Growth versus Value Stocks: Evidence for the US, the EU and the EMU

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Growth versus Value Stocks:

Evidence for the US, the EU and the EMU

Liga Miglane

Master’s Thesis, MSc BA Finance

Faculty of Economics and Business, University of Groningen

Supervisor:

Dr. Auke Plantinga

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Abstract

The financial literature has long debated whether value portfolios outperform growth portfolios. I attempt to prove that from 2004 to 2010 growth portfolios outperform value portfolios for time horizons longer than one year. I determine the economical outperformance of growth portfolios, but it is not significant. I also verify for the exposure of Fama–French factors to growth and value company returns. I find that factors such as size, book to market, beta, and market leverage have some explanatory power for growth and value company returns in the US, European Union, and European Monetary Union markets.

JEL Codes: C21, G11, G15

Keywords: growth portfolio, value portfolios, rebalancing, returns, cross-sectional analysis, factor analysis

Author: Liga Miglane Student number: 1946722

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Growth stocks are the stocks of companies with low book-to-market (B/M), cash-to-price, and earnings-to-price (E/P) ratios. In contrast, in value stocks these ratios are high (Lakonishok et al. (1994), Chan et al. (1991) and Bouwer and van der Put (1996)). The returns of growth and value stocks have been the topic of substantial research over the past two decades, most of which finds an outperformance for value stocks. However, despite the abundant theoretical and empirical evidence, investors still have a tendency to invest in growth stocks (Chan et al. (1991); Lakonishok et al. (1994)).

One rational explanation for the outperformance of value stocks is that it is due to the higher risk of value stocks (Fama and French (1992)). However, studying the US market, Lakonishok et al. (1994) cannot find a significant difference in the risk between growth and value stocks. Bouwer and van der Put (1996) say investors become too optimistic about growth stocks, since these stocks have done well in the past, and overprice them, while they are too pessimistic about value stocks. La Porta et al. (1997) examine this hypothesis and find that the superior return of value stocks is the result of errors in the expectations that investors have of future earnings. The authors find that the earnings announcement returns suggest that a significant portion of the return difference between value and growth stocks can be explained by earnings that are systematically more positive for value stocks. This conflicts with Fama and French’s risk-based explanation for the return disparity. Wouters and Plantinga (2004) find support for La Porta et al.’s (1997) expectational error hypothesis by distinguishing between stocks that switch between value and growth styles every year and stocks that have a fixed value or growth style. They also show that the difference in returns between value and growth stocks is frequently due to portfolio rebalancing.

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and Vishny (1990)). Block (1972) states that a portfolio’s time horizon is associated with risk, diversification, turnover, portfolio strategy, and so forth. Furthermore, he suggests that in a perfect world the time horizon should not be influenced by the investor’s and/or client’s desires to realize gains or losses. But this is not the case in the real world, where a portfolio’s time horizon is often shortened before the securities have a chance to fulfill their potential. Furthermore, Cella et al. (2010) show that stocks held by short-term investors experience more severe price drops and longer price reversals than those held by long-term investors, even after controlling for firm characteristics such as volatility, liquidity, and B/M. Last but now least, Gulen et al. (2008) find strong evidence that value companies are less flexible than growth companies in adjusting to declining economic conditions.

All these findings lead me to believe that time plays an important role in the investment decision making. Moreover, value and growth stocks have been a heavily debated topic for decades. Therefore, I propose the following two research questions.

 Do growth stock portfolios with time horizons longer than one year

significantly outperform value stock portfolios of similar time horizons and do portfolio rebalancing play a significant role?

 Does the exposure of Fama and French’s (1992) factors have a significant

explanatory power for growth and value company returns in the US, European Union (EU), and European Monetary Union (EMU) markets?

To answer these two research questions I examine stocks over seven years, from 2004 to 2010, which includes the recent credit crisis (starting in August 20071) and continues with the debit crisis in Europe (starting in late 2009). According to Gulen et al. (2008), value stocks are less flexible in a recession. Hence, I expect the outperformance of growth stock portfolios within the sample time frame. To find the answer to my first research question, I calculate market-weighted portfolio returns and test them for significance. To create the returns of portfolios with different time horizons, I estimate market-weighted weights, since this is the most common and advisable method (Elton et al. (2011)) in the finance literature. I then create portfolios with time horizons of up to seven years. Thus I study both long- and short-term

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investment horizons according to the definition of Droms and Straus (2003). As for determining a rebalancing effect on portfolio returns, I leave the portfolios unbalanced for each time horizon and later rebalance them every year according to the portfolios provided by MSCI. I predict that during worsening economic conditions, growth stock returns are higher in the short run and I expect value stock returns to be higher for long-term investments.

To answer my second research question, I run a least squares regression. I collect data from Datastream on stock returns, common equity, deferred taxes, total assets, earnings before interest and taxes, and price. I calculate the Fama–French (1992) factors the year before the companies are divided into growth and value portfolios to match the company returns (Fama and French (1992)). I study the US, the EU and the EMU markets. The US market is widely studied, but there is little evidence on EU and EMU value and growth company returns. This paper attempts to fill this gap.

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II. Literature Review

This section discusses the results of previous research on value and growth stocks. More specifically, it presents the main findings in the literature on the performance of growth and value stocks. This is followed by a review of the research on portfolio horizons and the importance of portfolio rebalancing.

Fama and French’s (1992) seminal paper investigates the joint roles of market beta, market equity, E/P, leverage, and book-to-market equity in the cross section of average returns on the New York Stock Exchange (NYSE), American Stock Exchange (AMEX), and NASDAQ stocks for the period 1963 to 1990. The authors could not support the hypothesis that average stock returns are positively related to market betas. They did find, however, that the average returns cannot be explained by betas and that a combination of market equity and book-to-market equity takes into account the roles of leverage and E/P in average stock returns. Furthermore, the authors state that market equity (ME) and book-to-market equity (BE/ME) provide a simple and powerful characterization of the cross section of average returns. These ratios are low for growth stocks, but high for value stocks. The authors show that companies with high ME and BE/ME are fundamentally riskier and have higher returns and therefore investors in such companies are compensated by higher returns.

Lakonishok et al. (1994) use contrarian models to determine why value stocks outperform growth stocks in the US market during 1968 to 1990. They state that the investment strategies for value stocks range from contrarian to “naïve” (trading with noise), thus producing higher returns. Lakonishok et al. (1994, p. 1542) argue that

These naive strategies might range from extrapolating past earnings growth too far into the future, to assuming a trend in stock prices, to overreacting to good and/or bad news, or to simply equating a good investment with a well-run company irrespective of price.

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future growth rates are known to be mean reverting. In other words, investors expect growth stocks to continue to grow faster than value stocks but are systematically disappointed.

