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Faculty of Economics and Business

Bachelor’s Thesis and Thesis Seminar Finance for Economics

BSc. Economics and Business Economics

Explaining stock returns in North American R&D-intensive

sectors, using the Fama-French 3- and 5-factor models

Eveline Wilgenkamp

Student number: 11871946

Supervisor: Yumei Wang

Date: June 30, 2020

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ii Abstract

This thesis researched above-average returns in R&D-intensive sectors through exposure to the Fama and French (1993, 2015) three- and five-factor models. It approached this problem with, on the one hand, times-series regressions on R&D-intensive portfolios sorted on size and book-to-market equity, after which a GRS-test on the joined alphas is computed. On the other hand, two-stage Fama-MacBeth regressions were run for individual assets to assess the risk-premia in R&D-intensive sectors. This study found that the Fama-French three- and five-factor models underperformed in R&D-intensive sectors. The proposed profitability and investment factors did not add any explanatory power in these sectors. The hypothesis follows that these findings were the result of an omitted risk factor in both models, which is correlated with the investment factor and explicitly applicable to R&D-intensive firms.

Statement of Originality

This document is written by Eveline Alice Wilgenkamp who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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iii Acknowledgements and preface

I want to thank my supervisor Yumei Wang for her understanding of the impact and repercussions of the global situation surrounding COVID-19 on the process of this thesis. She provided me with considerable flexibility in the planning and execution of the thesis process.

Furthermore, I am grateful for my family, friends, and partner who have been very helpful when dealing with personal matters during turbulent times, allowing me to fully focus on the thesis process. The quality of my final product would not have been achievable without their support.

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iv TABLE OF CONTENTS

ABSTRACT...ii

ACKNOWLEDGEMENTS AND PREFACE...iii

TABLE OF CONTENTS...iv

LIST OF TABLES...v

1. INTRODUCTION...1

1.1 Motivation and research question...1

1.2 Methodology and contribution...2

1.3 Structure...3

2. THEORETICAL FRAMEWORK...4

2.1 Early asset pricing models...4

2.2 Fama-French three-factor model...4

2.3 Fama-French five-factor model...5

2.4 Returns in R&D-intensive sectors...7

2.5 Hypotheses...7 3. METHODOLOGY...9 3.1 Sample selection...9 3.2 Variables...11 3.3 Factors...12 3.4 Portfolio construction...13 3.5 Descriptive statistics...14 3.6 Time-series regressions...15 3.7 GRS-test...16 3.8 Fama-MacBeth regressions...16

3.9 Newey-West standard errors...17

4. RESULTS...19 4.1 Time-series regressions...19 4.2 GRS-test...22 4.3 Fama-MacBeth regressions...23 5. DISCUSSION...26 5.1 Time-series regressions...26 5.2 Fama-MacBeth regressions...27 5.3 Future research...27 6. CONCLUSION...29 REFERENCES...30

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v LIST OF TABLES

Table 1: Studies of R&D-intensive SIC codes...9

Table 2: Industry name of SIC codes...10

Table 3: Factor construction...13

Table 4: Descriptive statistics...14

Table 5: Value-weighted portfolio returns...15

Table 6: Time-series regressions...20

Table 7: GRS-statistics...23

Table 8: First stage Fama-MacBeth regressions three-factor model...23

Table 9: First stage Fama-MacBeth regressions five-factor model...24

Table 10: Second stage Fama-MacBeth averages...25

Table 11: Second stage Fama-MacBeth regressions...25

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1 1. Introduction

1.1 Motivation and research question

Over the last years, popular media covered an increasing ratio of high-technology firms to regular companies. Firstly, there is the example of Tesla, who announced their design of the Cybertruck in 2019 and got over 250,000 pre-orders, despite online controversy (Wood, 2019). Another illustration of the phenomena is the everlasting competition between Samsung, Apple, and Huawei. Additionally, SpaceX sent NASA astronauts into space from American grounds for the first time in history (Potter, 2020). The common denominator of these popular high-technology firms: they invest generously in research and development (R&D).

These R&D-intensive firms have an interesting characteristic: on average, their stock return outperforms that of the market (Chambers, Jennings, and Thompson, 2002; Lev & Sougiannis, 1996). Two main explanations exist in academic literature: the first being mispricing due to accountancy methods, and the second comprising additional priced-in risk. The second explanation derives from the efficient market hypothesis, which implies that larger returns, such as in R&D-intensive sectors, come paired with increased risk. So, if the efficient market hypothesis holds, these returns should be prone to empirical measurement through above-average exposure to some risk factor.

The chosen asset pricing model to explain returns by risk factor exposure is the three-factor model by Fama and French (1993), which was extended to a five-factor model by Fama and French in 2015. The three-factor model attempts to explain variation in stock returns using a market, size, and book-to-market equity (also known as value) factor. The five-factor model adds a profitability and investment factor to the previous model.

One advantage of these models is that they are widely tested in academic literature. International tests (e.g., Fama & French, 2017) as well as sector-specific tests (e.g., Sarwar, Mateus, & Todorovic, 2018) are available. The general finding is that the five-factor model is an improvement of the three-factor model. Additionally, the models provide a practical advantage. The models are already commonly used for factor investing. Factor investing is a means of investing where one increases or decreases its exposure to a factor, depending on the sign of the risk premium of the factor, to expose the portfolio to higher returns. Exchange-traded funds (ETFs) are known to implement these practices. Glushkov (2016) finds that the main source of performance in ETFs is static factor exposure. Therefore, significant results in R&D-intensive sectors could provide ETFs – and other factor investors – with a new source of excess returns.

The aim of this thesis is to research whether the three- or five-factor model by Fama and French (1993, 2015) can successfully explain the source of risk of the excess returns of R&D-intensive firms. The analysis surrounds the following research question: to what extent do the

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2 Fama-French three- and five-factor models explain variation in stock returns of firms in North American R&D-intensive sectors? The analysis contains two hypotheses to assess this research question. The first hypothesis surrounds the idea that the five-factor model outperforms the three-factor model in explaining variation in stock returns across R&D-intensive firms. The second hypothesis concerns the risk premia of the factors. Are there any specific factor risk premia that R&D-intensive firms are especially exposed to, which could explain their high returns?

1.2 Methodology and contribution

Testing the two different hypotheses requires two different methods. To test the performance of each model in R&D-intensive sectors, a time-series regression approach was selected. These regressions estimate the monthly excess stock returns of portfolios consisting of R&D-intensive companies through exposure to the factors proposed by Fama and French (2015). Thus, this approach comprises the construction of portfolios, that sorts firms based on some benchmark(s). Working with regressions on portfolios rather than individual assets helps determine whether certain types of R&D-intensive firms (for example, those with high market capitalization and low book-to-market equity ratios) are particularly exposed to a risk factor. The method subsequently allows for analysis of the predictive power of a model in R&D-intensive sectors. On the one hand, by employing R-squared values and, on the other hand, by using GRS-statistics, which test whether the joined portfolio alphas are significantly different from zero. The second method applied to this thesis consists of regressions proposed by Fama and MacBeth (1973). Fama-MacBeth regressions consist of two parts. In the first stage, a time-series regression is run for each asset in the sample. That means that its monthly stock returns are regressed on the proposed Fama-French factors, which yields a beta representing each asset’s exposure to each factor. In the second stage, a cross-sectional regression is run for each period of the sample. That involves regressing the returns in time 𝑡 of each asset against their betas from the first stage. This yields factor gammas for each month. Taking the arithmetic average of the gammas of a factor yields the sample risk-premium for exposure to this factor. With this risk premium, the second hypothesis can be tested.

The sample used in the analyses consists of all firms listed on the NYSE, AMEX, and NASDAQ stock-exchanges, operating in an R&D-intensive sector. R&D-intensive sectors are selected utilizing standard industry codes, which are selected based on their prevalence in previous literature on R&D-intensity. The sample period ranges from July 1990 to December 2019.

