Fundamental indexation and collared indexation in Germany: Does it work?

1

Fundamental indexation and collared

indexation in Germany: Does it work?

Supervisor: Dr. R.O.S. Zaal Programme: MSc Finance

June, 26 2014

ABSTRACT

The aim of this paper is to test the principle of fundamental indexation for Germany. Moreover we test an alternative approach, called collared indexation. Existing literature shows evidence in favour of fundamental indexation, but the outcomes are not always consistent over time. Results of our paper are unambiguous, the fundamental indexes do not outperform the market capitalization index. Remarkably the market capitalization index is superior, followed by the collared index. Robustness checks across different time frames confirm these results. Further analysis shows that the superior performance of the market capitalization is caused by the bias towards growth stocks from the fundamental indexes.

JEL classifications

G10, G11, G12

Keywords

2

1. INTRODUCTION

Passive investment strategies become increasingly popular. In 2012, 17% of worldwide equity fund was invested in passive funds. This is a major increase, comparing to 10% in 2003 (Human, 2013). In the past, investing in indexes has outperformed active strategies in 69% of the cases (Malkiel, 2003). An example of passive investment strategies is investing in indexes. In the last years various alternative passive investment strategies have been introduced. For example market capitalization weighting, equal weighting and fundamental weighting. In this paper we focus on the concept of fundamental indexation and collared indexation.

The Capital Asset Pricing Model (CAPM) is broadly examined in academic literature and states that the linear relationship between the expected return and risk of securities is efficient (Sharpe, 1964; Lintner, 1965). This model implies that holding the market portfolio is optimal, considering the risk and return characteristics. The market portfolio consists of the capitalized weighted portfolio of public traded shares (Arnott, Hsu and West, 2011). Examples of capitalized weighted indexes are the S&P 500 in the United States, FTSE 100 in the United Kingdom and DAX in Germany. Most of these major indexes are weighted based on market capitalization (Hsu and Compollo, 2006). In these indexes, the weight of an individual stock in such an index depends on the market capitalization of that particular stock and is reweighted on a specific point in time. These capitalized indexes are very volatile and tend to fluctuate with the number of traded stocks (Arnott, Hsu and Moore, 2005).

3 exist when the stock price is much higher than the fair value of a firm, for example due to expectations of future earnings by investors.

Arnott, Hsu and Moore (2005) introduced fundamental indexation as an alternative weighting scheme to construct an optimal portfolio. Instead of using market capitalization, they adopt an economic-centric approach. Fundamental indexation bases the weights on economic fundamentals to create an index portfolio based on economic scale of firms. Arnott, Hsu and Moore (2005) use several proxies to represent true value, so that a firms’ value cannot be underprized or overpriced. The fundamentals that they use are book value of the equity, revenue, operating income, dividends and number of employees. In 2009, 8 billion dollar was invested in fundamental indexes in the US. Compared to the 604 billion dollar that was invested in the capitalized weighted index, it is only a small fraction (Droms, 2010).

In this paper we investigate whether the fundamental indexes perform better than the capitalized indexes, in terms of risk and return. We focus on the German market, where the DAX index is operating. The German market is the largest economy in Europe in GDP and has not specifically researched before (Worldbank data). The main goal is to determine whether fundamental indexation yields a superior return in Germany. We also look at the consistency of the performance from the indexes over time. Therefore the period under review is set from 1992 until and including 2012. We account for book value of the equity, cash flow, revenue, dividends and employees as size proxies. As new size proxies we introduce book value of assets and EBIT. In line with previous studies, a composite index is constructed. We also test an alternative method, called collared weighting. This principle is introduced by Arya and Kaplan (2006), where the market cap index is followed, but the fundamental index weights are used as boundaries. This leads to the following research question:

4 To answer this question we replicate indexes of each alternative. This is done by reweighing the portion of stocks in the index. After the creation of the indexes, we show the return and risk characteristics. We test the outperformance by several performance measures. Finally, we analyse the possible causes of excess returns.

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2. LITERATURE REVIEW

In this section we review different parts of literature. In the first place we outline the CAPM model and the Modern Portfolio Theory. In the second place the characteristics of capitalized indexes are discussed and we review the concept of passive investment strategies. In the third part we summarize the findings of prior literature, where we show the main results in the US, Europe and Australia. The fourth paragraph presents the main critics on fundamental indexation. In the fifth place the three factor model of Fama and French (1993) is illustrated. Finally, we introduce collared indexation of Arya and Kaplan (2006) as an alternative weighting scheme.

