be able to draw conclusions

on as to what variables may distort valuation results when using the multiples approach.

Furthermore, we will devote some time to the famous market efficiency hypothesis first

mentioned by Eugene Fama in 1970. In addition, we aim to investigate whether any model

can predict the price movements of the market indices. As a result, we will be able to

conclude whether the market efficiency hypothesis holds or not.

In order to reach these aims, we endeavor to address eight main research questions, which are

divided into three categories: Market Efficiency, Valuation Accuracy and Error Determinants:

A. Market Efficiency:

1. Is the S&P large-, mid-, and small-cap indices efficient in its weak form during year

2000 through 2014?

B. Valuation Accuracy:

2. What is the average valuation error for each multiple?

3. Which multiple gives the best, that is, closest approximation to market value?

4. On average, are there any notable differences in valuation errors for the different

indices?

5. Do equity value multiples outperform entity value multiples in terms of valuation

accuracy?

6. Do forward looking multiples outperform trailing multiples in terms of valuation

accuracy?

C. Error Determinants:

7. Is there any ‘error variable’ that can significantly influence the valuation error?

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8. Is there significant correlation between the valuation error of the present period (t) and

error variable observation from the previous period (t-1).

The study uses a hypothesis method to address each question, except questions 2 and 3.

Questions 2 and 3 are kept in their current form as it is not possible to rephrase them into

hypotheses.

1.3 Research Purpose

The purpose of our research is to provide answers to the questions listed above. The results

will further be compared to the results from previous papers written in the same field of

interest, that is, the papers by Kaplan & Ruback (1995), Lie & Lie (2002), Schreiner (2007),

and Ek & Lillhage (2012). From this, we will be able to provide an analysis based on

empirical observations on whether mid- and small-cap markets need to be valued differently

or not, as well as whether the U.S market can be approached in the same way as the Nordic

and the European market or not. In addition, we intend to investigate if the market efficiency

hypothesis holds for the markets and period we examine; that is, US large-, mid-, and small-

cap markets during the time span 2000 through 2014. Based on the results we will be able to

connect mispricing to market (in)efficiency.

1.4 Research Limitations

We would have liked to extend the research further by exploring two separate periods; that is,

before and after the economic crisis. Further, using more forward multiples would have given

us the opportunity to compare our results with previous research, including two year

multiples. Although, these are areas for future research, we feel that this could have been done

if time permitted. Instead, we have chosen to keep the methodology mainly intact compared to


the studies we draw on, and have been able to focus more on data collection and increasing

the sample. The final sample includes three-hundred (300) companies with annual

observations for each company over fifteen (15) years, that is, year 2000 through year 2014.

For each year and company we have collected twenty two (22) different variables (see

Appendix C for a full list of all the variables).

1.5 Outline of the Thesis

This thesis is separated into five (5) different chapters. Chapter 1 provides a general

introduction to the main topic of research, which is valuation accuracy using the multiples

approach. Moreover, the main questions we intend to answer will be presented in this chapter.

The literature review and the theoretical background is accounted for in Chapter 2. Chapter 3

contains the research approaches and the data analysis for all the prospects examined in this

thesis including the market efficiency, the valuation accuracy, the multiples and the error

determinants. Furthermore, this chapter, contains all the empirical approaches; that is,

statistical and econometric estimations and diagnostic tests. Chapter 4 presents the results of

our analysis, with an accompanying discussion of our findings. Finally, Chapter 5 includes all

the conclusions of our research along with answers to our initial hypothesis, followed by

recommendations for further research.

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2 Literature and Theoretical Review

There are a great many variables that play into the valuation of a corporate entity. Depending

on how thorough the analyst wants to be and how detailed the valuation needs to be, there

may be a need to adjust every single line item of a company’s financial statements. However,

for this research paper we have decided to limit ourselves to mainly investigating one

approach in particular; that is, the multiples approach. This being the case, our literature and

theoretical review will mainly delve into what others have discovered on the subject of

corporate valuation using multiples as well as the advantages and disadvantages of some of

the competing models mentioned in Section 1.1. Naturally, market efficiency, as it holds an

important place in this thesis, will be discussed.

2.1 Market Efficiency

Eugene Fama in his paper from 1970, tried to explain the market efficiency and created three

different forms. The first form is the weak form efficiency in which, future prices cannot be

predicted by analyzing the prices from the past. The second form is the semi-strong form

efficiency in which stock prices adjust to publicly available information rapidly and in an

unbiased fashion, so that no excess returns can be earned by trading on that information. The

third and last form is the strong form efficiency in which stock prices reflect all information,

both private and public, and no one can earn excess returns. Since then, many researchers

tried to investigate the weak form efficiency hypothesis in different periods and markets. For


instance, Gu (2004) used daily observation of the NASDAQ composite index from 1971 to

2001 and proved that there is no weak form efficiency. On the other hand, Chan, Gup and Pan

(1992), examined the United States and the major Asian Markets and came to the conclusion

that they are efficient in the weak form.

2.2 Discounted Cash Flow Model

The DCF-model, when used correctly, can estimate the entity value of a firm; that is, market

value of equity plus net debt and cash (e.g. Koller, Goedhart & Wessels, 2010; Damodaran,

2006). According to Koller et al. (2010) description of the model, it does so by discounting all

the future projected free cash flows to firm at an appropriate discount rate. They further point

out that the discount rate used is usually the firm’s weighted average cost of capital, or

WACC for short. Moreover, the WACC has two parts to it, the cost of equity and the cost of

debt. Depending on the firm’s capital mix, different weights are allocated to the different costs

to determine the WACC. At the end of the manually forecasted period a continuing value, CV

for short, is calculated by using an appropriate perpetuity formula. Once again, this value is

then discounted back to present time using the WACC. All the discounted cash flows are then

summed to arrive at entity or enterprise value. Then, according to Koller et al. (2010), once

the entity value is calculated it is then possible to subtract net debt to arrive at equity values.

In total, it is probably the most extensive and complete model in terms of flexibility and

ability to capture specific claims on or of the firm (Koller et al, 2010).

As such, it is very useful when, for example, valuing unorthodox transactions such as

management buyouts. Indeed, the DCF-model is what Kaplan & Ruback (1995) used in the

their research. In their study, Kaplan & Ruback (1995) looked at 51 high-leveraged

transactions spanning from 1983 to 1989. More specifically, they calculated the entity values

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of the firms in their sample by discounting the projected cash flows with the WACC, and then

calculating a CV-value for the year after projections ended. They used the information

provided by respective management for their cash flows and WACC projections. Doing this,

they found that the DCF-model performed very well when comparing the calculated entity

values to the market transactions, with a mean valuation error of 8% (median only 6%)

(Kaplan & Ruback, 1995).

Not surprising to anyone familiar with the model, Kaplan & Ruback (1995) also found that

the valuation errors changed drastically when they altered variables in the CAPM-formula

used to calculate the WACC. Specifically, they changed betas and market-risk premium. This

fact led the authors to raise one of the main drawbacks of the DCF-model, namely that it is

very dependent on the assumptions the user makes regarding growth rates, WACC, CV-year,

among many other things. Kaplan and Ruback (1995), however, maintain that their results are

based solely “on a number of ad hoc assumptions” (p.1060), that both professionals and

academics should be able to improve, which in turn should lead to more accurate valuations.

Regardless if this is true or not, there is still another major drawback with the DCF-method in

that it tends to be very time consuming to complete. When done fundamentally, every line

item of the financial statements should be forecasted, at least for a period of a few years

(Koller et al., 2010). As such, the model has an obvious disadvantage to other, less time-

consuming approaches such as using multiples when computing corporate value.

2.3 Multiples

At its core, a multiple is a ratio of some variables pertaining to corporate value, for example

stock price to earnings (P/E). Depending on how the market values other, comparable firms

one can quickly compute an approximate value of the target firm (Schreiner, 2007). The


procedure of calculating a firm multiple has four steps to it. Step one is to decide on which

numerator and denominator to use. For example, price to earnings and enterprise value to

EBITDA are two popular ones. In those instances the numerator would be price and enterprise

value respectively and the denominator or the value driver would be earnings and EBITDA

respectively. The second step is to decide on what peers to use (Schreiner, 2007). Essentially

one can do this through any design, however the consensus among the authors published in

the field is to use firms with similar industry codes (Lie & Lie, 2002; Schreiner, 2007). The

most commonly used industry classification systems are SIC, NAICS, FFIG, GICS and ICB

(Schreiner, 2007). Most systems rank a company with a four-digit code. For example code

6021 under the SIC-system is National Commercial Banks, code 602 is Commercial Banks,

and code 60-67 is Finance, Insurance, and Real Estate companies. Therefore, the more

numbers that match, the closer a firm is to the target company. The norm in the papers we

have examined, seem to use peers with at least a three-digit industry code match (Ek &

Lillhage, 2012; Lie & Lie, 2002; Schreiner, 2007). Evidently, at least three digits are used

because Alford (1992) found that multiple valuation accuracy improves when the industry

code is narrowed from zero up to three digits. Using four digits had no apparent advantage in

valuation accuracy versus only using three (Alford, 1992). Another issue that comes up when

selecting a peer sample, is the number of peers needed in order to form an adequate

comparable. Lie & Lie (2002) recommend using a peer sample of at least five firms. If there

are less than five firms for a given industry code, the code is then relaxed one level (Lie &

Lie, 2002). Thus, in our previous example, code 602 would be relaxed to 60 if there were less

than five comparable firms in the 602 industry. Schreiner (2007) on the other hand, maintains

that the optimal peer group consists of four to eight peers. Should there be less than four firms

for any given level-three industry code Schreiner (2007) suggests simply making do with the

smaller sample as relaxing the industry code level decreases comparability between the peers.