This thesis attempts to close the gap between two highly researched topics in finance: above-average returns in R&D-intensive sectors and the asset pricing models by Fama and French (1993, 2015). Therefore, it contributes to academic literature. Research on R&D-intensive samples

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3 has used the Fama-French three-factor model before. However, these papers generally have another research question to its basis, and the model was used as a control. The paper by Chambers et al. (2002) uses the three-factor model as control and finds that the model does not have high explanatory power in R&D-intensive sectors. Additionally, Gu (2016) researches the relationship between R&D-intensity and product market competition. She finds that alphas predicted by the five-factor model are significant in competitive R&D-markets and insignificant in concentrated markets. Nevertheless, she does not test the overall performance of the model in the R&D-intensive sample.

Fama and French (1993, 2015) find that the five-factor model outperforms the three-factor model explaining cross-sectional stock returns in North America. However, this thesis finds that both the three- and five-factor models do not perform well in North American R&D-intensive sectors. This finding implies that there is some unknown risk factor to which R&D-intensive firms are specifically sensitive, not included in the model. It is hypothesized that this risk factor is correlated with the investment factor. The discovery of the factor could provide investment opportunities with excessive returns through factor investing.

1.4 Structure

The next chapter discusses the previous literature on the topic. The first section explains the history of asset pricing models. The second and third sections introduce the theoretical concepts behind the factors of the three- and five-factor models by Fama and French (1993, 2015), respectively. In the fourth section, the two most common explanations of high returns in R&D-intensive sectors are presented. The last section proposes the hypotheses of this thesis. In the third chapter, the methodology of the analysis is put forth. This chapter will firstly include detailed information on sample selection. Subsequently, it demonstrates the construction of variables, factors, and portfolios. After that, it presents the descriptive statistics. The chapter finishes with an explanation of the time-series and Fama-MacBeth regressions and their relevant test statistics. Chapter four presents the results of the analysis, both for the time-series and the Fama-MacBeth methodology. Chapter five compares the results to previous literature and provides recommendations for future research on the topic. Chapter six synthesizes the results in a conclusion.

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4 2. Theoretical Framework

Chapter two describes the previous literature on the three- and five-factor models. It summarizes the development and theoretical concepts behind the factors proposed by Fama and French (1993, 2015) and the main findings from these papers. Furthermore, the chapter synthesizes the literature on high returns in R&D-intensive markets. Lastly, it introduces the proposed hypotheses to test the research question.

2.1 Early asset pricing models

In history, asset pricing surrounded a narrative on a trade-off between risk and return. Theories suggested that higher risk would come paired with higher returns, as investors demanded a risk premium. Risk consists of two parts: systematic (or market) risk and idiosyncratic risk, of which the latter could be diversified away by adding more stocks to the portfolio. The fundamental paper by Markowitz (1952) addresses the theories as it empirically shows that the movement of an asset’s returns respective to other assets’ returns measures an asset’s risk. This paper marked the start of modern portfolio theory (MPT).

Sharpe (1964) and Lintner (1965) extend the empirical framework of Markowitz (1952) with their famous capital asset pricing model (CAPM). The CAPM shows that if all investors are mean-variance optimizers (and thus hold the Markowitz optimal portfolio), the asset’s beta can measure the riskiness of an asset. The beta represents to what extent an asset’s returns co-move with the returns on the market portfolio. The higher the beta, the higher the undiversifiable market risk, and therefore the higher the required risk premium of an asset. The risk premium comes on top of the expected return of a free asset: the free rate. The combination of both the risk-free rate and the risk premium, as estimated by the CAPM, can be considered as the cost of equity.

2.2 Fama-French 3-factor model

However, Fama and French (1993) argue that the cross-sectional relationship between returns in the U.S. common stock market and the betas derived from the CAPM is small. They, therefore, propose an extension using variables that had positive explanatory power but were not necessarily well known in asset-pricing theory at the time. Using previous risk factor research by Fama and French (1992), they propose four variables. The first being size, measured by market capitalization. The second proposed factor is earnings/price, measured as earnings divided by the price of the asset. The third tested variable is leverage, measured by assets over either book or market equity value. The final proposed factor concerns a value factor, measured by an asset’s book-to-market equity ratio.

Using the four proposed factors, Fama and French (1993) test different asset-pricing models with a new approach: cross-sectional regressions using the methodology by Fama and

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5 MacBeth (1973) in combination with time-series regressions. From the wide variety of regressions follows that a model formed using the size and value factor, combined with the market beta from the CAPM, has the greatest explanatory power in both the stock and bond market. The size and value factors absorb most of the individual predictive power of the E/P and leverage factors. The theory behind the size and value factors comes from observed phenomena, rather than from theory. The size factor is based on the circumstance that, on average, small- and mid-cap stocks outperform large-cap stocks. The value factor relies on the notion that assets that are cheap relative to some value benchmark outperform those that are pricy. Fama and French (1993) conclude that the size and value factor should be related to some source of growth and profitability. However, this source is yet to be discovered.

2.3 Fama-French 5-factor model

Financial literature has widely tested the three-factor model by Fama and French (1993), and several researchers came up with subsequent statistically significant factors to add to the model. Firstly, Novy-Marx (2013) finds that a profitability factor has the same predictive power as the book-to-market value factor when explaining cross-sectional variation in returns. An interesting result, as Fama and French (2008) also researched profitability as a factor and did not find significant predictive power when combined with the 3-factor model. The main difference between the two approaches stems from the measurement of the profitability factor. Fama and French (2008) measure profitability as net cash flows, calculated as earnings minus investments. However, Novy-Marx (2013) measures the factor as a ratio of gross profits to assets, where gross profits were revenues minus costs of goods sold. Novy-Marx argues that gross profits to assets as a profitability measure has higher predictive power over cross-sectional return variation than net cash flows.

The philosophy behind the profitability factor is similar to that of the value factor. In a value hedge, one finances the acquisition of high book-to-market (value) stocks by selling low book-to-market (growth) stocks. Similarly, in a profitability hedge, one buys productive assets (which should yield more, and thus create higher returns) with the finances from selling unproductive assets. The profitability factor is related to size and value, as high profitability strategies usually are growth strategies, which comes paired with big size and low value firm characteristics.

Secondly, Aharoni, Grundy, and Zeng (2013) analyze the prior research that Fama and French (2006) had done on an investment factor. The idea behind the investment factor lies in the dividend discount model. More specifically, the theory comes from the firm valuation formula by

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6 Miller and Modigliani (1961). 1 When investment occurs – either through retained earnings or

stock issues – the change in book value of equity increases. An increase in book value of equity in turn results in lower firm value, and thus lower price. A decrease in price implies a decrease in returns due to lower capital gains. Therefore, the firm valuation formula by Miller and Modigliani predicts a negative correlation between investments and returns.

However, Fama and French (2006) find the investment factor coefficient positive and not statistically significant. Aharoni et al. (2013) discover that the methodology of Fama and French (2006) caused the result. It measures investment on a per-share basis, instead of a firm basis (like the valuation formula does). Aharoni et al. (2013) test two proxies of the investment factor on a firm basis: growth in total assets and growth in book equity. They find growth in total assets to have the highest predictive power over cross-sectional returns.

Fama and French (2015) take the priorly mentioned research into account and propose an extension of their 3-factor model by adding the profitability factor as defined by Novy-Marx (2013) and the investment factor as formalized by Aharoni et al. (2013) to their model. Their paper tests different combinations of the five factors: market exposure, size, value, profitability, and investment. These combinations result in various three-, four-, and five-factor models. They apply a variation of sorts based on the factors. For example, a 5 × 5 size-value sort formed 25 portfolios, each representing a combination of a quintile of size with a quintile of value.

From their regressions follows that all models were incomplete explanations of expected returns. However, the absolute intercept did decrease when upgrading from the three-factor model to the five-factor model. This happened especially for sorts on size, profitability, and investment, implying that the five-factor model performs best for firms that have high investment and profitability tilts. Besides that, they find that the value factor seemed to be redundant, as the five-factor model does not outperform the four-five-factor model that drops the value five-factor. However, they could not conclude that the factor was also redundant outside of their U.S. sample.