2.1 Capital Asset Pricing Model (CAPM)

The CAPM model is developed, amongst others by Markowitz (1952), Sharpe (1964) and Lintner (1965). Markowitz (1952) introduced the so called expected return-variance rule. Typical investment behaviour should be to diversify investments to construct a mean-variance portfolio. The reason for this is that an investment in more than one stock, reduces the total variance of the portfolio. Lintner (1965) and Sharpe (1964) developed this model further and constructed the Security Market Line. This line combines risk free assets and risky assets, which leads to the market portfolio. The market portfolio is mean-variance efficient and consists of securities weighted by their market capitalization. According to the efficient market hypothesis, holding this market portfolio is the optimal investment opportunity. The overall risk measure used in the CAPM model is the β. This represents the degree of sensitiveness of a particular stock compared to the market changes. The Capital Market Line is characterised by the following regression equation (Black, 1972):

(

)

( (

)

)

6 The CAPM is based on a number of assumptions, we summarize the main points. The capital market is assumed to be perfect. Where all investors are risk averse and maximize wealth. The investor cannot influence prices, hence is a price taker. In addition there are no information costs, transaction costs or taxes (Black, 1972). Despite the fact that the CAPM model is broadly used and easy applicable, there is also critique. Roll and Ross (1994) found evidence that the CAPM might be inefficient. Their research found only a small relation between the expected return and the risk, measured by beta. Markowitz (2005) confirms that in reality not all investors hold the mean-variance portfolio.

2.2 Capitalized indexation and passive investment strategy

As we have mentioned in the introduction, passive investment has become increasingly popular. Investors following a passive investment strategy use market capitalized weighted indexes, for example the S&P 500 (Elton, Gruber, Brown and Goetzmann, 2011). Moreover, Malkiel (2003) found evidence that passive investment strategies outperformed the active strategies in 69% of the cases.

7 2.3 Fundamental indexation

Arnott, Hsu and Moore (2005) introduced the principle of fundamental indexation. In this alternative method for creating an index, they use fundamental values to create the index. Arnott, Hsu and Moore (2005) focussed their research on the US market, with a sample period of 1962 until 2004. The following fundamentals were used: book value of equity, cash flow, revenue, sales, dividend and number of employees. The construction of the portfolio is done by ranking the companies by each metric. They select the upper 1000 firms in of each fundamental metric and create an index. Based on the magnitude of each metric, a weight is assigned to each firm and the return of the index is deviated. Moreover they constructed a composite index, consisting of book value of equity, cash flow, revenue and dividend. The composite index is created by combining the four weights of the fundamental index, each for an equal part of 25%. After construction, all indexes are compared to the S&P 500 index and a reference portfolio. The reference portfolio is constructed in the same way as the fundamental indexes, but is weighted based on market capitalization. Statistical evidence showed that all fundamental indexes are outperforming the capitalized index, based on a significance level of α=0.05. The average excess return, produced by the fundamental index is 1.97 percentage points. The volatility however, measured by standard deviation and beta, is of a similar level of the reference portfolio. The exact numbers are given in table 1.

8 fundamental indexes. It can be caused by superior construction of the indexes, inefficient market prices or additional risk exposure.

Hemminki and Puttonen (2007) tested fundamental indexation using European data. They examined the Dow Jones Euro Stoxx 50 in the period 1996 to 2006. The applied methodology is in line with the paper of Arnott, Hsu and Moore (2005). Similar fundamental indexes are created, only there is not accounted for revenue as a fundamental metric. Results show an average excess return of 1.76 percentage points. The book value of equity, dividend and composite index show significant outperformance over the reference portfolio. The sales, cash flow and employment show higher, but insignificant excess return compared to the market capitalization index.

Mar, Bird, Casaveccia and Yeung (2009) reviewed fundamental indexation for the Australian market. They formed indexes from 1995 until 2006 and accounted for the fundamental index of book value of equity, cash flow, revenue and a composite index. The performance of the fundamental indexes is, on average, 1.94 percentage points higher than the cap-weighted reference portfolio in the same period. Moreover, Mar, Bird, Casaveccia and Yeung (2009) also tested the drivers of fundamental indexation with the Cahart (1994) four factor model. This model tests the size, value and momentum factors. The only significant factor is the HML factor, which indicates that there is a bias towards value stocks.. This means that the index tends to overweight value stocks. Hence in the fundamental indexes, stock with low price to earnings ratios are selected (Fama and French, 1993). This model and its factors are further discussed in section 2.5.

9 Fundamental index Arnott et al (2005) Hemminki et al. (2007) Mar et al. (2009)

Market United States Europe Australia

Sample period 1962-2004 1996-2006 1995-2006

Measure GR STDEV GR STDEV GR STDEV

Reference portfolio 10.35% 15.20% 12.01% 24.00% 12.08% 11.03% Book value of equity 12.11% 14.90% 13.83% 24.51% 13.39% 11.14%

Cash flow 12.61% 14.90% 13.81% 23.04% 14.53% 11.32% Revenue 12.87% 15.90% NA NA 14.09% 11.96% Sales 12.91% 15.80% 13.63% 23.07% NA NA Dividends 12.01% 13.60% 14.92% 22.67% NA NA Employment 12.48% 15.90% 12.58% 24.30% NA NA Composite 12.47% 14.70% 13.77% 23.62% 14.01% 11.37%

Table 1: Return and risk characteristics of previous literature.