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The only time when Schreiner (2007) recommends relaxing the criteria or using a different

valuation method altogether, is when there are less than two peers.

Step three is concerned with combining each peer multiple into a single number. There are

several ways of doing this, for example using the arithmetic mean, geometric mean, harmonic

mean, or simply taking the median. Ek & Lillhage (2012) and Lie & Lie (2002) use the

arithmetic mean and the median in their papers. Schreiner (2007) however, argues that the

arithmetic mean is inappropriate to use when aggregating peer multiples as it relies too

heavily on outliers. He instead recommends using the median or harmonic mean (Schreiner,

2007).

Step four is the actual valuation and is very straight forward. The computed peer multiple

from step three is simply multiplied with the value driver, for example earnings, of the target

firm. It is plausible that it is the simplicity of this process that is attributable to the multiples

approach widespread practice. In fact, according to Dr. Klaus Spremann of the Swiss Institute

of Banking and Finance: “[a]ccounting based market-multiples are the most common

technique in equity valuation” (Schreiner, 2007, p.VII). Dr. Spremann further acknowledges

that multiples “are used in research reports…stock recommendations…in fairness opinions…

pitch books of investment bankers… [and even]…road shows of firms seeking an IPO”

(Schreiner, 2007, p. VII). With such widespread use, it is rather surprising to learn that there

is not much research on the subject. Out of the scarce sample of relevant research papers we

found, the most significant on the subject of valuation using multiples were written by Kaplan

& Ruback (1995), Lie & Lie (2002), Schreiner (2007), and Ek & Lillhage (2012). These

authors all raise important benefits of using multiples. For instance, the fact that they are

relatively quick to compute when compared to other more labor intensive models, such as the

DCF- or RIV-model. According Lie & Lie,


[t]he theoretical emphasis is usually on the discounted cash flow valuation (DCF)

technique, but it is cumbersome to use and sensitive to a host of assumptions.

Consequently, investment bankers and appraisers regularly use valuation by multiples

(Lie & Lie, 2002, p. 1).

Another attractive feature with multiples is the ease of use and simplicity, which makes the

concept very graspable to people not well versed in corporate finance (DeAngelo, 1990, cited

in Schreiner, 2007). In addition, they are also very useful when initially screening stocks for

investment purposes as relevant multiples are usually quoted in financial newspapers and on

trading platforms (Schreiner, 2007). In sum, multiples make for a very powerful and useful

valuation tool. Given this, a very relevant question tends to come up: which is in fact the best

multiple to use? Naturally, the answer depends on the context surrounding the question.

However, in general, Lie & Lie found that asset based multiples yielded more accurate and

less biased results than sales and earnings estimates did. Secondly, they found that adjusting

entity values for cash had little to no effect on valuation accuracy, while using forward

looking value drivers did. They also found EBITDA to be a better value driver than EBIT in

terms valuation accuracy for entity multiples. Lastly, they discovered that the overall accuracy

and bias of the valuation were greatly influenced by company size, profitability, and amount

of intangibles on the balance sheet (Lie & Lie, 2002). Schreiner (2007) on the other hand

found that earnings based multiples performed best, especially the two-year forward looking

price to earnings multiple, which had the overall best performance. Ek & Lillhage’s (2012)

findings support Schreiner’s in this regard. Although Ek & Lillhage (2012) did not look at the

two-year forward looking P/E multiple specifically, they found that the regular P/E multiple

performed the best in their sample. Schreiner (2007) also had another noteworthy discovery,

namely that equity multiples outperformed entity multiples in every regard. In addition, he

found, somewhat in line with the findings of Lie & Lie (2002), that knowledge related

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multiples, such as ratios based on R&D, outperform traditional multiples in science-based

industries (Schreiner, 2007).

However, one of the drawbacks of the multiples approach is that it combines all the

complexities of the business and provides one value for a given point in time (Schreiner,

2007). As such, it doesn’t require any fundamental analysis of the underlying business, which

arguably is very important from an investor’s perspective. In addition, since the multiples are

based on market values, there are instances where values will be somewhat inflated due to the

market being too hot (Schreiner, 2007).

2.4 Mispricing & Error Determinants

As described in the previous section, Lie & Lie (2002) found that company size and amount

of intangibles on the balance sheet affected the accuracy of a firm valuation. Especially

companies with a large part of their asset base consisting of intangible assets were severely

mispriced using traditional multiples, such as price to book or price to sales. Price to book

gave a median valuation error of -71%, while price to sales gave a median valuation error of -

151%. Based on their results Lie & Lie suggest that multiples are not suited well for valuing

tech companies. It should however, be noted that Lie & Lie identified tech companies by

searching for companies with a .com in their name. Their paper is also from 2002 essentially

right after the IT-crash, which may have also played into the valuation of especially IT- and

tech companies. Schreiner (2007) on the other hand found that multiples performed rather

well in valuing science-based companies, the trick is just to use the right multiple. He

proposed using knowledge-related multiples such as P/(EBIT+RD) or P/(E+R&D) for which


he received a better valuation result with a median valuation error of 29.8% and 28.07%

respectively. The results are not near as accurate as for valuing non-science based companies

with traditional multiples, but the improvement from the sample of Lie & Lie (2002) still

suggest that there may be some multiple combination out there that can capture the value of

science-based companies well. Nevertheless, it could be questioned why is it difficult to value

science-based companies. For one, many of these science-based firms are still to post profits

for the first time, which obviously pose a problem since most valuation models work by

discounting cash flows. Consequently, when valuing many of these firms it essentially

becomes a guessing game without any historic earnings to base future cash-flow predictions

on. The science-based companies that do post profits and expense intangible assets and

research, R&D for example, may experience severely decreased earnings in the short run.

However, according to Eberhart, Maxwell & Siddique (2004) a majority of firms that

suddenly increase their R&D expenses, later enjoy longer periods of above average returns,

something that markets are slow to incorporate - in essence another source of mispricing. In

support of the accounting treatment’s role in mispricing Lev, Sarath & Sougiannis (2005)

found consistent undervaluation of firms that expense R&D and consistent overvaluation of

firms that capitalize R&D, suggesting that markets have trouble valuing investments in R&D.

3 Methodology

In this section, we initially describe the Time Series Analysis, used in this thesis, in order to

examine the Market Efficiency in the three (3) different capitalization indices. The second

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part contains the main approach for our thesis, which is the Panel Data Analysis that will be

used to estimate the main models for the valuation accuracy and the error determinants.

3.1 Research Approach

As many researchers propose, the most appropriate approach for our investigative topic is a

quantitative method. That means that we are going to base our analysis on data gathered and

connect it to the topic we are trying to investigate. The fact that we are analyzing three

different capitalization indices and the first 100 firms of each index for a period of 15 years,

lead us to use the Panel Data Approach. Moreover, because we are examining market

efficiency for three indices in their weak form over a period of 15 years with daily

observations, the most appropriate method of analysis is the Time Series Approach. This

approach was proposed by Fama (1970) when he mentioned the market efficiency hypothesis.

This research project has also chosen the hypothesis approach in order to provide clear and

indisputable answers to our research questions.

3.2 Research Design

With this thesis we attempted to answer eight (8) questions divided into three main categories.

The first part aims to answer questions related to the Market Efficiency Hypothesis, the

second part is related to Valuation Accuracy, and the third part pertains to Error Determinants.

Regarding market efficiency, we attempted to answer if markets are efficient in its weak form

for all three (3) capitalization indices in US Market (large-cap, mid-cap, small-cap) during our

specified time period, that is, year 2000 through 2014.


Pertaining to valuation accuracy and mispricing, we attempted to shed light on whether or not

the different indices need to be valued differently as well as which multiple provides the best

approximation of market value. In addition, we tried to determine which of our specified

variables were connected to mispricing.

A. Market Efficiency

1. Is the S&P large-, mid-, and small-cap indices efficient in its weak form during year

2000 through 2014?

B. Valuation Accuracy




indices?


accuracy?

6. Do forward looking multiples outperform trailing multiples in terms of valuation

accuracy?

C. Error Determinants

7. Is there any ‘error variable’ that can significantly influence the valuation error?



In order to address these questions, we developed seven (7) hypotheses. The first three

hypotheses are connected to the market efficiency whereas the remaining hypotheses are

connected to the valuation accuracy and mispricing.

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H1: The large capitalization index (S&P500) is efficient in its weak form over the past 15

years.

H2: The mid capitalization index (S&P400) is efficient in its weak form over the past 15

years.

H3: The small capitalization index (S&P600) is efficient in its weak form over the past 15

years.

H4: Equity multiples outperform entity multiples in terms of valuation accuracy.

H5: There is no difference across the capitalizations by using the synthetic peer multiples.

H6: Forward-looking multiples outperform trailing multiples in terms of valuation accuracy.

H7: There is no connection between the valuation error and past observations of the error

determinants.