Bouwer and van der Put (1996) support the hypothesis that value stocks outperform growth stocks. They research stocks from Germany, France, the Netherlands and the UK from 1982 to 1993 and construct five portfolios for the following variables: E/P, the ratio of cash flow to price, B/M, and dividend yields. They find that the hedged returns of value stock portfolios outperform those of growth stock portfolios. This difference is especially significant for the ratio of cash flow-to-price, which shows an outperformance of 20%. The authors explain this strong outperformance with Shefrin and Stateman’s (1995) argumentation, where, according to behavioral asset pricing theory, noise traders make cognitive errors that lead them to believe that the good stocks are the stocks of good companies, thus leading them to prefer the stocks of growth companies.

La Porta et al. (1997) specifically test the hypothesis that the superior returns of value stocks are due to investors making expectational errors. In particular, the past growth of value companies is extrapolated too far into the future. The authors study the NYSE, AMEX, and NASDAQ firms from 1971 to 1993. They find that higher returns of value strategies continue to last for four to five years and therefore investors can expect these strategies to yield long periods of positive earnings. They determine a difference in annual announcement returns of 25–30% between value and growth stocks in the first two to three years after portfolio formation and a difference of 15– 20% over the fourth and fifth years. They attribute these differences to investor desire to invest in companies with high profitability and superior management.

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negative and the earnings growth rate is low. The authors propose a behavioral finance explanation in that investors are unable to process the information properly.

A more recent study by Gulen et al. (2008) tests the hypothesis that value stocks are less flexible than growth stocks in adjusting to a declining economic situation. They use the Markov switching framework of Perez-Quiros and Timmermann (2000) to do so, as well as the ratio of fixed assets to total assets, the frequency of disinvestment, financial leverage, and operational leverage as proxies for flexibility. They also use a short-term interest rate and a default spread as proxies for worsening economic conditions. Their results strongly support their projected hypothesis, since the expected excess returns of value stocks are most strongly influenced by bad economic states and the expected excess returns of growth stocks are the least influenced in a recession. The sample period of their study is from January 1954 until December 2007. Therefore, they find support for the claim that value stocks are less flexible than growth stocks under bad economic conditions. Their evidence is supported by theoretical predictions from the emerging investment-based asset pricing literature.

Shleifer and Vishny (1990) point to the investment horizon as the main reason for mispricing, motivated by arbitrage pricing theory. They state arbitrage is cheaper for short-term assets than for long-term assets because the former cannot stay mispriced for long, whereas long-term assets can. Arbitrage for long-term assets is therefore pricier than for short-term assets since the former must be more mispriced in equilibrium for net returns to be equal. This leads to superior mispricing in long-term assets in equilibrium. Since managers and/or institutional investors fear being fired, they tend not to underprice company equity. Thus, they tend to avoid investments that raise the equity’s costs of arbitrage. Shleifer and Vishny (1990) conclude that long-term investments take longer to pay off and managers and institutional investors therefore tend to avoid them, choosing, instead, short-term investments with shorter payoff horizons.

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share price reactions to bad news in the market. The authors argue that short- and long-term investors have different goals and limits that have direct impact on their trading behavior during severe market drops. They find that stocks held by short-term investors experience more severe price drops and larger price reversals than those held by long-term investors, even after controlling for firm characteristics such as liquidity, volatility, size, and B/M. The authors note that short horizon-oriented investors amplify the effect of severe stock market drops.

Block (1972) discusses the difference between expected and actual holding periods. The expected holding period should be a deliberate decision to optimize performance but, instead, it is the result of circumstances. According to Block (1972), these circumstances are the life span of the accounts held by an organization, the people involved, the investment strategies selected by the company, and so forth. Therefore, most of the time the actual holding period is shortened by the customer’s desires to realize gains and/or losses, often before the security has had a chance to fulfill its role in the portfolio. Block (1972) discusses the expectational time horizon, that is, the maximum distance in the future investors feel they can accurately forecast fundamentals such as earnings and dividends. When investors feel confident about predicting the market direction, say, four years in the future, they estimate the discounted price. But Block (1972) points out that in good times the market is more eager to discount growth reasonably far into the future and to emphasize returns rather than risk. But when market uncertainty is high, the market demands a higher rate of return and shortens its discounting period, shortening investment periods. The author criticizes long-term investors because they tend to make long-term investment decisions based primarily on short-term information, no matter the phase of the market.

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years), and long term (seven years or more). Garmaise (2006) proposes five time horizons: one year or less, one to two years, three to four years, five to seven years, and seven years more. Given the lack of consensus, Grabel et al. (2009) interviewed 22 financial specialists from the US and Canada and analyzed their answers on this topic. All participants agreed that there is no one standardized definition for investment time horizons and the majority were using their own definitions or ones their company created. In the end, the authors define five time horizons: ultra-short term (nine months or less), short term (more than nine months to 2.5 years), short intermediate (more than 2.5 years to five years), long intermediate (more than five years to 10 years), and long term (more than 10 years). The authors conclude that these time horizons definitions can help better tailor asset allocation advice to a client’s time horizon.

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III. Data and Descriptive Statistics

This section presents information on the data collection for portfolio formation and the data for the regression analysis. To empirically analyze whether the growth portfolio significantly outperforms the value portfolio when similar time horizons and/or portfolio rebalancing are taken into account, I use MSCI’s composed value and growth indices1 as the foundation to estimate the portfolio returns. In 2003 MSCI began applying a two-dimensional framework to characterize growth and value companies. It subsequently began composing relevant indices, using different attributes such as the book-to-price ratio, the 12-month forward E/P, dividend yields, long-term forward earnings per share (EPS) growth rates, short-term forward EPS growth rates, current internal growth rates, long-term historical EPS growth trends, and long-term historical sales per share growth trends. From these variables it estimates z-scores for value and growth, which are used to determine the style of each security. MSCI explains that non-value stocks do not always mean growth stocks and vice versa in their two-dimensional framework and that some securities have the characteristics of both value and growth stocks while others do not qualify as either. It argues its methodology reflects a more accurate investor’s view on style definition and segmentation (MSCI Barra (2007)). The MSCI data set includes several companies in both the growth and value data sets since their characteristics are ambiguous. According to earlier research (e.g., Wouters and Plantinga (2004)), these securities are considered to be in the middle, or switching stocks. Since this research focuses on value and growth stocks, I exclude switching stocks from the data set to avoid double counting.

This research is one of several recent studies providing evidence on the US, EMU, and EU markets, the world’s biggest and most influential markets. Since the last decade the markets have gone through stable, ascending, and descending economic states, my sample period from 2004 to 2010 covers both economic activity and recession.

1_{The MSCI data contained herein is the property of the MSCI. MSCI, its affiliates, and any other party}

involved in, or related to, making or compiling any MSCI data, make no warranties with respect to any such data. The MSCI data contained herein is used under license and may not be further used,

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The limitation of this thesis, as mentioned, is that it excludes companies without clear growth or value characteristics. It also excludes companies that went bankrupt or which had no available data. The final numbers of companies from which the portfolio returns are composed in each year are shown in Table I.