From all their analyses, it becomes apparent that the model had one significant shortfall in explaining returns: it lacks predictive power in portfolios of small stocks with negative relationships to the profitability and investment factors. Those lethal portfolios thus comprise small stocks that have high investment despite having low profitability. Their conclusion follows that despite its downfalls, the 5-factor model outperforms the 3-factor model in estimating cross-sectional variance in returns on the U.S. stock market.

1 𝑉(𝑡) = ∑ 𝐸(𝑌(𝑡+𝜏))−𝐸(∆𝐵(𝑡+𝜏))

(1+𝜌)𝜏

𝜏=1 . Where 𝑉(𝑡) is the value of a firm at the end of time 𝑡, 𝑌(𝑡 + 𝜏) is

income after interest and taxes at the end of time 𝑡 + 𝜏, ∆𝐵(𝑡 + 𝜏) is the change in book value of equity between 𝑡 and 𝑡 + 1, and 𝜌 is the discount factor.

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7

2.4 Returns in R&D-intensive sectors

As briefly covered in the introduction, academic literature generally concludes that R&D-investment and stock returns are positively related. Lev and Sougiannis (1996) research R&D expensing under GAAP mandates. They find that there is an intertemporal relationship between R&D capital and subsequent returns of stocks. R&D capital consists of capitalized investment expenses and is, in turn, a proxy of R&D-investment. They conclude that the result may stem from two reasons. The first being that the underreaction of the market to R&D-related information leads to mispriced stocks. The second hypothesis is that R&D-investment comes paired with increased priced risk, which would show up in a complete factor model of returns.

Penman and Zhang (2002) research the first hypothesis by analyzing the effect of R&D-investment in combination with conservative accounting on stock returns. They find a change in investment level in a conservative accounting environment is negatively related to current earnings. Consecutively, these current earnings are used to forecast future earnings, and therefore determine the value that drives returns.

Chambers et al. (2002) synthesize these results as it investigates the two hypotheses using extensive data analyses. Firstly, they establish that stock returns for R&D-intensive firms are indeed higher than for non-R&D-intensive firms in their sample. Secondly, they investigate the reason why these returns are higher. They find that returns due to changes in R&D-investment are most likely under the mispricing hypothesis. Additionally, Chambers et al. (2002) use the three-factor model by Fama and French (1992) as a control and find that returns due to the level of R&D-investment are most likely a result of the risk hypothesis. They substantiate this result by proving that, on the one hand, R&D-intensive stocks outperform non-R&D-intensive stocks in the long run and, on the other hand, there is an undiversifiable excess variability in R&D-intensive portfolios. Nevertheless, when estimating the three-factor model’s performance in their R&D-intensive sample, they find the model to be an incomplete measure.

2.5 Hypotheses

To tackle the research question of this thesis, two hypotheses are proposed, based on the empirical analysis of the three- and five-factor models above. Based on the findings by Fama and French (2015), the first alternative hypothesis states that the five-factor model outperforms the three-factor model in explaining cross-sectional stock returns. The analysis tests this hypothesis by comparing the alphas of the time-series regressions using either the three- or five-factor models. The alphas represent the estimated unexplained returns of the model. The comparison of alphas is executed using the joined test on alphas by Gibbons, Ross, and Shanken (1989).

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8 𝐻0: The unexplained returns of the three- and the five-factor model are equal.

𝐻1: The unexplained returns of the three-factor model are greater than those of the five-factor

model.

The second and third alternative hypotheses aim to test the linear relationship between risk premia allocated to assets and higher exposure to their individual risk factors. These hypotheses are tested by analyzing the risk premia forthcoming from cross-sectional regressions using the Fama and MacBeth (1973) methodology.

𝐻0: The risk premia associated with exposure to the factors of the three-factor model are

insignificant.

𝐻1: The risk premia associated with exposure to the factors of the three-factor model are

significant.

𝐻0: The risk premia associated with exposure to the factors of the five-factor model are

insignificant.

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9 3. Methodology

Chapter 3 firstly describes the process of sample selection and data gathering. Secondly, it explains the method of and variable, factor, and portfolio construction. Additionally, the sample descriptive statistics are put forth and interpreted. It then gives a detailed description of the times-series regression method and the subsequent GRS-test on the joined alphas. Lastly, it illustrates the two-stage Fama-MacBeth regression method and the reasoning and theory behind the choice of applying Newey-West standard errors to this method.

3.1 Sample selection

The sample used in the analyses consists of North American listed companies. Using North American companies eases the comparison between the R&D-intensive sample used in this analysis and the sample used by Fama and French (1993, 2015), as both papers used North American returns. This puts the focus on R&D-intensity, rather than geographic location. The period chosen for the analysis is from July 1990 to December 2019. The starting date matches the sample used in Fama and French (2017), and data restrictions apply after December 2019.

The first part of the dataset used for the analyses were stock prices, used to calculate returns. For this, the CRSP database on the monthly stock prices of all North American firms was used. From the same database, data on firm SIC codes and shares outstanding was extracted. The CRSP monthly stock price dataset includes all stocks listed on NYSE, AMEX, and NASDAQ, concurrent with the sample that Fama and French (1993, 2015) used. Only firms with at least 12 consecutive observations were kept in the sample. The next step was to establish which of the firms were operating in sectors deemed “R&D-intensive”. Previous research suggests sampling by SIC (standard industry code) of industries that are R&D-intensive by nature. Table 1 provides an overview of used or suggested SIC codes for R&D-intensive sectors in previous academic literature. Table 2 provides the industry names allocated to the SIC codes and the number of occurrences of the in the reviewed literature of table 1.

Table 1: Study names with their respective used or suggested R&D-intensive SIC codes

Name of study SIC code

Bernstein & Mamuneas (2006) 28, 35, 36, 37

Chan, Lakonishok, & Sougiannis (2001) 283, 357, 36, 37, 38, 48, 737 Clem, Cowan, & Jeffrey (2004) 283, 357, 361-367, 37, 382, 737,

Kile & Phillips (2009) 283, 357, 366, 367, 382, 384, 481, 482, 489, 737, 873 Lev, Sarath, & Sougiannis (2005) 283, 357, 36, 37, 38, 48, 737

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10 Table 2: SIC codes with industry name and prevalence in studied literature

SIC code Industry name Count

28 Chemicals and pharmaceutics 2

283 Drugs and pharmaceuticals 4

35 Machinery and computer hardware 2

357 Computers and office equipment 4

36 Electrical and electronics 4

361-367 Electrical and electronics minus miscellaneous 1

366 Communication equipment 1

367 Electronic components and accessories 1

37 Transportation vehicles 4

38 Scientific instruments 3

382 Laboratory, optic, measure, control instruments 2 384 Surgical, medical, dental instruments 1

48 Communications 2

481 Telephone communications 1

482 Miscellaneous communication services 1

483 Communication services, NEC 1

737 Computer programming, software, and services 4 873 Research, development, testing services 1

Based on the counts of SIC codes shown in table 2, the SIC codes that were most prominent were left in the sample. That means, that when a SIC code (which is a 4-digit number) has both its 2-digit category and a 3-2-digit subcategory mentioned, the (sub)category that was used in more papers is selected. Despite being used only once, the sample included SIC code 873 as well as it is an R&D-specific sector. Conclusively, the final sample of SIC codes encompassed 283, 357, 36, 37, 38, 48, 737, and 873. All firms which did not operate in any of these sectors were dropped from the dataset.

The second part of the dataset involved annual firm accounting data, which was needed to construct portfolios sorted on size and book-to-market equity. Using the Compustat database on firm characteristics, data on stockholders’ equity, deferred taxes and investment tax, and preferred stock were extracted. As North American companies listed on NYSE, AMEX and NASDAQ also include Canadian companies, some of these characteristics were given in Canadian Dollars. We applied the exchange rate from CAD to USD to these characteristics. The applied exchange rate was derived from Federal Reserve data from July 1990 up to and including January 2019, and

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11 Bank of Canada data for February 2019 up to and including December 2019. The characteristics were merged with the dataset on prices using a linking table containing the company identifiers permco of CRSP and GVKEY of Compustat.