2.4 Critics

Despite the previous evidence in favour of fundamental indexation, there is also critique. Blitz and Swinkels (2008) state about fundamental indexation: ‘it is a new breed of value indexes’. In the 1980’s investigators already found that stocks with low price-to-earnings ratios generated superior returns (Siegel, 2006). Hence a portfolio consisting of value stock outperforms the market. A fundamental index simply overweighs value stocks and underweights growth stocks. Blitz and Swinkels (2008) tested this tendency with the Fama and French (1993) three factor model, which will be discussed in section 2.5. Blitz and Swinkels (2008) found highly significant evidence that the fundamental indexes have a bias towards value stocks. We saw similar results before in the paper of Mar, Bird, Casaveccia and Yeung (2009). Moreover, Kaplan (2008) states: ‘Because value-biased portfolios historically have outperformed unbiased portfolios, it is no surprise that a fundamentally weighted index outperforms a market-cap index’.

10 The third point of critique is that fundamental indexes do not represent a feasible opportunity set (Kaplan, 2008). In market equilibrium, not every investor can hold the fundamental index. With a capitalization weighted index this is possible, since it represents the market portfolio. Hence a portion of investors cannot hold an optimal portfolio (Blitz and Swinkels, 2008). This is a theoretical point, one can conclude that if every investor wants to hold the fundamental index, the market mechanism will hold and prices will rise as the demand increases.

Next to these criticisms, we see that the excess return of fundamental indexation is not consistent over time (Blitz and Swinkels, 2008). Similar results have been shown by Arnott, Hsu and Moore (2005), where even negative outperformance of the fundamental indexes has been measured in certain years. This negative outperformance is also showed by Estrada (2008). In order to anticipate on this effect, we test the robustness of our findings across different time frames in chapter 4.

2.5 Fama and French three factor model

As we have seen in the papers mentioned before (e.g. Blitz and Swinkels, 2008; Mar, Bird, Casaveccia and Yeung, 2009), the Fama and French (1993) model is often used to determine the drivers of performance. This approach is an extension of the CAPM model to increase the explanatory power of the model. Two factors are added next to the factor from equation 1. First, the SMB factor, stands for small minus big and accounts for the size premium. If this factor is positive in a time frame, the small firms produced a higher return than the large firms. If the factor is negative, the large firms had a higher return. Second, the HML factor stands for high minus low and accounts for the value premium. A positive HML factor means that the value stocks produced a higher return than the growth stocks. When the factor is negative the growth stocks outperformed the value stocks. The regression equation of the Fama and French (1993) model is,

11 where is the return of the portfolio, is the risk free rate and is the excess return. The is the measure of systematic risk, the coefficient of the size factor and of the value factor. The is

the error term. In the end of this paper we also use this model to find the drivers of outperformance in the German market.

2.6 Alternative method: Collared indexation

We have discussed advantages and disadvantages of capitalization weighted and fundamental weighted indexes. In the capitalization weighted index, a stock price can rise which creates a large position of that stock in the index. This decreases the diversification of the overall portfolio and increases risk. While fundamental indexing should decrease risk (Kaplan, 2008). In the fundamental index, one needs to sell stocks that performed well, because its weight has increased. When the stock performed badly, an investor needs to buy more, to increase the weight (Blitz and Swinkels, 2008). The extend of these rebalancing effects depends on the rebalancing period.

12 Figure 1: The boundaries of the collared approach (Arya and Kaplan, 2006).

Arya and Kaplan (2006) researched collared indexation for the US market in the sample period of 1997 until 2005. They found a higher return for the fundamental index, but lower risk, measured by standard deviation for the collared index. This is shown in table 2. We apply this method of indexing for the German market.

Return Standard deviation

Market index 6.08 17.43

Collared index 8.01 16.76

Fundamental index 9.07 17.11

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3. DATA COLLECTION AND METHODOLOGY

In the first section we show our data collection and sample size. In the second paragraph we review the construction of the different fundamental indexes and the composite index. Here we also show the calculation of geometric return. In the third part of this chapter the construction of the collared indexes is explained. In the fourth section we show different types of performance measures, which we apply to measure the optimal index. In the fifth part we show the formulas of the liquidity measures. Finally, we give our hypothesis.

3.1 Data collection

The data that we use comes from the German market. The sample is drawn in the time frame of 1993 until and including 2012, a 21 year period under review. Table 3 gives the sample size of different years across the sample period. All the data is extracted from Thomson Datastream. We first collected the data of the fundamental values. These were, market capitalization, equity, total assets, cash flow from operations, EBIT, net sales, dividends and number of employees. The cash flow of operations was only available up from 1998. To compute the returns and volatility of the indexes, we retrieved the daily return index. The return of each share was calculated as follows:

(3),

where RI is the return index. This is computed daily, to measure volatility and annually to measure returns. Further we extracted static data, such as ISIN code and firms operating sector.