3.3 Data Collection Method

Our main sources for datasets are Thomson Reuters - Datastream Professional 5.1 as well as

the NASDAQ website (NASDAQ, 2015). Specifically, the list with firms under each

Capitalization Category (S&P500, S&P400, S&P600) were downloaded from the NASDAQ

(NASDAQ, 2015) webpage. The same source was used in order to identify the SIC Code for

each firm separately. The rest of our variables were gathered in Thomson Reuters -

Datastream Professional 5.1 (see Appendix C, Table C1)


Regarding data frequency, we use annual observations for all of the variables pertaining to the

panel data analysis, as well as the multiples calculations. For the market efficiency time series

analysis, the observations are daily. All variables have been gathered from Thomson Reuters -

Datastream Professional 5.1 (see Appendix C, Table C1).

3.4 Data Analysis

Having as purpose to analyze different aspects of valuation accuracy and the error

determinants, it is prudent to separate the analysis into subsections so that it will be easier for

the reader to follow the procedure.

3.4.1 Market Efficiency - Time Series Approach

The term Time Series Analysis is used to describe the different econometric approaches that

can be used in order to make estimations and forecasts on time-series data. Conceivable from

the name itself, time series data is a dataset that contains observations for a specific variable

of interest over a specific period of time. For instance, a time-series dataset can be daily

observations of a stock index over the last ten years.

Halkos (2011a) explains that there are both parametric and non-parametric methods that can

be used while working on time series analysis datasets. In the parametric approaches, the

underlying stochastic process has a specific configuration that includes an certain number of

parameters such as Autoregressive model (AR) or Moving Average model (MA) or even a

combination of both like the ARMA or ARIMA approach. Moreover, Halkos (2011a) also

mentions that there can be a separation between linear and non-linear approaches as well.

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In the case of Market Efficiency, we are going to use the time-series analysis because the

dataset for each index examined will contain daily observations over the last 15 years (2000-

2014). Moreover, the estimations and forecasts for each index will be done separately and

without any combined estimations. Our goal is to model the movements of each index

autonomously and not in regard to the other indices.

As in any statistical or econometric procedure, before the estimation and the forecast, a

descriptive analysis is required. A descriptive analysis will provide an opportunity to the

researchers or analysts to get a general idea of the observations they are going to use in their

estimations. The most important indicators that require our attention are the mean value and

the standard deviation. Moreover, skewness and kurtosis give a general idea whether the

observations are normally distributed or not. However, we should not jump into conclusions

only based on the descriptive statistics. We also need to test the datasets as a number of

different problems may occur.

Problems may occur in Time-series datasets

1. Autocorrelation

One of the assumptions of an OLS estimation is that the error terms are assumed to be

independent over time. Autocorrelated error terms are the most important consideration for a

practicing forecaster because when the problem of the autocorrelation occurs, the estimation

and the forecast will be biased. (Halkos, 2011a; Brooks, 2008)

In order to test for autocorrelation we can use a number of different tests, such as Durbin-

Watson statistics (DW).

H0= independent error terms over time, the error terms are completely random and serially

uncorrelated.


If there is a serial correlation issue, autocorrelation may occur because the residuals are not

serially uncorrelated.

2. Heteroskedasticity

One of the assumptions of an OLS estimation is that the variance of the error terms are

assumed to be constant (homoscedastic). However, if the variance of the residuals is not

constant but depend upon the value of x, then the residuals are heteroskedastic. (Halkos,

2011a)

In order to test for Heteroskedasticity, we can use the Goldfeld-Quandt test (Halkos, 2011a),

Breusch – Pagan – Godfrey test (Halkos, 2011a), or the White test (Halkos, 2011a)

H0= Error term variance is constant (homoscedastic)

3. Multicollinearity

With the term Multicollinearity we identify the issue when two or more independent variables

(x) are excessively linearly correlated with each other then autonomous influence cannot be

determined (Halkos, 2011a; Brooks, 2008). What is more, the problem of Multicollinearity

does not occur due to the estimation but due to data and variable specification. (Brooks,

2008).

In order to test for Multicollinearity will can check the R2. A high R2 with low values for t-

statistics of the coefficients indicates Multicollinearity issues. Moreover, the case of (Near)

Multicollinearity can be tested through the correlation matrix, where if: Corr(x i,xj)>=0.80,

then those two variables are highly correlated.

25


However, in our case, Multicollinearity will not occur due to the fact that the independent

variables will be AR and MA terms and not specific variables that can be linearly correlated

(explain the same thing).

4. Non-normality

The assumption for normality is that the residuals follow the normal distribution. In order to

test for normality we use the skewness, the kurtosis and the Jarque-Bera test (Brooks, 2008;

Halkos, 2011a)

In order for a series to be normally distributed the value for skewness should be equal to zero

(0) and the value for kurtosis should be equal to three (3). The Jarque-Bera test assumes to

follow the Chi-squared distribution.

H0= Residuals are normally distributed

5. Non-stationarity

A common assumption in many time series techniques is that the data is stationary, which

means that the mean value, the variance and the autocorrelation structure do not change over

time.

In order to test for stationarity we can use either the correlogram or the Augmented Dickey-

Fuller test and the Phillips-Perron test.

H0= Mean value, variance and autocorrelation structure are constant over time

6. Non-linearity

The issue of non-linearity describes the situation where the relationship between the

dependent and the independent variables is not a linear one (Brooks, 2008; Halkos, 2011a).


That is not a serious problem, because the most obvious solution is to try and estimate the

model with a non-linear approach, such as the exponential one.

In order to test for non-linearity we can the BDS test (Halkos, 2011a).

H0= Residuals are independent and identically distributed (i.i.d)

The ARIMA Model

The ARIMA model (AutoRegressive Integrated Moving Average) is a well-known and useful

estimation, which is widely used in Time Series Analysis. This approach is a generalization of

an autoregressive moving average (ARMA) model. Their effectiveness derives from the fact

that these models can help the researchers or the analysts to understand the available data or

even make predictions (forecasts) based on those series.

The general reference to the model is ARIMA(p,d,q) where p,d and q are the parameters refer

to the order of autoregressive, integrated and moving average terms respectively. This model

constitutes one of the most important parts of the Box-Jenkins approach, which was described

in the Time Series Analysis: Forecasting and Control (1971) book by George Box and

Gwilym Jenkins.

As a rule of thumb, it is widely accepted that the first 80% of the observations are used for the

estimation of the model while the remaining 20% are used for the forecasting procedure.

These are the percentages we are going to use for our estimations as well. The procedure of

estimation, diagnostic testing and forecast will be described in the next subsection.

The ARIMA procedure

The procedure is as follows. We aim to start with descriptive statistics of the market returns so

as to get a sense of the variables we are using. Afterwards we make ARIMA estimations

27


starting with an ARIMA (10,1,10), meaning we will include AR terms (autocorrelation) from

1 to 10 and MA terms (moving average) from 1 to 10 and 1 integration term because we are

using the returns of the prices generated as the first difference of the logarithm of the prices.

That means:

ARIMA (10,1,10) = maxAR(10), maxIntegration (1), maxMA(10)

and in those estimations we are going to exclude AR and MA terms which are insignificant

with the purpose of reaching the most optimal model by using the AIC and the Loglikelihood

criterion. Note that the lower the AIC, the higher the Loglikelihood, the better the estimation.

Thus, the estimations with the lowest AIC and highest Loglikelihood will be the most

appropriate.The same procedure will be followed both for the GARCH/T-GARCH and E-

GARCH. The residuals will be tested on all these different tests already mentioned. What is

important to mention is that we are going to use 80% of our sample (01/03/2000-12/30/2011)

for the estimations and the last 20% (01/02/2012-12/31/2014) for the forecast.

The results of the forecast will be qualified based on four (4) values: the Root Mean Squared

Error, the Mean Absolute Error, the Mean Abs. Percent Error and the Theil Inequality

Coefficient[1]. Note that the forecast model that gives the lowest values on those criteria or

most of them is the best possible forecast of all.

If the Random Walk (RW) (see Appendix A, eq. 1)appears to be the best forecast estimation

we can assume that the market is efficient in its weak form because there is randomness in the

returns and there is no model that can predict the market movements. Otherwise, we can

assume that the market is inefficient in its weak form.

In this thesis, we are going to investigate three different American capitalization indices

(S&P500, S&P400, S&P600) for a period of 15 years (2000-2014). In addition, we are going


to use daily observation for the last 15 years (01/03/2000-12/31/2014). By using different

estimations such as ARIMA, GARCH/T-GARCH, E-GARCH and Random Walk for all three

indices, we aim to find the best forecast method and prove market (in)efficiency. Lazar and

Ureche (2007) investigated the market efficiency of the emerging markets and they proved

that most of the markets in their sample are not efficient in their weak form. The tests used in

that paper were, BDS, LM test, Q-statistics and Runs test. In our case we are going to test the

residuals of the ARIMA models with the following tests: Q-statistics (for serial correlation),

Jarque-Bera (for normality), ARCH test (for heteroskedasticity), LM test (for linear

dependence), BDS (for non-linearity).

