The persistence of excess returns – A value perspective Master Thesis Finance By J.W. de Vries (s1780131) Under supervision of T. Dijkstra

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The persistence of excess returns – A value perspective

Master Thesis Finance By J.W. de Vries (s1780131) Under supervision of T. Dijkstra

Abstract

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Table of content

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Introduction

One of the most central questions in the field of business is the question how to generate value. In the book “Valuation”, Koller et al. (2010 p.113) propose a formula to estimate the value of a company. Some central metrics here are growth, return on invested capital (ROIC), return on new invested capital

(RONIC) and the weighted average cost of capital (WACC). According to them a company is able to create value with growth by having a return on invested capital higher than the cost of capital. When this is the case it is said that the company is able to create excess returns. When a company is able to create (sustainable) excess returns it is said that it has a competitive advantage. This paper will investigate the ability of companies to create and maintain these excess returns.

An important notion with respect to the sustainability and level of excess returns is the competitive structure of an industry. In his book Competitive Strategy Porter (1980) introduced his five forces framework, which helped to analyze the competitive structure of an industry. The competition in an industry according to him is determined by the threat of new entry, pressure from substitute products, bargaining power of buyers, the bargaining power of suppliers and the degree of rivalry amongst competitors within the industry. One can see that these characteristics are industry specific, therefore it is important to take into account the industries to which a company belongs when assessing the

generation of excess returns. Hawawini et al.(2003) investigated the importance of industry specific characteristics relative to firm specific characteristics, with regards to value. They found that for most companies industry specific factors are most important in assessing firm value, only a few value leaders or losers are able to significantly outperform / underperform the market respectively.

This paper will build on the work of Nissim and Penman (2001) and on the master thesis of Derk Mulder (2012). Nissim and Penman have cleared the ground for using accounting ratios for (equity) valuation purposes. Furthermore they investigated the change in several important accounting ratios, including measures resembling return on invested capital. Derk Mulder has performed a regression analysis, which includes a decay rate and long term level of excess returns and additionally included the return on net investments in his model. This thesis will build upon the work of Derk Mulder by solving some of the estimation problems, which remained in his analysis and additionally this paper will add the distinction between the value leaders and losers from other companies.

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 Is there a difference in the decay rate of excess returns and the level of long run excess returns between industries?

 Does a distinction between the value leaders and losers from the other companies impact the decay rate and long-term level of excess returns.

The rest of this paper will be organized as follows. First in paragraph 2, a literature review will be given explaining what drives value, explains why and how industry variables are relevant and shows the results of past studies. In paragraph 3 the literature will be re-examined, but this time from a more practical point of view. This paragraph will show why and which accounting variables we will use and introduce the model to be estimated. Then paragraph 4 will give a description of the eventual data and paragraph 5 will present the methodology which is needed to tackle the estimation problems with the model. Then paragraph 6 presents the results of the study and this paper ends with a conclusion in paragraph 7.

Literature Review

What drives value

When valuating companies it is very important to have a clear understanding of the drivers of value. Several authors such have already investigated different drivers. Consider for example the key value driver formula as described in Damodaran (2007), which is represented in equation 1.

( ) (

)

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The key drivers here are EBIT which stands for the Earnings Before Interest and Taxes, which is a proxy for operating income, t is the operating tax rate, ROIC is the Return on Invested Capital, g is the stable growth grate and WACC is the weighted average cost of capital. This formula is used in practice to calculate the terminal value of a specific company. This formula shows some of the dynamics of value creation. First it assumes that growth is not bigger than the WACC. Another important implication of the formula is that growth is only able to create value if ROIC is higher than the WACC. Consider the

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5 ∑₍ ( )₎ ₍ ₎ ( ) (

)

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This formula distinguishes between an explicit forecast period (from time i = 1 to n) which is taken care of in the first part of the formula (∑ ₍ ( )₎) and the eventual stable state (at time = n + 1) which is

calculated with the last term ( ( ) (

)

) (Most of the time and is

considered to be equal to the EBIT and WACC at period n). Note that the stable state needs to be discounted to the present, which is done with the middle term (₍ ₎ ) Also note that in formula 2 ROIC has been replaced with RONIC which is the return on new invested capital. RONIC can be seen as a stable state of ROIC. Here we can also see some key questions practitioners have to ask themselves. In first case they should ask themselves what are good estimates for the different variables. But they also need to decide how long the explicit forecast period should be. This paper investigates whether excess returns decay to an economy wide average or an industry average. This paper can give practitioners some insight in what way excess returns decay and how long it takes to enter a stable state. Practitioners can use findings of this paper to see if their estimates for the future are realistic.

The major lesson from a value perspective thus is that a company is able to create value when its return on invested capital is higher than its cost of capital. When managers make decisions to invest their money in a project they should only invest in a project when the return on invested capital is higher than the cost of capital or otherwise their decisions would be value destroying. In addition a company would not be able to continue making decisions where the return on invested capital is lower than the cost of capital. Because if they do so, their company would soon go bankrupt or would be taken-over by another party. Thus in general we would find that companies on average would have zero or higher excess returns.

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6 economies of scale. Some companies might have very low marginal costs. When scale increases it can spread their fixed costs over more products, thus leading to higher cost-efficiency. Consider for example companies such as Amazone. Because they do not own physical stores where they sell their goods to their customers, they can keep their marginal costs per additional customer very low, while at the same time they can spread their fixed costs over more customers. While the hierarchy of investments and economies of scale might be important ingredients for determining a decay rate of excess returns. There is an additional force which might be very important, namely competition.

Industry characteristics and competitive forces

Consider for example Stigler (1963 p. 54) as in Fama and French (2000): “There is no more important proposition in economic theory than that, under competition, the rate of return on investment tends toward equality in all industries. Entrepreneurs will seek to leave relatively unprofitable industries and enter relatively profitable industries.” Instead of the return on investment itself, this paper argues that it is the level of excess returns which returns toward the mean (which is the return on investments minus the weighted average cost of capital). Entrepreneurs would not enter a specific market if it does not compensate them for the risk they take. Additionally it seems only natural to assume that different industry have different risk characteristics.

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7 erode excess returns becomes all too clear. When there are more participants in one industry a specific company is less able to set its price, namely if you set your prices higher than your competitor, without providing superior quality, buyers might decide to buy your competitors products.

From a more practical point of view there are several things which might influence the decay rates of excess returns. In some industries products may have a very short product life-cycle, which might follow from the fact that the particular industry has a very high rate of innovation. If this is the case products which are superior in this year might significantly underperform next year’s products. If this is the case a company can only shortly enjoy superior returns on that specific product. Even when innovation rates would not be high it is questionable if a company can continue enjoy high returns on their product as competitors will try and imitate your product. If you are unable to protect your product, for example through patents, your excess returns will erode quickly.