The third part of the dataset consisted of data on the factors and risk-free rate. For this, the Fama/French North American 5 Factors monthly dataset was used, as it is available on Ken French’s website. Data on North American factors and risk-free rate are available from July 1990 onwards and are updated regularly. Using the timeframe of this analysis, data up to December 2019 was used. This data was then merged to the master dataset using time as the linking variable. The construction of these factors is explained in section 3.3.

The last part of the dataset were NYSE quintile breakpoints on size and book-to-market equity data. This data was needed to form portfolios on size and value. Data on every fifth percentile of size and book-to-market equity of all listed NYSE firms at each time 𝑡 were extracted from Ken French’s website. Size percentile data is calculated monthly, available from December 1925 onwards, and is updated regularly. Book-to-market equity data is calculated yearly, available from 1926 onwards, and is also updated regularly. From both datasets, data for July 1990 until December 2019 was used. Specifically, the data on the 20th, 40th, 60th, and 80th percentiles. This data was merged with the master dataset using the linking variable time.

3.2 Variables

Firstly, monthly stock return (𝑟𝑖,𝑡) was calculated by dividing the difference between the

price in time 𝑡 and the price in time 𝑡 − 1 by the price of time 𝑡 − 1.2 Extremely high returns were

generated in this process, due to stock splits. In order to prevent bias in the sample, upside returns were nominally winsorized to 200%. Trimming was not a viable option, as it would create gaps in the time-series of the panel data. It is not uncommon for stocks to reach high monthly returns, such as 200%, especially shortly after being listed. The threshold of 200% was chosen by randomly sampling high returns and going though financial news to find the origin of the high return. It was found that all sampled high returns above 200% were the result of stock splits.

Secondly, a market capitalization (𝑀𝐸𝑖,𝑡) variable was created by multiplying the stock

price of firm 𝑖 in month 𝑡 with the shares outstanding of firm 𝑖 in month 𝑡. This variable was adjusted to be expressed in millions to match the NYSE quintile breakpoints from Ken French’s

2The return variable was transformed into a percentage by multiplying by 100 to match the format of the

factors and risk-free rate of the Fama/French North American 5 Factors database. Furthermore, CRSP uses month closing prices as price data. However, when this data is not available, it uses the end-of-month bid-ask average. When the bid-ask average is used, the price is displayed as a negative price. Therefore, a new price variable was used to calculate returns, defined as the absolute value of the CRSP price variable

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12 website. The variable serves as a proxy of firm size and is used to sort portfolios on size, explained in section 3.4.

Thirdly, a book-to-market equity (𝐵 𝑀⁄ 𝑖,𝑡) variable was constructed following Fama and French (2015). Book equity is defined as “the book value of stockholders’ equity, plus deferred taxes and tax credit, minus the book value of preferred stock” (French, n.d.). Market equity is the market capitalization constructed before. Book-to-market equity is calculated in June of every year, as portfolios are formed in June of every year, and is calculated as book equity in December of the previous year divided by market equity in December of the previous year. The book-to-market equity ratio is used to sort portfolios on value, explained in section 3.4.

3.3 Factors

On Ken French’s website it is explained how the market, size, B/M, profitability, and investment factors were constructed.3 Factor construction formulas are given in table 3. The process of factor construction is repeated every month.

The market factor (𝑟𝑀 − 𝑟𝑓) is calculated as the value-weighted return on the market portfolio minus the one-month Treasury bill rate. All NYSE, AMEX, and NASDAQ listed stocks are in this market portfolio, provided that they are available on CRSP or Compustat, are common stocks and thus carry share code 10 or 11, and have available data on size and book-to-market equity (B/M).

To construct the other four factors, a variety of portfolios are required to capture the difference in return between factor groups, for example, to capture the difference between small-cap stocks and large-small-cap stocks. Three different 2 × 3 sorts are applied to create a total of eighteen portfolios. The first sort is on size and B/M, the second sort is on size and profitability, and the third sort is on size and investment. For size, small firms are those falling into the 10th percentile of market capitalization in North America. Big firms are those above the 10th percentile. B/M is broken into three groups: value, neutral, and growth. For this the 30th and 70th percentile B/M ratio breakpoints are used. Profitability is also split into three groups: robust, neutral, and weak, using the 30th and 70th percentile of operating profitability (OP). Lastly, investment is again divided into three groups: conservative, neutral, and aggressive, using the 30th and 70th percentile of investments. A portfolio is then formed by combing characteristics of two groups. For example, firms with small size and value B/M are assigned to the SV (small value) portfolio.

The size factor (SMB) is constructed by subtracting the average return of the nine big portfolios from the average return of the nine small portfolios. Hence, SMB stands for small minus

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13 big. The book-to-market equity factor (HML) is constructed using the portfolios from the 2 × 3 size-B/M sort. It is calculated by subtracting the average return of the two growth, or low, B/M portfolios from the average return of the two value, or high, B/M portfolios. Due to the nature of this factor’s construction, its abbreviation HML can be interpreted as high minus low. The profitability factor (RMW) is constructed using portfolios forthcoming from the 2 × 3 sort on size and operating profitability. It is determined by subtracting the average return of the two weak portfolios from the two robust portfolios. Therefore, its abbreviation RMW can be elucidated as robust minus weak. The investment factor (CMA) is created from the portfolios of the 2 × 3 sort on size and investment. It is calculated by subtracting the average return on the two aggressive portfolios from the average return of the two conservative portfolios.

Table 3: factor construction functions Factor Function Size 𝑆𝑀𝐵𝐵 𝑀⁄ = 1 3(𝑆𝑉 + 𝑆𝑁 + 𝑆𝐺) − 1 3(𝐵𝑉 + 𝐵𝑁 + 𝐵𝐺) 𝑆𝑀𝐵𝑂𝑃=1 3(𝑆𝑅 + 𝑆𝑁 + 𝑆𝑊) − 1 3(𝐵𝑅 + 𝐵𝑁 + 𝐵𝑊) 𝑆𝑀𝐵𝐼𝑛𝑣 =1 3(𝑆𝐶 + 𝑆𝑁 + 𝑆𝐴) − 1 3(𝐵𝐶 + 𝐵𝑁 + 𝐵𝐴) 𝑆𝑀𝐵 =1 3(𝑆𝑀𝐵𝐵 𝑀⁄ + 𝑆𝑀𝐵𝑂𝑃+ 𝑆𝑀𝐵𝐼𝑛𝑣) B/M 𝐻𝑀𝐿 =1 2(𝑆𝑉 + 𝐵𝑉) − 1 2(𝑆𝐺 + 𝐵𝐺) Profitability 𝑅𝑀𝑊 =1 2(𝑆𝑅 + 𝐵𝑅) − 1 2(𝑆𝑊 − 𝐵𝑊) Investment 𝐶𝑀𝐴 =1 2(𝑆𝐶 + 𝐵𝐶) − 1 2(𝑆𝐴 + 𝐵𝐴)

Variables are value-weighted returns of portfolios based on combinations of two characteristics after sorting. Size characteristics: S small, B big. B/M characteristics: V value, N neutral, G growth. Profitability characteristics: R robust, N neutral, W weak. Investment characteristics: C conservative, N neutral, A aggressive. I.e., SV stands for small value, SN stands for small neutral, etcetera.

3.4 Portfolio construction

The time-series regressions and the accompanying GRS-test require excess value-weighted returns on test portfolios as the dependent variable. In this analysis, a 5 × 5 sort on size and B/M was chosen, as this is the portfolio the paper by Fama and French (2015) starts out with, thus providing comparability. The portfolio creation works in a similar way as the first step in factor construction. The breakpoints used for both size and book-to-market equity are the 20th, 40th,

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14 60th, and 80th percentiles of market capitalization and the book-to-market equity ratio, respectively. The 5 × 5 double sort results in 25 portfolios, each a different combination of a size group and a B/M group. The returns for each portfolio 𝑖 in month 𝑡 are the value-weighted returns of the portfolio. It is calculated by weighing the returns of each stock in portfolio 𝑖 in month 𝑡 by the share of market capitalization it contributes to the total market capitalization of portfolio 𝑖 in month 𝑡. Then the weighted returns of all stocks within that portfolio 𝑖 in month 𝑡 are summed. The risk-free rate in time 𝑡 was subsequently deducted from the value-weighted returns of portfolio 𝑖 in time 𝑡 to calculate the value-weighted excess return of portfolio 𝑖 in time 𝑡.

