Fundamental indexing
An analysis of the returns, risks and
costs of applying the strategy
Author:
Roelf C. Houwer
Contact information:
Roelf C. Houwer, Theodoor Gilissen Bankers, Institutional Asset Management, PO Box 3325, 1001 AC Amsterdam. Tel +31-20-5276529. E-mail: r.houwer@gilissen.nl
Abstract
1. INTRODUCTION
The Capital Asset Pricing Model by Sharpe (1964), Lintner (1965) and Mossin (1966) states that the “market portfolio” is mean variance efficient. This leads to the conclusion that a passive investor can do no better than holding a combination of the market
portfolio and a riskless asset. The power of CAPM lies in the fact that if one finds the market portfolio, one has simultaneously found the mean variance optimal portfolio. The passive investment industry and academic finance society have used the argument above to state that the market capitalization weighted index is sufficiently representative for the “market portfolio” to be mean variance efficient. Furthermore, weighting the stocks in an index by market capitalization brings some very desirable traits that account for its popularity. Because market capitalization is depends on price, indices weighted by market capitalization require very little rebalancing and thus have low turnover costs. Also, market capitalization is highly correlated with trading liquidity and availability of the stocks, allowing for lower transaction costs and large scale investing (for example by pension funds).
A number of authors have criticized on the market capitalization portfolio being
representative for the market portfolio and thus mean variance efficient. Mayers (1976), for example argues that the market portfolio should include all risky assets, not just equity. Stambaugh (1982) uses this idea and tests the CAPM using a market portfolio that includes non equity assets and finds improved results over the traditional CAPM tests. There is another aspect of capitalization weighting, one that is central to this thesis, which shows that capitalization weighting cannot be mean variance efficient. Treynor (2005) shows that if there are overpriced and underpriced stocks in the market, capitalization weighting will overweight the overvalued stocks and underweight the undervalued stocks, causing a performance drag. He pleads for weighting stocks equally in the index, thereby making the weights of the individual stocks in the index independent of price. Hsu (2004) concludes that if prices do not reflect fundamentals, capitalization weighting is sub-optimal. He also demonstrates that the performance drag of capitalization
weighting is an increasing function of price inefficiency and that portfolios based on price insensitive weights achieve better return.
Arnott, Hsu and Moore (2004) propose a weighting scheme that uses fundamental values of a firm as proxies for size instead of market capitalisation. They find that by using fundamental weighting, a passive investor can do much better than the market
annum. The t-statistics for the excess performance, reported by Arnott, Hsu and Moore (2004), are significant for all fundamental indices (almost four for the composite index). The only time that the fundamental indices fall behind the reference index in performance is in particular bull markets, where a small group of stocks grossly outperform the
average stock (for example during the “tech bubble” in the ninety’s and at the time of the “nifty-fifty” of 1972). The fundamental indices, however, more than make up for this lag as prices of these stocks revert to a level that is more in line with their fundamental values. The average turnover of the fundamental indices is 13.09%. This is reasonable compared to the 6.30% turnover of the reference index and lowers the average excess return of the fundamental indices by only 0.14% to 1.99% per annum (with a very safe transaction rate of 1% both ways). The liquidity of the fundamental indices is about half the liquidity of the reference index (measured in weighted dollar trading volume of the stocks in the index).
As the numbers above demonstrate, fundamental indexing seems to generate alpha compared to its market capitalization equivalent. Arnott, Hsu and Moore (2004) are not clear about the source of the excess return. It’s up to the reader whether the excess return comes from improvement of the performance drag of capitalization weighting or from hidden risk factors such as the Fama and French (1992) size and value effects. Bernstein (2006) performs Fama and French regressions on the Research Affiliates Fundamental Index and demonstrates that the excess returns can be partly explained by these hidden risk factors, however he does not address the issue of managing the fundamental indices (like turnover and liquidity costs) which may well annihilate the rest of the excess return. Thus, up to this point the source of any excess returns that fundamental indexing may generate remains unclear.
The aim of this thesis is to shed some light on this matter by analyzing both the risk and return characteristics of fundamental indexing, in terms of Fama and French (1993) risk factors and CAPM Beta, and by analyzing the costs that come with managing a
fundamental index. This results in the following research question:
Does the fundamental index show any excess return compared to its benchmark market capitalization weighted index when we correct for Fama and French (1993) risk factors, CAPM Beta and portfolio management costs?
This research is performed on a broad European stock index (the Dow Jones STOXX 600). Up until now, little research has been done on weighting European stock indices by fundamental values. This follows one of the recommendations of Arnott, Hsu and Moore (2004) to investigate the performance of fundamental indexing abroad.
2. LITERATURE REVIEW
In academics there has been a widespread debate between proponents and opponents of active investment strategies, referred to as “the active versus passive debate”. Active management is defined as trying to outperform a benchmark and passive management as simply trying to track a benchmark. As Javier Estrada (2006) explains, they have one thing in common: “In the vast majority of cases, the assets in the benchmark are weighted by capitalization.” Estrada gives one main reason why this is so. Modern portfolio theory suggests that a capitalization weighted index is mean-variance efficient and thus offers the highest return given a certain level of risk. Another merit of a capitalisation weighted index is that there is no rebalancing as Hsu (2004) points out, resulting in low turnover. A third advantage of market capitalization is its high correlation with trading liquidity and investment capacity, allowing for lower transaction costs and large scale investing (Arnott, Hsu and Moore 2004).