I collect the annual return index of companies from December 2003 to December 2010 from Datastream to estimate their returns in US dollars. The entire data set is thus in one currency, facilitating the comparison of outcomes. After estimating company returns, I calculate the market-weighted portfolio returns, which are analyzed in Section IV. I estimate a total of 168 portfolio returns in all three markets, that is, 28 growth and 28 value portfolios each for the US, EU, and EMU. These portfolios are held for at least one year and up to seven years, thus covering both short- and long-term investments (Droms and Straus (2003)).

Table I presents descriptive statistics of the company returns in each market, including the mean, median, maximum, minimum, and standard deviation of the returns, as well as their distribution. It is common in the financial data for returns to not always be normally distributed, which is the case in this data set. The Jarque–Bera test shows non-normality in a couple of the years, as in 2004 for EMU companies.

In Table I, the mean indicates that 2008 was the least successful year for EU and EMU companies, with EU growth and value companies dropping by 143% and 383%, respectively, and EMU growth and value companies dropping by 150% and 370%, respectively. Companies in the US market experienced negative returns in 2008 as well, with drops of 211% and 310% for US growth and value companies, respectively. The highly negative returns in all three markets that year are attributable to credit crunch resulting from the US subprime crisis (Mizen (2008)). It is interesting to note that growth companies in all three markets achieve positive mean returns in 2010 while value companies are still struggling with negative mean returns. This may indicate that growth companies recover more quickly than value companies under economic pressure (Cella et al. (2010)).

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the growth companies in all three markets outperform the value companies. On the other hand, the difference between the standard deviations of growth and value companies is small in the EU and EMU markets, but more significant in the US market. Therefore I expect growth portfolios to outperform value portfolios.

From the descriptive statistics in Table I, I can conclude two things: (i) growth company returns are higher than value company returns in all three markets and (ii) recover faster since the downturn in 2008.

To determine which variables explain growth and value company returns, I use Fama and French’s (1992) factors to run the regressions. Their methodology includes estimating the logarithm of market equity, the logarithm of book value to market equity, the logarithm of total assets to market equity, and E/P. Therefore I collect data on shares outstanding from the MSCI database and data on total assets, common shares of equity, deferred taxes, earnings before interest and taxes, and the price of companies from Datastream for 2003 to 2009. To match the returns in year t, I collect the fundamentals for the year t - 1, as suggested by Fama and French (1994). The data on deferred taxes presented a complication because they were often missing since not all companies calculate them or reveal them in their balance sheets. Therefore I assumed that deferred taxes equaled zero for the companies with no such data.

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IV. Methodology

This section explains the methodology. It first describes the construction of the portfolios and then presents the regression analysis.

A. Methodology of Portfolio Formation

To test my first research question— does growth stock portfolios with time horizons of more than one year significantly outperform value stock portfolios of similar time horizons and does portfolio rebalancing plays a significant role—I calculate the portfolio returns. Therefore, I first collect the annual return index of companies from 2003 to 2010 and calculate the company returns (Ri):

(1) Ri= (RIi,t/RIi,t-1) -1

I reweight the market weights of each company stock:

(2) Wi,t = Wi,t /∑Wi,t

I then estimate the portfolio returns by multiplying Wi,t with Ri and summing the

acquired values. Therefore, the annual return of a portfolio (Rt) is calculated as

(3) Rt= ∑ (Ri,t* Wi,t)

The composition of companies in a non-rebalanced portfolio stays the same throughout the portfolio’s holding period. The composition of companies in a rebalanced portfolio changes every year, since companies can change their value or growth characteristics.

Next, I test the difference between growth and value portfolios returns, both non-rebalanced and rebalanced, with a Welch test. The hypotheses for this test are

H0: The mean of the growth portfolio equals the mean of the value portfolio

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The null hypothesis, H0, tests whether the mean of the growth portfolio return equals

the mean of the value portfolio return. If H0 is rejected, hypothesis H1 says that the

mean of the growth portfolio return is higher than the mean of the value portfolio return.

I also calculate the betas of the portfolios. First, before sorting the value and growth companies into their characteristic groups, I estimate the beta for each company as a slope calculated on 12 to 48 monthly returns (depending on data availability) during four years (Fama and French (1992)). Next, I estimate the portfolio betas by multiplying Wi,t with βi and summing the acquired values.

Therefore, the annual betas of the portfolios (βt) are calculated as

(4) βt = ∑ (β i,t* Wi,t)

As a last step, when the annual betas of portfolios are estimated, I calculate the average betas of the portfolios (β) with different time horizons for both rebalanced and non-rebalanced portfolios:

(5) β= (βt,0 + βt,1 +…+ βtn) /(tn)

Next I explain the regression analyses to check for Fama–French (1992) factors in market-weighted company returns from 2004 until 2010.

B. Regression Analysis

To analyze which control variables influence the returns of value and growth companies from 2004 to 2010, I run a linear regression for each year. I use Fama– French (1992) factors as the control variables. I check the exposure of Fama and French (1992) factors to growth and value company returns from 2004 to 2010 in the EU, EMU, and US. I run the following cross-sectional regressions of market-weighted company returns:

(6) Rgi –= βt + ln(ME(t-1)) + ln(BE/ME(t-1)) + ln(A/ME(t-1)) +

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(7) Rvi –= βt + ln(ME(t-1)) + ln(BE/ME(t-1)) + ln(A/ME(t-1)) +

+ E/P(t-1)+error term

I use equations (6) and (7) to analyze the value and growth company returns. I mainly use control variables based on Fama and French’s (1992) research to explain the returns. I run the regression a total of 112 times for all three markets, that is, 56 times for each market, respectively: 28 times for growth stocks and 28 times for value stocks. The main difficulty in running the regressions was the non-normal distribution. To solve this problem I followed Brooks (2008) and used dummy variables to exclude outliers. This is a good solution, though not the best, since it artificially improves the data set, but since I was unable to obtain better data from credit crunch to improve the significance of the data set, excluding outliers was the best second option.

In equations (6) and (7) I explain the company returns via beta, a size ratio, B/M, market leverage, and a price-to-earnings ratio. Although beta lost some of its fame as a result of empirical tests by Fama and French (1992), it still retains its theoretical role as a measure of risk (Shalit and Yitzhaki (2002)). Therefore, in equations (6) and (7), beta represents company systematic risk. According to Elton et al. (2011), a stock’s beta is a good tool for deciding whether to include it in a portfolio. Here it is calculated over 12 to 48 monthly returns (depending on data availability) during four years before the value and growth companies are sorted into their characteristic groups (Fama and French (1992)).

The proxy for size is the logarithm of market equity (ln(ME)), where ME is the result of multiplying shares outstanding by price. The data on shares outstanding are from the MSCI database and the prices represent the official closing prices for equities, obtained from Datastream. The size proxy partly explains the cross section of average returns presented by the market betas. The book to market equity ratio (BE/ME) as well as ME include information on the cross section of average stock returns. The ratio BE/ME is a division of book equity by market equity, where book equity is the sum of common share equity and deferred taxes (Fama and French (1992)).