1998 2002 2007 2012 Market capitalization 449 687 720 639 Total equity 451 690 726 646 Total assets 452 691 726 646 Cash Flow 261 619 650 601 EBIT 419 659 701 632 Net sales 452 694 723 654 Dividends 420 676 654 592 Employees 431 673 674 600

14 3.2 Construction of indexes

The way we construct the indexes is similar to the existing literature (Arnott, Hsu and Moore, 2005). We construct fundamental indexes based on the following size metrics: book value of equity, book value of the assets, cash flow, EBIT, net income, revenue, dividends and number of employees. Total assets and EBIT are introduced as a new metrics compared to existing literature. Firstly, total assets are used, since the assets of a company are used to generate income. We test whether this size metric is good to use for construction of a fundamental index. Secondly, the EBIT metric has similar characteristics as net income, but the firms’ costs are subtracted. Hence it gives a better view of profitability. All fundamental values where collected on an annual basis, at the end of each year. Next, values are ranked by each metric, hence the firms with the largest value are on top. The 200 largest firms, in terms of value of metric, are used to compose the fundamental index. Then weights are assigned to each stock, by the following formula:

(4),

Where, is weight assigned to the stock, is the value of the fundamental metric of stock i and is the sum of the 200 fundamentals in index. Based on this weight we compute the return of the index, the beta and the standard deviation. We use geometric return as return number of each index. This measure is used in the existing studies (e.g. Arnott, Hsu and Moore, 2005; Hemminki and Puttonen, 2007; Mar, Bird, Casaveccia and Yeung , 2009). It is a better measure, because the observation returns are multiplied instead of added. In an index, wins and losses are alternated and thus multiplication of the returns is a better form. Geometric return is computed by (Elton, Gruber, Brown and Goetzmann, 2011):

15 where GR is geometric return and R is the return in a specific year. The formula is powered by the fraction 1 divided with n, where n is the number of observations. As a measure of systematic risk we use β. This measure is computed as follows (Markowitz, 2005):

( )

( ) (6),

Where is the systematic risk of the security i, ( ) is the covariance of the individual security, and the market portfolio. ( ) is the variance of the market portfolio. The overall measure of risk is standard deviation. We computed this on a daily basis, hence we annualized this measure with the following formula (Sironi and Resti, 2007):

√ (7),

Where is the annual standard deviation, is the daily standard deviation and T is the number of trading days. Next to the fundamental indexes we also construct a composite index. In this index we combine selected fundamental indexes. These individual weights are set together based on equal weight, this is shown in the following formula:

(8),

In this formula N is the number of indexes in the composite index and FI are the fundamental indexes. The number of firms is this index is also restricted to 200. Hence the 200 largest weights of the formula are used in the composite.

3.3 Collared indexation

16 { (9),

Where L is the lower bound, X is the weight of the market capitalization index and U is the upper bound. Hence if the market capitalization index assigns a higher or lower weight than the boundaries the weight is limited to the fundamental weight. The total weight of the collared index is 1.

3.4 Performance measures

To assess the performance of the different indexes, several measures are used. First of all, we use the ratio of Sharpe (1966). This ratio measures the slope of the Security Market Line and thus represents the premium return per unit of increase in risk. An investor can increase his performance by achieving a higher slope of this ratio. Hence the higher the Sharpe ratio, the better the performance. The ratio is calculated as follows:

( ) (10),

Where ( ) is the expected return of the index, we used the average return as a proxy. is the risk free rate and is the standard deviation of the portfolio, which is the volatility of the fund. We compare the Sharpe ratio with the ratio of each index. A close alternative of this measure is the index of Treynor (1965), however it accounts for the systematic risk measured by β instead of the standard deviation. It is computed as follows:

( ) (11),

17 higher the Jensen’s alpha the more outperformance of the index. This risk-adjusted measure for performance can be characterised by the following regression equation:

( ) (12),

Where is the return of the portfolio, in this case the index, is the risk free rate and is the risk adjusted return parameter Jensen’s alpha. The is the return of the market, in this case the DAX index and is the error term. We measure the significance of the alpha with a t-test.

3.5 Liquidity measures

Next to the performance of the fundamental indexes, we also measure their liquidity. We use the CAP and the concentration ration, this is in line with Arnott, Hsu and Moore (2005). An investor could hold a portfolio with superior performance, but it must also be possible to sell the shares from the portfolio. A benefit from the capitalized indexes is that these indexes are very liquid. However, fundamental indexes may hold smaller positions in stocks that are not noted in the DAX index. Therefore we use the liquidity measures. First of all we use CAP ratio (Mar, Bird, Casaveccia and Yeung, 2009). This ratio is computed as follows:

(13),

Where is the average capitalization of the fundamental weighted indexes and is the

average capitalization of the capitalized indexes. The second measure we use is the concentration ratio. When this ratio is high, the index’ 10 highest stocks have a large portion of the market capitalization and hence the index is concentrated. When the ratio is low the index is more dispersed. The ratio is computed as follows:

(14),

18 3.6 Hypothesis

To check whether fundamental indexes perform better than the capitalized indexes, we set the following hypotheses:

Hypothesis 1:

H0: The fundamental weighted index and capitalization weighted have equal performance ( )

H1: The fundamental weighted index performs better than the capitalization weighted index. ( )

Hypothesis 2:

H0: The collared weighted index and capitalization weighted have equal performance ( )

19 0 100 200 300 400 500 600 700 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

Risk free rate DAX Market capitalization Total equity Total assets Cash flow EBIT Net sales Dividends Employee Composite Collared 4. RESULTS

In this section we present our results. In the first place we show the performance of all indexes, including the collared index. In the second place the liquidity measures are given, to test whether the indexes are liquid. In the third place we carry out robustness checks, where we test the consistency of the results across time frames. In the fourth place we search for possible sources of outperformance of certain indexes. In the fifth place Fama and French regressions are shown, to find the drivers of excess return.

