Smoothed Capitalization Weighted Indexation

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University of Groningen

Faculty of Economics and Business

MSc Finance

Smoothed Capitalization Weighted Indexation

European Evidence

Tom J. Gortemaker

Master’s Thesis

Groningen, August 4

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Abstract

In this paper I examine the performance of smoothed capitalization weighted indexes relative to a market capitalization weighted index, and a fundamental index. The smoothed capitalization weighted indexes are formed on the basis of a simple moving average of market capitalization values. The constructed indexes cover European data during the period 2003 to 2013. I analyze whether smoothed capitalization weighted indexes generate a positive alpha after correcting for risk factors. I use the four factor model of Carhart to correct for risk. The significant alpha coefficients present evidence that smoothed capitalization weighted indexes generate higher risk-adjusted returns than market capitalization weighted indexes. I also find that the smoothed capitalization weighed indexes and the fundamental index produce equal risk-adjusted returns.

Keywords: Capitalization-weighted index; Smoothed capitalization-weighted index; Fundamental-based portfolio; Price inefficiency; Value bias

JEL Classifications: G11

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Preface

The course Institutional Investment Management lectured by mister Van der Meer enlarged my interest in the field of investment theory. Subsequently I bought the books Buffet – The Making Of

An American Capitalist and The Intelligent Investor of Benjamin Graham. Inspired by value investing,

the relative new concept Fundamental Indexation seemed as an interesting research area for my thesis. I would like to emphasize my appreciation for the assistance of my supervisors Damm and Plantinga, whereas I sincerely wish strength and recuperation for mister Damm. Mister Plantinga stimulated me to take a view by a different angle, smoothed capitalization weighting, and challenged me to develop my skills in Microsoft Excel. To obtain my data from Datastream I have regularly occupied the computers for my associate students, therefore I would like to make my apologies. I have to admit that the overload of data faced me with my lack of programming skills. For the arrangement of data and useful assistance in programming I express my appreciation for my pal Tim Kuipers. Furthermore, I am thankful for my internship opportunity at KroeseWevers Corporate Finance. During four months I have had the opportunity to learn from the valuation of companies in practice. I’m thankful for the inspiring working environment where I could discuss investment topics, especially with Berto Janssen. During my research I faced substantial physical distress and I would like to thank my family, friends and especially my girlfriend for their support. I learned a lot more about investment theory during the research and I hope this study will add new insights in its research area.

I. Introduction

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percent of all U.S. funds underperformed (after expenses) their benchmarks or had been liquidated from 2008 to 2012.

This paper focuses on passive managed portfolios. The most popular passive strategy is constructing a portfolio by weighting each individual stock based on its market value1 relative to the market value of the total stock market. These portfolios are market capitalization weighted. Market capitalization weighting has several advantages: it incurs lower fees and trading costs than active strategies, it provides a convenient way to participate in the broad equity market, it is highly correlated with trading liquidity thereby reducing portfolio transaction costs, and it is highly correlated with investment capacity and so allowing the use of passive indexing on an immense scale. However, if market prices appear to be inefficient, market capitalization weighted portfolios would be sub-optimal. Treynor (2005) and Hsu (2006) explain that market capitalization weighting will, as a price-related weighting method, lead to a performance drag due to overweighting overvalued stocks and underweighting undervalued stocks.

Portfolio construction methods which do not depend on prices, could eliminate the potential bias due to over- and undervaluation of stocks. In contemporary research, several price-indifferent construction methods are examined. A much studied alternative construction method is based on equally weighting, but it does not preserve all benefits of market capitalization weighting. Another portfolio construction method is fundamental indexation, as introduced by Arnott et al. (2005). This passive strategy retains the benefits of cap weighting. The fundamental indexation method constructs portfolios by weighting stocks on an array of price-indifferent measures of company size. These measures of company size are: book value, cash flow, revenues, gross sales, gross dividends and total employment. This strategy constructs a portfolio by weighting each stock by the company’s metric value relative to the sum of metric values of the total stock market. A composite fundamental index equally weights multiple of the fundamental metrics of company size. As a result this construction method seems to be able to break the link between over- and undervaluation and portfolio weight, and weights companies by a intuitive metric of company size. Empirical evidence shows that fundamental indexation is able to produce higher returns than market capitalization weighted indexation over a long-time horizon in various equity markets. However, this strategy does have disadvantages. None of the measures of company size capture perceived growth opportunities of the companies. Therefore, these metrics of company size which deemphasize growth

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characteristics do not necessarily serve as an appropriate proxy for the company’s fair value. Moreover, fundamental indexation requires several company size metrics. If these metrics are combined, which is quite common, this strategy requires more data and computational effort than market capitalization weighting.

Perold (2007) and Kaplan (2008a) argue that market capitalization weighting does not, by itself, create a performance drag. An intense debate between proponents and critics of fundamental indexation appeared in the Financial Analyst Journal2. Critics dispute the claim that investors can outperform a market capitalization weighted index, in inefficient markets, without knowing the fair value. The formula describes the components of a company’s market price in inefficient markets.

Advocates of the fundamental indexation approach assume that the pricing error is uncorrelated with the fair value. Perold (2008) argues that, if the pricing error is random and uncorrelated with fair value and if investors have no knowledge of the fair value, then the fair value must be randomly distributed around the observed market price. So conditional on knowing the fair value, the pricing error is independent of the fair value. Therefore, for investors who have no knowledge of fair value, investing in market capitalization weighted funds entails no performance drag. Investors who have knowledge of fair value can take advantage of that, however this essentially distinguishes active from passive management. Hsu (2008) argues that fair value has no place in constructing an optimal portfolio, it should only include expected return and risk. In contrast, Kaplan (2008b) notes that fair value plays an essential role in portfolio construction if market prices contain errors that mean-revert to zero. The more investors assess a stock to be undervalued, the higher they will set their expectations of its return, and vice versa. Earlier, Arnott et al. (2005) expressed their concern that market capitalization is a volatile way to measure a company’s size or its true value, because prices are too noisy relative to fundamentals. So fundamental indexation seems to assign stock weights by a more accurate estimate of fair value than market prices. Therefore, the passive fundamental indexation strategy seems to have an active dimension.