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with a rational-pricing story for the role of ME and BE/ME in average returns. Further research by Fama and French (1995) proves that ME and BE/ME are interconnected with profitability, which means that in a rational market a short-term variation in profitability should have little effect on stock price or BE/ME. Therefore BE/ME should be associated with long-term differences in profitability, which also supports the findings of Fama and French (1995).

Leverage is an important financial tool in explaining returns. Fama and French (1992) calculate market leverage as the logarithm of the ratio of total assets to market equity and book leverage as the logarithm of the ratio of total assets to book equity. Higher market leverage is assumed for higher returns, and higher book leverage for lower returns (Bhandari (1988)). I exclude book leverage from the regression since it is perfectly collinear with the rest of the explanatory variables. Therefore I investigate how market leverage affects company returns.

According to Ball (1978) and Fama and French (1992), E/P is a good proxy for forecasting returns when earnings are positive. Basu (1983) proves that E/P explains the cross section of average returns on US stocks when size proxy and market risk are taken into account. Further, Balsu(1983) states that unidentified factors in returns can be attributed to E/P; hence, E/P is a catchall proxy for unidentified factors.

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V. Results

This section discusses the results of the research. It first discusses the returns of growth and value portfolios and their betas and then the results of the regression analysis.

A. Portfolio Returns and Their Betas

As discussed earlier, growth and value stocks have been the topic of significant research over the past two decades, most of which supports the outperformance of value stocks. Table II shows the returns of US growth and value portfolios, with different results from those of earlier studies (Fama and French (1992); Lakonishok et al. (1994); Bouwer and van der Put (1996)). I calculate the portfolio returns of the first through seventh years of holding (see the holding periods in Table II). In the US market, non-rebalanced value portfolio returns are higher only when the portfolio is composed in 2004 and held for the first five years. When the portfolio returns are positive, the growth portfolios outperform the value portfolios in nearly all the rest of the cases. For, example, holding US growth portfolios in 2006 achieves a return of 20.45% in the first year, but US value portfolios yield a return of only 14.46%, a difference of 6% in favor of growth portfolios. The difference is even greater if one rebalances the portfolios after the first year: The return in the second year rises to 31.67% for growth portfolios and only up to 13.33% for value portfolios, a difference of 18% in favor of growth portfolios. This finding may be attributed to worsening economic conditions and the credit crunch in 2009. According to Gulen et al. (2008), value companies are less flexible than growth companies in adjusting to declining economic conditions. Economics events and world market downturns may be the reason for growth portfolio outperformance. The economic outperformance of growth portfolios is cogent in almost all holding periods, but Welch’s significance test fails to prove its significance.

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Table II. US Growth and Value Company Portfolio Returns

The holding period is the number of years one holds a portfolio and this table shows the returns of portfolios for different holding periods. The entry year is the year one starts holding a portfolio; non-reb indicates that the company composition of a portfolio is the same throughout the holding period, reb indicates the portfolio composition is reevaluated every year

Entry year /holding period US growth 1st_Y ₂nd_Y ₃rd_Y ₄th_Y ₅th_Y ₆th_Y ₇th_Y 2004 non-reb 0.0969 0.0892 0.1216 0.1364 -0.3018 0.2576 0.0907 2004 reb 0.0969 0.2157 0.2045 0.3167 -0.2586 0.3195 0.2220 2005 non-reb 0.2157 0.1280 0.1682 -0.3274 0.2690 0,1047 2005 reb 0,2157 0,2045 0,3167 -0,2586 0,3195 0.2220 2006 non-reb 0.2045 0.1834 -0.3531 0.2893 0.1096 2006 reb 0.2045 0.3167 -0.2586 0.3195 0.2220 2007 non-reb 0.3167 -0.3630 0.3126 0.1218 2007 reb 0.3167 -0.2586 0.3195 0.2220 2008 non-reb -0.2586 0.2405 0.1106 2008 reb -0.2586 0.3195 0.2220 2009 non-reb 0.3195 0.1314 2009 reb 0.3195 0.2220 2010 non-reb 0.2220 2010 reb 0.2220 Entry year /holding period US value 1st_Y ₂nd_Y ₃rd_Y ₄th_Y ₅th_Y ₆th_Y ₇th_Y 2004 non-reb 0.1775 0.1329 0.1621 0.1364 -0.1928 -0.2573 0.0581 2004 reb 0.1775 0.1187 0.1446 0.1333 -0.1233 -0.1512 0.1100 2005 non-reb 0.1187 0.1601 0.1221 -0.2080 -0.2612 0.0563 2005 reb 0.1187 0.1446 0.1333 -0.1233 -0.1512 0.1100 2006 non-reb 0.1446 0.1163 -0.2089 -0.2704 0.0574 2006 reb 0.1446 0.1333 -0.1233 -0.1512 0.1100 2007 non-reb 0.1333 -0.1500 -0.2371 0.0786 2007 reb 0.1333 -0.1233 -0.1512 0.1100 2008 non-reb -0.1233 -0.1622 0.0991 2008 reb -0.1233 -0.1512 0.1100 2009 non-reb -0.1512 0.1194 2009 reb -0.1512 0.1100 2010 non-reb 0.1100 2010 reb 0.1100

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Table III. EU Growth and Value Company Portfolio Returns

The holding period is the number of years one holds a portfolio and this table shows the returns of portfolio for different holding periods. The entry year is the year one starts holding a portfolio; non-reb indicates that the company composition of a portfolio is the same throughout the holding period, reb indicates the portfolio composition is reevaluated every year.

Entry year/ holding period EU growth 1Y 2Y 3Y 4Y 5Y 6Y 7Y 2004 non-reb 0.1425 0.2264 0.1527 0.1194 -0.1328 -0.0279 0.1331 2004 reb 0.1425 0.2909 0.2601 0.2801 -0.0652 -0.0287 0.2678 2005 non-reb 0.2909 0.1977 0.1103 -0.1212 -0.0306 0.1013 2005 reb 0.2909 0.2601 0.2801 -0.0652 -0.0287 0.2678 2006 non-reb 0.2601 0.1888 -0.1464 -0.0641 0.1290 2006 reb 0.2601 0.2801 -0.0652 -0.0287 0.2678 2007 non-reb 0.2801 -0.1217 -0.0878 0.1428 2007 reb 0.2801 -0.0652 -0.0287 0.2678 2008 non-reb -0.0652 -0.0581 0.1480 2008 reb -0.0652 -0.0287 0.2678 2009 non-reb -0.0287 0.1921 2009 reb -0.0287 0.2678 2010 non-reb 0.2678 2010 reb 0.2678 Entry year/ holding period EU value 1Y 2Y 3Y 4Y 5Y 6Y 7Y 2004 non-reb 0.1303 0.2470 0.2545 0.1296 -0.2306 -0.1489 0.0359 2004 reb 0.1303 0.2387 0.1775 0.1093 -0.2113 -0.0456 0.0580 2005 non-reb 0.2387 0.2422 0.1199 -0.2400 -0.1379 0.0441 2005 reb 0.2387 0.1775 0.1093 -0.2113 -0.0456 0.0580 2006 non-reb 0.1775 0.1163 -0.2338 -0.1189 0.0300 2006 reb 0.1775 0.1093 -0.2113 -0.0456 0.0580 2007 non-reb 0.1093 -0.2370 -0.0952 0.0309 2007 reb 0.1093 -0.2113 -0.0456 0.0580 2008 non-reb -0.2113 -0.0668 0.0779 2008 reb -0.2113 -0.0456 0.0580 2009 non-reb -0.0456 0.0626 2009 reb -0.0456 0.0580 2010 non-reb 0.0580 2010 reb 0.0580