4.1 performance results

In figure 2, the final value of each fundamental portfolio is displayed. The final value based on an initial investment of €100 in the beginning of the sample period. Our data collection started in 1992, however in this figure we start in 1998. This since the data of the cash flow, composite and collared index was only available since 1998. Due to this different sample period of these indexes, we report all our results in the years 1998 until 2012 to avoid wrong comparison of final value.

20 In figure 2 we see the economic situations in the sample year. A clear loss is visible in the global financial crisis of 2008. All indexes tend to make the same movement, but in a differing extend. The most remarkable aspect is that the market capitalization has the highest final value. Followed by the collared index and the EBIT index. This is inconsistent with existing literature. The DAX index has, after the total asset index the lowest final value. This is remarkable, since both the DAX and market capitalization index are based on the value of their market capitalization. The DAX index consists of only 30 stocks and the market capitalization reference index exists of 200 stocks and both indexes have a different rebalancing date. The return figure presented above, does not incorporate risk. Therefore we show the risk and return characteristics of all fundamental indexes in table 3. The excess return in this table is calculated as the geometric return of the index minus the geometric return of the DAX index. The results are distinct. Market capitalization has the highest Sharpe and Treynor ratio, Hence is the best mean-variance index. The total assets index is performing relatively bad, even worse than the DAX index. After the market capitalization index the collared index has the highest ratios. The EBIT is the best performing fundamental index followed by the composite index. Based on the results in table 4 we see that all other fundamental indexes outperform the DAX index. However to incorporate risk we use the alpha from Jensen (1966) to measure excess return.

Index GR STDEV Beta Excess Sharpe Treynor

DAX 3.96% 0.232 1.000 0.00% 0.005 0.001 Market capitalization 13.23% 0.197 0.762 9.27% 0.476 0.123 Total equity 8.43% 0.205 0.792 4.47% 0.224 0.058 Total assets 1.50% 0.242 0.817 -2.46% -0.097 -0.029 Cash flow 8.51% 0.208 0.784 4.54% 0.225 0.059 EBIT 9.44% 0.208 0.784 5.48% 0.270 0.071 Net sales 7.49% 0.198 0.758 3.53% 0.184 0.048 Dividends 6.70% 0.190 0.730 2.74% 0.150 0.039 Employee 8.24% 0.195 0.750 4.27% 0.225 0.059 Composite 8.63% 0.199 0.774 4.66% 0.241 0.062 Collared 11.91% 0.196 0.769 7.94% 0.411 0.105

Risk free rate 3.84%

21 In table 5 we show the results of the Jensen’s alpha regression and the T-test to measure the significance. The results confirm the superior performance of the market capitalization portfolio. The alpha of 8.8% is highly significant with a p-value of 0.000. Next we see that the collared approach has a highly significant alpha of 7.5%. The EBIT index is the best performing fundamental index, with a significant alpha of 5.1%. Next, the composite index, cash flow index and equity index are the best performing fundamental indexes. With significant returns of 4.2%, 4.1% and 4.0% respectively. The total assets index is worst performing, although the t-statistic is insignificant.

Jensen’s alpha t-statistic p-value

Market capitalization 0.088 5.550 0.000 Total equity 0.040 3.087 0.009 Total assets -0.020 -0.833 0.420 Cash flow 0.041 2.836 0.014 EBIT 0.051 2.691 0.019 Net sales 0.032 1.805 0.094 Dividends 0.023 1.773 0.100 Employee 0.039 2.501 0.027 Composite 0.042 2.830 0.014 Collared 0.075 5.507 0.000

Table 5: Results of Jensen’s alpha regressions.

4.2 Liquidity measures

22 to the liquidity in Arnott, Hsu and Moore (2005) where the lowest CAP ratio is 0.66, we can conclude that all are indexes are sufficiently liquid, as they all are above the ratios compared to Arnott, Hsu and Moore (2005).

Ratio Concentration CAP

Market capitalization 0.481 1.000 Total equity 0.431 0.999 Total assets 0.260 0.997 Cash flow 0.423 0.925 EBIT 0.416 0.933 Net sales 0.415 0.986 Dividends 0.437 0.933 Employee 0.346 0.975 Composite 0.426 0.998 Collared 0.467 0.995

Table 6: Liquidity ratios.

4.3 Robustness checks

23 -40% -30% -20% -10% 0% 10% 20% 30% 40% 50% Re tu rn Re tu rn Re tu rn Re tu rn Re tu rn Re tu rn Re tu rn Re tu rn Re tu rn Re tu rn Re tu rn Re tu rn Re tu rn Re tu rn Re tu rn 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Market Capitalization Composite Collared EBIT

Figure 3: index returns across sample period.