3.4.2 Multiples

As touched upon in section 2.3, there are four basic steps to any multiple valuation:

Step 1 consists of selecting a target firm, that is, the corporate entity one wish to value and

selecting the numerator and the denominator of the multiple. The most common selection for

the numerator is usually price or enterprise value. The choice of denominator/value driver is

usually more flexible. Some of the more commonly quoted and used ones are earnings, sales,

assets, EBIT, and EBITDA (see Appendix C, Table C2 for full list of multiples). It should be

noted that Schreiner (2007) bring up the matching principle, that is, value drivers that capture

claims of both debt and equity holders such as EBITDA should be matched with the

corresponding numerator, in this example enterprise value. We have chosen to ignore that

principle in this thesis, as one of our main goals is to find which multiple best approximates

market value. We therefore find it pertinent to examine all possible combinations we have

time for, even if they may violate the matching principle.

29


Step 2 consists of selecting an appropriate peer group. For this thesis we started by taking the

one hundred (100) largest firms seen to market capitalization of the S&P large-, mid-, and

small-cap indices. We chose these particular indices because of the ease of access to data in

Datastream 5.1. The reason we only included the one hundred largest firms from each index is

simply because time limitations did not allow us to collect and examine any more data. With

our sample at hand, we then assigned each firm their respective SIC code as listed on Nasdaq.

We chose to use the SIC-system solely because its availability. Schreiner (2007) argued that

the GICS or ICB system yield a better estimation of peers than does the SIC system.

However, both the GICS and ICB system are professionally managed and as such there is a

fee to use it.

Step 3 consists of compiling each target firm’s peers’ multiples into a single number. As noted

in section 2.3 there are several ways of doing this, for example using the arithmetic mean,

harmonic mean, or simply taking the median. Ek & Lillhage (2012) and Lie & Lie (2002) use

the arithmetic mean and the median in their papers. Schreiner however, argued that the

arithmetic mean is inappropriate to use when aggregating peer multiples as it relies too

heavily on outliers. He instead recommended using the median or harmonic mean (Schreiner,

2007). We decided to use all three ways in this thesis. Once again, one of our main objectives

is to find which multiple provides the best approximation of market value. We therefore think

it is prudent to employ all of the previously cited methods so nothing is left unchecked. Due to

our sample size we sometimes found that we did not have enough peers for a given SIC-code

to compute a peer multiple. Lie & Lie recommend using a peer sample of at least five firms. If

there are less than five firms for a given industry code, the code is then relaxed one level (Lie

& Lie, 2002). So for example, code 602 would be relaxed to 60 if there were less than five

comparable firms in the 602 industry. Schreiner on the other hand, maintains that the optimal

peer group consists of four to eight peers. Should there be less than four firms for any given


level-three industry code he suggests simply making do with the smaller sample as relaxing

the industry code level decreases comparability between the peers (Schreiner, 2007). We

decided to do a hybrid version where we relaxed the SIC-code one level if there were less than

three peers for a given SIC-code. We decided on three because our limited sample had a lot of

instances where there only were three or four companies for a given SIC-code. According to

Alford (1992) the valuation accuracy decreases substantially when moving from an industry-

code level of at least three down to two. So in order to maintain the highest valuation accuracy

possible, we opted for going with Schreiner’s (2007) recommendations instead and to

decrease the number of peers first hand and then relax the SIC-code one level if absolutely

necessary. Just like Lie & Lie (2002) we use one year estimations when compiling the peer

multiples. So peer values at time t are compiled into one number, which is then used in step 4

to calculate the estimated value for the target firm at time t.

Step 4 consists of the actual valuation and is, as noted in Section 2.4, very straight forward.

The calculated peer/SIC-multiple from step 3 is simply multiplied with the target firm’s value

driver in order to arrive at theoretical market price or enterprise value. For example, if the

calculated peer/SIC P/E-multiple is 10 and the target firm’s earnings are 2, we get a

theoretical market price of 20. Note that we get market price and not enterprise value in this

example as the numerator in the multiple, that is, P is price and not enterprise value.

3.4.3 Valuation Accuracy - Statistical Approach

In order to have good comparability with previous papers on multiples valuation, we opted to

use the same method in calculating the valuation error. Kaplan & Ruback (1995), Lie & Lie

(2002), Schreiner (2007), and Ek & Lillhage (2012) all calculate the valuation error by taking

the natural logarithm of the ratio of the estimated value and the observed/market value.

31


Valuation Error=ln EV∗¿EV

¿

Using this equation we were able to calculate a mean valuation error for each multiple for our

different indices, which arguably provides some insight into which multiple works the best.

However, before assigning the title of best multiple to one of the ratios it is also interesting to

look at what percentage of the sample has a valuation error of less than a certain percentage.

Kaplan & Ruback (1995), Lie & Lie (2002), Schreiner (2007), and Ek & Lillhage (2012)

crown the best multiple by looking at what multiple had the largest part of the sample with a

valuation error of less than 15%. For comparability, we did this as well.

In order to obtain these values, descriptive statistics by classification will be used. As

classification we are going to use the period dimension. Moreover, by using the Simple

Hypothesis Test, the number observations which are placed out of the range of (+/-) 0.15 will

allow the researchers to calculate the percentage of the observations included in the range

over the total number of observations.

3.4.4 Error Determinants - Panel Data Approach

The term Panel Data Analysis is used to describe the econometric approach that can be used

to combine two dimensions in the same estimation. In other words, when in an analysis the

researchers include both cross sectional units and period dimension, which means

observations for more than one year for each firm, they are using the Panel Data Analysis.

This analysis is preferable in many cases as it can provide a solution to more complex

problems than Time Series Analysis or Cross Section Analysis when used separately.

Moreover, by combining both dimensions, the analysts are increasing the degrees of freedom

and as a result the significance of the tests (Brooks, 2008).


A panel data can be either balanced or unbalanced. The balanced panel data has no missing

values in periods in any cross-section unit whereas the unbalanced panel dataset has fewer

observations in some cross-section units (Brooks, 2008).

Once again, before the final estimation is specified both the regressions and their residuals

should be tested for a number of different problems that may occur.

Problems may occur in Panel Data Analysis


With the term Multicollinearity refers to the issue when two or more independent variables (x)

are excessively linearly correlated with each other and an autonomous influence cannot be

determined (Halkos, 2011a; Brooks, 2008). What is more, the problem of Multicollinearity

does not occur due to the estimation but due to data and variable specification. (Brooks,

2008).

In order to test for Multicollinearity we can check the R2. A high R2 with low values for t-

statistics of the coefficients indicates Multicollinearity issues. Moreover, the case of Near

Multicollinearity can be tested through the correlation matrix, where if: Corr(xi,xj)>=0.80,

then those two variables are highly correlated (Brooks, 2008; Halkos, 2011a).

2. Heterogeneity

One of the main problems that appear when using Panel Datasets is Heterogeneity. With the

term Heterogeneity, econometric theory refers to the difference across the cross section units

being examined that can occur when using Panel Dataset. (Brooks, 2008)

H0= no difference across the cross section units (homogeneity)

33


3. Endogeneity

Another problem that needs to be taken into consideration is the Endogeneity issue. The four

assumptions of the OLS is that there should be no relationship between the error term and the

corresponding x variable or mathematically expressed Cov (ui,t,xi,t)=0. If that assumption does

not hold, then there is a correlation between the error term and the corresponding variable. So

in that case the independent variable is endogenous. (Angrist, Pischke, 2009)

H0= no correlation between the independent variable and the error term (exogenous variable)

There are four different factors that can cause endogeneity to an estimation. Briefly, these

factors are: 1. Omitted Variables, 2. Simultaneity, 3. Measurement Error, 4. Selection Bias.

(Angrist, Pischke, 2009)


One of the assumptions of an OLS estimation is that the variance of the error terms are

assumed to be constant (homoscedastic). However, if the variance of the residuals are not

constant but depend upon the value of x, then the residuals are heteroskedastic. (Halkos,

2011a; Brooks, 2008)

H0= Error term variance is constant (homoscedastic)

5. Autocorrelation

One of the assumptions of an OLS estimation is that the error terms are assumed to be

independent over time. Autocorrelated error terms are the most important consideration for a


practicing forecaster because when the problem of the autocorrelation occurs, the estimation

and the forecast will be biased. (Halkos, 2011a; Brooks, 2008)

H0= independent error terms over time,

the error terms are completely random and serially uncorrelated

6. Non-normality

The assumption of normality is that the residuals follow the normal distribution. In order to

test for normality we use the skewness, the kurtosis and the Jarque-Bera test (Brooks, 2008;

Halkos, 2011a)

In order for a series to be normally distributed the value of skewness should be equal to zero

(0) and the value of kurtosis should be equal to three (3). The Jarque-Bera test assumes to

follow the Chi-squared distribution.

H0= Residuals are normally distributed

What are the consequences of those problems?


In case that two or more independent variables are highly correlated, the regression becomes

very sensitive to small changes in its specification (Brooks, 2008)

2. Heterogeneity

When the sample is heterogeneous and the analysts ignore that problem, then the result will be

a pooled regression. That can lead to another potential problem the poolability. Of course, a

35


pooled regression will not be an appropriate estimation since the estimated coefficients will be

biased and unreliable (Brooks, 2008).

3. Endogeneity

By ignoring the endogeneity issue, the estimation will be biased. That means that the

outcomes will not be reliable and future expectations can not be based on them (Angrist,

Pischke, 2009).


The non-constant variance on the residuals can lead to biased estimations. That means that the

estimated values do not represent reality, so forecasts should not be based on those

estimations (Halkos, 2011a; Brooks, 2008).