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growth portfolio returns increase remarkably. As expected, value portfolio returns decrease when the portfolio is rebalanced. Further, even though it is obvious that growth portfolios have higher returns within the scope of this research, Welch’s test fails to prove the significance of this outperformance for non-rebalanced and rebalanced growth portfolios.

The results of the EMU growth and value portfolio returns are shown in Table A1 (Appendix A). The EMU growth portfolios show outperformance in all holding periods but, just as for the US and EU markets, this outperformance is not significant.

The findings together make me refute my first research question that growth stock portfolios with time horizons more than one year significantly outperform value stock portfolios of a similar time horizon and that portfolio rebalancing plays a significant role. Therefore I cannot prove that growth portfolios held for more than one year outperform value portfolios, since the significance test fails to support this conclusion. Nor can I prove that rebalancing has a significant impact on portfolio returns. From an economic standpoint, portfolio rebalancing is important, since growth portfolio returns increase remarkably and value portfolio returns tend to decrease with rebalancing. However, the statistical test fails to underpin the significance of these findings.

In addition, I check for risk factors and calculate the betas for portfolios (see Appendix B). Of 56 (non-rebalanced and rebalanced) US growth portfolio betas, 33 are higher than the value portfolio betas. This reveals a slightly higher systematic risk for 33 US growth portfolios and 23 US value portfolios. The findings for the EMU and EU portfolio betas are presented in the table B1 and table B2 (see Appendix B) and show that the betas for value portfolios are higher than for growth portfolios (both rebalanced and non-rebalanced). This indicates that the value portfolios bear higher systematic risk than the growth portfolios for the EU and EMU markets. It is interesting that the betas for both value and growth rebalanced portfolios for all three markets increase every year. This indicates that the systematic risk for rebalanced portfolios has a tendency to increase for rebalanced portfolios.

B. Regression analysis

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the growth characteristics of companies every year, from 2004 to 2010. Jarque–Bera statistics confirm a normal distribution of the residuals. I try to improve the Jarque– Bera statistics by excluding outliers. The non-normality in 2005 and 2007 may be explained by market changes (Sheik). The R-squared and adjusted R-squared values indicate that the data has some explanation power. Durbin–Watson statistics show no serial correlation between variables in any of the seven regressions. I also test the linearity of the regressions with Ramsey’s RESET test, which affirms the linearity of models.

The US growth company returns seem to be more dependent on B/M and beta. Both B/M and beta are significant at both the 1% and 5% significance levels. Here B/M has a positive sign, indicating that the return increases when the value of B/M increases. Similar findings are presented by Stattman (1980) and Rosenberg et al. (1985) on US company returns, where beta switches signs over time. A positive relation between company returns and beta is also found by Black (1972) and Fama and MacBeth (1973), although a later study by Fama and French (1992) does not support it. Surprisingly, size does not explain US growth company returns very well; it is significant only in 2010, with a negative sign. Here E/P appears to have a flat relation with returns, since the coefficient is zero throughout the research period. Market leverage is insignificant for US growth, with a negative sign, contradicting Bhandari (1988), who finds a positive relation between leverage and return.

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Table IV. US Growth Company Returns

This table represents the results of regressions for US growth company returns in 2004 to 2010. The company compositions of the portfolios are reevaluated every year. Therefore this table presents the results of ordinary least squares (OLS) only for obvious growth companies. Here C is a constant; Beta’04 (where ’04 stands for the year 2004, ’05 for 2005, etc.) is systematic risk for 2004; Size’04 (where ’04 stands for the year 2004, ’05 for 2005, etc.) is a ratio for 2004 companies returns, calculated as the logarithm of market equity; BE/ME’04 (where ’04 stands for the year 2004, ’05 for 2005, etc.) is a B/M ratio for 2004 company returns, calculated as the logarithm of market equity divided by book equity; E/P’04 (where ’04 stands for the year 2004, ’05 for 2005, etc.) is E/P for 2004 company returns; LgA/M’04 (where ’04 stands for the year 2004, ’05 for 2005, etc.) is market leverage for 2004 company returns, calculated as the logarithm of total assets divided by market equity; and DUM1 is a dummy variable that represents all the outliers of the residuals in the regression.

Companies reevaluated in 2004 Companies reevaluated in 2005 Companies reevaluated in 2006 Companies reevaluated in 2007 Variable Coeff Prob. Variable Coeff Prob. Variable Coeff Prob. Variable Coeff Prob.

C 0.4868 0.0552 C 0.5816 0.0607 C 0.3645 0.1790 C 0.2765 0.3662

Beta'04 -0.1553 0.0000 Beta'05 -0.0326 0.2236 Beta'06 0.0672 0.0342 Beta'07 0.0093 0.7745 Size'04 -0.0047 0.7788 Size'05 0.0085 0.6764 Size'06 -0.0066 0.7170 Size'07 0.0169 0.3854 BE/ME'04 0.0985 0.0042 BE/ME'05 0.1596 0.0000 BE/ME'06 0.0187 0.5171 BE/ME'07 0.1152 0.0004 E/P'04 0.0000 0.9426 E/P'05 0.0000 0.0503 E/P'06 0.0000 0.5274 E/P'07 0.0000 0.2408 LgA/M'04 -0.0395 0.1134 LgA/M'05 0.0090 0.7492 LgA/M'06 0.0245 0.3399 LgA/M'07 -0.0005 0.9884

DUM1 0.9482 0.0001 DUM1 1.2327 0.0000 DUM1 1.3276 0.0000 DUM1 1.4303 0.0000

R2 0.3121 R2 0.4130 R2 0.1804 R2 0.3158

Adj. R2 _0.2843 _{Adj. R}2 _0.3865 _{Adj. R}2 _0.1596 _{Adj. R}2 _0.2870

F-stat. 1.1229 F-stat. 1.5544 F-stat. 8.7071 F-stat. 1.0992

Prob(F-stat.) 0.0000 Prob(F-stat.) 0.0000 Prob(F-stat.) 0.0000 Prob(F-stat.) 0.0000 Durbin–Watson 1.6739 Durbin–Watson 1.9714 Durbin–Watson 1.9884 Durbin–Watson 1.9730 Jarque–Bera 3.6181 Jarque–Bera 17.0912 Jarque–Bera 3.3154 Jarque–Bera 36.1407

Prob. 0.1638 Prob. 0.0002 Prob. 0.1906 Prob. 0.0000

Companies reevaluated in 2008 Companies reevaluated in 2009 Companies reevaluated in 2010

Variable Coeff Prob. Variable Coeff Prob. Variable Coeff Prob.