3.5 Descriptive statistics

Table 4 provides the summary statistics of the main variables of the sample. The 1.168% average of monthly excess return in the R&D-intensive sample is higher than the monthly market excess return of 0.683%. This finding is in line with previous literature suggesting that R&D-intensive companies outperform the market on average (Chambers et al., 2002; Lev & Sougiannis, 1996).

However, the median of sample excess returns is negative, meaning that more than 50 percent of all observations on returns were negative. An explanation for this phenomenon could be the inclusion of two significant market downturns in our sampling time. On the one hand, the burst of the dot-com bubble between 1997 and 2001 was included. The bubble burst especially hit tech firms, which are a big part of this R&D-intensive sample. On the other hand, the financial crisis of 2007 is included, which hit all firms, including the R&D-intensive sample. All factors have positive means, which is in line with Fama and French (2015).

Table 4: descriptive sample statistics

Variable 𝑟𝑖 𝑟𝑖− 𝑟𝑓 𝑟𝑀− 𝑟𝑓 SMB HML RMW CMA 𝑁 525,722 525,722 353 353 353 353 353 Mean 1.408 1.168 0.683 0.108 0.153 0.327 0.243 Median 0.000 -0.420 1.150 0.060 0.060 0.290 -0.020 Std. Dev. 22.345 22.349 4.210 2.754 3.260 2.395 2.616 Min -97.217 -97.227 -18.410 -13.870 -14.070 -15.450 -10.780 Max 200 200 11.560 16.700 17.580 13.940 14.390

The zero median of the return variable in table 4 seems irregular at first. However, the high amount of zero monthly returns for R&D-firms in the sample explains the result. Zero returns are most prominent during the years 1990-1999. Specifically, 2.05% of the sample comprises zero returns.

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15 The data suggests that this is the result of illiquidity in the R&D-intensive market.4 The data

findings corroborate with the article by Boone and Raman (2001). This article states that higher off-balance R&D (i.e., uncapitalized R&D-expense) leads to higher market illiquidity. Most zero return observations were found from 1990 to 1999 due to lower market accessibility.

Table 5 summarizes the average value-weighted excess returns of the 25 test portfolios used in the time-series regressions. The phenomenon that small-cap firms outperform large-cap firms is visible within each of the B/M columns. However, there are some irregularities, such as the medium size, second-highest B/M portfolio. The return effect of book-to-market equity is also visible. However, the relationship is less apparent than the size relationship. The effect seems especially strong for big firms, and less strong for firms of size group three or one. When one compares table 4 to table 5, the value-weighted excess portfolio returns generally seem higher than the mean excess sample return. This implies that losses of smaller firms within one portfolio were made up for by extremer gains of bigger firms within the same portfolio.

Table 5: average value-weighted excess portfolio returns

Low B/M 2 3 4 High B/M Small 4.270 4.401 3.508 3.663 4.979 2 2.749 2.736 2.407 2.136 3.393 3 2.044 1.897 2.944 3.548 1.354 4 1.693 1.551 2.170 1.519 3.398 Big 0.568 0.594 0.698 1.086 1.825

Average value-weighted returns of portfolios sorted on quintile NYSE breakpoints of size and B/M.

3.6 Time-series regressions

In order to test the first hypothesis, which regards the explanatory power of the three- and five-factor models, a time-series regression was run for every one of the 25 test portfolios for every model. The three-factor model is as proposed by Fama and French (1993), and the five-factor model is as proposed by Fama and French (1995). For both models, the dependent variable in this regression is the value-weighted excess portfolio return of portfolio 𝑖 at time 𝑡. For the three-factor model, the independent variables are the market, size, and value factors. For the five-factor model, they are the market, size, value, profitability, and investment factors at time 𝑡.

4Liquidity is measured by the share turnover ratio (shares of stock 𝑖 traded in month 𝑡 / shares outstanding

of stock 𝑖 in month 𝑡). Liquidity in the whole R&D-intensive sample has a mean of 2.063 and a median of 1.090. Liquidity among the firm-month observations with zero returns has a mean of 0.871 and a median of 0.448. The liquidity of the latter is substantially lower than that of the former.

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16 The three-factor time-series regression model is mathematically described as:

𝑟𝑖,𝑡 − 𝑟𝑓,𝑡 = 𝑎𝑖 + 𝑏𝑖(𝑟𝑀,𝑡− 𝑟𝑓,𝑡) + 𝑠𝑖𝑆𝑀𝐵𝑡+ ℎ𝑖𝐻𝑀𝐿𝑡+ 𝑒𝑖,𝑡

The five-factor time-series regression model is mathematically described as:

𝑟𝑖,𝑡− 𝑟𝑓,𝑡 = 𝑎𝑖 + 𝑏𝑖(𝑟𝑀,𝑡− 𝑟𝑓,𝑡) + 𝑠𝑖𝑆𝑀𝐵𝑡+ ℎ𝑖𝐻𝑀𝐿𝑡+ 𝑟𝑖𝑅𝑀𝑊𝑡+ 𝑐𝑖𝐶𝑀𝐴𝑡+ 𝑒𝑖,𝑡

These regressions yield an intercept, 𝑎𝑖, which stands for the estimated returns of portfolio 𝑖 that could not be explained by exposure to the factors. The coefficients 𝑏𝑖, 𝑠𝑖, ℎ𝑖 and 𝑐𝑖 describe the exposure of portfolio 𝑖 to each of the respective factors. Error term 𝑒𝑖,𝑡 captures the difference between the estimated and actual returns of portfolio 𝑖 in time 𝑡.

3.7 GRS-test

We test whether the predicted alphas from the time-series regressions are jointly zero to examine each of the two models’ predictive power. Gibbons et al. (1989) find a test-statistic to assess portfolio efficiency: the GRS-test. It is designed so that high predicted alphas of a model lead to a high GRS-test statistic.5

The test-statistic put forth by Gibbons et al. is described as follows: 𝑓𝐺𝑅𝑆 = (𝑇 − 𝑁 − 𝑘

𝑁 )

1 1 + 𝜇𝑓′Σ𝑓−1𝜇𝑓

𝛼̂′Σ̂−1𝛼̂ ~ 𝐹(𝑁, 𝑇 − 𝑁 − 𝑘)

The test assumes that error terms 𝑒𝑖,𝑡 are normally distributed and are independent and identically distributed (iid). The formula can be separated into three parts. In the first part of the formula, 𝑇 is the number of periods in the data, 𝑁 is the number of portfolios used, and 𝑘 is the number of factors in the model. In the second part of the formula, 𝜇𝑓′ is the transpose of a 1 × 𝑘 vector with the mean factor returns, Σ𝑓 is the 𝑘 × 𝑘 covariance matrix of the factors and 𝜇𝑓 is the normal 1 × 𝑘 vector with mean factor returns. In the last part of the formula, 𝛼̂′ is the transpose of an 𝑁 × 1 vector of

the 𝑁 estimated alphas, Σ̂ is the 𝑁 × 𝑁 covariance matrix of the residuals, and 𝛼̂ is the normal 𝑁 × 1 vector of the 𝑁 estimated alphas. The GRS test-statistic follows an F-distribution with 𝑁 degrees of freedom in the nominator and 𝑇 − 𝑁 − 𝑘 degrees of freedom in the denominator.

3.8 Fama-MacBeth regressions

To test the significance of the risk premia associated with the factors from the three- and five-factor models, cross-sectional regressions are run using the methodology by Fama and

5 The test requires that the amount of assets or portfolios does not exceed the number of periods. Therefore,

we use portfolios instead of individual assets in the time-series methodology. In this analysis there are 25 portfolios and 336 monthly periods.