Results of Past Studies

Several authors have already investigated the question whether returns erode to a certain level. For example Nissim and Penman (2001) created ranked portfolios based on specific ratios such as the return on assets and the return on equity. They found that returns converge rather quickly to an economy wide average. Additionally Fama and French (2000) found that returns quickly revert to the mean (about 38% per year). However, they also noted that the rates of reversion are largely non-linear. According to Fama and French mean reversion is the quickest for returns below the mean and is quicker when it is far from its mean in either direction. Fairfield et al. (2001) investigated whether industry characteristics would increase the explanatory power, measured as the adjusted r-square, would significantly add to the analysis. While they did find industry characteristics increased the power of explaining reversion to the mean for growth factors, they did not found significant results for industry specific characteristics.

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8 because of a gradual decreasing return on new investment (Derk Mulder 2012). To fully grasp this insight one needs to distinguish between return on existing investments, which erode due to increased

competition and returns on new invested capital which erode due to decreasing marginal returns on capital, due to a hierarchy in investment decisions.

One needs to take away from these studies that there is quite some evidence for mean reverting returns, however so far it is unclear whether returns are reverting to an industry average or an economy wide average. Additionally, one has to consider that the pattern of mean reversion is not homogenous among different companies, Hawawini et al. (2003) have proposed to distinguish between under- or

outperformers and regular industry members. Additionally Fama and French (2000) noted that mean reversion is non-linear, and that both the magnitude and the sign of the difference from the mean matter for mean reversion.

Model and Variables

Using Accounting Data

When valuing companies we are often in need of accounting data. We need accounting data to assess the value of a specific company. Damodaran (2007) and Nissim and Penman (2001) give an extensive discussion how to use accounting data when valuating companies. Here Damodaran focuses on how to get good estimates for different variables or ratios and Nissim and Penman focus on the stability of these ratios.

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9 Another thing to notice is that we focus on the accounting or book value of different assets within our ratios. This is only logical, because book values are often based on a type of cost accounting, which does not reflect the possible earning potential these assets have for a specific company. Consider for example the market value of equity, this market value already captures the earnings potential of growth assets. However these are not yet generating any cash flows. This would bias the return on invested capital downwards since the market value of equity can not be linked to the existing investments, which generate a cash flow today. Even without the existence of growth assets, using market values marks up the value of existing assets. Damodaran gives an example of a single project company which invests €50 million in a project, the company has a cost of capital of 10% and the project will earn €10 million in perpetuity. The market values this project at a value of €100 million. When evaluating the returns on a market value basis we see a return on invested capital of 10%, which equals the weighted average cost of capital and thus no excess returns are made. If we compare it to the actual investment, which is given by the book value of the project of €50 million, then the return on invested capital is 20% leading to an excess return of 10%. Which seems far more reasonable.

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10 decay rate of excess returns. However, the target crowd of this paper are the practitioners and the researchers in the field of valuation. It is important to note that this paper focuses on the value of operations of different companies from an organizational perspective and one needs to know that this does not always have to be correlated with the value the company brings to an investor.

Model Specification

So far it has been discussed why and when industry or firm specific factors matter when trying to identify decay rates and long-term excess returns. It is still required to specify the correct model for mean

reversion. Fairfield et al. (2009) specify a very simplistic model for mean reversion, namely:

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Where = the return on invested capital of company i at time t and = the return on invested

capital of company i at time t-1. However this model is far too simplistic. First of all, it does not take into account a time-varying cost of capital (k). Without including this in the estimation, too little insight is given into the value generation capabilities of a company. Focusing on excess returns would further alter the analysis to:

( ) ( ) (4)

However, we are interested in the question whether, companies or industries are able to create some sustainable form of excess returns (γ). Equation 4 assumes that any form of excess returns fully erodes, because of competition. Incorporating the γ further alters the formula to:

( ) (( ) ) (5)

The constant disappears because we include the variable Furthermore Derk Mulder noted that the equation could be further improved by including an term for net investments. First we need to create nominal values of the ratios and then implement the return on net investments as a proxy for the return on new invested capital:

( ) (( ) ) ( ) (6)

In equation 6 , is the invested capital at time t-1 and is the invested capital at time t-2.

Here i is the return on new investments, and the net investments at time t-1 (= - ).

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11 excess returns ( (( ) ) ) and a level of excess returns on new investments

( ) . Basically this follows the model for Economic Profit.

However, this equation gives absolute measures of economic profit. When comparing different

companies with each other it is better to just look at the percentages. That is why everything is divided by . To come to:

( ) (( ) )

( ) (7)

With some rearranging we get:

( ) ( ) ( ) (8)

However there is perfect multicollinearity between

and

. Recall that = - + .

When using this information in the past equation we get: ( ) ( ) - + ( ) (9) Or when rewritten: ( ) ( ) ⁄ ⁄ (10)

Here = (1-δ)* , =(1- δ) and = (i-k) - (1-δ)* . Where δ is the eventual decay factor.

While this regression would be optimal, there are extensive problems with estimating the return on new invested capital. Damodaran (2007) proposes to estimate it by dividing the difference in earnings before interest and taxes between years divided by the difference in invested capital between years. However, when doing this, severe estimation biases arise. While it can be expected that the second regression term would be rather small, it will be better to leave it out of the estimation. Additionally it is impossible to estimate B2 directly, however this would imply an equal return on new invested capitals between companies, which is not a probable assumption. Therefore for practical reasons it is best to leave the estimation to:

( ) ( )

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12 Here = (1-δ) and = (1-δ)* .

Variables under investigation

This thesis requires estimation of the different variables which are given in equation (10). These are Return on Invested Capital (ROIC), Weighted Average Cost of Capital (WACC), Invested Capital (A) and New Invested Capital (I). With I simply being the change in invested capital between t=0 and t=-1. This section will discuss how to get appropriate measures for the different variables, Appendix A will give an overview of the different raw variables and list the sources of the data.

Damodaran (2007) proposes to use earnings before interest and taxes (EBIT) minus the operating taxes ( ) divided by the Invested Capital as a measure for the Return on Invested Capital. Here the operating tax rate can be calculated as follows:

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Here is the marginal tax rate and is the Interest Expenditures on Debt.

When measuring Invested Capital he proposes to use book values instead of market values. This because market values include the expected value of growth assets and therefore mark up the value of the existing assets by including their earnings potential. Then there are two ways of measuring invested capital, one way is to use the asset-based approach which sums the value of the fixed assets and the non-cash working capital. This paper however will use the capital-based method, which sums the book value of debt and equity and deducts the excess cash balance and goodwill. Excess cash need to be removed because most of the time cash is invested in low return investments and therefore not removing the cash balance from invested capital gives a wrong view with regards to value from operations. While no clear cut measure for operating cash exist, Koller et al. (2010 p.145 ) propose to estimate the operating cash as 2% of the total revenue in that year. Additionally goodwill will be deducted from the invested capital as goodwill normally constitutes a premium over the book value of assets, which are acquired in a take-over. Removing goodwill therefore gives a better estimate for the value of operations. If however someone is interested in the problem from an investor point of view goodwill does not need to be removed. This because an investor actually pays the goodwill for the assets. Therefore in order to assess the profitability of the investment, goodwill needs to be included. In most cases both the asset-based and the capital-based method will provide similar outcomes.