Chen et al. (2007) address the smoothed capitalization weighting strategy, implementing the idea of fundamental indexation without some of the corresponding disadvantages. This portfolio construction approach is easier to implement than fundamental indexation. The smoothed

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capitalization weighting strategy replaces the use of accounting data by the time series of market capitalization. Thereby, smoothed capitalization weighting replaces the required data of several size metrics with only one size metric, market capitalization. This strategy constructs a portfolio by weighting each individual stock based on its moving average of market capitalization values relative to the moving average of market capitalization values of the total stock market. Chen et al. (2007) find that smoothed capitalization weighting outperformed market capitalization weighting by approximately 1 percent a year in the United States between 1962 and 2003.

So market capitalization weighted indexes have a potential bias for over- and undervaluation of stocks if markets are inefficient. The fundamental indexation strategy tries to avoid this potential bias, however it has disadvantages. The smoothed capitalization weighting strategy is able to reduce these disadvantages and generates excess returns in the United States. This study uses European data to examine the performance of smoothed capitalization weighted indexes.

The research purpose of this study is two-fold and defined by the following research questions:

Do European smoothed capitalization weighted indexes generate higher absolute and risk-adjusted returns than market capitalization indexes?

Do European smoothed capitalization weighted indexes generate the same risk-adjusted returns as fundamental indexes?

By using European data from 1998 to 2013, I examine whether smoothed capitalization weighting generates higher absolute and risk-adjusted returns than market capitalization weighting. Therefore, I construct four smoothed capitalization weighted indexes and a market capitalization index. The annual excess returns of the smoothed cap indexes over the capitalization weighted indexes are tested on significance by a T-test. I find that the smoothed capitalization weighted indexes produce higher returns than the market capitalization index, however the excess return is not statistically significant.

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factors. All smoothed cap weighted indexes produce a significant positive alpha after correcting for the four risk factors.

Then I examine whether smoothed capitalization weighted indexes produce the same risk-adjusted return as the fundamental index. The annual excess return of the fundamental index over the smoothed cap index is regressed on the annual European market risk factors. I find that the best performing smoothed cap index generates a small alpha compared to the fundamental index. However, the alpha coefficient is not significant.

The remainder of this paper is structured as follows. The following section describes the relevant literature. Section III presents the methodology used in this study, whereas section IV outlines the data characteristics. The findings are presented in section V along with more details of the performance analysis. Section VI presents a brief summary of the major findings of this paper.

II. Literature Review

Market index origin

Popular market indexes are usually market capitalization weighted. The popularity of this portfolio construction method dates back to the formalisation of the Capital Asset Pricing Model (CAPM) by Sharpe (1964). He was one of the founding fathers of the CAPM3, who all worked upon the foundation of portfolio theory of Markowitz (1952). Markowitz developed a portfolio model based on a set of assumptions, e.g. that investors are rational, full-informed, and only care about expected risk and return. His model enables the construction of a mean-variance efficient frontier. The CAPM added several assumptions, in particular that all investors are able to borrow and lend limitless and at the same risk-free rate. As a result, the curved efficient frontier changed into a straight capital market line. The true market portfolio lies on the point of tangency of the capital market line with the efficient frontier. This true market portfolio is both mean-variance efficient and market cap weighted. So the CAPM provides the logic and origin of market capitalization weighting as dominant index construction method until today. The construction of a mean-variance-efficient portfolio is an intellectually challenging and resource intensive task. It is complicated to forecast expected returns and the covariance matrix of a countless number of stocks. This complexity supports the belief that

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cap-weighted market indexes are sufficiently representative of the CAPM market portfolio and to be nearly mean-variance efficient.

Fundamental indexation as alternative indexing method

Treynor (2005) and Hsu (2006) explain that capitalization weighting implies overweighting overvalued stocks and underweighting undervalued stocks if market inefficiencies exist. To make the stock weights unrelated to the pricing error, Treynor (2005) suggests equally weighted indexation. Pricing errors tend to cancel each other out by eliminating the structural link between over- and undervaluation and the portfolio weight. Equally weighting, however, is unable to adequately reflect the economy and lacks scalability due to its tilt toward small capitalization stocks. Arnott et al. (2005) present an alternative weighting method mentioned as fundamental indexation. Fundamental indexation uses accounting data in attempt to establish more accurate estimates of company value compared to noisy market prices. If market prices do revert to the company’s fair values, the fundamental index is able to produce excess returns over the market cap index.

Several authors challenge the theoretical validity of fundamental indexation. Some authors declare that fundamental indexation is not really a passive index because of its active dimension. Assness (2006) argues that a strictly defined index should describe a combination of assets we can all invest in without distorting prices. Since market capitalization derives from a set of prices and corresponding company values on which the market currently agrees, any deviations from market-cap weights are deviations from that agreed-upon centre. In such a way the fundamental index takes active bets against the crowd and the definition of index may not be appropriate. Other critics argue that fundamental indexation is a value strategy and exploit its exposure toward the market risk factors value and size. Asness (2006) as well as Bogle and Malkiel (2006) draw attention to the value and small-cap tilt in a fundamental index and describe it as a quantitative value investing method. Historically, value and small-cap stocks generated higher risk-adjusted returns. These anomalies are mentioned as the value effect and the size effect. It is still ambiguous whether these stocks have produced higher returns because of higher (hidden) risk or because of mispricing (or a combination). If value and small-cap stocks outperform due to systematically mispricing, then fundamental indexation will (along with other value funds) outperform in the future.

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of fundamental indexation assume that the construction method of fundamental indexation is price-indifferent, whereas market-cap indexation is price-related. In contrary to Treynor (2005) and Hsu (2006), Perold (2007) disputes the assumption that market cap weighting, by itself, causes a performance drag. According to Perold (2007), it is incorrect to conclude that the pricing error is correlated with the market value. Even though prices may revert to fair value, without knowing the fair value, the direction of the movement is random. Kaplan (2008) invalidates the assumption that fundamental weights are unbiased estimators of fair value weights that are statistically independent of market values. He focuses on the variance of errors in market capitalization relative to the variance of error in fundamental weights for the fair value of stocks. Since criticism mainly concerns the theoretical validity, empirical evidence could give more insight in the performance of fundamental indexation.