24 Index GR STDEV Beta Excess Sharpe Treynor Alpha

Panel A. Results in period 1998-2002

DAX -7.41% 0.261 1.000 0.00% -0.467 -0.122 0.00% Market capitalization 6.87% 0.217 0.716 14.28% 0.096 0.029 10.82% Total equity 0.29% 0.217 0.707 7.69% -0.207 -0.064 4.12% Total assets -7.60% 0.234 0.677 -0.20% -0.529 -0.183 -4.14% Cash flow -1.38% 0.230 0.713 6.03% -0.268 -0.086 2.53% EBIT -0.67% 0.230 0.720 6.74% -0.237 -0.076 3.33% Net sales -2.00% 0.202 0.622 5.41% -0.335 -0.109 0.80% Dividends -0.15% 0.197 0.622 7.26% -0.250 -0.079 2.65% Employee -1.06% 0.199 0.615 6.35% -0.293 -0.095 1.65% Composite 0.45% 0.210 0.688 7.86% -0.206 -0.063 4.05% Collared 5.49% 0.211 0.704 12.89% 0.033 0.010 9.29% Panel B. Results in period 2002-2007

DAX 22.77% 0.171 1.000 0.00% 1.104 0.189 0.00% Market capitalization 27.96% 0.144 0.758 5.19% 1.669 0.317 9.76% Total equity 24.99% 0.148 0.775 2.22% 1.422 0.272 6.47% Total assets 22.65% 0.163 0.811 -0.12% 1.151 0.231 3.45% Cash flow 25.95% 0.150 0.772 3.18% 1.467 0.286 7.49% EBIT 27.37% 0.150 0.778 4.60% 1.567 0.302 8.79% Net sales 25.67% 0.149 0.772 2.91% 1.464 0.282 7.20% Dividends 23.33% 0.140 0.726 0.56% 1.384 0.267 5.72% Employee 25.59% 0.146 0.751 2.82% 1.481 0.289 7.53% Composite 25.78% 0.147 0.770 3.01% 1.487 0.284 7.35% Collared 26.89% 0.144 0.761 4.12% 1.594 0.302 8.64% Panel C. Results in period 2007-2012

DAX -1.15% 0.269 1.000 0.00% -0.149 -0.040 0.00% Market capitalization 6.15% 0.232 0.827 7.31% 0.143 0.040 6.62% Total equity 1.70% 0.250 0.896 2.86% -0.046 -0.013 2.44% Total assets -7.72% 0.335 1.068 -6.57% -0.316 -0.099 -6.30% Cash flow 2.84% 0.247 0.867 4.00% 0.000 0.000 3.47% EBIT 3.62% 0.245 0.862 4.77% 0.032 0.009 4.22% Net sales 0.84% 0.249 0.886 1.99% -0.080 -0.023 1.54% Dividends -1.36% 0.236 0.821 -0.20% -0.178 -0.051 -0.92% Employee 2.04% 0.245 0.867 3.20% -0.033 -0.009 2.67% Composite 1.44% 0.244 0.864 2.60% -0.057 -0.016 2.05% Collared 4.69% 0.237 0.843 5.85% 0.078 0.022 5.22%

25 4.4 causes of outperformance

The results are conclusive. Based on Jensen’s alpha we see that the fundamental indexes do not outperform the index created of market capitalization. We now try to find the causes of the outperformance of the market capitalization index. In table 8, we show the 10 largest companies in selected indexes with their assigned weight in 2012. The names in all the indexes are no surprise. Most striking is the large weight attached to the first three firms of the total assets index. We see 31.1% weight in Deutsche Bank. This means that Deutsche Bank can have large influence on the return of the index. Moreover, this large weight reduces the diversification effect and increases the standard deviation of the index. Further notable things are the large weight of 16.7% of Volkswagen in the EBIT index. Further the presence of Lanxess in the top 10 of the DAX index is strange, it is not in any other top 10.