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13 classified as debt. Examples are pension, or healthcare obligations. However, the capital based approach can also be biased when a company has holdings in other companies. This would increase the measure of invested capital and reduce the measure of return on invested capital. This paper will average the invested capital capital in a given year in order to smooth the measure for invested capital (Invested Capital of the beginning of a year + the Invested Capital at the end of the year, divided by two). Damodaran (2007) also discusses some other biases which arise due to the fact that some items are expensed, while in fact they should be capitalized (and depreciated at an appropriate rate). Examples are, R&D expenditures and marketing expenditures. An additional problem is that EBIT is susceptible to different accounting measures with regards to depreciation. A possible adjustment would be to use the Cash Flow Return on Invested Capital, which uses EBITDA instead of EBIT and adds back accumulated depreciation to the Invested Capital. However, these kind of adjustments are beyond the scope of this paper.

The Weighted Average Cost of Capital can be calculated with the following formula:

( ) (13)

Where is the pre-tax cost of debt, D is the level of debt E is the level of equity and the return on equity. is estimated by dividing the Interest Expense on Debt by the average debt in a year. The cost of equity can be estimated with the following equation:

( ) (14)

Here is the risk-free rate, is a smoothed beta according to Blume’s (1975) beta smoothing method. Which can be done with equation 15.

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Where = Covar( , )/Var( ,), is the market return and is the return on security i. The beta needs to be smoothed because of sampling errors when estimating betas. The argument is that large betas have a higher potential to be biased upwards and lower betas have a higher chance to be biased downwards. Blume’s method effectively solves this problem.

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14 flows for a specific period and then take the return on invested capital in the last period as the return on new invested capital to estimate the continuing value. This paper does not explicitly forecast any cash flows, thus another way needs to be found to estimate the return on new invested capital. The problem is that it is not directly observable with standard accounting methods. One possible way to estimate the return on new invested capital is with equation 16. However as already said, this measures often gives unreasonable measures for return on new investment and therefore return on new invested capital is left out of the regression model.

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Data Description

Data on the companies constituting the S&P500 index from 1988-2012 has been collected from Datastream and Worldscope. For a full list of variables with their mnemonics look in Appendix A. Over the years 1062 companies have been part of the S&P500 index. For 50 companies Datastream had no data available and therefore they have been excluded from the analysis. While the balance sheets of companies in the financial sector (ICB code 8000) are hard to interpret and because the measures proposed in this paper have little to say about this sector, they have also been removed from the analysis. This reduces the total data set with an additional 172 companies and leaves us with 840 companies.

This dataset still has several problems. The first problem is that a lot of data points are missing. Little and Rubin (1987) provide an extensive discussion on how to deal with missing data. First one needs to make assumptions about the pattern of the missing data. Data may be either missing completely at random (MCAR), missing at random (MAR) or not missing at random (NMAR). MCAR means that the missing data depends neither on the independent variables, nor on the dependent variable. MAR means that the missing data is dependent on the independent variables, but not dependent on the dependent variable. Finally NMAR, means that both the MCAR and MAR assumptions do not hold. Missing data in this

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15 data is different from the level of excess returns from the companies with complete information.

Effectively, this would mean that the missing data is NMAR. Using simple imputation methods therefore could seriously bias the results. In chapter 11 of their book, Little and Rubin (1987 p.218-241) give an extensive discussion how to deal with these kind of data problems.

One possible solution they give is the use of the Expectation-Maximization Algorithm (EM algorithm). The EM algorithm has 2 steps, an expectation step and a maximization step. Within the estimation step it gives an expectation of the missing value and then in the maximization step it maximizes the

log-likelihood given the expectation. When the distribution is of the exponential family then the EM algorithm has some nice properties, that is with each iteration the log-likelihood increases. However, there is no guarantee that you will find the most likely value as the algorithm might get stuck at a local maxima. Additionally and probably more problematic, when the real distribution of the total population is not of the exponential families, or that the distribution is not correctly specified, the EM algorithm might bias the data (Little and Rubin 1987 p. 225-227). It is plausible that the real distribution of excess returns might not follow a normal distribution and therefore the EM algorithm might introduce a bias into the results. When looking at table 3 we can see that the distribution of the sample is skewed to the right. At the same time the current sample is also biased to the right as it focuses on the survivors, which should have higher excess returns than the non-survivors. It seems to be so that with particular

assumptions the EM algorithm might actually give better predictions of the total population. However, for practical reasons this thesis will use pairwise deletion to deal with missing data points. This

introduces a certain survivorship bias to the data, as the dataset now only contains the companies with a long track record (which are the survivors and generally also the bigger companies). This means that we can also only infer conclusions on these companies. With the use of pairwise deletion it is known that the data will be biased towards the survivors, the use of the EM algorithm might overcome this bias, but at the same time it is uncertain to what extent it might introduce a new one (if the real distribution is non-normal). The problem with this pairwise deletion is that 546 additional companies were excluded from the analysis, seriously reducing the degrees of freedom in the sample.

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16 and a negative invested capital. This company will have a positive return on invested capital; this variable however has no connection to the true performance of the company. This is why negative estimates of invested capital should be removed from the dataset. Also consider companies with a very small amount of invested capital. If the estimation of invested capital were accurate, then it would not create any problems. However, consider a company with an EBIT of $50.000 and an estimated amount of invested capital of $100.000 the return on invested capital would in this example be 50%, however if the real invested capital would be $200.000 so the estimation would be off by $100.000 then the return on invested capital would be 25%. However, when EBIT would be $500.000 and the estimated Return on Invested Capital would be $1.000.000 while the true Invested Capital is $1.100.000 then the difference between the estimated return on invested capital and the real return on invested capital would be much lower (5% versus 25%). Therefore it might be wise to set the cut-off point somewhere higher than just an estimated invested capital of 0. Fama and French chose such a cut-off point. This paper will do the same. Therefore an additional 51 companies are excluded from analysis. Eventually this leaves us with 243 different companies.

Table 1 Number of Companies

Total Companies S&P 500 1062

Not Available 50

ICB code 8000 172

Full Data Unavailable 546

Too low invested capital 51

Total Remaining for Analysis 243

This leaves us with a total of 5589 individual observations. Which is equal to the amount of companies (243), times the amount of years (23). Take a note that while the data ranges from 1988-2012, there is a lagged variable of two years in the regression estimation, which effectively means that the period under estimation is from 1990-2012.

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Table 2, Number of companies per industry Industry Name Oil & Gas Basic Materials Industrials Consumer Goods Healthcare Consumer Services

Telecommunications Utilities Technology

Industry Code 1 1000 2000 3000 4000 5000 6000 7000 9000

Nr. of

Companies 20 20 52 43 18 43 4 29 14

Table 2, presents a description of the number of companies per industry, Financials have been excluded, because financial information from these companies can not be interpreted the same way as with the other companies.