Empirical Evidence

Arnott et al. (2005) introduce the fundamental indexation concept and present an U.S. study over 42 years from 1962 through 2004. The fundamental indexes produce on average 1.97 percent higher returns than the S&P 500 and even 2.15 percent higher returns than the reference portfolio4. The study of Hemminki and Puttonen (2007) covers European data from January 1996 to December 2006 and supports the U.S. findings. Eight fundamental portfolios of the largest 50 firms outperform the DJ Euro Stoxx 50 by on average 1.76 percent a year. Research of Mar et al. (2009) also supports the U.S. results in an Australian context for the period 1995 to 2006. They find an average excess return of 1.94 percent and argue that the superiority of fundamental indexation can largely be explained by its inherent bias toward value stocks. Estrada (2008) focuses on international asset allocation using fundamental indexation and also finds support for the findings of the other studies. Arnott et al. (2008) present more extensive empirical research regarding fundamental indexation. The fundamental indexation method is tested in a U.S. index of large caps, small caps, growth stocks, value stocks, and REITs5. The construction method produces average excess returns of respectively 210, 340, 160, 180, and 220 basis points a year. The fundamental index outperforms the market cap index with on average 2.6 percent in countries outside the United States. The returns of a global portfolio of countries outside the U.S. exceed the market-cap index returns with 3.3 percent a year. Above all, the fundamental emerging market index outperforms the market cap index by 10.7 percent annually.

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Market capitalization weighted 1000 index

-9- Risk-adjusted return analysis

Several studies identified anomalies which generated consistently higher returns across different time periods and countries. Banz (1981) and Reinganum (1981) are two of the first researchers who found that firms with smaller market capitalization generate, on average, higher risk-adjusted returns than those with higher market capitalizations. This observation is called the size value and proxies for one of the risk factors in the Fama French three factor model. Another risk factor of the Fama French model is the value effect, initially recognized by Rosenberg et al. (1985). They find a positive relationship between stock returns and their BE/ME. Fama and French (1992) determine that size and value are both significant explanatory variables to explain the variation in stock returns. These factors are, along with the market risk factor, superior to the CAPM for accounting for stock returns. Jegadeesh and Titman (1993, 2001) introduce the momentum factor. They demonstrate that stocks which perform well in recent months significantly outperform stocks with recent poor performance for the next several months. Carhart (1997) adds the one-year momentum factor to the Fama French three factor model, thereby he improves the explanatory power of the model.

The empirical evidence shows that fundamental indexation is able to outperform market cap weighting. A risk-adjusted return analysis identifies whether these excess returns can be explained by market risk factors. Blitz and Swinkels (2008) examine the risk-adjusted performance of fundamental indexes between 1962 and 2005. The returns on the RAFI 10006 are regressed on the returns of traditional market risk factors. The fundamental index seems to contain a large and highly significant exposure toward the value factor. After adjustment for style exposure, fundamental indexation produces no significant added value. In addition to the style exposure, the fundamental index does not represent a buy-and-hold strategy and requires subjective choices. Blitz and Swinkels (2008) conclude that fundamental indexation is essentially an active value strategy disguised as an index. The risk-adjusted performance of European fundamental indexes is analyzed by Houwer and Plantinga (2009) over the time period 1993-2007. These fundamental indexes generate a significant and positive alpha after risk-adjustment by the Fama French three factor model. The annual turnover lies in between the turnover percentages of market cap indexes and active strategies. Houwer and Plantinga (2009) conclude that fundamental indexation is neither a passive nor an active strategy.

-10- Smoothed capitalization weighted indexation

Chen et al. (2007) introduce the smoothed capitalization weighting method. Similar to fundamental indexation, this strategy assumes that stock prices are noisy approximations of its fair value and that market prices revert to their fair value. The intuition is that smoothing a company’s market value mitigates the pricing noise. Their study uses U.S. data over the period 1962 to 2003. The smoothed capitalization weighted index outperforms a capitalization weighted index by approximately 1 percent per annum.

Chen et al. (2007) estimate fair value weights by a simple moving average of capitalization weights for the previous t periods. The estimated fair value weight is denoted by Wi,t (fund), whereas Wi,τ

(cap) represents the market capitalization weights.

(1)

Implementation

In this study, fair values are estimated by using the simple moving average of a company’s market capitalization. Companies are ranked by their estimated fair value and the top hundred companies are included in the index. A company’s weight is its estimated fair value as a percentage of the sum of estimated values of the hundred constituents.

(2)

Vi,t (comp) is the estimated value and Vi,t (cap) is the company’s market capitalization for period t.

I construct four smoothed-cap indexes based on 2-year, 3-year, 4-year, and 5-year averages. The averages are calculated at the last trading day of December of each year and held for 12 months. Weights are rebalanced at the end of the calendar year.

FTSE supplies a relevant FTSE market-cap benchmark7 and a relevant FTSE European fundamental index8. Therefore, this study uses the FTSE ground rules for FTSE European Index Series. The FTSE Eurotop 100 is selected as market cap benchmark. However, a constructed market cap index is set as the reference portfolio to make direct comparisons uncomplicated by subjective selections, market impact, float, and so forth. For example, the FTSE Eurotop 100 treats the incorporation and deletion

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FTSE Eurotop 100

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of constituents somewhat different than the constructed market index (and smoothed-cap indexes). Companies have to rise to the 90th position or above to be inserted into the index and have to fall to the 111th position or below to be deleted, whereas the smoothed-cap index includes the hundred highest ranked companies. Although, the FTSE Eurotop100 and the reference portfolio should deliver approximately the same risk and returns. The fundamental index, FTSE RAFI Europe, includes a larger amount of constituents. Instead of hundred constituents for the market cap index, thousand constituents are used in the fundamental index. Despite of being a suboptimal benchmark, it is the only European fundamental index available over the relevant time period.

This portfolio construction approach generates a constant number of hundred constituents for any year without further adjustments needed. The fundamental index uses trailing 5-year9 averages of company size metrics for index construction. The smoothed cap construction method is quite comparable with fundamental indexation, albeit the one approach uses market capitalizations and the other uses fundamental metrics. Chen et al. (2007) use monthly market capitalization data and estimated the weight by taking the median over the estimation period. This study calculates the return on each portfolio on a yearly basis. I decided to calculate yearly returns to present the most intuitive return metric. In addition, computational constraints led to the current portfolio return methodology.