5. Autocorrelation

The estimators that derived from the regression are unbiased but ineffective. Once again, that

means that the estimated values do represent the reality, so forecasts should not be based on

those estimations. Even in large samples, the coefficients are not efficient which means that

they do not have the minimum variance (Brooks, 2008; Halkos, 2011a)

6. Non-normality

There are no serious consequences deriving from the non-normality problem.

How to test for those problems?


In order to test for Multicollinearity, a correlation matrix is required. Through that matrix it is

easy to identify if two corresponding variables are highly correlated. If two corresponding


variables have a correlation value equal to or over 0.80, then near Multicollinearity occurs and

those two variables explain the same thing.

2. Heterogeneity

The formal test for Heterogeneity is the Redundant Fixed Effects – Likelihood Ratio. When

using fixed effects specification in both dimensions, the Redundant Fixed Effects -

Likelihood Ratio test gives two different values, both the F-test and Chi-square test for both

dimensions. If the probability of these values is lower than 0.05 (5% level of significance),

then the null hypothesis is rejected for the specific dimension and there is heterogeneity. It is

possible to have heterogeneity in both dimension or only in one (Brooks, 2008).

3. Endogeneity

The test for endogeneity is one that needs to be done manually because the software used, E-

Views 8, does not have an endogeneity test. The manual test is as follows. Based on theory

the researcher should decide which of the independent variables can be endogenous. This

variable should be used in a new estimation as dependent variables where all the other

independent variables will follow on the RHS. The residuals of the regression should be

saved. These residuals will afterwards be included in the first estimation specification. If the

residuals appear to be significant, which mean that the p-value will be lower than 0.05 and the

t-statistics are higher than 2 in absolute value (based on the Rule of thumb), then the null

hypothesis is rejected and the examined independent variable is endogenous (Angrist,

Pischke, 2009).


In order to test for Heteroskedasticity, we can use the Goldfeld-Quandt test (Halkos, 2011a),

Breusch – Pagan – Godfrey test (Halkos, 2011a), White test (Halkos, 2011a)

37


However, these tests are not applicable on Panel Data, thus the estimation needs to be tested

manually for Heteroskedasticity. This manual test is as follows. From the estimated

regression, that included the possible heterogeneity and endogeneity specifications, the

residuals should be saved and squared. Those residuals will be used afterwards as dependent

variables followed by all the independent variables in the RHS of the regression but without

the heterogeneity and endogeneity effects. If the probability of the F-statistics from that

estimation are lower than 5%, then the null hypothesis is rejected and the estimation is has

Heteroskedasticity issues.

5. Autocorrelation

In order to test for autocorrelation we can use a number of different tests, such as Durbin-

Watson statistics (DW). A DW value equal to 2 indicates that there is no autocorrelation. On

the other hand, DW value lower than 2 indicates negative autocorrelation and DW value

greater than 2 indicates positive autocorrelation (Halkos, 2011a; Brooks, 2008)

6. Non-normality

The formal test of Normality is the Jarque – Bera test. If the probability of Jarque – Bera is

lower than 0.05, then the null hypothesis is rejected and the residuals are not normally

distributed.

Moreover, when the residuals are normally distributed the value of skewness is equal to zero

(0) and the value of kurtosis is equal to three (3). If these values are not reached, it can be


concluded that the residuals do not follow the normal distribution (Halkos, 2011a, Halkos,

2011b, Brooks,2008).

How can the problems be solved?


The solution to Multicollinearity is a straight forward procedure. Because the two highly

correlated independent variables explain the same thing, it is up to the researchers to decide

which one of the two corresponding highly correlated variables will be excluded (Brooks,

2008).

2. Heterogeneity

If the Redundant Fixed Effects – Likelihood Ratio indicates that heterogeneity occurs in the

estimation, there is a number of different solutions.

The first and most preferable solution is to introduce Random Effects (RE) in the model

because it is the specification that gives more degrees of freedom compared to the Fixed

Effects specification. However, in order to use that specification, the RE need to be well-

specified. To test the specification of RE, the Correlated Random Effects – Hausman Test is

used. The null hypothesis for the test is that the RE are well specified. If the null hypothesis is

rejected, the Random Effects are not a suitable solution for heterogeneity. In that case the

Fixed Effects should be used instead (Brooks,2008).

Last but not least, there is a possibility that combined effects may be required. That means

that one of the dimensions may have well specified RE but the other one does not. However,

if the software cannot run a combined effect regression, the Within Transformation is the

solution to the problem. The same solution applies to when RE are needed in both dimensions

of an unbalanced panel data. Once again, the software cannot estimate a regression with RE

39


in both dimensions when the panel dataset is unbalanced. Thus, one of the dimensions should

be transformed by using the Within Transformation (Brooks, 2008).

3. Endogeneity

When at least one of the independent variables is endogenous, the Valid Instrument Variables

need to be used in order to mitigate the problem of endogeneity. With the term Valid

Instrument Variable (IV), we actually mean a variable which is partially correlated with the

endogenous independent variable and not correlated with the error term. However, because

the error term is not observable we cannot test the correlation between the IV and the error

term. Instead, the correlation between the dependent variable and the IV has to be tested.

Thus, in that case, it is important that the dependent variable and the error term are

uncorrelated (Angrist, Pischke, 2009).


The solution to the Heteroskedasticity issue is either to transform the variables which will

reduce their size or to make use of the White “Robust” standard errors (Brooks,2008).

5. Autocorrelation

One of the methods that can be used to solve the autocorrelation issue is to include both the

dependent and independent variables in the estimation lags of the variables (Halkos, 2011a).

The term lag is indicating the use of the value from the previous period of the specified

variable.

6. Non-normality

The issue of non-normality can be solved by either transforming the variables through the log

of the variables or by excluding a few outliers. However, in the case that the sample is big

enough that problem can be ignored (Brooks,2008).


The Estimation Procedure

The variables we use in this part will be the valuation errors that have been calculated based

on description in Section 3.4.3 as dependent variable and as error explanatory variables the

researchers decided to use some firm-based information that can affect the investors decision

and lead to mis-valuation. Based on Ek & Lillhage’s (2012) findings, some explanatory

variables are the natural logarithm of the total assets, the Market/Book ratio, and the annual

volatility and the R&D intensity (see Appendix A, eq. 2) of each firm. In our case some other

explanatory variables will be included. One of the variables will be a dummy variable

indicating if the credit rating of the firm is investment grade or not, by assigning the value one

(1) if so, and zero (0) otherwise (Moody’s, 2015). The decision to include the credit rating

variable was based on the notion that mis-valuation may be caused by investor bias and how

investors perceive the firm in question. Because the credit rating of each firm in our sample is

easily accessible to investor, it may be a source of information that can influence the

valuation. Another explanatory variable will be the Tobin’s Q (see Appendix A, eq.3), which

is a performance measure for a firm. Specifically, it is total market value of the firm divided

by total asset value of the firm. We included this variable as we believe investors may be

influenced and show some bias due to the historic performance of a firm. Finally, another

variable we believe may lead to mis-valuation is the profit margin. Much like in the case of

Tobin’s Q, we believe that miv-valuation may be caused by investor bias stemming from too

high of a reliance on a firm’s historic performance. Thus, the analysis consists of determining

which of these error variables are significant and in which cases. The analysis is as follows.

The first step is to present the descriptive statistics of the sample to gain a general sense the

variables we are using, which then will be followed by the correlation matrix. This matrix will

give us the opportunity to check for highly correlated variables before we start the

estimations. The next step is to specify the regression. We will use the valuation errors

41


calculated in Section 3.4.3 as the dependent variables and the previously listed terms, such as

Tobin’s Q as explanatory variables. Through this procedure we will try to identify which of

these explanatory variables can significantly influence the valuation errors. The estimation has

the following expression:

Valuation errori,t= α+β1*X1,i,t+β2*X2,i,t+β3*X3,1i,t+β4*X4,i,t+β5*X5,i,t +β6*X6,i,t+β7*X7,i,t+ui,t

The independent variables are as follows:

X1,i,t: ln (Total Assets)

X2,i,t: Market/Book (M/B)

X3,i,t: Volatility

X4,i,t: R&D intensity (see Appendix A, eq.2)

X5,i,t: Credit Rating

X6,i,t: Tobin’s Q (see Appendix A, eq.3)

X7,i,t: Profit Margin

With the expression at hand, a pooled regression is used in order to attain a benchmark result.

Obviously the benchmark will not be used because that means that the sample is a cross

sectional sample and has no period dimension. The next step is to run the Redundant Fixed

Effects – Likelihood Ratio which will indicate the heterogeneity issue and will specify the

variables that face that problem. Afterwards, Random Effects will be introduced in the

regression because, as explained above, they are more preferable. However, these RE need to

be well-specified which leads us to the Correlated Random Effects – Hausman Test. That test


will give us the solution to the heterogeneity issue by indicating the specification needed,

either the Random Effects or the Fixed Effects or perhaps a combined specification.

The next step is the endogeneity testing procedure, which will provide a solution if that

appears in our estimations. Since we do not know which of the seven (7) explanatory

variables that can be endogenous, all of the variables will be tested consecutively and if any

variable appears to be endogenous, then the procedure described in this Section will be used

in order to mitigate endogeneity.