A description of the dataset of the 243 companies with truncated data at 1% to remove the biggest outliers can be found below in table 3. The descriptive statistics per industry can be found in Appendix B, additionally this appendix also includes a graph which shows how the excess returns, ROIC and the WACC evolve over time.

Table 3 Descriptive Statistics Full Sample

ROIC WACC Excess Returns B1 B2

Mean 0.1844 0.0595 0.1248 0.1132 0.9639 Median 0.1526 0.0582 0.0901 0.0806 0.9536 Maximum 0.9591 0.1230 0.9136 0.9419 2.0502 Minimum -0.3428 0.0106 -0.3899 -0.4443 0.3579 Std. Dev. 0.1430 0.0192 0.1449 0.1407 0.1863 Skewness 1.291 0.327 1.290 1.425 1.103 Kurtosis 6.914 3.052 6.805 8.539 7.716 Jarque-Bera 5070.107 99.123 4870.590 8947.362 6249.317 Probability 0 0 0 0 0

This table gives the description of the dataset containing all 243 companies of which full data is available of companies which were part of the S&P500 from 1990-2012. The data has been truncated at 1%. Roic is return on invested capital, wacc is the weighted average cost of capital, b1 is the first regression term and b2 is the second regression term

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18 Table 4 Correlation between parameters

ROIC 1 -0.033 0.991 0.738 0.050

WACC 1 -0.167 -0.172 -0.031

Excess Returns 1 0.751 0.054

B1 1 0.030

B2 1

This table gives the correlation coefficients of the different paramaters. Roic is return on invested capital, wacc is the weighted average cost of capital, b1 is the first regression term and b2 is the second regression term

Logically we find a strong positive correlation between excess returns and return on invested capital. Additionally we see a relatively small but still negative correlation between the weighted average cost of capital and excess returns. Furthermore we find a low correlation between the different explanatory variables, signaling no problem of multicollinearity.

Methodology

From a theoretical point of view it would be best to try and estimate equation 10. However, the real return on new invested capital is hard to estimate. At the same time the expected value of the in equation 10 is quite small as it takes a percentage of a percentage. Therefore excluding it from analysis should not bias the results too much. For these reasons this paper will focus on equation 11, which is repeated below.

( ) ( )

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This regression equation simply has two different regression coefficients, where is equal to (1-δ) and is equal to (1-δ)* . Note that this regression equation does not contain any constant. For this reason it is not possible to make full use of the panel structure of the data, with either a fixed effects model or a random effects model. For this reason the equation has been rearranged, by dividing each variable with

to get equation 17. ( ) ( ) (17)

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19 Generally, choosing between a random or fixed effects model would require performing a Hausman-Test. The random effects model requires that the independent variables are uncorrelated with the error term. The fixed effects model does not require this assumption. When the assumption is met, the random-effects model is more efficient than the fixed effects model. When comparing the fixed effects model, the random effects model and a model which simply pools the data and performs an OLS, we can see that each require different assumptions. Simply pooling the data assumes that there are no time-specific or company-time-specific effects on the constant. Choosing a random or fixed effects method allows the constant to vary cross-sectional or over time. Then the pattern of these effects determines whether to use a fixed- or random-effects model. When the effects are random than the random-effects model is preferred, however when the effects are non-random a fixed effects method is preferred.

The advantage of the period or cross-sectional fixed effects method is that it is able to capture omitted variables when the effect of the omitted variable is fixed either cross-sectional, for the period method, or over time for the cross-sectional method. A simple example would be the relationship between educational level and income, the relationship might depend on an omitted variable “ability”, which is fixed over time but can vary between individuals. A cross-sectional fixed effects model can implicitly take ability into account.

Consider using a fixed effects model for our problem at hand. It would allow for different intercepts either cross-sectional or over time. It assumes that the decay rate of excess returns is constant over time and between companies, however it allows for varying levels of long-term excess returns either over time (for the period-fixed effects method) or between companies (for the cross-sectional fixed effects model). Using a period fixed effects model would allow for varying constants between periods, which would imply that the long-term level of excess returns varies over time, this would not be a troublesome assumption. However, when using a company fixed effects model it is impossible to find useful estimates for the long-term level of excess returns, as the long-term level of excess return is allowed to cross-vary between companies, which no longer implies that those companies converge to the same level. This leads to the conclusion that the long-term level of excess returns is no longer interpretable.

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20 In the literature section already two approaches to do this have been discussed. For example there might exist differences in the long-term level of excess returns and the decay rate of excess returns between companies of different industries and between winners / losers and normal companies. This paper will run regressions on the whole sample, on the different individual industries and on the normal companies (i.e. the winners and losers are excluded) at the economy level and the industry level. The winners and losers are chosen on the basis of their average level of excess returns over the whole time-period. For the economy wide analysis the top 10% and the bottom 10% are excluded from the analysis and for the industry specification the top 2 and bottom 2 are excluded from the analysis.

Additionally there exists the potential problem of autocorrelation and heteroskedasticity in the error term. When these problems exist the estimation at hand would still be the unbiased, however it would no longer be efficient, or in other words the standard deviations would be inappropriate. Different ways exist to deal with these problems. One potential solution is discussed by Newey and West (1987). Another possible solution, specifically for panel data are the panel corrected standard errors, these are discussed in Beck and Katz (1995). For the simple OLS, which is performed in Matlab, the method by Newey and West will be used and for the fixed effects methods in eviews the panel corrected standard errors will be used.

Results

Table 12 in Appendix C presents the results of the pooled OLS of the regression in equation 11, both the regression parameters of the economy wide estimation and the per industry estimation have been included in this table. Additionally table 5 below presents the fundamental parameters of the same test. First notice that all of the regression coefficients in table 12 are significant at the 1% level (except for the telecommunications industry, which are significant at the 5% level). When looking at the fundamental parameters, all of the parameters are significant at the 1% level. Furthermore it has to be said that the standard deviation of the δ is equal to the standard deviation of the estimate for b1 and the standard deviation of the γ is equal to:

] * S * [

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21 Here is the partial derivative of / with respect to and is the partial derivative of / with respect to and S is the covariance matrix of the regression of dimension 2x2.

Table 5 Fundamental Parameters OLS equation 11

Coefficient Estimate

Standard Deviation

t-statistic Coefficient Estimate

Standard Deviation t-statistic All Healthcare δ 0.2166*** 0.0228 9.500 δ 0.2759*** 0.0578 4.773 γ 0.0472*** 0.0047 10.012 γ 0.1073*** 0.024 4.471

Oil & Gas Consumer Services

δ 0.3781*** 0.0598 6.323 δ 0.2230*** 0.0542 4.114

γ 0.0519*** 0.0095 5.467 γ 0.0431*** 0.0096 4.491

Basic Materials Telecommunications

δ 0.4301*** 0.0914 4.706 δ 0.1459** 0.0730 1.999

γ 0.0828*** 0.0243 3.408 γ 0.0224** 0.0103 2.171

Industrials Utilities

δ 0.2099*** 0.0453 4.634 δ 0.4576*** 0.0944 4.847

γ 0.0490*** 0.0105 4.665 γ 0.0501*** 0.0175 2.866

Consumer Goods Technology

δ 0.1368*** 0.0339 4.035 δ 0.3787*** 0.0824 4.596

γ 0.0370*** 0.0077 4.799 γ 0.1357*** 0.0425 3.193

This table gives the estimates of the fundamental parameters of equation 11 (( ) ( ) , the estimate of

is equal to (1-δ) and is equal to (1-δ)* . Where a is the return on invested capital, k is the cost of capital, A is the invested capital, δ is the decay rate of excess returns and is the long term rate of excess returns.