Hypothesis

The research objective of this study is twofold. Thereof, the first research question requires two analyzes. In order to answer the first research question I examine whether smoothed cap indexes produce absolute excess returns and whether they produce higher risk-adjusted returns. I use a two-sided t-test to test whether the smoothed-cap excess returns differ from the market-cap excess returns. Excess returns are defined as the index return (Rit) minus the risk free rate (Rft). The benchmark returns are denoted by Rbt.

H1:

Several studies show significant excess returns of fundamental indexes over market cap indexes. Chen et al. (2007) find that smoothed cap weighted indexes also generate significant excess returns over the market cap index. Therefore, I expect to reject the null hypothesis of no different excess returns between smoothed cap indexes and market cap indexes.

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This study uses a Carhart four factor regression to examine whether smoothed cap indexes generate higher risk-adjusted returns. The alpha coefficient captures the return unexplained by the market risk factors. Positive alpha coefficients denote higher risk-adjusted returns on the smoothed cap indexes. The studies of Blitz and Swinkels (2008), Mar et al. (2009), and Houwer and Plantinga (2009) do not agree upon the risk-adjusted performance of fundamental indexation. Chen et al. (2007) have not executed a risk-adjusted analysis of the smoothed cap indexes. Therefore, the literature presents no evidence to expect that smoothed cap indexes are able to generate significant risk-adjusted returns.

H2: The smoothed capitalization weighted indexes generate higher risk-adjusted returns than market capitalization weighted indexes

The second research question is whether smoothed cap indexes produce the same risk-adjusted returns as fundamental indexes. Therefore, the annual return differences between the fundamental index and the best performing smoothed cap index are regressed on the market risk factors. We only know that both portfolio construction methods have produced significantly higher returns than the market cap indexes. Therefore I expect to accept the null hypothesis of equal risk-adjusted returns on the smoothed cap index and fundamental index.

H3: The risk-adjusted return of smoothed capitalization weighted indexes is not equal to the risk-adjusted return of the fundamental indexes

III. Methodology

Absolute Return analysis

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The risk level of the portfolios is initially measured by the standard deviation of returns. Before taking into account market risk factors, the Sharpe ratio can provide some insight in the risk-adjusted performance. The Sharpe ratio is defined as:

(3)

Rit is the annual index return, Rf is the annual risk-free rate, and σit is the standard deviation of the annual index returns.

Relative performance measures focus on the index performance relative to a benchmark, without adjustments for systematic risk. The tracking error σte defines the risk relative to the benchmark. This measure indicates to what extend the portfolio deviates from the benchmark Rbt. Therefore, it could present an indication of the incurred trading costs due to rebalancing.

(4)

The information ratio is a widely used measure for portfolio managers and combines the relative return and relative risk.

(5)

Risk-adjusted returns by CAPM regression

The index returns are adjusted for risk in order to find explanations for possible outperformance (or underperformance). The risk-adjusted performance is initially measured by a traditional CAPM time series regression.

(6)

Rit is the annual return on the index, Rft is the risk-free rate as supplied by Kenneth French10 and RMt is the return on the reference portfolio. The βiM coefficient measures the excess returns explained by the market risk. The αit resulted from the regression is the Jensen’s measure and indicates excess returns unexplained by market (or systematic) risk.

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The Treynor ratio is used to compare index performance adjusted for systematic risk.

(7)

The outcome of the Treynor ratio is directly comparable with the equity premium11. If the Treynor ratio exceeds the equity premium, a portfolio adds value relative to the passive market index.

Risk-adjusted returns by Fama-French-Carhart four factor model

This study uses a Carhart four factor model to determine whether the smoothed cap weighted indexes and fundamental index exhibit size, value or momentum characteristics relative to the reference portfolio:

(8)

Rit is the annual return on the index, Rbt represents the annual return on the benchmark index, Rmt

denotes the market return, and Rft is the risk free rate. The size factor SMBt stands for small minus

big, the value factor HMLt stands for high minus low, and the one-year momentum factor is MOMt.

The European market risk factors supplied by French are used as proxy for the factors (RMt – Rft), SMBt, HMLt and MOMt.

IV. Data

The dataset contains European company data for the period December 1998 to December 2013. Total stock returns and the year-end market capitalizations are obtained from Thomson’s Datastream. The portfolios are constructed for 2003 to 2013, an 11-year period covering both bear and bull markets. The market capitalization data covers sixteen years to enable portfolio construction of the 5-year smoothed cap index for 2003. According to the rules of the FTSE European Index Series, companies of sixteen European countries are included in the sample. The database contains both listed and delisted stocks to avoid a survivorship bias. Listed stocks are defined as companies still listed on one of the sixteen stock exchanges. Delisted stocks denote once listed but currently unavailable stocks. Delisted stocks are commonly caused by mergers, acquisitions, nationalization by government, or bankruptcy. Table 1 shows the distribution of the companies in the database by its located country, listed stock exchange, and actual stock exchange condition.

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Table 1. Distribution characteristics of the European companies in database, 1998-2013.

The companies in the dataset are from sixteen European countries and thereby sixteen stock exchanges. The number of companies are identified by country, stock exchange, and current stock exchange condition.

Country Exchange Listed Delisted Total

Austria Vienna SE 95 170 265

Belgium Euronext Brussel 169 399 568

Denmark Copenhagen SE 179 271 450

Finland Helsinki SE 140 187 327

France Euronext Paris 842 1,504 2,346

Germany Frankfurt SE 798 827 1,625

Greece Athens SE 237 252 489

Ireland Dublin SE 39 112 151

Italy Milan SE 318 455 773

Netherlands Euronext Amsterdam 107 344 451

Norway Oslo SE 208 448 656

Portugal Euronext Lissabon 68 182 250

Spain Madrid SIBE 163 155 318

Sweden Stockholm SE 580 925 1,505

Switzerland SIX Swiss 265 390 655

United Kingdom London SE 1,435 3,449 4,884

Sample 5,643 10,070 15,713

The data is obtained from Datastream and is not immediately useable for portfolio construction. Companies which are already withdrawn from stock exchanges for reasons such as mergers and acquisitions have inaccurate data. Datastream prolongs their latest actual market capitalization and stock price infinitely instead of transforming it into zero or not available. The data of the relevant delisted stocks in the sample are corrected manually to avoid unrealistic portfolio compositions.