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17 MacBeth (1973). The procedure comprises two stages of regressions. The first stage of regressions is a time-series regression for each asset 𝑖, which is similar to the time-series regression described in section 3.6. However, value-weighted excess portfolio returns were used as the dependent variable in the time-series regressions used to calculate the GRS-statistic, whereas for the Fama-MacBeth regressions, excess returns of individual assets are used as the dependent variable. Thus, the dependent variable for both the three- and five-factor model in the first-stage regression is the excess return of asset 𝑖 at time 𝑡. The independent variables of the three-factor model are the market, size, and value factors at time 𝑡. The five-factor model’s independent variables are the market, size, value, profitability, and investment factors at time 𝑡. This regression yields betas for every factor 𝑘, for every asset 𝑖, used in the second stage.

The first-stage three-factor model is mathematically described as:

𝑟𝑖,𝑡− 𝑟𝑓,𝑡 = 𝛽𝑎,𝑖+ 𝛽𝑏,𝑖(𝑟𝑀,𝑡− 𝑟𝑓,𝑡) + 𝛽𝑠,𝑖𝑆𝑀𝐵𝑡+ 𝛽ℎ,𝑖𝐻𝑀𝐿𝑡+ 𝑒𝑖,𝑡

The first-stage five-factor model is mathematically described as:

𝑟𝑖,𝑡 − 𝑟𝑓,𝑡 = 𝛽𝑎,𝑖 + 𝛽𝑏,𝑖(𝑟𝑀,𝑡− 𝑟𝑓,𝑡) + 𝛽𝑠,𝑖𝑆𝑀𝐵𝑡+ 𝛽ℎ,𝑖𝐻𝑀𝐿𝑡+ 𝛽𝑟,𝑖𝑅𝑀𝑊𝑡+ 𝛽𝑐,𝑖𝐶𝑀𝐴𝑡+ 𝑒𝑖,𝑡 The second stage involves cross-sectional regressions for each time 𝑡. The dependent variable in the cross-sectional regressions for both the three- and five-factor models is again the monthly excess return of asset 𝑖 at time 𝑡. The independent variables of the three-factor model regressions are the factor betas 𝛽̂𝑏,𝑖, 𝛽̂𝑠,𝑖 and 𝛽̂ℎ,𝑖 of each asset 𝑖 (which are consistent over time 𝑡) retrieved from the first-stage regressions. The independent variables of the five-factor model regressions are 𝛽̂𝑏,𝑖, 𝛽̂𝑠,𝑖, 𝛽̂ℎ,𝑖, 𝛽̂𝑟,𝑖 and 𝛽̂𝑐,𝑖. This regression yields gammas for every factor 𝑘, for every time 𝑡.

The second-stage three-factor model is mathematically described as: 𝑟𝑖,𝑡− 𝑟𝑓,𝑡 = 𝛾𝑎,𝑡 + 𝛾𝑏,𝑡𝛽̂𝑏,𝑖+ 𝛾𝑠,𝑡𝛽̂𝑠,𝑖 + 𝛾ℎ,𝑡𝛽̂ℎ,𝑖+ 𝜀𝑖,𝑡 The second-stage five-factor model is mathematically described as:

𝑟𝑖,𝑡− 𝑟𝑓,𝑡 = 𝛾𝑎,𝑡+ 𝛾𝑏,𝑡𝛽̂𝑏,𝑖+ 𝛾𝑠,𝑡𝛽̂𝑠,𝑖+ 𝛾𝑎,𝑡𝛽̂ℎ,𝑖+ 𝛾𝑟,𝑡𝛽̂𝑟,𝑖+ 𝛾𝑐,𝑡𝛽̂𝑐,𝑖+ 𝜀𝑖,𝑡

The risk premium of factor 𝑖 is then described by the average of the 𝑡 amounts of 𝛾̂𝑖, which is calculated with the formula 𝛾̂̅𝑖 = ∑

𝛾̂𝑖,𝑡

𝑇 𝑇 𝑡=1 .

3.9 Newey-West standard errors

In the risk-premium analysis we are dealing with panel data, which can bring along several issues. The most common issue in financial datasets is a correlation between the variables of interest, both cross-sectionally and serially (Gow, Ormazabal, & Taylor, 2010). This results in the

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18 violation of the assumption of independence of regression errors, which is problematic when using standard errors in test statistics, as they depend on this assumption. The idea behind the methodology by Fama and MacBeth (1973) is that estimating 𝑡 cross-sectional regressions in the second stage addresses the cross-sectional correlation of error terms. However, this leaves serial correlation (or time-series correlation) to affect the standard errors. A common approach in financial literature is to reduce the impact of this problem by applying Newey and West (1987) standard errors in the second stage.

Literature shows mixed results of the effectiveness of a Fama-MacBeth approach with Newey-West standard errors. Richardson, Sloan, Soliman, and Tuna (2006) argue that this estimating method generally provides moderate estimates of standard errors, which would address overestimating statistical significance associated with correlation in standard errors. However, Gow et al. (2010) find that a combination of Fama-MacBeth regressions with Newey-West standard errors does not consistently provide robust standard errors when both cross-sectional and time-series correlation is present in large samples. Due to the limited amount of econometric testing on the combination of Fama-MacBeth regressions using Newey-West standard errors, the risk-premium analysis relies on the theoretical substantiation of both Fama and MacBeth (1973) and Newey and West (1987) and applies the combined methodology.

To address the time-series correlation, the procedure by Newey and West (1987) applies an adjustment to the regular standard errors. The regular standard errors are calculated by taking the square-root of the formula 𝑠𝑒2(𝛾̂̅𝑖) =

1 𝑇∑ 𝛾 ̂𝑖,𝑡−𝛾̂̅𝑖 𝑇−1 𝑇

𝑡=1 . The Newey-West adjustment is applied by

the multiplication of the standard error with √𝑁𝑊, where 𝑁𝑊 = 1 + ∑𝑛𝑖=1(1 − 𝑖 𝑛⁄ + 1)𝜌𝑖. In

this formula, 𝑖 is the lag, 𝑛 is the total number of lags for which autocorrelation is expected to be present, and 𝜌𝑖 is the autocorrelation at lag 𝑖.

There are developed methods of automatic lag selection for one-stage regressions using Newey-West standard errors, such as Newey and West (1994) developed themselves. However, these automatic selection methods are generally not applied in a methodology where the Newey-West standard errors are combined with two-stage Fama-MacBeth regressions. In a combinative methodology, arbitrary lags are used. For example, Core, Guay, and Rusticus (2006) use a lag of one, whereas three to eleven lags depending on the overlap in test periods are used in the case of Doyle, Lundholm, and Soliman (2003). Gow et al. (2010) used different lags in their analysis of the Fama-MacBeth-Newey-West methodology and found that lag of one to provide the least biased results. Therefore, a lag of one was used when calculating the Newey-West standard errors of the Fama-MacBeth regressions in this analysis.

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19 4. Results

Chapter 4 presents the results of the time-series regressions and Fama-MacBeth regressions for both the three- and five-factor models. Additionally, GRS-test outcomes are displayed and interpreted.

4.1 Time-series regressions

The right panels of table 6 provide the regression coefficients of the three-factor model following the time-series regression methodology, alongside the R-squared of each portfolio and the amount of firm-month observations used per portfolio for each time-series regression. The alphas of the three-factor model time-series regressions are significant on a 5% level for all portfolios of size groups one to four. We see that the alphas of small-cap portfolios are especially high, numerating from 2.75 to 4.017 percentage points of nominal returns per month. However, we see that alphas are no longer significant for big size portfolios, except for the big, high B/M portfolio.

The regression coefficients of the market factor of all 25 portfolios are positive and significant. Furthermore, all 25 betas are close to one, implying that excess market return and excess value-weighted portfolio returns of R&D-intensive sectors move in the same direction and with the same magnitude.