Composite index Total Assets index EBIT index

1 VOLKSWAGEN 9.0% DEUTSCHE BANK 31.1% VOLKSWAGEN 16.7%

2 ALLIANZ 7.2% ALLIANZ 10.6% ALLIANZ 6.3%

3 E.ON 5.1% COMMERZBANK 9.8% BASF 5.7%

4 DEUTSCHE TELEKOM 5.1% VOLKSWAGEN 4.7% DAIMLER 5.2%

5 BASF 5.1% MUNCHENER RUCKVER 3.8% BAYER. MOTOREN WERKE 5.0%

6 SIEMENS 5.0% DEUTSCHE BOERSE 3.4% SIEMENS 4.8%

7 DEUTSCHE BANK 4.9% DEUTSCHE POSTBANK 3.0% AUDI 3.8%

8 DAIMLER 4.5% DAIMLER 2.5% E.ON 3.1%

9 BAYER. MOTOREN WERKE 4.1% E.ON 2.1% MUNCHENER RUCKVER 2.9%

10 MUNCHENER RUCKVER 3.2% BAYER. MOTOREN WERKE 2.0% COMMERZBANK 2.8%

Collared index Market Cap index DAX index

1 VOLKSWAGEN 7.5% VOLKSWAGEN 7.2% LANXESS 9.4%

2 SIEMENS AG 6.3% SAP 6.5% BAYER 8.5%

3 BASF 6.2% SIEMENS 6.0% VOLKSWAGEN 7.8%

4 BAYER 5.6% BASF 5.9% SIEMENS 7.7%

5 SAP 4.6% BAYER 5.4% SAP 7.0%

6 BAYER. MOTOREN WERKE 4.5% BAYER. MOTOREN WERKE 4.3% BAYER. MOTOREN WERKE 5.6%

7 ALLIANZ 4.5% ALLIANZ 4.3% ALLIANZ 5.6%

8 DAIMLER 4.1% DAIMLER 4.0% BASF 5.2%

9 DEUTSCHE TELEKOM 3.5% DEUTSCHE TELEKOM 3.4% DAIMLER 4.4%

10 DEUTSCHE BANK 2.9% DEUTSCHE BANK 2.8% DEUTSCHE TELEKOM 3.6%

26 Based on the results of table 8, we further investigate the weights assigned to a specific sector in four indexes. To every stock in the index the sector is attached, then the weights per sector are summed to determine the total part of the sector in the index. This is done for every year in the sample, hence we can see the development. The results are visible in figure 4, 5, 6 and 7. In figure 4 we see the weights of the total assets weighting index. The results are obvious. The index consists for approximately 70%-80% of the financial sector. Hence, almost all returns of this index are focussed towards one sector. Moreover the large part towards financial institutions may cause a low diversification effect due to the concentration towards this sector. If the financial firms perform badly, for example due to non-systematic risk effects, the fundamental index of total assets may become worthless. We conclude that the total assets index is not a good metric to create a fundamental index.

Figure 4: Sector weights of the total assets index.

Next we evaluate figure 5, 6 and 7. These graphs show the market capitalization index, collared index and the composite index respectively. First of all the market capitalization index is more spiked compared to the others. The collared index behaves in between. This is logical, given the methodology that this is in fact the market capitalization index, with the composite index as a boundary. In the last graph, we see that the fundamental composite index is less spiked and has a

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Total Assets index

27 smoother movements of weights across different sectors. The movement is less erratic. These findings are similar with Arnott, Hsu and Moore (2005), where they explain that the market capitalization shifts strongly due to changing investor preferences.

Figure 5: Sector weights of the market capitalization index.

Figure 6: Sector weights of the collared index. 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Market Capitalization index

28 Figure 7: Sector weights of the composite index.

4.5 Fama and French Regression

In this section we aim to find drivers of excess performance with the Fama and French (1993) model. In order to do so, the SMB and the HML factor are added to the CAPM regression model, we discussed this model in chapter 2. A positive SMB factor means that the small shares outperformed the large shares and vice versa if the factor is negative. A positive HML factor means that the value stocks outperformed the value stocks. If this factor is negative, the growth stocks outperform the value stocks (Fama and French, 1993). In the regression, the adjusted R squared measures the explanatory power of the model. We executed the Fama and French (1993) regression for four indexes, namely market capitalization, composite, collared, EBIT and total assets index.

In table 9, the results of the regression of the market capitalization index are given. The alpha is highly significant, but negative. This is a large difference comparing to the one factor model we regressed in table 4. The SMB factor is almost zero and insignificant, hence has no influence on the excess return. However the HML factor has a coefficient of -0.240, with a p-value of 0.07. This means that this factor has influence on the performance of the index. Since the factor is negative, the index is biased towards growth stocks. This is consistent with expectations (Mar, Bird, Casaveccia and

29 Yeung, 2009). The adjusted R squared is 0.945, which means that the model has high explanatory power. Last is valid for all regressions, since all adjusted R squared lie on a similar level.

General

R squared 0.956

Adjusted R squared 0.945 Number of observations 15

Variable Coefficient Standard error T-statistic P-value

Alpha -0.078 0.020 -3.846 0.003

Beta 1.069 0.079 13.574 0.000

SMB 0.003 0.191 0.017 0.987

HML -0.240 0.120 -2.009 0.070

Table 9: Fama and French three factor regression for market capitalization index.

In table 10 we give our second regression result of the composite fundamental index. The alpha has a coefficient of -0.024. The SMB factor yields a coefficient of -0.044, but is insignificant with its p-value of 0.732. However, the HML factor with a high coefficient of 0.351 has a p-value of 0.001 and thus highly significant. This means, that there is a bias towards growth stocks, even with a higher coefficient as within the market capitalization. This is striking, since existing literature states that the fundamental index has a bias towards value stock and this bias should be the main driver of outperformance.