C 0.1316 0.5549 C 0.5023 0.2478 C 0.9402 0.0007

Beta'08 -0.1416 0.0000 Beta'09 0.0063 0.8997 Beta'10 0.1823 0.0000

Size'08 -0.0179 0.2217 Size'09 0.0094 0.7389 Size'10 -0.0640 0.0003

BE/ME'08 0.0185 0.3169 BE/ME'09 0.0658 0.1648 BE/ME'10 -0.0139 0.5939

E/P08 0.0000 0.2102 E/P'09 0.0000 0.1583 E/P'10 0.0000 0.1634

LgA/M'08 -0.0237 0.3423 LgA/M'09 0.0566 0.2348 LgA/M'10 -0.0926 0.0029

DUM1 3.1864 0.0000 DUM1 -1.2922 0.0021 DUM1 0.7390 0.0042

R2 0.6513 R2 0.1360 R2 0.3821

Adj. R2 _0.6384 _{Adj. R}2 _0.1096 _{Adj. R}2 _0.3585

F-stat. 5.0438 F-stat. 5.1494 F-stat. 1.6215

Prob(F-stat.) 0.0000 Prob(F-stat.) 0.0000 Prob(F-stat.) 0.0000

Durbin–Watson 2.2020 Durbin–Watson 2.2079 Durbin–Watson 1.7703

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Table V. US Value Company Returns

This table represents the results of regressions for US value company returns in 2004 to 2010. The company compositions of the portfolios are reevaluated every year. Therefore this table presents the results of OLS only for obvious value companies. Here C is a constant; Beta’04 (where ’04 stands for the year 2004, ’05 for 2005, etc.) is systematic risk for 2004; Size’04 (where ’04 stands for the year 2004, ’05 for 2005, etc.) is a ratio for 2004 companies returns, calculated as the logarithm of market equity; BE/ME’04 (where ’04 stands for the year 2004, ’05 for 2005, etc.) is a B/M ratio for 2004 company returns, calculated as the logarithm of market equity divided by book equity; E/P’04 (where ’04 stands for the year 2004, ’05 for 2005, etc.) is E/P for 2004 company returns; LgA/M’04 (where ’04 stands for the year 2004, ’05 for 2005, etc.) is market leverage for 2004 company returns, calculated as the logarithm of total assets divided by market equity; and DUM1 is a dummy variable that represents all the outliers of the residuals in the regression.

C 0.8710 0.0012 C 1.2181 0.0001 C -0.0050 0.9860 C 0.1363 0.6277

Beta'04 -0.1031 0.0000 Beta'05 -0.0330 0.2023 Beta'06 -0.0497 0.0254 Beta'07 0.0613 0.0139 Size'04 -0.0119 0.3620 Size'05 -0.0038 0.8093 Size'06 0.0069 0.6271 Size'07 0.0056 0.6793 BE/ME'04 0.0354 0.0142 BE/ME'05 0.1430 0.0000 BE/ME'06 -0.0137 0.6038 BE/ME'07 0.0795 0.0002 E/P'04 0.0000 0.3637 E/P'05 0.0000 0.8074 E/P'06 0.0000 0.4189 E/P'07 0.0000 0.0813 LgA/M'04 0.0192 0.1910 LgA/M'05 -0.0130 0.4452 LgA/M'06 0.0220 0.2036 LgA/M'07 -0.0531 0.0009

DUM1 0.5927 0.0004 DUM1 0.8292 0.0000 DUM1 0.6132 0.0003

R2 0.3690 R2 0.3347 R2 0.0472 R2 0.2530

F-stat. 1.2863 F-statistic 1.2139 F-stat. 2.0610 F-stat. 8.2552

Prob(F-stat.) 0.0000 Prob(F-stat.) 0.0000 Prob(F-stat.) 0.0716 Prob(F-stat.) 0.0000 Durbin–Watson 2.0461 Durbin–Watson 1.9409 Durbin–Watson 1.9562

Durbin–

Watson 1.9287 Jarque–Bera 6.8530 Jarque–Bera 5.7380 Jarque–Bera 5.9764 Jarque–Bera 3.2064

C 1.2885 0.0000 C 0.2957 0.1988 C 1.1454 0.0009

Beta'08 -0.0521 0.0481 Beta'09 -0.1932 0.0000 Beta'10 -0.0068 0.8131 Size'08 -0.0413 0.0027 Size'09 -0.0075 0.4589 Size'10 -0.0371 0.0126 BE/ME'08 0.1281 0.0000 BE/ME'09 0.0508 0.0031 BE/ME'10 0.0095 0.7152

E/P08 0.0000 0.0134 E/P'09 0.0000 0.8857 E/P'10 0.0000 0.3628

LgA/M'08 -0.0851 0.0000 LgA/M'09 -0.0461 0.0009 LgA/M'10 0.0165 0.4188

DUM1 0.5166 0.0002 DUM1 4.4952 0.0000

R2 0.2271 R2 0.4524 R2 0.7207

Adj. R2 _0.2099 _{Adj. R}2 _0.4291 _{Adj. R}2 _0.7127

Jarque–Bera 2.3410 Jarque–Bera 4.7333 Jarque–Bera 3.7504

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I can therefore say that beta is not positively related to company returns for the US market and support Fama and French’s (1992) findings. Market leverage is significant at the 1% significance level, but with a negative sign for growth companies. This finding indicates that market leverage captures some negative risks and partly supports Bhandari’s (1988) findings for the US market. Size is more significant in explaining US value company returns, but mostly with a negative sign. This finding shows that increases in market equity have a negative relation to company returns. The E/P for the US market, for both growth and value company returns, is almost never significant and has flat explanatory power.

The results for the EU and EMU markets are slightly different than for the US market. Table VI presents the results of EU growth company returns. According to the Jarque–Bera and Durbin–Watson tests, the residuals are normally distributed and there is no serial correlation, respectively. The R-squared value is relatively low but shows that the data still fit the model.