We observe that the coefficient of the size factor is big and significant for small firms with low book-to-market equity and becomes smaller and less significant as size and B/M increases, yet the effect of size seems to decrease more heavily. A similar effect is seen in the significance of the value coefficients: the HML factor performs best for small firms with low book-to-market equity and performs worse when size and B/M increases. The lower explanatory power of the SMB and HML factors in big, high B/M firms is also visible in the portfolio’s adjusted R-squared. Adjusted R-squared is high for low B/M firms and deteriorates as book-to-market equity increases. The variance in adjusted R-squared is less apparent for different firm sizes. Comparing the results of the alpha coefficients with the results on adjusted R-squared provides interesting interpretations. Alphas stand for the estimated amount of returns that are not explained by factor exposure. Yet we see that for portfolios with insignificant alphas, the adjusted R-squared value is not necessarily close to 1. This implies big variation in the number of unexplained returns by the three-factor model over the time-series, resulting in higher standard errors (𝑒𝑖,𝑡) and lower alphas.

The left panels of table 6 provide the time-series regression coefficients of the five-factor model, in addition to the adjusted R-squared values and the number of firm-month observations per portfolio. The market, SMB, and HML coefficients of the five-factor model regressions exhibit

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Table 6: time-series regression coefficients three- and five-factor model

Five-factor model Three-factor model

Low B/M 2 3 4 High B/M Low B/M 2 3 4 High B/M

a a Small 3.646***(0.273) 3.871***(0.408) 2.963***(0.299) 3.080***(0.308) 3.870***(0.679) 3.450***(0.283) 3.664***(0.391) 2.750***(0.278) 2.920***(0.302) 4.017***(0.689) 2 2.070*** (0.197) 2.025*** (0.267) 1.480*** (0.245) 1.261*** (0.268) 2.705*** (0.651) 1.969*** (0.203) 1.960*** (0.254) 1.582*** (0.234) 1.246*** (0.247) 2.750** (0.689) 3 1.534***(0.176) 1.171***(0.210) 2.189***(0.775) 2.221***(0.687) 0.714***(0.232) 1.349***(0.178) 1.145***(0.209) 2.156***(0.711) 2.529***(0.780) 0.529**(0.226) 4 1.083***(0.158) 0.766***(0.205) 1.224***(0.381) 0.823**(0.328) 2.556***(0.852) 0.982***(0.160) 0.769***(0.209) 1.228***(0.397) 0.632**(0.312) 2.544***(0.846) Big -0.104 (0.172) 0.072 (0.279) 0.101 (0.261) 0.317 (0.341) 1.133** (0.453) 0.019 (0.146) -0.004 (0.208) 0.137 (0.253) 0.321 (0.300) 1.165** (0.474) b b Small 1.145*** (0.078) 0.962*** (0.099) 0.962*** (0.071) 0.948*** (0.082) 1.051*** (0.226) 1.177*** (0.075) 0.987*** (0.099) 1.026*** (0.071) 0.974*** (0.090) 0.967*** (0.195) 2 1.165*** (0.053) 1.080*** (0.070) 1.169*** (0.064) 1.193*** (0.070) 1.060*** (0.133) 1.176*** (0.052) 1.084*** (0.069) 1.111*** (0.061) 1.180*** (0.063) 1.001*** (0.131) 3 1.040*** (0.046) 1.063*** (0.051) 1.135*** (0.196) 1.574*** (0.167) 1.117*** (0.065) 1.109*** (0.043) 1.057*** (0.053) 1.131*** (0.136) 1.392*** (0.129) 1.175*** (0.060) 4 1.139*** (0.043) 1.141*** (0.060) 1.218*** (0.106) 1.236*** (0.097) 1.312*** (0.121) 1.166*** (0.042) 1.114*** (0.055) 1.200*** (0.084) 1.292*** (0.089) 1.303*** (0.125) Big 1.030*** (0.035) 0.940*** (0.075) 0.936*** (0.085) 1.09*** (0.088) 1.082*** (0.112) 0.974*** (0.034) 0.958*** (0.046) 0.898*** (0.079) 1.093*** (0.092) 1.059*** (0.110) s s Small 1.552*** (0.147) 1.630*** (0.216) 1.451*** (0.145) 1.564*** (0.202) 1.941*** (0.532) 1.812*** (0.167) 1.936*** (0.308) 1.638*** (0.185) 1.783*** (0.267) 1.951*** (0.452) 2 1.149*** (0.094) 1.268*** (0.180) 0.946*** (0.101) 0.959*** (0.095) 0.640* (0.382) 1.303*** (0.099) 1.378*** (0.237) 0.950*** (0.096) 1.031*** (0.091) 0.754** (0.355) 3 0.903*** (0.085) 0.785*** (0.112) 0.414* (0.223) 0.549 (0.380) 0.204* (0.114) 1.019*** (0.090) 0.851*** (0.120) 0.487** (0.195) 0.589* (0.331) 0.356*** (0.115) 4 0.550*** (0.076) 0.573*** (0.115) 0.552** (0.218) 0.383** (0.162) -0.124 (0.229) 0.649*** (0.073) 0.660*** (0.147) 0.605*** (0.217) 0.555*** (0.213) -0.066 (0.222) Big -0.164** (0.067) -0.098 (0.083) -0.375*** (0.130) -0.118 (0.177) -0.319 (0.260) -0.208*** (0.064) -0.014 (0.086) -0.314** (0.128) -0.136 (0.177) -0.301 (0.220) h h Small -1.212***(0.192) -1.100***(0.265) -0.670***(0.189) -0.827***(0.247) (0.569)0.125 -1.079***(0.144) -0.893***(0.212) -0.729***(0.152) -0.706***(0.198) (0.609)0.461 2 -1.087***(0.115) -0.780***(0.197) -0.465***(0.129) -0.307**(0.130) -1.056***(0.340) -0.974***(0.085) -0.685***(0.160) -0.237**(0.110) -0.187***(0.070) -0.717***(0.230) 3 -0.863***(0.088) -0.465***(0.118) (0.455)-0.314 -0.736**(0.301) (0.154)-0.032 -1.011***(0.077) -0.379***(0.110) (0.167)-0.228 (0.173)0.008 (0.097)-0.104 4 -0.903*** (0.084) -0.495*** (0.133) 0.186 (0.369) -0.289 (0.205) -0.254 (0.233) -0.906*** (0.070) -0.303*** (0.097) 0.307 (0.379) -0.333** (0.152) -0.157 (0.134) Big -0.701*** (0.090) -0.327** (0.147) -0.303* (0.167) 0.221 (0.178) -0.272 (0.371) -0.529*** (0.050) -0.311*** (0.111) -0.098 (0.110) 0.192 (0.134) -0.166 (0.312) 20

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Five-factor model Three-factor model

Low B/M 2 3 4 High B/M Low B/M 2 3 4 High B/M

r -Small -0.859*** (0.207) -1.011*** (0.321) -0.618*** (0.223) -0.722*** (0.241) -0.030 (0.494) 2 -0.509***(0.130) (0.235)-0.364 (0.170)-0.013 (0.186)-0.237 (0.446)-0.374 3 -0.387*** (0.119) -0.218 (0.145) -0.242 (0.426) -0.128 (0.336) -0.504*** (0.108) 4 -0.330***(0.103) -0.288*(0.166) (0.269)-0.175 -0.568***(0.215) (0.234)-0.191 Big 0.145* (0.082) -0.277** (0.125) -0.198 (0.187) 0.059 (0.220) -0.059 (0.311) c -Small 0.566** (0.263) 0.754** (0.379) 0.141 (0.257) 0.493** (0.261) 0.589 (0.740) 2 0.394**(0.170) (0.222)0.306 0.397**(0.188) (0.205)0.299 (0.453)0.730 3 (0.138)-0.103 (0.169)0.234 (0.454)0.244 1.330***(0.451) (0.181)0.076 4 (0.126)0.124 0.443**(0.187) (0.393)0.275 (0.236)0.148 (0.255)0.241 Big 0.238**(0.121) (0.292)0.136 (0.266)0.430 (0.236)-0.072 (0.406)0.206 Small 0.801 0.647 0.728 0.719 0.228 0.770 0.605 0.712 0.692 0.229 2 0.848 0.743 0.677 0.679 0.216 0.831 0.735 0.673 0.674 0.210 3 0.858 0.713 0.158 0.161 0.641 0.849 0.709 0.161 0.150 0.621 4 0.854 0.704 0.287 0.575 0.095 0.847 0.689 0.288 0.559 0.100 Big 0.756 0.596 0.399 0.400 0.218 0.750 0.588 0.387 0.403 0.221 Small 79206 40314 33930 37297 66869 79206 40314 33930 37297 66869 2 27972 13294 10076 7221 7929 27972 13294 10076 7221 7929 3 18031 9228 5544 3552 5568 18031 9228 5544 3552 5568 4 15732 7496 4536 2604 4416 15732 7496 4536 2604 4416 Big 18096 6816 3860 2352 2900 18096 6816 3860 2352 2900 𝐴𝑑𝑗. 𝑅 𝑁 𝐴𝑑𝑗. 𝑅 𝑁

The left (right) panel shows the coefficients of the five-factor model (three-factor model) time-series regressions on 25 size-B/M portfolios, with robust standard errors between brackets, as well as adjusted R-squared and number of observations per portfolio. Statistical significance indicated by stars, *** at 1% level, ** at 5% level, and * at 10% level.