***, **, * respectively mean significance at the 1%, 5% and 10% level.

It can be seen that the decay rate of excess returns and the long term level of excess returns differ substantially between industries. When using the economy wide estimation we have a decay rate of 22%, while the industry decay rates range from 14% in the consumer goods industry to 46% in the utilities industry. The same goes for the long term rate of excess returns. For the economy wide

estimation one can find a long-term rate of excess returns of 4,7%, while for the industries the long-term rate of excess returns range from 2,2% to 13,6% for the technology industry.

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22 parameters. Note that the telecommunications industry is not included as this industry only contained 4 companies. Additionally table 9 will summarize all of the fundamental parameters of the different regressions into one table.

Table 6 Fundamental Parameters OLS equation 11 Value Leaders

and Losers Excluded

Standard Deviation

Standard Deviation t-statistic All Healthcare δ 0.3168*** 0.0293 10.812 δ 0.3729*** 0.0662 5.633 γ 0.0651*** 0.0075 8.685 γ 0.1548*** 0.0380 4.075

δ 0.4433*** 0.0567 7.818 δ 0.2532*** 0.0581 4.358

γ 0.0602*** 0.0111 5.421 γ 0.0478*** 0.0100 4.780

δ 0.4742*** 0.1252 3.788 δ - - -

γ 0.0979** 0.0416 2.354 γ - - -

δ 0.2445*** 0.0510 4.794 δ 0.5439*** 0.0826 6.585

γ 0.0557*** 0.0128 4.353 γ 0.0691*** 0.0221 3.125

δ 0.1664*** 0.0378 4.402 δ 0.4220*** 0.1094 3.857

γ 0.0437*** 0.0093 4.695 γ 0.1450** 0.0592 2.449

This table gives the estimates of the fundamental parameters of equation 11 (( ) ( )

with the value winners and losers removed. The estimate of is equal to (1-δ) and is equal to (1-δ)* . Where a is the return on invested capital, k is the cost of capital, A is the invested capital, δ is the decay rate of excess returns and is the long term rate of excess returns.

It can be seen that most parameters are still considered significant at the 1% level (except for the long-term rate of excess returns for the basic materials and the technology industry which are significant only at the 5% level). It seems that excluding the industry leaders and losers from the analysis actually increases the decay rate of excess returns and increases the long term rate of excess returns that is estimated.

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23

( )

( ) (17)

Results from the redundancy test are given in table 16 in Appendix C. For the economy wide estimation and most industries the period and cross-section fixed effects are highly significant. When the value leaders and losers are included there are several exceptions, which are the basic materials industry, where the cross-sectional fixed effects are only significant at the 10% level and the healthcare industry, where the cross-sectional fixed effects are not significant (p-value of 0.15). However, when the value leaders and losers are excluded a few things happen. The cross-sectional fixed effects are no longer significant for the Oil & Gas Industry, the healthcare and the technology industry, at the same time the basic materials industry is only significant at the 10% level. The methodology section has given an extensive discussion on this topic and explains what kind of effect the existence fixed effects has on the regression. To sum up here it suffices to say that the existence of period fixed effects would not alter the interpretability of the data too much. However, when cross-sectional fixed effects are present we lose interpretability of the long-term rate of excess returns. The reason behind this is that, the constant is allowed to vary per cross-section, practically giving each cross-section an individual level of long-term excess returns. In contrast to this the pooled OLS without fixed effects, forces the different cross-sections to have the same intercept and therefore assumes an equal intercept for each cross-section. With period fixed effects included the long-term level of excess returns is no longer equal between periods. While for some industries there appear to be no cross-sectional fixed effects, to be consistent all the estimations will include period and cross-sectional fixed effects.

Furthermore a Hausman test has been performed to test whether a random-effects or a fixed effects measure should be used. The Hausman test favored the fixed effects measure for both the cross-sectional and the period specific model.

Table 14 in Appendix C gives the results of the regression on estimates for and . It can be seen that all parameters are highly significant at the 1% level. These estimates lead to the decay rates which are reported in table 7. Again we can see that all estimates are highly significant at the 1% level (except for the telecommunications industry which is significant only at the 5% level). We can see that the decay rate of excess returns has substantially increased. For the economy wide estimation the decay rate of excess returns increased from 22% (with the pooled OLS estimation) to 38% to the fixed effects

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24 Table 7 Cross-Sectional and Period Fixed Effects regression on

equation 11

Industry Coefficient Estimate

Standard Deviation

t-Statistic

All δ 0.3825*** 0.0188 20.379

Oil & Gas δ 0.5594*** 0.0645 8.673

Basic Materials δ 0.3891*** 0.0602 6.468 Industrials δ 0.3997*** 0.0409 9.784 Consumer Goods δ 0.2719*** 0.0356 7.644 Healthcare δ 0.3546*** 0.0560 6.337 Consumer Services δ 0.4287*** 0.0421 10.174 Telecommunications δ 0.3541** 0.1765 2.007 Utilities δ 0.5564*** 0.0718 7.753 Technology δ 0.3937*** 0.0611 6.448

This table gives the regression estimates of the fundamental parameters of equation 17 (( )

( ) ), where equation 17 is

regressed with cross-sectional and period fixed effects. is a constant and the estimate of is equal to (1-δ). Additionally a is the return on invested capital, k is the cost of capital, A is the invested capital and δ is the decay rate of excess returns.

Table 8 Cross-Sectional and Period Fixed Effects regression on equation 11 Without winners and losers

Industry Coefficient Estimate

Standard Deviation

t-Statistic

All Δ 0.4512*** 0.0230 19.609

Oil & Gas Δ 0.6415*** 0.0707 9.079

Basic Materials Δ 0.4685*** 0.0746 6.280 Industrials Δ 0.4280*** 0.0442 9.681 Consumer Goods Δ 0.3282*** 0.0362 9.055 Healthcare Δ 0.4251*** 0.0666 6.379 Consumer Services Δ 0.4178*** 0.0435 9.603 Telecommunications Δ - - - Utilities Δ 0.6454*** 0.0598 10.789 Technology Δ 0.4190*** 0.0758 5.525

This table gives the regression estimates of the fundamental parameters of equation 17 (( )

( ) ), where equation 17 is

regressed with cross-sectional and period fixed effects. is a constant and the estimate of is equal to (1-δ). Additionally a is the return on invested capital, k is the cost of capital, A is the invested capital and δ is the decay rate of excess returns. Here the value leaders and losers have been excluded.