After solving the two main issues of the regression, the estimation will be tested for

heterogeneity and White Robust SE’s will be used if needed. After mitigating any potential

heterogeneity issue, the estimation will be tested for autocorrelation by using the DW ratio

given in the statistics following the estimation. If the DW ratio indicates autocorrelation,

either positive or negative, the lags of both the dependent or independent variables will be

used till a DW close to two (2) is achieved, while at the same time providing the best AIC.

Lastly, the residuals of the final estimation will be tested for normality. In the case that the

residuals are not normally distributed, we can ignore that issue because of the sufficient size

of our sample.

By repeating the above described procedure, the researchers will have the ability to identify

which error variables significantly influence the valuation errors depending on the way the

valuation errors were calculated each time. That means, answers will be given for all different

cases. Specifically, the valuation errors, based on Section 3.4.2, will be calculated for all

different multiples (11 in total), three different approaches (median, average and harmonic)

and all different sample categorization (total sample and each capitalization separately). That

43


gives a final number of 132 estimations and outcomes that will be presented and discussed in

Section 4.3.

4 Analysis and Discussion

In this chapter we present the results of our different analysis. The chapter is divided into

three main Sections; Market Efficiency, Valuation Accuracy, and Error Determinants.

4.1 Market Efficiency

4.1.1 Descriptive Statistics


The results of the descriptive statistics of the market returns are as follow:

Table 4.1.1 Descriptive Statistics of market returns

Indices S&P500 S&P400 S&P600

Mean 0.075913 0.016055 0.086034

Std. Dev 0.248609 0.237141 0.261584

Skewness -0.638427 -0.834145 -0.697049

Kurtosis 3.310569 3.222872 3.290829

JB p-value 0.604320 0.437687 0.553482

Normality yes yes yes

From the table above (Table 4.1.1) we can conclude that the lowest returns are observed in the

mid-cap index with a value equal to 0.016055 or 1.6055% while the highest returns are

observed in Small Cap with a value equal to 0.086034 or 8.6034%. The market risk, measured

by using the standard deviation, indicates that the riskiest of all indices is the Small Cap and at

the same time the least risky is the Mid Cap. The negative skewness indicates that the lower

deviations from the mean are larger than the upper deviations, suggesting a greater probability

of large decreases than rises. What is more, Kurtosis, in all cases, has coefficients greater than

3 (but really close to 3) and Skewness has values close to 0, so we can assume that the returns

seem to follow the asymptotic chi-squared distribution, as required. Normality can also be

proved with the use of Jarque-Bera test and its probability. As we can see, the probabilities, in

45


all cases, are greater than 0.05, so we cannot reject the null hypothesis in a 5% level of

significance.

4.1.2 Model Approach

The next step is to estimate the most appropriate model based on AIC and the Loglikelihood

Criterion. After repeating the procedure for all different combinations we came to the

conclusion that there is a specification for each model that gives the best estimation. The table

below (Table 4.1.2) presents the results with the best specifications and the terms that have

been excluded:

Table 4.1.2 Best Model Approach

Indices ARIMA GARCH/T-GARCH E-GARCH

S&P500 ARIMA (10,1,10) GARCH (2,2)

With ARIMA (10,1,10)

E-GARCH (2,1)


- excluded No No AR(4)

AIC -5.781425 -6.237441 -6.277221

S&P400 ARIMA (10,1,10) GARCH (2,1)


E-GARCH (1,2)


- excluded AR(4), MA(1), MA(4) AR(3), MA(3) AR(1), AR(8), MA(8)


AIC -5.4498221 -5.991598 -6.007784

S&P600 ARIMA (10,1,10) GARCH (2,2)


E-GARCH (1,1)


- excluded AR(3), AR(5), MA(5) AR(8), MA(8) AR(4), AR(7), AR(8)

AIC -5.567518 -5.789050 -5.809214

4.1.3 Residual Diagnostics

The residuals for each test:

Jarque-Bera: H0: Skewness being equal to 0 and kurtosis being equal to 3

Q-statistics: H0: Residuals have no serial correlation

LM Test: H0: Residual have no autocorrelation

ARCH Heteroskedasticity Test: Ho:Residuals are homoskedastic

BDS Test: H0: Residuals have linearity

The residuals of all these estimations were tested and the results are the following: [1] None

of the residuals meets the normality requirements because their skewness in most cases is far

from 0 and their kurtosis is far form 3. At the same time, the probability is below 5%, which

means that we can reject the null hypothesis of having a skewness equal to 0 and kurtosis

equal to 3; following a normal distribution, so all residuals suffer from non-normality. [2]

Based on Q-statistics we can support the belief that apart from ARIMA estimations and

GARCH (2,2) for S&P500, none of the estimations have a serial correlation problem using up

to 36 lags because the probabilities of Q-statistics are greater than 5% in all cases, with the

exception of ARIMA and S&P500 GARCH (2,2) estimations where the probabilities are

below 5%, so only in these cases the null hypothesis can be rejected and it can be assumed

that there is serial correlation. [3] Regarding the LM test, it should be noted that this test is

47


applicable only in an ARIMA approach and not in any GARCH approach. For that reason we

have tested the residuals only for the ARIMA estimations. Our conclusions is that all the

ARIMA based LM tests have insignificant residuals, which mean that their t-statistics are

lower than 1.96. Note that when t-statistics is lower than 1.96, there is no significance on 55

level of significance. As an alternative, we can use the Rule of Thumb: significance |t-

statistics|>2 suggests significance. That means that we can reject the null hypothesis of the test

and assume that there is no autocorrelation. [4] The next test is the Heteroskedasticity ARCH

test. With a low probability of F-statistics in that test for ARIMA estimations and E-GARCH

(1,1) for the S&P600, we can reject the null hypothesis of the test and suggest that there is

heteroskedasticity instead. However, we cannot reject the null hypothesis for any other case.

[5] Last test is the BDS test for linearity issues. For all indices and for all different

approaches, there is significance for the test. That means that the probability of the z-statistics

in all dimensions are lower than 0.05 and the z-statistics are greater than 3 in all cases. That

leads us to reject the null hypothesis of the test and come to the conclusion that none of our

estimations have linearity in its residuals.

4.1.4 Forecasting

After presenting the results of the residual diagnostic tests, it is time to present the results of

the forecasts which will give us the answer to the main question of this Section: Is the market

is efficient in its weak form or not? If the market is efficient in its weak form then a Random

Walk should be followed by the price movements and there should be no correlation between

the past and the future price movements, otherwise the market will be inefficient and a

number of investors will be able to gain abnormal returns. As mentioned above, for the

forecast the last 20% of our observations will be used.


4.1.4.1 Large CapitalizationThe table below (Table 4.1.3) presents the results from the forecast for all four estimations.

Four different critical values are presented. Based on these values we can conclude if the

market if efficient in its weak form. The model that reaches the lowest values for each critical

value, or at least most of them, is the model that gives the best estimation. For the large cap

(S&P500), we can suggest that because Random Walk has only one of the lowest values of

the four, while GARCH has two and E-GARCH has one, it is not the best model to use order

to describe the market prices. That means that, for the S&P500 index the stock price

movements do not follow the RW, which indicates that there is no market efficiency in its

weak form for the large capitalization.

Table 4.1.3 Large Capitalization Forecasting Results

ARIMA GARCH (2,2)

E-GARCH (2,1)

Random Walk

Root Mean Squared Error

0.007316 0.007274 0.007285 0.007290

Mean Absolute Error 0.005374 0.005324 0.005375 0.005329

Mean Abs. Percent Error 114.6901 145.7314 180.5384 99.20992

Theil Inequality Coefficient

0.936366 0.936503 0.917324 0.995350

49


4.1.4.2 Mid CapitalizationThe table below (Table 4.1.4) presents the results from the forecast for all four estimations.

Four different critical values are presented and based on those we can conclude if the market

is efficient in its weak form. The model that reaches the lowest values for each critical value,

or at least most of them, is the model that gives the best estimation. For the mid-cap index

(S&P400), we can suggest that because Random Walk has only one of the lowest values out

of the four, while GARCH has three, it is not the best model to describe the market prices.

That means that, for the S&P400 index the stock price movements do not follow the RW,

which indicates that there is no market efficiency in its weak form for the mid capitalization.

Table 4.1.4 Mid Capitalization Forecasting Results

ARIMA GARCH (2,1)

E-GARCH (1,2)

Random Walk


0.008669 0.008559 0.008622 0.008566




0.883868 0.262480 0.908428 0.971812

4.1.4.3 Small CapitalizationThe table below (Table 4.1.5) presents the results from the forecast for all four estimations.

Four different critical values are presented and based on those we can conclude if the market

is efficient in its weak form. The model that reaches the lowest values for each critical value,

or at least most of them, it is the model that gives the best estimation. For the small-cap index

(S&P600), we can suggest that because Random Walk has three out of the four lowest critical

values, while GARCH has only one, is the best model to describe the market prices. That


means that, for the S&P600 index the stock price movements do follow the RW, which

indicates that there is market efficiency in its weak form for the small capitalization.

Table 4.1.5 Small Capitalization Forecasting Results

ARIMA GARCH (2,2)

E-GARCH (1,1)

Random Walk


0.009616 0.009498 0.009583 0.009450




0.905076 0.902495 0.915511 0.972271

4.2 Valuation Accuracy


In the table below we present the average multiple valuation error for the total sample. All the

valuation errors for the different indices can be found in Appendix B (See Appendix B9-B12).