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22 similar patterns as those of the three-factor model regressions. Again, all alphas are significant on a 5% significance level except for the big-cap stocks of B/M group one to four. The high alphas, especially those of small-cap portfolios, imply that the five implemented risk factors do not sufficiently explain the excess returns of R&D-intensive firms. Market betas are again close to one and significant for all portfolios.

In the five-factor regression model, the size factor again loses significance as size and book-to-market equity increases, where the size effect is most prominent. The size factor’s nominal coefficients are very similar to those of the three-factor outcomes, implying that the addition of the profitability and investment factors did not take away any explanatory power of the size factor. Coefficients of the HML factor are again negative and decrease in significance as B/M and size jointly increase. The profitability factor’s coefficients are negative, but only significant for small-cap stocks and low B/M stocks.

The overall predictive power of the profitability factor in R&D-intensive sectors seems minimal. The investment factor appears to perform even worse in R&D-intensive sectors, relative to the profitability factor. The profitability factor was significant on the 5% level for 10 out of 25 portfolios, the investment factor is only significant on the 5% level for 8 out of 25 portfolios. R-squared values of the five-factor model regressions are very similar to those of the three-factor model. This is no surprise as the new variables, profitability and investment, have low predictive power in R&D-intensive sample.

Table 6 contains the same panel for both models, showing firm-month observation per portfolio. They are identical, as the same portfolios and value-weighted returns were used as the dependent variable in both the three- and five-factor model regressions. It becomes clear from the panel that most companies in R&D-intensive sectors are small firms, falling within the 20th percentile of market capitalization of the NYSE. The trend is obvious: the higher the market capitalization percentile, the less firm-month observations are in the portfolio. Most R&D-intensive companies have low book-to-market equity, and firm-month observations generally decrease up to the 80th percentile, after that it increases again for the high B/M group. Firm size and B/M are thus both left-skewed, but portfolios are sorted proportionally on quintiles. This leads to unbalanced portfolio sizes. Working with value-weighted portfolio returns, as done in this analysis, enables us to compare the portfolio returns of unbalanced portfolios.

4.2 GRS-test

From table 7, we learn that the GRS-test easily rejects both the three- and five-factor model. However, the GRS-statistic of the five-factor model is lower than that of the three-factor model. A lower GRS-statistic implies a higher likelihood for the hypothesis that alphas are jointly zero,

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23 relative to the hypothesis that the alphas are not jointly zero. However, as both statistics are not significant at the 5% level, there is no evidence that the three- or five-factor models are complete models for estimating returns in R&D-intensive sectors. The average absolute alpha of the three-factor model is about 0.046 percent point lower than the alpha of the five-three-factor model, however, its adjusted R-squared is about 1 percentage point lower.

Even though the GRS-statistic is slightly lower for the five-factor model than the three-factor model, their p-values are equal. Therefore, there is no evidence supporting the first alternative hypothesis that the five-factor model outperforms the three-factor model in explaining stock returns in R&D-intensive sectors when sorting portfolios on size and book-to-market equity. Table 7: GRS statistics, average absolute alpha, adjusted R-squared

Model GRS P(GRS) |𝛼̂̅| 𝐴𝑑𝑗. 𝑅2

FF-3 11.674 0.000 1.673 0.538 FF-5 9.511 0.000 1.719 0.548

Table 7 shows the nominal GRS-statistic and its p-value, the average absolute alpha (intercept), and the average adjusted R-squared values for 25 portfolios sorted on NYSE quintiles of size and value.

4.3 Fama-MacBeth regressions

During the first stage of the Fama-MacBeth regressions, a time-series regression was run for every asset 𝑖, which yielded a beta for every risk factor 𝑘 included in the model. Table 8 shows the descriptive statistics of the first-stage betas for the three-factor model regressions. We find that market and size betas are somewhat higher than one on average. The average value beta is negative because most firms in our sample have low book-to-market, which implies negative exposure to the HML factor.

Table 8: descriptive statistics first-stage regressions (three-factor model) FF-3 𝛽̂𝑏,𝑖 𝛽̂𝑠,𝑖 𝛽̂ℎ,𝑖 𝑁 4677 4677 4677 Mean 1.141 1.172 -0.607 Median 1.111 1.062 -0.556 Std. Dev. 1.113 1.513 1.618 Min -7.162 -10.757 -17.111 Max 9.788 10.362 11.952

Table 8 shows the descriptive statistics of the coefficients for the first-stage three-factor model regression: ri,t – rf = βa,i + βb,i(rM,t – rf,t) + βs,iSMBt + βh,iHMLt + ei,t

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24 Table 9 provides the descriptive statistics of the estimated betas of the five-factor model first-stage regressions. The mean of both the market and size betas have decreased, as the profitability and investment betas have soaked up some of the variations in returns. The investment beta is small, therefore, exposure of R&D-intensive firms to the investment factor is low on average. The value beta is still negative, and higher than in the three-factor regressions.

Table 9: descriptive statistics first-stage regressions (five-factor model) FF-5 𝛽̂𝑏,𝑖 𝛽̂𝑠,𝑖 𝛽̂ℎ,𝑖 𝛽̂𝑟,𝑖 𝛽̂𝑐,𝑖 𝑁 4677 4677 4677 4677 4677 Mean 1.031 1.072 -0.443 -0.474 -0.139 Median 1.032 0.956 -0.401 -0.332 -0.010 Std. Dev. 1.353 1.790 2.446 3.080 3.110 Min -8.398 -20.474 -21.158 -30.638 -26.046 Max 13.025 14.119 17.955 22.652 29.103

Table 9 shows the descriptive statistics of the coefficients for the first-stage five-factor model regression: ri,t – rf = βa,i + βb,i(rM,t – rf,t) + βs,iSMBt + βh,iHMLt + βr,iRMWt + βc,iCMAt + ei,t

In the second stage of the Fama-MacBeth regressions, a cross-sectional regression is run for every month 𝑡, where the excess return of asset 𝑖 is regressed on the estimated betas from the first-stage regressions. From table 10 follows that the average amount of observations per monthly regression is 1489.297, which are the sets of asset betas. Furthermore, the adjusted R-squared is 5% for the three-factor regressions and 7.3% for the five-factor model regressions. This low result will be explained in further detail in the discussion of this analysis.

The gamma of the alpha coefficient is statistically significant coefficient at a 1% significance level for both models, as shown in table 11. This means that there is some – or more than one – risk factor, not included in the three- or five-factor model, that carries a significant risk premium. The risk premium of SMB is significant at the 10% level for the three-factor model. The coefficient of 0.264 means that if one increased its beta exposure to the SMB with 1, it would receive 0.264% higher monthly returns. For the five-factor model, none of the risk factor premia are significant. The profitability risk premium is negative, meaning that if one were to increase its exposure to the profitability factor by 1, returns would decrease with 0.219%. The investment risk premium is negative as well.

When a factor is an excess return, the risk premium should be equal to the population mean of the factor. Therefore, we test the estimated risk premia against their relevant factors. Table 12 shows the results of a t-test of the risk premium against its factor average. All risk premia are statistically significantly different from their factor at the 5% level, both in the three- and

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