It is interesting that size is significant at the 1% and 5% significance levels. Therefore it plays a more important role in explaining EU company returns than US company returns. Size mostly has a negative sign. In addition, Bouwer et al. (1996) also find a significant negative effect for four European countries’ companies. This means, smaller European companies tend to do better in the following year than big ones. Market leverage is significant at the 1% and 5% significance levels and is mostly positive. This supports Bhandari’s (1988) findings, that market leverage positively explains company returns. Unlike US returns, beta has no significant explanatory power for EU growth company returns, but the sign is mostly positive, which would support the results of Black (1972) and Fama and MacBeth (1973). Here B/M as well as beta is not a significant explanatory variable for EU growth company returns, but it indicates a positive company relation with returns, similar to Stattman’s (1980) findings for the US market.

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Table VI. EU Growth Company Returns

This table represents the results of regressions for EU growth company returns in 2004 to 2010. The company compositions of the portfolios are reevaluated every year. Therefore this table presents the results of OLS only for obvious growth companies. Here C is a constant; Beta’04 (where ’04 stands for the year 2004, ’05 for 2005, etc.) is systematic risk for 2004; Size’04 (where ’04 stands for the year 2004, ’05 for 2005, etc.) is a ratio for 2004 companies returns, calculated as the logarithm of market equity; BE/ME’04 (where ’04 stands for the year 2004, ’05 for 2005, etc.) is a B/M ratio for 2004 company returns, calculated as the logarithm of market equity divided by book equity; E/P’04 (where ’04 stands for the year 2004, ’05 for 2005, etc.) is E/P for 2004 company returns; LgA/M’04 (where ’04 stands for the year 2004, ’05 for 2005, etc.) is market leverage for 2004 company returns, calculated as the logarithm of total assets divided by market equity; and DUM1 is a dummy variable that represents all the outliers of the residuals in the regression.

C 1.4895 0.0000 C 1.4181 0.0000 C 0.6789 0.0109 C 1.5221 0.0000

Beta'04 0.1007 0.2472 Beta'05 -0.0636 0.3281 Beta'06 0.0286 0.6037 Beta'07 0.0009 0.9845 Size'04 -0.0483 0.0045 Size'05 -0.0305 0.0437 Size'06 -0.0020 0.8831 Size'07 -0.0492 0.0008 BE/ME'04 0.0161 0.5481 BE/ME'05 0.0084 0.7085 BE/ME'06 -0.0090 0.6651 BE/ME'07 0.0196 0.3382 E/P'04 0.0000 0.4870 E/P'05 0.0000 0.5908 E/P'06 0.0000 0.8345 E/P'07 0.0000 0.0474 LgA/M'04 0.0174 0.5039 LgA/M'05 0.0553 0.0070 LgA/M'06 0.0720 0.0002 LgA/M'07 0.0008 0.9666

DUM1 2.2669 0.0000 DUM1 1.2017 0.0000 DUM1 1.1495 0.0000 DUM1 0.9262 0.0001

R2 0.3835 R2 0.4189 R2 0.3198 R2 0.3095

C -0.5903 0.1010 C 0.6374 0.0621 C 0.6029 0.0000

Beta'08 -0.0472 0.3354 Beta'09 -0.1399 0.0245 Beta'10 0.1258 0.0583

Size'08 0.0146 0.3753 Size'09 -0.0301 0.0423 Size'10 0.0194 0.7319

BE/ME'08 0.0106 0.6620 BE/ME'09 0.0099 0.6377 BE/ME'10 0.1057 0.0004

E/P08 0.0000 0.8184 E/P'09 0.0000 0.0294 E/P'10 0.0000 0.2505

LgA/M'08 -0.0306 0.1380 LgA/M'09 -0.0217 0.2018 LgA/M'10 -0.0636 0.0216

DUM1 0.7813 0.0000 DUM1 0.9522 0.0000 DUM1 1.7283 0.0000

R2 0.1910 R2 0.1757 R2 0.2588

Adj. R2 _0.1535 _{Adj. R}2 _0.1477 _{Adj. R}2 _0.2389

Jarque–Bera 3.9536 Jarque–Bera 3.2537 Jarque–Bera 5.9640

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Table VII. EU Value Company Returns.

This table represents the results of regressions for EU value company returns in 2004 to 2010. The company compositions of the portfolios are reevaluated every year. Therefore this table presents the results of OLS only for obvious value companies. Here C is a constant; Beta’04 (where ’04 stands for the year 2004, ’05 for 2005, etc.) is systematic risk for 2004; Size’04 (where ’04 stands for the year 2004, ’05 for 2005, etc.) is a ratio for 2004 companies returns, calculated as the logarithm of market equity; BE/ME’04 (where ’04 stands for the year 2004, ’05 for 2005, etc.) is a B/M ratio for 2004 company returns, calculated as the logarithm of market equity divided by book equity; E/P’04 (where ’04 stands for the year 2004, ’05 for 2005, etc.) is E/P for 2004 company returns; LgA/M’04 (where ’04 stands for the year 2004, ’05 for 2005, etc.) is market leverage for 2004 company returns, calculated as the logarithm of total assets divided by market equity; and DUM1 is a dummy variable that represents all the outliers of the residuals in the regression.

C 0.5782 0.0503 C 0.7835 0.0063 C 1.2447 0.0000 C 0.0795 0.7232

Beta'04 -0.1277 0.1070 Beta'05 -0.1061 0.1328 Beta'06 -0.0103 0.8638 Beta'07 0.0624 0.1231 Size'04 -0.0111 0.4796 Size'05 -0.0141 0.3152 Size'06 -0.0406 0.0026 Size'07 0.0144 0.1616 BE/ME'04 0.0380 0.1653 BE/ME'05 0.0173 0.4840 BE/ME'06 -0.0461 0.0584 BE/ME'07 0.0657 0.0002 E/P'04 0.0000 0.1395 E/P'05 0.0000 0.8884 E/P'06 0.0000 0.4619 E/P'07 0.0000 0.1039 LgA/M'04 -0.0096 0.6317 LgA/M'05 0.0199 0.2751 LgA/M'06 0.0810 0.0000 LgA/M'07 -0.0257 0.0422

DUM1 1.9365 0.0000 DUM1 1.3979 0.0000 DUM1 1.6961 0.0000 DUM1 1.0239 0.0000

R2 0.3384 R2 0.4872 R2 0.4743 R2 0.4085

C -0.3606 0.1662 C 0.3034 0.3622 C 0.3007 0.3867

Beta'08 -0.0387 0.2455 Beta'09 -0.1085 0.0024 Beta'10 -0.0270 0.5468

Size'08 0.0099 0.3792 Size'09 -0.0019 0.8970 Size'10 0.0027 0.8557

BE/ME'08 0.0396 0.0110 BE/ME'09 0.0344 0.0353 BE/ME'10 0.0922 0.0001

E/P08 0.0000 0.7279 E/P'09 0.0000 0.0947 E/P'10 0.0000 0.9799

LgA/M'08 -0.0272 0.0139 LgA/M'09 -0.0027 0.8363 LgA/M'10 -0.0628 0.0003

DUM1 0.8526 0.0000

R2 0.2247 R2 0.1509 R2 0.1222

Adj. R2 _0.1974 _{Adj. R}2 _0.1199 _{Adj. R}2 _0.0944

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Size, on the other hand, is negatively related. This finding strengthens the conclusions of Bouwer et al. (1996), that smaller European companies perform better in the future. As for EU growth company returns, the beta for EU value company returns has no significant explanatory power, but it has a negative sign. This finding supports Fama and French’s (1992) finding that beta is not positively related to company returns. It differentiates between EU growth and value company returns, where the former is positively related to beta and the latter is negatively related. Market leverage is not significant and has a negative sign. This also contradicts the results of the regressions for EU growth company returns.