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25 Additionally, the same regression is again estimated with the value leaders and losers excluded. The regression estimates are again significant at the 1% level and presented in table 15 in Appendix C. The fundamental parameters are reported in table 8 above.

We again can see that excluding the value leaders and losers seems to increase the decay rate of excess returns. For a full overview of decay rates per specification take a look in table 9.

In table 9 the differences between the regressions becomes really apparent. When looking at the decay rate of excess returns the decay rate increases when moving from the pooled OLS estimation to the fixed effects estimation. Second, it also increases when the value leaders and losers are excluded from

analysis.

With respect to the long-term rate of excess returns we can only make inference about the change between including and excluding the value leaders and losers from the pooled OLS estimation. In this sense we see that in every industry the long-term rate increases. Additionally, the long-term excess returns for most industries is closer to the industry median. This is not a strange finding. The higher the decay rate of excess returns, the closer the long-term level of excess returns should be with the industry median. As it presupposes that most companies can not continue to underperform or outperform the industry.

Table 9 also presents the adjusted r-squared of the different models. The adjusted r-squared is a

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26 excess returns actually increases when the value leaders and losers are excluded. For this reason it would be appropriate to also test a non-linear specification with fixed effects. However, due to limited time, this is left for further research.

Table 9 Summary of Fundamental Parameters

1a 1b 2a 2b Coefficient 1a 1b 2a 2b

All Healthcare

δ 0.2166 0.3168 0.3825 0.4512 δ 0.2759 0.3729 0.3546 0.4251

γ 0.0472 0.0651 - - γ 0.1073 0.1548 - -

Adjusted R-Squared 0.569 0.601 0.604 0.489 Adjusted R-Squared 0.446 0.441 0.466 0.326

δ 0.3781 0.4433 0.5594 0.6415 δ 0.2230 0.2532 0.4287 0.3282

γ 0.0519 0.0602 - - γ 0.0431 0.0478 - -

δ 0.4301 0.4742 0.3891 0.4685 δ 0.1459 - 0.3541 -

γ 0.0828 0.0979 - - γ 0.0224 - - -

Adjusted R-Squared 0.302 0.189 0.463 0.396 Adjusted R-Squared 0.649 - 0.519 -

δ 0.2099 0.2445 0.3997 0.4280 δ 0.4576 0.5439 0.5564 0.6454

γ 0.0490 0.0557 - - γ 0.0501 0.0691 - -

δ 0.1368 0.1664 0.4287 0.3282 δ 0.3787 0.4220 0.3937 0.4190

γ 0.0370 0.0437 - - γ 0.1357 0.1450 - -

Adjusted R -Squared 0.707 0.709 0.722 0.694 Adjusted R -Squared 0.399 0.415 0.550 0.497

This table gives an overview of all the fundamental parameters which were found in the paper. In the model specification a 1 stands for the data found from the pooled OLS estimation of equation 11 (( ) ( ) ) and a 2 stand for the cross-sectional and

period fixed effects regression of equation 17 (( )

( ) ). At the same time an a stands for value leaders and losers

included and a b stands for the value leaders and losers excluded. Here a stand for the return on invested capital, k is the cost of capital, A is the amount of Invested Capital, δ is the decay rate of excess returns and γ is the long term rate of excess returns.

Note that for industry 6 the b estimations are missing, due to a too small sample size and for the 2 estimations the long-term rate of excess rate is excluded because it lacks interpretability with that estimation method.

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27

Figure 1 gives the evolution of excess returns over time. The portfolios are based on a ranking of excess returns in the base year, then the median value of these portfolios are followed over the consecutive years.

Figure 1 shows some major differences between the different groups. First consider the lowest group. This group converges rather quickly to a reasonable amount. However, do note that this group is probably most affected by the survivorship bias, as companies which were taken-over or went bankrupt, are excluded from analysis. Therefore the rate of convergence for this group is probably overstated. Second we can see that the highest group also converges rather quickly. However, for the other groups the average median rate is quite constant over the different periods. While it is the average median value, it is hard to infer that excess returns do not decay, however we could argue for the fact that there is no common long term rate of excess returns. If there was a common long-term rate of excess returns we should see more convergence and it would be more probable that the rank of the portfolio in the beginning should not be this similar at the end of the period. However, precise conclusions are hard to make, based on such a graph alone. However, this graph does show that big differences exist between different companies. Therefore it is questionable if the simple pooled OLS is able to fully capture the differences between the different companies, especially when considering the finding of significant fixed effects. It also partially supports the finding that the adjusted r-squared is higher for the fixed effects estimation which includes the value leaders and the value losers, as it seems to be so that the model fits best for the value leaders and losers. At the same time it also shows the need to address the potential non-linearity in the estimation.

-0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 1 2 3 4 5 level of excess Returns period

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28 The same portfolio approach has also been performed on the industries. Inference from these graphs is however difficult as the sample size of each industry is rather small. Still I would cautiously argue that it seems to be so that there are differences between industries. At the same time the distinction between industries does not seem to reduce the differences between individual companies a lot, as there still are big differences between the different portfolios at the end of period 5.

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29 While this paper does find some evidence that the model with decaying excess returns is more appropriate for companies with excess returns further away from the mean. In order to be conclusive, the linearity has to be tested. However, due to a lack of time, this is left for further research.

Additionally Hawawini et al. (2003) coined the notion that distinguishing between value leaders, losers and “normal” companies might improve the estimation. This paper gives some evidence which supports their findings. This paper both finds different decay rates and different levels of adjusted r-squared for the group with and without value leaders and losers. The findings are partially contradictory to the expectations. The decay rate of excess returns increases when value leaders are excluded. However, at the same time (at least for the fixed effects estimation) the adjusted r-squared is higher for the full sample, compared to the sample which excludes the value leaders and losers. Signaling that the model of decaying excess returns is more appropriate for the value leaders and losers. However, more research is needed to be conclusive.

Conclusion

This paper gives some insights into the mean reversion of excess returns. Several different methods have been tested which are in correspondence with the existing literature on the topic. A simple pooled OLS has been performed on an economy wide specification and an industry specific specification.

Additionally a fixed effects method has been estimated in order to cope with potentially varying levels of long-term excess returns between companies. These models have been tested on a sample which includes the value leaders and value losers and on a sample which excludes them.