General

R squared 0.981

Adjusted R squared 0.976

Number of observations 15

Variable Coefficient Standard error T-statistic P-value

Alpha -0.024 0.012 -1.911 0.082

Beta 1.094 0.052 20.927 0.000

SMB -0.044 0.127 -0.351 0.732

HML -0.351 0.078 -4.517 0.001

30 The third regression result is given in table 11 of the collared index. The alpha has a negative, significant coefficient of -0.067. The beta is 1.085 and significant, hence the index is slightly riskier than the market. Again, the SMB factor is insignificant. The HML factor has a coefficient of -0.196 and a p-value of 0.083.The coefficient of the HML factor is lower than in de the market capitalization index and the composite index, but there is a bias towards growth stocks.

General

R squared 0.966

Adjusted R squared 0.957 Number of observations 15

Variable Coefficient Standard error T-statistic P-value

Alpha -0.067 0.017 -3.930 0.002

Beta 1.085 0.068 16.008 0.000

SMB -0.065 0.165 -0.392 0.703

HML -0.196 0.103 -1.907 0.083

Table 11: Fama and French three factor regression for collared index.

In the fourth place, we execute the three factor model regression for the EBIT fundamental index in table 12. This is the best performing fundamental index. The SMB factor is insignificant. The HML factor has a coefficient of -0.320 and is significant.

General

R squared 0.958

Adjusted R squared 0.946 Number of observations 15

Variable Coefficient Standard error T-statistic P-value

Alpha -0.028 0.186 -1.523 0.156

Beta 1.064 0.077 13.818 0.000

SMB -0.259 0.196 -1.324 0.212

HML -0.320 0.116 -2.748 0.019

31 The last regression we show is in table 13 of the total asset index. These results show a different image. A positive significant alpha, with a coefficient of 0.052 and a significant beta with a coefficient of 0.0935, hence it is slightly less risky than the market portfolio. The SMB factor has a negative coefficient, but is not significant. Finally, the HML factor yields a highly significant coefficient of -0.425. This means that there is a bias towards growth stocks.

General

R squared 0.966

Adjusted R squared 0.957

Number of observations 15

Variable Coefficient Standard error T-statistic P-value

Alpha 0.052 0.016 3.215 0.008

Beta 0.935 0.061 15.436 0.000

SMB -0.297 0.177 -1.677 0.122

HML -0.425 0.104 -4.090 0.002

Table 13: Fama and French three factor regression for total assets index.

From these results we find that all the indexes have a bias towards growth stocks. This means that the indexes consist for a large part of growth stocks. Growth stocks are characterized by a high price-to-earnings ratio (Fama and French, 1993). For the market capitalization index, this is in line with the expectations. For the fundamental indexes this is striking, since existing literature (e.g. Blitz and Swinkels, 2008; Mar, Bird, Casaveccia and Yeung, 2009) found a bias towards value stocks as a driver of the excess performance. These value stocks typically have a low price-to-earnings ratio (Fama and French, 1993). The coefficient of the HML factor of the market capitalization index is -0.24, while the coefficient for the EBIT index is -0.32, for the composite index is -0.351 and for the total assets index -0.425. Hence the economic meaning of the HML factor in the fundamental indexes is larger. We conclude that the bias towards growth stocks of the fundamental indexes causes the outperformance of the market capitalization index.

32

5. CONCLUSION

This final chapter is divided in two section. In the first section we give the general conclusion of our study. In the second section we give options for further research.

5.1 Conclusion

In this paper, we examined the performance of the market capitalization, fundamental and collared indexes. We focussed on the German market. Statistical evidence shows that there is no significant outperformance of fundamental indexes or collared index compared to market capitalization indexes. The best performing fundamental index was EBIT, which we introduced as an alternative profitability size metric. The results are conclusive the market capitalization index outperforms the alternatives indexes consistently, hence fundamental indexation is flawed. We cannot reject our null hypotheses.

Existing literature of among others, Arnott, Hsu and Moore (2005) shows evidence in favour of fundamental indexation. However these results are not consistent over time. In the period 1-1-1990 until 31-12-1999, the market capitalization indexes outperformed the fundamental indexes. On average, the fundamental indexation indexes look superior, but this is over a long sample period of 42 years. The average investor does not hold a portfolio for that period of time. Next another important criticism stays upstanding, namely the claim that fundamental indexation is an active investment strategy instead of a passive one. Fundamental indexes need periodic rebalancing, which leads to higher transaction costs.

33 We also tested collared indexation, as an alternative. This hybrid approach shows results in between the capitalized indexes and fundamental indexes. This is logical, since collared indexation is based upon these two indexes. However results show that the geometric return is higher than the fundamental index, but it has a lower standard deviation as both the market capitalization and fundamental indexes. If there was indeed a bias towards value stocks, this method might be superior. Based on this study, the principle of fundamental indexation is not appealing for investor. However the existing literature shows conflicting evidence compared with this study. In the end markets always behave different and react on several events. Past performance is no guarantee for future success.

5.2 Further Research

Further research could focus on other alternative approaches. Chen (2007) introduced a so called ‘smoothed cap’ approach. In this approach a market index is created that outperforms the standard capitalization weighted index. However, this is done without the fundamental data, but with an estimation. They estimated the fundamental value based on the median of previous capitalization weight in a past estimation window on a stock. The fact that the fundamental accounting metrics are not needed, may save the time consuming process of sorting and creating the fundamental index.

34

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