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Table 2. Descriptive statistics of smoothed cap indexes and benchmark indexes, 2003-2013.

The percentages are the annual returns and the annual standard deviation of returns.

Year

FTSE Eurotop

100 Reference portfolio Smoothed cap 2y Smoothed cap 3y Smoothed cap 4y Smoothed cap 5y

FTSE RAFI Europe 2003 14.92% 14.34% 16.49% 19.27% 19.18% 19.42% 22.00% 2004 9.71% 10.32% 10.27% 9.67% 9.13% 9.53% 14.74% 2005 24.93% 24.22% 24.11% 24.39% 24.06% 23.89% 28.94% 2006 15.49% 16.24% 15.98% 15.61% 15.53% 15.24% 23.50% 2007 5.83% 7.04% 6.27% 6.00% 5.68% 5.86% 4.89% 2008 -40.76% -39.54% -39.92% -40.09% -39.76% -39.63% -45.29% 2009 29.73% 26.03% 32.30% 33.99% 33.74% 33.07% 42.52% 2010 7.98% 7.64% 7.31% 7.31% 7.08% 7.01% 9.62% 2011 -6.69% -7.44% -7.62% -7.05% -7.87% -8.79% -12.39% 2012 14.15% 14.62% 15.63% 15.27% 14.69% 14.29% 15.90% 2013 19.16% 19.71% 19.91% 19.90% 20.31% 20.77% 24.79% Arithmetic Mean 8.59% 8.47% 9.16% 9.48% 9.25% 9.15% 11.75% Standard Deviation 19.03% 18.38% 19.29% 19.61% 19.55% 19.52% 23.60% Geometric Mean 6.64% 6.65% 7.19% 7.46% 7.25% 7.16% 8.81% Maximum return 29.73% 26.03% 32.30% 33.99% 33.74% 33.07% 42.52% Minimum return -40.76% -39.54% -39.92% -40.09% -39.75% -39.63% -45.29% Skewness -1.64 -1.74 -1.53 -1.47 -1.43 -1.44 -1.28 Kurtosis 5.26 5.35 4.96 4.87 4.74 4.68 4.24 Jarque-Bera 7.28** 8.08** 6.08** 5.57* 5.15* 5.08* 3.73 Observations 11 11 11 11 11 11 11

** Denotes significance at the 5% level * Denotes significance at the 10% level

The annual returns are skewed, whereas the significant Jarque-Bera values indicate that the returns are not normally distributed. However, these descriptive statistics do not cause difficulties for the execution of a regression analysis. After the regression, I would be concerned about the normal distribution of the residuals because it could invalidate the statistical tests of significance. Therefore, this study provides a ARCH-LM test for possible existence of heteroscedasticity.

V. Results

Absolute returns

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and 6.65 percent. These indexes bear also the lowest risk as given by the volatility of 18.38 percent and 19.03 percent. The Sharpe ratio adjusts the returns by their volatility. The fundamental index has the highest Sharpe ratio, closely followed by the 3-year smoothed cap index.

The substantial higher tracking error of the fundamental index could be declared partially by the different universe of included stocks. The smoothed cap indexes contain hundred constituents, whereas the fundamental index contains thousand constituents. The fundamental index also delivers the highest information ratio. Therefore, it seems fair to say that the fundamental index provides the best absolute return characteristics. Figure 1 plots the value creation of a starting portfolio of hundred Euro. An investment of hundred Euro in the reference portfolio in 2003, would have more than doubled in 2013, to 203.08 Euro. In comparison, the smoothed cap using 3-year averages would end up with 220.66 Euro and the fundamental index concluded with even 253.23 Euro.

All smoothed cap indexes produce higher returns than the reference portfolio. Of the smoothed cap weighted indexes, the index based on 3-year averages delivers the highest average excess return of 0.81 percent. In comparison, the fundamental index offers an excess return of annually 2.16 percent. However, this average return increase of 2.16 percent is combined with an average volatility increase of more than 5 percent a year. The excess returns are not significant for any of the indexes. Therefore, the H0 hypothesis can not be rejected.Contrary to the findings of Chen et al. (2007), the results do not confirm that smoothed cap weighted indexes generate higher absolute returns than market cap indexes. Although the insignificance can possibly be explained by the relative small sample size of eleven observations.

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Table 3. Return characteristics of smoothed capitalization weighted indexing portfolios and benchmarks, 2003-2013.

The indexes are constructed from 2003 to 2013. Indexes are rebalanced on the last trading day of December. Each year, all firms in the sample are ranked according to each estimated fair value. The highest hundred firms form the respective indexes at their relative fair value weight. The geometric return is computed from annual index returns. The volatility is the annual standard deviation. The Sharpe ratio, tracking error, and information ratio are computed by annual returns. The table presents the excess return of the indexes over the reference portfolio, even like the corresponding t-Statistic.

** Denotes significance at the 5% level * Denotes significance at the 10% level

Figure 1. Wealth accumulation: various indexing portfolios, 2003-2013.

100 150 200 250 300 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 FTSE Eurotop 100 Reference portfolio Smoothed-cap 3y FTSE RAFI Europe

Index Ending Value €100 Geometric Return Volatility Sharpe Ratio Excess Return vs. Reference Tracking Error vs. Reference Information Ratio Excess Return t-Statistic for

FTSE Eurotop 100 202.76 6.64% 19.03% 0.264 -0.02% 1.34% 0.09 0.27 Reference portfolio 203.08 6.65% 18.38% 0.276 - - - - Smoothed-cap 2y 214.67 7.19% 19.29% 0.289 0.54% 2.04% 0.34 1.13 Smoothed-cap 3y 220.66 7.46% 19.61% 0.298 0.81% 2.87% 0.35 1.19 Smoothed-cap 4y 216.04 7.25% 19.55% 0.288 0.60% 2.82% 0.28 0.91 Smoothed-cap 5y 213.96 7.16% 19.52% 0.284 0.51% 2.73% 0.25 0.81

-19- CAPM adjusted returns

The portfolios are adjusted for market risk by a CAPM time series regression. The return on the reference portfolio represents the market risk factor. Table 4 shows that the index returns are highly correlated with the returns on the reference portfolio. All portfolios contain a beta coefficient that is larger than 1, which indicates that the smoothed cap indexes and the fundamental index bear more market risk than the reference portfolio. The fundamental index bears the highest market risk with a beta coefficient of 1.266, whereas the smoothed cap portfolio using three year averages contains the second highest beta coefficient of 1.063.