Results are comparable to similar studies. The simple OLS measure provides a decay rate of excess returns of 22% and shows some variation between different industries. This specification assumes an constant level of long-term excess returns, which is equal amongst the different companies. This means that for the economy wide estimation, it is assumed that the excess returns of all the companies converge to this level and for the industry specific estimation it is assumed that this level is different between industries and equal between companies within industries. A fixed effects redundancy test shows that for the economy wide estimation and for most industries this assumption might not be true. Also the portfolio analysis, following Nissim and Penman (2001) in figure 1 has provided some evidence that the long-term levels of excess returns might differ between companies. Specifically it provides some evidence that companies who outperform will continue to outperform, while the magnitude of

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30 increases from 22% to 38%. Again we see huge differences between industries. Still one has to note that for some industries, such as the healthcare industry the question whether excess returns converge to a similar level was not rejected. Additionally when value leaders and losers are excluded, this assumption might not be rejected for some additional industries, such as the Oil & Gas and the Technology industry. Additionally when the assumption of equal levels of long-term excess returns is abandoned, the adjusted r-squared of the fixed effects model without value leaders and losers decreases. This in combination with the findings of figure 1 provides some evidence that the effects of decaying excess returns are more appropriate for these value leaders and losers. However, more research is needed in order to be conclusive.

Still several problems remain unsolved. The most important problem is the missing data. About 30% of the full dataset consisted of missing data. This paper chose to use pairwise deletion, leading to a survivorship bias towards the bigger companies which have a long track record. Several imputation methods exist which calculate probable values for these missing values. One example would be to use the EM algorithm. While the approach of pairwise deletion has introduced a survivorship bias and eats away degrees of freedom, which decreases the efficiency of the results. The EM-algorithm also has the potential problem of introducing a bias if the true distribution of the population does not follow a normal-distribution (or any other distribution of the exponential family).

Another thing which could be done is to use a likelihood approach to estimate the different parameters. Basically what it does, is that it assumes a particular distribution and then tries to maximize the

probability of finding the observed values, given the model. Part of this paper already incorporated a likelihood approach, namely the fixed effects redundancy test. One of the nice properties of likelihood approach is that it is quite intuitive to compare different models with a likelihood ratio test, of which this redundancy test is an example. This paper tried to test which model specification is actually the best, with a likelihood approach this could be done more easily.

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31 The last problem which still is unaddressed is whether a non-linear model would fit the data better. Fama and French (2000) found that a linear model might be more appropriate, this because the decay rate is higher when the level of excess returns is further away from the mean and is higher when the level of excess returns is below the mean.

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Damodaran, A., (2007). Return on Capital (ROC), Return on Invested Capital (ROIC) and Return on Equity (ROE): Measurement and Implications. Stern School of Business p. 1-69

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Hawawini, G., Subramanian, V., Verdin, P., (2003). Is Performance Driven by Industry-or Firm-Specific Factors? A New Look at the Evidence. Strategic Management Journal, Vol. 24, Issue 1, p. 1-16. Koller, T., Goedhart, M., Wessels, D., (2010). Valuation, Measuring and Managing the Value of Companies, 5th edition, John Wiley & Sons Inc., New Jersey.

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32 Nissim, D., Penman, S., (2001). Ratio Analysis and Equity Valuation: from Research to Practice. Review of Accounting Studies, Vol. 6, Issue 1, p. 109-154.

Porter, M.E., (1980). Competitive Strategy. The Free Press, New York. Stigler (1963). Capital and rates of returns in manufacturing industries

Mater Thesis Mulder, D., (2013). A More General Approach to Estimate the Effects of Competition on Performance (unpublished)

http://www.irs.gov/pub/irs-soi/02corate.pdf accessed 5 october 2013

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33

Appendix

Appendix A Description of variables

Table 10 Description of Variables Employed

Raw Variables Shortcut Source Code

Company Code ISIN DATASTREAM ISIN

Industry Code ICB DATASTREAM ICB

Earnings Before Interest and Taxes EBIT WORLDSCOPE WC18191

Cash Balance C WORLDSCOPE WC02005

Common Equity E WORLDSCOPE WC03501

Preferred Stock Ps WORLDSCOPE WC03451

Total Debt D WORLDSCOPE WC03255

Goodwill G WORLDSCOPE WC18280

Interest Expense on Debt IED WORLDSCOPE WC01251

Revenues Sales WORLDSCOPE WC01001

Reported Taxes Tr WORLDSCOPE WC01451

Marginal Tax Rate Tm http://www.irs.gov/pub/irs-soi/02corate.pdf

Monthly Return Index RI DATASTREAM RI

Market Return RI DATASTREAM (S&P500) RI

Risk Free Return Rf http://www.federalreserve.gov/releases/h15/data.htm

Adjusted Variables Shortcut Calculation

Operating Cash OC 2% x Sales*

Excess Cash EC C – OC

Invested Capital A E + Ps + D - EC – G

Operating Tax Rate To (Tr - Tm * IED)/EBIT Return on Invested Capital ROIC (EBiT * (1-To)) / A

Monthly Returns Ri LN(RI2/RI1)

Beta B cov(Ri,Rm)/Var(Rm)

Beta Smoothed B* 0,33 + 0,66B

Return on Equity Re Rf + B*(5%)**

Return on Debt Rd IED / D

Weighted Average Cost of Capital WACC (E/(E+D)*Roe + D/(E+D)*(1-tm)Rd

Excess Returns ER ROIC – WACC

* Koller (2010) states that operating cash can be estimated by taking 2% of the total revenues. ** Koller (2010) states that the true market premium is around 5%.

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34

Appendix B Descriptive Statistics per Industry

Table 11 Descriptive Statistics per industry

Oil & Gas

Mean 0.1304 0.0682 0.0621 0.0512 0.9210 Median 0.1198 0.0675 0.0528 0.0430 0.9269 Maximum 0.6165 0.1174 0.5471 0.5189 1.6689 Minimum -0.2753 0.0306 -0.3234 -0.3660 0.3886 Std. Dev. 0.0945 0.0170 0.0951 0.0877 0.1647 Skewness 0.717 0.331 0.740 0.430 0.519 Kurtosis 6.979 2.735 6.665 7.117 6.037 Jarque-Bera 342.920 9.698 299.394 339.034 197.026 Probability 0 0.008 0 0 0 Basic Materials

Mean 0.1658 0.0646 0.1000 0.0925 0.9611 Median 0.1511 0.0633 0.0879 0.0845 0.9521 Maximum 0.7255 0.1218 0.6724 0.8659 1.8668 Minimum -0.3334 0.0119 -0.3899 -0.4004 0.4584 Std. Dev. 0.1142 0.0197 0.1151 0.1179 0.1795 Skewness 0.548 0.331 0.564 1.049 1.023 Kurtosis 6.497 3.141 6.344 11.280 7.157 Jarque-Bera 255.750 8.606 237.167 1389.312 405.169 Probability 0 0.014 0 0 0 Industrials

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35 Table 11 continued

Consumer Goods

Mean 0.2215 0.0573 0.1643 0.1539 0.9800 Median 0.1927 0.0555 0.1317 0.1178 0.9569 Maximum 0.9434 0.1219 0.8560 0.9298 1.9731 Minimum -0.3198 0.0107 -0.3630 -0.4443 0.3760 Std. Dev. 0.1488 0.0190 0.1523 0.1543 0.1986 Skewness 0.850 0.413 0.844 1.020 1.252 Kurtosis 5.723 3.103 5.422 6.747 7.221 Jarque-Bera 421.584 28.211 356.656 744.119 980.560 Probability 0 0 0 0 0 Healthcare