51



For large cap the P/EBITDA 1 calculated with the median proved to be the best multiple

with an average valuation error of only 0.0879% or 8.70 bp, and a standard deviation of

0.393. However, P/E 1 calculated with the median proved to be the best multiple in terms of

Table 4.1.6:Average Valuation Errors - Total Sample


percentage of the sample falling within the fraction of 0.15. 57.16% percent of the sample had

a valuation error less than 15% for P/E (1).

For mid cap P/TA calculated with the median proved the have the lowest valuation error on

average of only 0.1199% or 11.99 bp, and a standard deviation of 0.659. In terms of

percentage of the sample falling within the fraction of 0.15, EV/EBITDA 1 proved to be the

best multiple with 49.26% of the sample with a valuation error less than 15%.

For small cap EV/EBITDA 1 calculated with the median was the best multiple with an

average valuation error of only 0.21% or 21 bp, and a standard deviation of 0.5075. In terms

of percentage of the sample falling within the fraction of 0.15, P/E 1 calculated with the

median proved to be the best one with 49.31% of the sample having a valuation error of less

than 15%.


indices?

Forward-looking earnings based multiples perform the best for all indices, in terms of

percentage of the sample having a valuation error less than 15%. P/S and P/TA perform the

worst in the same regard, which is notably since assets based multiples performed very well in

the study by Lie & Lie (2002). In addition, there’s a slight difference in absolute value of the

valuation errors for the different caps, where large cap has the smallest absolute valuation

error for the best performing multiple, mid cap somewhat larger and small cap somewhat

larger than mid cap. The conclusion we draw from this is that it is harder to value smaller

companies, albeit the difference is very small. Drawing on other knowledge however, it

makes sense. Arguably there is less media coverage and insight into smaller companies than

53


there generally is for larger companies, which we believe could explain some of this

mispricing.


accuracy?

In terms of accounting for the largest part of the sample within the valuation fraction of 0.15,

equity based multiples performed better than entity based multiples for all indices except mid-

cap where EV/EBITDA 1 performed the best. The difference for the mid-cap index was

however, very small with EV/EBITDA 1 accounting for 49.26% of the sample and P/E 1

accounting for 47.93% of the sample. Both multiples were calculated with the median.

5. Do forward-looking multiples outperform trailing multiples in terms of valuation

accuracy?

Yes, it would seem so. All of our best performing multiples were indeed forward-looking

multiples.

All of our samples, that, is the total sample, large-cap, mid-cap, and small-cap showed

undervaluation for the SIC-multiple compiled by using the median and harmonic mean, while

it showed overvaluation for the average. From an investors perspective it therefore seems

better to use either the median or harmonic mean when compiling the peer multiple, as it has a

tendency to undervalue the stock, essentially resulting in an extra cushion or margin of safety

for said investor. Another nice feature is the fact that the peer multiples calculated with the

median performed the best in all of our tests. From a practical viewpoint this is nice, as the

method is very easy to understand and quick to calculate. In accordance with Schreiner’s

(2007) findings, we also discovered that forward-looking multiples outperform trailing ones.


Once again, just like Schreiner we found that the 12-month forward-looking price to earnings

multiple performed especially well.

Total Sample Large Cap Mid Cap Small Cap0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

All SIC LevelsSIC Level (3 & 4)

Figure 4.1.1: Difference in Valuation Error for Different SIC-levels

Another interesting discovery is that valuation accuracy improved when we excluded the SIC-

multiples calculated at a SIC-level less than three. This is also agreement with Schreiner’s

(2007) argument that the industry code level should only be relaxed when absolutely

necessary, as the similarity of peers is paramount to getting an accurate valuation.

Interestingly, P/TA performed the worst for many of our samples, which is the opposite of

what Lie & Lie (2002) found in their study, where asset based multiples performed the best.

4.3 Valuation Error Determinants

The main questions of this Section are the following:

1. Is there any error variable that can significantly influence the valuation error?55




As already mentioned in Section 3.4.4, the researchers used seven (7) explanatory variables

with the purpose to determine the valuation errors. The initial step was the descriptive

statistics for all valuation errors and explanatory variables. Through this the authors got a

general idea of the sample they have to use, specifically, from looking at the mean values and

the standard deviation. Moving forward, the correlation matrix indicated that there is no

Multicollinearity between the valuation errors and the error determinants. That means there is

no reason to exclude any of the explanatory variables.

The next part was the estimation procedure that started with a pooled (OLS) regression as a

benchmark, which will not be used in the results. The researchers repeated the procedure for

every valuation error calculated in Section 3.4.3 and all the results, both the tests and the final

estimated coefficients can be found in Appendix B (Tables B13 –B45). One of the results,

specifically the estimation of P/E median is presented in the table below (Table 4.1.7)

The table is separated into two parts, where on the left side of the table the reader can observe

all the final estimations of the coefficients and the regression in total, while on the right side

of the table the reader can obtain information about all the tests the researchers used and the p-

values which will lead either to acceptance or rejection of the null hypotheses briefly

described in Section 3.4.4. What is important to mention is that the values of

Heteroskedasticity and Autocorrelation presented on the right side of the table with all the

tests are those initially estimated, before any correction was made, while the values presented

on the left side are the final values after taking into consideration any potential problem and


correcting the errors. All the hypotheses were checked in 5% level of significance, which

means that if the p-value is lower than 0.05, the null hypothesis was rejected.

In the table 4.1.7 the level of significance is presented with the use of (*). Specifically,

*indicates significance at the 0.1level, **indicates significance at the 0.05 level and ***indicates

significance at the 0.01 level.

Focusing the discussion on table 4.1.7, it is easily recognizable that the greatest fit is given in

the Small Cap index, which has a fit of 51.0834%. That means that almost 51.1% of the error

variables can explain the valuation error of P/E median.

Moreover, in none of the four (4) categories Total Assets were found to be significant in terms

of explaining the valuation error. The M/B ratio appears to be significant only in the Large

capitalization index and seems to have a negative impact on valuation error. That means that

57

Table 4.1.7: P/E Median Error Determinants & Diagnostic Tests


the higher the M/B, the lower the valuation error and vice versa. What appears to be

significant in all cases, or almost all cases, is the R&D intensity variable and Tobin’s Q. Both

of them have a negative effect on the valuation error just like M/B. Moving now to the lags, it

is obvious that the Credit Rating from the previous period can cause a significant valuation

error both in the Large Cap and Small Cap indices. Due to the fact that lags were used only in

order to solve Autocorrelation, some of the lags were not included in the estimation because

they were either exaggerating the problem or they were giving a higher AIC. Compared to the

current period, there is still significance on Tobin’s Q, although only in the total sample

estimation. R&D intensity, however, showed no significance compared to the current period.

Not surprising, the Profit margin from the previous period is significant, which lead us to the

conclusion that the investor decisions can be influenced by the previous period profits. The

difference between the two periods is that the significant explanatory variables from time t

appear to reduce the valuation error; whereas the significant explanatory variables from time

t-1 appears to worsen the valuation error. What is essential to mention is that the current

valuation error can be influenced by the previous periods valuation error.

Pertaining to the overall results, initially, all the estimations were suffering from

autocorrelation and a high percentage of the estimations were facing Heteroskedasticity

issues. None of the estimations had endogenous variables, which means that the problem of

endogeneity did not appear and the researchers did not have to deal with that issue. Finally,

all the residuals from the final estimation are not normally distributed, but due to the large

sample size that is an issue that can be ignored.

The graph below (Graph 4.1.2) present the percentage of significance of all coefficients

estimated for time t.


Constat_term

ln(TA) M/B Volatility R&D int dummy CR

Tobin's Q Profit Margin

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

Total SampleLarge Cap.Mid Cap.Small Cap.

Figure 4.1.2: Percentage of significance of Error Determinants (time t)

As we can see, in general, the highest significance can be found in Tobin’s Q and the Profit

Margin with the Total sample and Large Cap index reaching the highest values, where the

credit rating from that period is the one that has the lowest percentages.

These percentages were calculated based on the number of coefficients that were significant at

5% level of significance over the total number of coefficients (33 in time t).

The next graph (Graph 4.1.3) presents the significance of the coefficient of the previous

period.

In comparison with the previous graph, it is recognizable that the most significant of all

coefficients appear to be previous year’s valuation error, which actually reaches 100% for the

total sample, and almost 40% for the Small Cap, the lowest one of all four. The Total Assets

59


come in second place with more than 63% significant coefficients on the Large Cap index,

which is followed by Volatility and Tobin’s Q. However, what is important to mention is that

both volatility and R&D intensity do not have any significance in the Small Cap index for

time t-1 while at the same time, Tobin’s Q has the lowest value of all existing percentages in

the Small Cap index. In time t-1, the percentage was calculated based on the number of

significant coefficients divided by the total number of coefficients, which differs since some

of the lags were excluded.

Lastly, we have a graph presenting the Goodness of Fit (R2). In this graph (Graph 4.1.4), the

researchers are trying to present the percentage of Goodness of Fit that goes under each of the

three categories. The three categories are as follows:

0%=<R2< 40% Low fit

40%=<R2<80% Medium fit

ln(TA)(-1) M/B(-1) Volatility(-1)

R&D int (-1)

dummy CR (-1)

Tobin's Q (-1)

Profit Margin (-

1)

Valuation Error(-1)

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

90.00%

100.00%

Total SampleLarge Cap.Mid Cap.Small Cap.