The market risk factor does not entirely explain the excess returns since all indexes produce a positive alpha coefficient. The alpha coefficients of the portfolios range from 0.28 for the 5-year smoothed cap index to 1.43 for the fundamental index. Although, none of the corresponding T-statistics are significant. Therefore, these results do not confirm that smoothed cap indexes produce a higher risk-adjusted return. The Treynor index adjusts the index returns for its market risk. All indexes provide a higher Treynor index than the reference index. The fundamental index generates the highest equity premium of 5.71 percent given by the Treynor index. In comparison, the reference portfolio produced an equity premium of 5.09 percent.

Table 4. CAPM characteristics of smoothed cap indexes and benchmark indexes, 2003-2013.

The indexes are constructed from 2003 to 2013. Indexes are rebalanced on the last trading day of December. Each year, all firms in the sample are ranked according to each estimated fair value. The highest hundred firms form the respective indexes at their relative fair value weight. The geometric return, The Sharpe ratio and Treynor index are computed using yearly returns. The annual European risk-free rates are supplied by French. The annual return on the reference portfolio represents the market risk factor. The beta is derived from the regression of annual excess return of the indexes on the annual excess return of the market cap index. The Jensen’s measure is the intercept term from these regressions.

Index Geometric Return

Correlation with Reference CAPM Beta vs. Reference CAPM Alpha vs. Reference t-Statistic for Jensen’s

Alpha Treynor Index

FTSE Eurotop 100 6.64% 0.998 1.036 -0.14% -0.32 4.89% Reference portfolio 6.65% - - - - 5.09% Smoothed-cap 2y 7.19% 0.995 1.048 0.35% 0.57 5.36% Smoothed-cap 3y 7.46% 0.991 1.063 0.57% 0.65 5.53% Smoothed-cap 4y 7.25% 0.991 1.059 0.37% 0.41 5.36% Smoothed-cap 5y 7.16% 0.991 1.057 0.28% 0.32 5.28%

FTSE RAFI Europe 8.81% 0.985 1.266 1.43% 1.04 5.71%

-20- Fama French Carhart four factor model adjusted returns

The Fama French Carhart model includes, in addition to the market risk factor, the risk factors for value, size, and momentum. These factors, or anomalies, delivered higher risk-adjusted returns in the past or carried additional hidden risk. Earlier studies drew attention to the size and especially value bias of fundamental indexes. I analyze whether the constructed indexes have exposure to these market risk factors.

Table 5 presents the results of the four factor regression. All indexes produce excess returns over the reference portfolio. The momentum factor has a negative and significant coefficient for all indexes. Moreover, all smoothed cap indexes generate a positive and significant alpha. The alpha coefficients of the smoothed cap indexes using 2-, 3-, and 4-year averages are significant at a 5% significance level. The smoothed cap 5-year index has a significant alpha coefficient at a significance level of 10%. The significant alpha coefficients imply that the excess returns could not be explained by the market risk factors. These results confirm that smoothed cap indexes are able to generate higher risk-adjusted returns than market cap indexes. Therefore the null hypothesis of equal risk-risk-adjusted returns on smoothed cap indexes and market cap indexes can be rejected. This study adds a new insight to the literature, since no literature exist regarding risk-adjusted performance of smoothed cap indexes.

The alpha coefficient of the fundamental index is remarkable. Despite being the second highest absolute value, the alpha coefficient is not significant. The fundamental index generates a 1.49 percent alpha which is almost as high as the alpha of the smoothed-cap 3-year portfolio of 1.59 percent. The insignificance could probably be explained by the relative high, doubled relative to the smoothed cap indexes, standard deviation of the unexplained returns for the fundamental index. The fundamental index is the only index with a significant alpha coefficient for the size factor. An explanation could be that the fundamental index uses a larger universe of stocks for the index composition. Consequently, it has more exposure to relative smaller stocks.

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represents an unexplained risk-adjusted return premium generated by the smoothed-cap 3-year index relative to the fundamental index. The alpha coefficient of -0.1 percent is minimal and not significant. Therefore, we can accept the null hypothesis of equal risk-adjusted returns generated by the smoothed-cap index and fundamental index.

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Table 5. Risk-adjusted performance of index portfolios versus the reference portfolio, 2003-2013.

The results are derived from the Carhart four factor model. The yearly returns of the indexes are regressed on the annual European market risk factors. The β , δ (SMB), γ (HML), θ (MOM) are coefficients of respectively the market risk premium, size, value, and one-year momentum. The t-Statistics are presented next to the coefficients. The corresponding p-values are given in between the quotation marks.

Portfolio / Index α t-Statistic for α β t-Statistic for β δ (SMB) t-Statistic for δ γ (HML) t-Statistic for γ θ (MOM) t-Statistic for θ R-squared Adjusted ARCH-LM

FTSE Eurotop 100 0.31% 1.1113 0.0023 0.1624 0.0815 2.0218* -0.0707 -2.3738* -0.0422 -3.8059** 0.7517 0.0005 (0.3090) (0.8763) (0.0897) (0.0552) (0.0089) (0.9826) Reference portfolio - - - - Smoothed-cap 2y 1.09% 4.6945** 0.0061 0.5315 0.0608 1.8272 -0.0366 -1.4901 -0.0772 -8.4387** 0.9191 0.5974 (0.0033) (0.6142) (0.1174) (0.1868) (0.0002) (0.4396) Smoothed-cap 3y 1.59% 3.7747** 0.0012 0.0569 0.0761 1.2648 -0.0119 -0.2677 -0.1087 -6.5677** 0.8641 0.3183 (0.0092) (0.9565) (0.2529) (0.7979) (0.0006) (0.5726) Smoothed-cap 4y 1.34% 2.6283** -0.0087 -0.3471 0.0945 1.3036 0.0086 0.1602 -0.1068 -5.3611** 0.8064 0.0000 (0.0391) (0.7404) (0.2401) (0.8780) (0.0017) (0.9945) Smoothed-cap 5y 1.10% 1.9859* -0.0139 -0.5073 0.1000 1.2662 0.0430 0.7371 -0.0984 -4.5321** 0.7582 0.0624 (0.0943) (0.6300) (0.2524) (0.4889) (0.0040) (0.8028)

FTSE RAFI Europe 1.49% 1.5306 0.0796 1.6512 0.3764 2.7143** -0.0109 -0.1062 -0.1013 -2.6581** 0.8570 0.5758

(0.1767) (0.1498) (0.0349) (0.9189) (0.0376) (0.4480)

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Table 6. Risk-adjusted performance of index portfolios versus the reference portfolio, 2003-2013.