Mean 0.2836 0.0554 0.2290 0.2048 0.9590 Median 0.2666 0.0551 0.2172 0.1894 0.9393 Maximum 0.8742 0.1176 0.8201 0.9288 2.0258 Minimum -0.2559 0.0124 -0.3141 -0.4153 0.4004 Std. Dev. 0.1728 0.0194 0.1760 0.1743 0.2209 Skewness 0.346 0.224 0.319 0.568 1.341 Kurtosis 3.513 2.964 3.341 4.756 7.404 Jarque-Bera 12.677 3.421 8.962 74.925 453.091 Probability 0.002 0.181 0.011 0 0 Consumer Services

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36 Table 11 continued

Telecommunications

Mean 0.1456 0.0518 0.0944 0.0856 0.9468 Median 0.1491 0.0529 0.1032 0.0760 0.9733 Maximum 0.2964 0.0861 0.2401 0.2384 1.2606 Minimum -0.0513 0.0106 -0.0916 -0.0845 0.4265 Std. Dev. 0.0625 0.0183 0.0667 0.0646 0.1630 Skewness -0.652 -0.254 -0.540 -0.047 -1.197 Kurtosis 4.075 2.612 3.507 3.499 4.779 Jarque-Bera 10.824 1.552 5.390 0.976 33.372 Probability 0.004 0.460 0.068 0.614 0 Utilities

Mean 0.1038 0.0502 0.0537 0.0504 0.9588 Median 0.1042 0.0491 0.0521 0.0481 0.9626 Maximum 0.4634 0.0911 0.4148 0.3218 1.7451 Minimum -0.1317 0.0112 -0.1700 -0.2034 0.3579 Std. Dev. 0.0339 0.0147 0.0336 0.0334 0.1164 Skewness 2.033 0.166 1.859 1.149 0.600 Kurtosis 33.830 2.734 31.838 23.657 14.529 Jarque-Bera 26874.570 5.031 23495.900 12005.720 3728.661 Probability 0 0.081 0 0 0 Technology

Mean 0.2138 0.0626 0.1502 0.1273 0.9645 Median 0.1739 0.0612 0.1164 0.0995 0.9477 Maximum 0.9591 0.1224 0.9059 0.9309 2.0099 Minimum -0.3054 0.0149 -0.3518 -0.4352 0.4082 Std. Dev. 0.2031 0.0184 0.2054 0.1944 0.2103 Skewness 0.884 0.148 0.909 1.004 1.021 Kurtosis 4.544 2.873 4.516 6.067 5.879 Jarque-Bera 70.480 1.393 71.684 173.092 166.145 Probability 0 0.498 0 0 0

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37 0 0.05 0.1 0.15 0.2 0.25 19 90 19 92 19 94 19 96 19 98 20 00 20 02 20 04 20 06 20 08 20 10 20 12 R a t e Year

Figure 2 Median Level of Variables

over time

Excess Returns ROIC

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38

Appendix C Regression Coefficients

Table 12 Pooled OLS of equation 11

Standard Deviation

Standard Deviation t-statistic All Healthcare B1 0.7834*** 0.0228 34.360 B1 0.7241*** 0.0578 12.528 B2 0.0370*** 0.0027 13.704 B2 0.0777*** 0.012 6.475

B1 0.6219*** 0.0598 10.400 B1 0.7770*** 0.0542 14.336

B2 0.0323*** 0.0040 8.075 B2 0.0335*** 0.0054 6.204

B1 0.5699*** 0.0914 6.235 B1 0.8541*** 0.073 11.700

B2 0.0472*** 0.0070 6.743 B2 0.0191** 0.0074 2.581

B1 0.7901*** 0.0453 17.442 B1 0.5424*** 0.0944 5.746

B2 0.0387*** 0.0063 6.143 B2 0.0272*** 0.0049 5.551

B1 0.8632*** 0.0339 25.463 B1 0.6213*** 0.0824 7.540

B2 0.0319*** 0.0055 5.800 B2 0.0843*** 0.0164 5.140

This table gives the regression estimates of equation 11 (( ) ( ) , the estimate of is equal to (1-δ) and

is equal to (1-δ)* . Where a is the return on invested capital, k is the cost of capital, A is the invested capital, δ is the decay rate of excess returns and is the long term rate of excess returns.

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39 Table 13 Pooled OLS of equation 11 with leaders and losers removed Coefficient Estimate

Standard Deviation

Standard Deviation t-statistic All Healthcare B1 0.6832*** 0.0293 23.317 B1 0.6271 0.0662*** 9.473 B2 0.0445*** 0.0034 13.088 B2 0.0971 0.0148*** 6.561

B1 0.5567*** 0.0567 9.818 B1 0.7468 0.0581*** 12.854

B2 0.0335*** 0.0043 7.791 B2 0.0357 0.0050*** 7.140

B1 0.5258*** 0.1252 4.200 B1 - - -

B2 0.0515*** 0.0102 5.049 B2 - - -

B1 0.7555*** 0.051 14.814 B1 0.4561 0.0826*** 5.522

B2 0.0421*** 0.0071 5.930 B2 0.0315 0.0044*** 7.159

B1 0.8336*** 0.0378 22.053 B1 0.578 0.1094*** 5.283

B2 0.0364*** 0.0062 5.871 B2 0.0838 0.0200*** 4.190

This table gives the regression estimates of equation 11 (( ) ( )

with the value winners and losers removed. The estimate of is equal to (1-δ) and is equal to (1-δ)* . Where a is the return on invested capital, k is the cost of capital, A is the invested capital, δ is the decay rate of excess returns and is the long term rate of excess returns.

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40 Table 14 Cross-Sectional and Period Fixed Effects For Equation 17

Standard Deviation

Standard Deviation t-statistic All Healthcare B0 0.0590*** 0.0026 22.715 B0 0.1078*** 0.0143 7.547 B1 0.6175*** 0.0188 32.894 B1 0.6454*** 0.0560 11.534

B0 0.0446*** 0.0052 8.584 B0 0.0591*** 0.0054 11.029

B1 0.4406*** 0.0645 6.832 B1 0.5713*** 0.0421 13.558

B0 0.0482*** 0.0076 6.332 B0 0.0518*** 0.0180 2.883

B1 0.6109*** 0.0602 10.154 B1 0.6459*** 0.1765 3.660

B0 0.0633*** 0.0059 10.675 B0 0.0332*** 0.0040 8.371

B1 0.6003*** 0.0409 14.694 B1 0.4436*** 0.0718 6.182

B0 0.0575*** 0.0062 9.248 B0 0.0751*** 0.0118 6.384

B1 0.7281*** 0.0356 20.474 B1 0.6063*** 0.0611 9.929

This table gives the regression estimates of equation 17 (( )

( ) ) with cross-sectional and period fixed effects, the

standard errors are panel corrected standard errors. Here is a constant and is equal to (1-δ) Where a is the return on invested capital, k is the cost of capital, A is the invested capital and δ is the decay rate of excess returns.