80%=<R2=<100% High fit

Total Large Mid Small0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

80%=<R^2=<100%40%=<R^2<80%0%=<R^2<40%

Figure 4.1.4: Goodness of Fit

As we can see from the graph, in the Total Sample 50% of the estimations have a medium

goodness of fit, while only 15.63% of estimations are reaching a high R2. In the Large Cap

index the percentage of the medium fit increases at 54.55% while at the same time the

percentage of the high fit increases at 24.24% which leads to a decrease on the low fit. The

highest percentage of the low fit is observed on the Mid Cap index with a value of 63.64%,

which at the same time we see really low percentage of the high fit, only 9.09%. Finally, the

Small Cap index has a high percentage on the high R2, leading to equal percentages to the

other two categories (low and medium) with a value of 24.24%.

Once again, in order to calculate the percentages the researchers used the number of observed

values under each category over the total number of observations, which equals 33. However,

61


for the Total Sample, the total number of observation is not 33 but 32. The reason for that is

the fact that one of the estimations in the category has an R2 equal to 100%, which is the P/TA

harmonic estimation (see Appendix B, table B30). Such a high Goodness of Fit is not

reasonable, because it actually means that the explanatory variables can completely explain

the valuation error and there are no standard errors in that estimation. That derives from the

formula of R2 (see Appendix A, eq. 4). In order to have a reasonable estimation on the

percentages presented above and more realistic results we decided that it would be fair to

exclude such an irrational value, which is probably not reflecting reality.

With this said, it is respectable to suggest that there are error variables that can explain the

valuation error. That means that the valuation errors are not random but they are influenced by

other factors. These error variables can be values from the current period but also values from

the previous period. Moreover, the valuation error by itself from the previous period can have

an impact on the current valuation error. Based on the Credit Rating dummy, we can suggest

that the investors’ decisions can be influenced by investment credit ratings and cause an

increase in the valuation error.

5 Conclusion

Our analysis suggest that earnings-based multiples are the best multiples to use when valuing

firms through the multiples approach, that is, earnings-based multiples yield the closest

approximation of market value. We found that this is true both for equity and entity multiples,

where P/E 1 performed very well for equity multiples and EV/EBITDA 1 performed very well

for entity multiples. Interestingly, one of our hybrid multiples performed very well for the


large-cap index, namely P/EBITDA 1, which is rather surprising since both Schreiner (2007)

and Ek & Lillhage (2012) are adamant about the importance of matching theory. Overall,

equity-based multiples, that is, multiples with price or capitalization in the numerator

outperformed enterprise-based multiples and forward-looking multiples, that is, multiples that

incorporate next year’s expected earnings, outperformed trailing ones. Both of these findings

are in accordance with what Schreiner (2007) discovered. Schreiner’s (2007) best performing

multiple was P/E 2, and ours was P/E 1. We expect that P/E 2 would have performed even

better than P/E 1 in our sample as well, unfortunately earnings estimations for the next two

years were not available in Datastream 5.1.

Regarding the different indices, we discovered that the average valuation error for our best

performing multiples increased as we moved from the large-cap index down through and

towards the small-cap index, suggesting that valuation accuracy becomes worse for smaller

firms. The error, however, was marginal and the best multiples were still forward-looking,

earnings-based equity multiples suggesting that this is still the best way to value firms through

the multiples approach, regardless of company size.

We can also conclude that using the median when compiling the peer multiples is the best

approach (see section 3.4.2). All of our best performing multiples were computed with the

median. The median also tended to have negatively biased results, which is a nice feature for

investors on the buy side. Lastly, in accordance with Schreiner’s (2007) argument, we found

that the valuation errors decreased when we excluded the multiples computed with a SIC-level

of 2 or 1, confirming that similarity of peers is highly important in order to achieve high

valuation accuracy.

Regarding the market efficiency theory, we can conclude that our econometric analysis

yielded results in line with previous research findings. Out of the three indices we analyzed;

63


that is, the S&P large-, mid-, and small-cap, only the small-cap index is efficient in its weak

form. Our results suggest that for the other two; that is, the large- and mid-cap index, there are

approaches which can explain price movements and let the investors exploit the market

inefficiency.

For the valuation error determinants, we can conclude that there is a significant connection of

the valuation error with both current and past period observations. Moreover, we found that

the Large Cap index is has better Goodness of fit compared to the other two capitalizations.

Contradictory to Ek and Lillhage’s (2012) findings, we can prove that R&D intensity has

significance in some of the estimations; whereas in their study R&D intensity has no

significance. That leads us to conclude that investors active in the US markets are influenced

by the R&D intensity; whereas the Scandinavian investors seem to not be influenced by the

R&D intensity.

5.1 Practical Implications

We believe our findings can be of interest for investors, both institutional and private, in their

endeavors to invest successfully. After all, price paid for any given financial instrument is one

of the most important variables of a successful investment: in order to make sure it is a fair

and appropriate price, a proper valuation is needed. We also encourage students and

academics to continue the research within this field.


5.2 Future Research

Including this thesis, there have now been studies looking at multiples valuation for American

and European large cap stocks. To the best of our knowledge, this is the first study to look at

mid-cap and small-cap firms. However, we believe that there is still room for more research.

For example, it would be interesting to see a more comprehensive study, incorporating more

firms - for example the whole S&P small cap. In addition, there is to our knowledge still no

study looking at Asian companies or emerging markets. It would also be interesting to see a

study that focused more on the difference in valuation accuracy between various industries.

Regarding the error determinants, we believe that there is still room to improve on the model

and add on more error determinants. It will also be interesting to see a study with more,

unconventional multiples included, more specially, one will emerge that can reduce the

valuation error for science-based firms.

65


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Appendix AExpressions

RandomWalk :StockReturns=c+Stock Returns−1+u i (1)

R∧Dintensity= R∧DSales (2)

Tobi n' sQ=Total Market V alueTotal Assets (3)

R2=1− SSESST (4)


Appendix B

69

B1 – B8: Valuation Errors - Descriptive Statistics


71


B9: Average Valuation Errors - Total Sample


B10: Average Valuation Errors - Large Cap.

73


B11: Average Valuation Errors – Mid Cap.


B12: Average Valuation Errors – Small Cap.

75


B13: P/E Median Error Determinants & Diagnostic Tests

B14: P/E Average Error Determinants & Diagnostic Tests


77

B15: P/E Harmonic Error Determinants & Diagnostic Tests

B16: P/S Median Error Determinants & Diagnostic Tests


B17: P/S Average Error Determinants & Diagnostic Tests

B18: P/S Harmonic Error Determinants & Diagnostic Tests


79

B19: P/EBITDA Median Error Determinants & Diagnostic Tests

B20: P/EBITDA Average Error Determinants & Diagnostic Tests


B21: P/EBITDA Harmonic Error Determinants & Diagnostic Tests

B22: P/EBIT Median Error Determinants & Diagnostic Tests

B23: P/EBIT Average Error Determinants & Diagnostic Tests

B24: P/EBIT Harmonic Error Determinants & Diagnostic Tests

B25: P/(EBIT+RD) Median Error Determinants & Diagnostic Tests

B27: P/(EBIT+RD) Harmonic Error Determinants & Diagnostic Tests

B29: P/TA Average Error Determinants & Diagnostic Tests


81

B31: EV/EBITDA Median Error Determinants & Diagnostic Tests

B32: EV/EBITDA Average Error Determinants & Diagnostic Tests

B33: EV/EBITDA Harmonic Error Determinants & Diagnostic Tests

B34: PEV/EBIT Median Error Determinants & Diagnostic Tests

B35: EV/EBIT Average Error Determinants & Diagnostic Tests

B36: EV/EBIT Harmonic Error Determinants & Diagnostic Tests

B37: P/e (1) Median Error Determinants & Diagnostic Tests


B39: P/E (1) Harmonic Error Determinants & Diagnostic Tests

B40: P/EBITDA (1) Median Error Determinants & Diagnostic Tests

B41 : P/EBITDA (1) Average Error Determinants & Diagnostic Tests

B42: P/EBITDA (1) Harmonic Error Determinants & Diagnostic Tests

B43: EV/EBITDA (1) Median Error Determinants & Diagnostic Tests


83

B45 : EV/EBITDA (1) Harmonic Error Determinants & Diagnostic Tests


Appendix C

C1: Variable Codes

Variable Code Variable Code

Assets WC02999 Market/Book PTBV

Volatility WC08806 R&D WC01201

Enterprise Value WC18100 EBIT WC18191

EBITDA WC18198 Sales DWSL

Earnings WC07250 Stock Price P

P/S FTSPS Profit Margin WC08316

S&P400 S&PMID P/E PE

10-year gov index U.S BMUS10Y Capitalization MV

12-month forward Enterprise Value DIEV S&P500 $SPX

12-month forward P/E PEFD12 S&P600 S&P600I

12-month forward EBITDA EBD1FD12 10-year treas. bond U.S S00311

C2: List of Multiples

List of MultiplesP/EP/E (1)P/SP/EBITP/(EBIT+RD)P/EBITDAP/EBITDA (1)P/TAEV/EBITEV/EBITDAEV/EBITDA (1)

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