The results are derived from the Carhart four factor model. The yearly excess returns of the FTSE RAFI Europe over the smoothed-cap 3-year portfolio are regressed on the annual European market risk factors. The β , δ (SMB), γ (HML), θ (MOM) are coefficients of respectively the market risk premium, size, value, and

one-year momentum. The t-Statistics are presented next to the coefficients. The corresponding p-values are in between the quotation marks.

Portfolio / Index α t-Statistic for α β t-Statistic for β δ (SMB) t-Statistic for δ γ (HML) t-Statistic for γ θ (MOM) t-Statistic for θ R-squared Adjusted ARCH-LM

FTSE RAFI Europe -0.10% -0.0934 0.0784 1.4081 0.3764 2.7143** -0.0109 -0.1062 -0.1013 -2.6581** 0.8570 0.5758

- Smoothed-cap 3y (0.9287) (0.2087) (0.0349) (0.9189) (0.0376) (0.4480)

-24- Liquidity and Turnover

The possible higher returns on the constructed indexes might be offset by other advantages of market cap indexes, e.g. high liquidity and low turnover. Less liquid stocks may be thinly traded thereby incurring higher transaction costs. Table 7 and Table 8 indicate liquidity characteristics of the smoothed cap indexes. The CAP ratio determines the investment capacity of the constructed indexes relative to the cap-weighted market index. Therefore, the CAP ratio provides a measure of relative capacity. We can see that the average liquidity of smoothed-cap indexes and slightly higher than the market index.

Table 7. CAP ratios of smoothed capitalization weighted indexes, 2003-2013.

Year Reference portfolio Smoothed cap 2y Smoothed cap 3y Smoothed cap 4y Smoothed cap 5y

2003 100% 122.59% 138.74% 143.15% 134.15% 2004 100% 93.83% 105.19% 116.28% 120.15% 2005 100% 95.99% 90.90% 97.53% 105.41% 2006 100% 90.09% 84.74% 79.78% 82.69% 2007 100% 93.82% 85.97% 80.68% 75.98% 2008 100% 97.03% 92.26% 85.72% 80.77% 2009 100% 133.14% 141.55% 141.04% 135.20% 2010 100% 88.90% 102.50% 107.62% 107.77% 2011 100% 97.20% 89.24% 97.57% 101.23% 2012 100% 103.93% 103.65% 97.78% 104.99% 2013 100% 94.40% 94.93% 94.01% 89.47% Mean 100% 100.99% 102.70% 103.74% 103.44%

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Table 8. Concentration ratios of smoothed capitalization weighted indexes, 2003-2013.

Year Reference portfolio Smoothed cap 2y Smoothed cap 3y Smoothed cap 4y Smoothed cap 5y

2003 31.05% 30.33% 30.05% 29.54% 28.37% 2004 28.85% 30.10% 30.09% 30.11% 29.82% 2005 27.57% 28.03% 28.96% 29.33% 29.48% 2006 26.45% 27.23% 27.66% 28.53% 28.94% 2007 23.15% 24.80% 25.83% 26.48% 27.34% 2008 22.71% 22.86% 23.77% 24.62% 25.32% 2009 26.64% 24.24% 23.91% 24.48% 25.06% 2010 24.91% 25.42% 24.33% 24.06% 24.51% 2011 23.66% 24.01% 24.59% 24.03% 23.90% 2012 26.21% 24.87% 24.65% 25.01% 24.26% 2013 25.29% 25.59% 24.89% 24.66% 24.86% Mean 25.29% 26.13% 26.25% 26.44% 26.53%

Illiquidity only becomes a problem when one seeks to trade. Therefore a measure of the degree of trading would be useful. Unfortunately, this study does not provide a turnover measure. However, the tracking error could serve as an indicative measure of relative turnover. The tracking error indicates to what extent the constructed index deviates from the market index.

-26- Discussion

This section evaluates whether, and to what extent, the results are able to provide answers to the research questions. In addition, I discuss whether these results are in line with the expectations based on the existing literature. The first research question is:

Do European smoothed capitalization weighted indexes generate higher absolute and risk-adjusted returns than market capitalization indexes?

This study finds that the smoothed capitalization weighted indexes generate higher absolute returns than market capitalization weighted indexes. However, none of the smoothed-cap indexes generates significant annual excess returns. This is not in line with the findings of Chen et al. (2007), who find a significant excess return of smoothed cap indexes over the market cap index by approximately 1 percent per annum. The smoothed-cap 3-year index, the best performing smoothed cap index, generates an absolute excess return of 0.81 percent a year. Despite positive excess returns of all smoothed cap indexes, the results could not confirm the U.S. findings of Chen et al. (2007). Statistically, the smoothed cap indexes and market cap index seem to generate equal absolute returns.

The CAPM regression indicates that smoothed cap indexes produce higher risk-adjusted returns, given the positive alpha coefficients. Although, the alpha coefficients are not significant. The Carhart four factor model regression generates also positive alpha coefficients for the smoothed cap indexes. These alpha coefficients are all significant. Since Chen et al. (2007) present no risk-adjusted analysis, there is no existing literature on the risk-adjusted performance of smoothed cap indexes. This study presents evidence that smoothed cap indexes are able to generate higher risk-adjusted returns than market cap indexes.

Do European smoothed capitalization weighted indexes generate the same risk-adjusted returns as fundamental indexes?

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the fundamental index. The excess returns of the fundamental index over the smoothed-cap 3-year index are regressed on the market risk factors. The alpha coefficient is negative and insignificant. Therefore, it seems that fundamental index and smoothed cap indexes generate equal risk-adjusted returns. If we look at the absolute returns, both the smoothed cap indexes and the fundamental index produce yearly excess returns over the market cap index. In case of the CAPM regression, both construction methods produce a positive and insignificant alpha coefficient. These results do not contradict the statement of equally risk-adjusted returns on smoothed cap indexes and the fundamental index.