The results of the least squares regression for EMU growth and value company returns are presented in Table C1 (Appendix C) and Table C2 (Appendix C), respectively. The data for EMU growth and value company returns regression are normally distributed, show no serial correlation, and are linear in the model. In the regression of EMU growth company returns, the significance of the explanatory variables changes from year to year. Size, beta, B/M, E/P, and market leverage all have some explanatory power over time for EMU growth company returns. Size seems to have more explanatory power for EMU growth than for the US market and has a negative sign, as for the EU market. Market leverage changes signs over time and therefore shows positive and negative relations with growth company returns. The same applies for beta (Fama and French (1992)). Here B/M is significant for a couple of years at the 1% and 5% significance levels and has a positive sign, supporting Stattman’s (1986) earlier results

The results of the least squares regression for EMU value companies show the significance of the explanatory variables changing from year to year. In most years the B/M and market leverage are significant at both the 1% and 5% significance levels. As for the US and EU markets, B/M is positively related to EMU company returns. Beta, on the other hand, changes its sign from year to year. In addition, market leverage seems to change sign over time, from positive to negative and back again. This is similar to the regression of EU value company returns.

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VI. Conclusions

I research MSCI-composed growth and value stock portfolios in the US, the EU and the EMU markets with a time horizon from 2004 until 2010. I pose two research questions and attempt to shed some light on the debated topic of growth and value portfolio returns.

First, I must refute my first research question that growth stock portfolios with time horizons of more than one year significantly outperform value stock portfolios of the same time horizon and that portfolio rebalancing plays a significant role. The growth portfolio returns are higher than for value portfolios from an economic point of view. The outperformance of growth stock portfolios is not common in the earlier research. Lakonishok et al. (1994), Fama and French (1992, 1995), and Bouwer and van der Put (1996) research the US and a couple of European countries and determine the outperformance of value stock portfolios. Although Iconfirm the outperformance of growth portfolios, it is not statistically significant in any of the three markets. Therefore I cannot prove that a growth portfolio held for more than one year will outperform an equivalent value portfolio. Nor can I prove that rebalancing has a significant impact on portfolio returns: Even though portfolio rebalancing is important, growth portfolio returns increase remarkably and value portfolio returns tend to decrease with rebalancing. However, the Welch’s test fails to underpin its significance.

The economic outperformance of growth portfolios can be biased to a particular research period and data set. Several negative events took place within my research period, such as the credit crunch in 2009. According to Gulen et al. (2008), growth stocks tend to be more flexible in worsening economic conditions than value stocks. Therefore my findings cannot be applied to the entire market. In addition, I calculate the portfolio betas for growth and value portfolios. Portfolio betas tend to be higher for value portfolios in the EU and EMU markets and for growth portfolios in the US market. Interestingly, portfolio betas tend to increase from year to year for US, EU, and EMU rebalanced growth and value portfolios. Why betas increase every year for rebalanced portfolios could be a topic for future research.

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Fama–French (1992) factors can explain growth and value company returns from 2004 to 2010. The significance of the explanatory variables changes over time. However, E/P seems to have no important explanatory power in any of the three markets, since it has a flat relation with company returns and is barely significant. The main conclusions I can draw for the US market are the following:

i. Size does not seem to be of great importance in explaining US company returns.

ii. Here B/M explains US growth and value company returns better than size, supporting Stattman (1980), Rosenberg et al. (1985), and Fama and French (1992).

iii. Beta is an important explanatory variable for US growth and value company returns. It has a negative relation with US value company returns, which supports Fama and French’s (1992) findings.

The exposure of Fama–French (1992) factors in the EU market is slightly different than in the US market. The main findings for the EU market are as follows:

i. Size is a significant explanatory variable for EU company returns. It has a negative sign, which supports the findings of Bouwer and van der Put (1996). ii. Market leverage has a significant, mostly positive relation to EU growth

company returns, which supports Bhandari’s (1988) findings. But market leverage for EU value company returns is neither significant nor positive. iii. Here B/M is significant and positively related to EU value companies returns,

as in the US market.

The significance of Fama–French (1992) factors changes over time in the EMU market. The main findings from a regression of least squares for EMU company returns are as follows:

i. Here B/M is positively related to EMU company returns. This finding supports earlier research, like, Stattman (1980), Rosenberg et al. (1985), and Fama and French (1992).

ii. Size has a more significant negative relation to EMU growth company returns than to EMU value company returns, it supports Bouwer and van der Put(1996).

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of Fama and French (1992), that beta does not have a positive relation with company returns.

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APPENDIX A

Table A1. EMU Growth Portfolio Returns

The holding period is the number of years one holds a portfolio and this table shows the returns of portfolio for different holding periods. The entry year is the year one starts holding a portfolio; non-reb indicates that the company composition of a portfolio is the same throughout the holding period, reb indicates the portfolio composition is reevaluated every year.

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APPENDIX B

Table B1. EMU Growth and Value Portfolio Betas

This is a table of betas for EMU growth and value portfolios. The entry year is the year when one starts holding a particular portfolio and the holding period is the number of years a particular portfolio is held; non-reb indicates that the company composition of a portfolio is the same throughout the holding period, reb indicates the portfolio composition is reevaluated every year.

Entry year/ holding period

EMU growth portfolio betas

1Y 2Y 3Y 4Y 5Y 6Y 7Y 2004 non-reb 0.1017 0.1238 0.2094 0.5633 0.6229 0.8452 0.8752 2004 reb 0.1017 0.0770 0.1802 0.6374 0.7017 1.0297 1.0802 2005 non-reb 0.0770 0.2021 0.5737 0.6265 0.9485 0.9655 2005 reb 0.0770 0.1802 0.6374 0.7017 1.0297 1.0802 2006 non-reb 0.1802 0.6421 0.7182 1.0252 1.0427 2006 reb 0.1802 0.6374 0.7017 1.0297 1.0802 2007 non-reb 0.6374 0.7422 1.0713 1.0626 2007 reb 0.6374 0.7017 1.0297 1.0802 2008 non-reb 0.7017 0.9612 0.9047 2008 reb 0.7017 1.0297 1.0802 2009 non-reb 1.0297 1.0001 2009 reb 1.0297 1.0802 2010 non-reb 1.0802 2010 reb 1.0802 Entry year/ holding period

EMU value portfolio betas