The smoothed cap indexes and fundamental index produce excess returns over the market cap index, although the excess returns are not significant. Additionally, both strategies generate a positive and insignificant alpha coefficient from the CAPM regressions. The insignificances could possibly be explained by the relative small sample size of eleven observations. All annual return data and market risk factor coefficients are correct. However, we should be cautious regarding the significance of the test outcomes. In hindsight, it would be more decent to analyze the monthly returns instead of the annual returns for the statistical robustness of the findings.

VI. Conclusion

This study contains two research questions. The first is whether smoothed cap indexes generate higher absolute and risk-adjusted returns than market cap indexes. In absolute terms, the smoothed cap indexes produce a positive excess return over the market cap index. However, the excess returns are not significant. Contrary to the findings of Chen et al. (2007), the smoothed cap indexes and market cap index seem to generate equal absolute returns.

No existing literature concerns the risk-adjusted performance of smoothed cap indexes. The Carhart four factor model regression generates positive and significant alpha coefficients for all of the smoothed cap indexes. Therefore, this study provides evidence that the smoothed cap indexes do produce higher risk-adjusted returns than market cap indexes.

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are regressed on the market risk factors. The alpha coefficient is small, negative and insignificant. Thereby, I conclude that the fundamental index and smoothed cap indexes generate equal risk-adjusted returns.

The smoothed cap indexes have similar liquidity characteristics as the market index. Unfortunately, this study does not provide turnover measures. However, the tracking error seems to indicate that smoothed cap indexation does not incur substantial additional trading costs.

A limitation of this study concerns the sample size. The sample size of eleven observations results from the use of annual returns over the period 2003 to 2013. Additionally, the associated costs deserve more in-depth analysis. These limitation, however, could be interesting research areas for future studies regarding the smoothed capitalization weighted construction method.

References

Arnott, R., Hsu, J., Moore, P., 2005. Fundamental indexation. Financial Analysts Journal 2, 83-99. Arnott, R., Hsu, J., West, J., 2008. The Fundamental Index – A Better Way To Invest. John Wiley & Sons, Inc., Hoboken, New Jersey.

Arnott, R., Markowitz, H., 2008. Fundamentally flawed indexing: comments. Financial Analysts Journal 2, 12-14.

Asness, C., 2006. The value of fundamental indexing. Institutional Investor (October), 67-71. Banz, R., 1981. The relationship between return and market value of common stocks. Journal of Financial Econoimics (vol. 9), 3-18.

Blitz, D., Swinkels, L., 2008. Fundamental indexation: an active value strategy in disguise. Journal of Asset Management 4, 264-269.

Bogle, J., Malkiel, B., 2006. Turn on a paradigm. Wall Street Journal (June), 14-14.

-29-

Estrada, J., 2008. Fundamental indexation and international diversification. Journal of Portfolio Management 3, 93-109.

Fama, E., 1970. Efficient capital markets: a review of theory and empirical work. Journal of Finance 2, 383-417.

Fama, E., French, K., 1992. The cross-section of expected stock returns. Journal of Finance 2, 427-465. Fama, E., French, K., 1993. Common risk factors in the returns on stocks and bonds. Journal of

Financial Economics 1, 3-56.

Gruber, M., 1996. Another puzzle: the growth in actively managed mutual funds. The Journal of Finance 3, 783-810.

Hemminki, J., Puttonen, V., 2008. Fundamental indexation in Europe. Journal of Asset Management 6, 401-405.

Houwer, R., Plantinga, A., 2009. Fundamental indexing: an analysis of the returns, risks and costs of applying the strategy. Working paper, University of Groningen.

Hsu, J., 2006. Cap-weighted portfolios are sub-optimal portfolios. Journal of Investment Management 4, 44-53.

Hsu, J., 2008. Why fundamental indexation might – or might not – work: a comment. Financial Analysts Journal 2, 17-18.

Jegadeesh, N., Titman, S., 1993. Returns to buying winners and selling losers: implications for stock market efficiency. Journal of Finance 1, 65-91.

Jegadeesh, N., Titman, S., 2001. Profitability of momentum strategies: an evaluation of alternative explanations. Journal of Finance 2, 699-720.

Kaplan, p., 2008a. Why fundamental indexation might – or might not – work. Financial Analysts Journal 1, 32-39.

Kaplan, P., 2008b. Why fundamental indexation might – or might not – work: author response. Financial Analysts Journal 2, 18-18.

Lintner, J., 1965. The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics 47, 13–37.

Mar, J., Bird, R., Casavecchia, L., Yeung, D., 2009. Fundamental indexation: an Australian investigation. Australian Journal of Management 1, 1-20.

Markowitz, H., 1952. Portfolio selection. The Journal of Finance 1, 77-91.

-30-

Perold, A., 2008. Fundamentally flawed indexing: author response. Financial Analysts Journal 2, 14-17.

Reinganum, M., 1981. Misspecification of capital asset pricing: empirical anomalies based on earning yield and market values. Journal of Financial Economics 1, 9-17.

Rosenberg, B., Reid, K., Lanstein, R., 1985. Persuasive evidence of market inefficiency. Journal of Portfolio Management 3, 9-16.

Sharpe, W., 1966. Mutual fund performance. Journal of Business 1, 119-138. Siegel, J., 2006. The ‘noisy market’ hypothesis. The Wall Street Journal (June), 14-17. Treynor, J., 1961. Market value, time, and risk. Unpublished manuscript.

Treynor, J., 1962. Toward a theory of market value of risky assets. Unpublished manuscript.

Treynor, J., 2005. Why market-valuation-indifferent indexing works. Financial Analysts Journal 5, 65-69.

Treynor, J., 2008. Fundamentally flawed indexing: comments. Financial Analysts Journal 2, 14-14.

Ground Rules for the Management of FTSE European Index Series. Version 10.0 january 2014. Standard & Poor’s (2013). S&P Indices Versus Active Funds Scorecard.

Gregg Fisher (2013)

http://www.forbes.com/sites/greggfisher/2013/08/28/in-mutual-funds-is-active-vs-passive-the-right-question