Burton Malkiel (2003) is a strong proponent of passive investing. Malkiel’s (2003) arguments are based on the former mentioned characteristics of capitalization weighted indices. Building on the efficient market hypothesis, he states that stock markets are in general efficient and thus there are no possibilities to successfully predict winning and losing stocks in the long run. The market portfolio thus gives the best trade-off between risk and return and should be preferred by all investors. This generates an equilibrium in which prices are such that markets will clear. This implies that the weights in the market portfolio are equal to their market capitalization. Malkiel (2003) acknowledges that there are anomalies in the market and refers to a number of authors like Campbell (1997), DeBondt and Thaler (1995), Lo and MacKinlay (1999) and Shiller (2000). He concludes, however, that these anomalies have not given rise to profitable active investing strategies. The efficient market hypothesis brings us to a shortcoming of capitalization weighting. If there are overpriced and underpriced stocks in the market, capitalization weighting will overweight the overvalued stocks and underweight the undervalued stocks, causing a performance drag. Treynor (2005) shows this in his article by mathematically deriving this performance drag. He pleads for weighting stocks independent of price by equal weighting. Hsu (2004) concludes that if prices do not reflect fundamentals, capitalization weighting is sub-optimal. He shows this with the following simple example. Two
companies A and B, with both one stock outstanding. The fair values (which are
unobservable to the investor) of the stocks are €10, however stock A costs €12 and stock B costs €8. The expected return over the fair value of the stocks is 10% (€1). How does this affect returns when comparing market capitalization weighting of the stocks to weighting the stocks by fair value and the stocks value revert to their fair values?
As an alternative to market capitalization weighting, Arnott, Hsu and Moore (2004) propose weighting based on fundamental values. They construct portfolios using gross earnings, gross revenue, gross dividends, gross sales and number of employees as weights. Using data for the US over the period between 1962 and 2004, they find these indices to perform better. They demonstrate these indices to achieve a higher average annual return of 213 basis points, with lower variance and slightly lower CAPM Beta than the S&P 500. Arnott, Hsu and Moore (2004) attribute this superior return to price inefficiencies or hidden risk factors as described by Fama and French (1992), but stay agnostic about this issue. The best performing fundamental index (gross sales) has an excess return over the reference index of 2.50% per annum over the 42 year period and a CAPM Beta of 0.99. The worst performing fundamental index (gross dividends)
performs 1.64% per annum better than the reference market capitalization index, but has a CAPM Beta of only 0.84. In the best and worst quarters of the composite fundamental index, returns are better than in the best and worst quarters of the reference market capitalization index. Also, the fundamental indices perform better under different market conditions. This is with the exception of particular bull markets, where a small group of stocks grossly outperform the average stock, like the tech bubble in the late ninety’s. After the burst of this bubble, however, the fundamental indices more than make up for this slight shortfall in returns by showing excess returns of 10.86% per annum from 2000 until 2003.
Arnott, Hsu and Moore (2004) state that there are three major advantages to fundamental indexing compared to capitalization weighting. First, since the fundamentals used are price insensitive, the resulting performance is not subject to the performance drag which capitalization weighting bears with it. Second, fundamental indexing exhibits higher return with lower volatility and therefore is more mean variance efficient. Finally, fundamental indexing exhibits the preferable characteristics of the cap-weighted index: high liquidity, high investability and low transaction costs.
However there is also substantial criticism on fundamental indexing. An important question comes to mind. Where should we put fundamental indexing in light of the “active versus passive” debate? Arnott, Hsu and Moore (2004) present fundamental indexing as a passive strategy. Another way of looking at this is by seeing a fundamental index as a benchmark that can be tracked. From this point of view, fundamental indexing is a passive strategy. An important point to note, is that fundamental indexing requires periodic rebalancing. Furthermore, it is presented as a strategy that produces alpha compared to a capitalization weighted index. This leads some to conclude that it is therefore an active strategy pretending to be a passive one. Although the labels “active” and “passive” seem trivial for investors, the implications that come with these labels are definitely not. As Malkiel (2003) and Estrada (2006) point out, active strategies often bring with them higher turnover and higher transaction costs.
Bernstein (2006), however, shows that the higher performance of the RAFI index (Research Affiliates Fundamental Index) can be partly explained by higher exposures to the Fama and French (1993) risk factors.
Although we assume the three-factor model of Fama and French (1993) as known to the reader, we want to expand on this issue a little further since it plays an important role in our research. Fama and French (1992) find that market value and book-to-market ratio do a good job in explaining average returns in the American stock market over the period 1963-1990. Fama and French (1993) expand on this issue by introducing a three factor model using the CAPM market premium, the size premium and the value premium. They derive the size premium by subtracting the average return of the 30 percent largest stocks (according to their market value) from the return of the 30 percent smallest stocks. The value premium is derived in a similar fashion by subtracting the average return of
3. DATA REQUIREMENTS AND METHODOLOGY
We will now describe the data that we have used for this research, the way we constructed the indices and the methodology that we applied to answer our research question. The data requirements and methodology is given in two subsections, one for the description of the way we constructed the indices and the raw data used (3.1) and one for the methodology we used to analyze the return and risk characteristics of the indices(3.2).
3.1 Constructing the indices
We perform this research on fundamental indexing using data obtained from Thomson’s Datastream on the stocks from the Dow Jones Stoxx 600 (Stoxx) over the period between December 1992 and May 2007. To check whether our data is accurate and to analyze the results of our research, we subdivide the period under investigation into two subperiods: December 1992-December 2001 and December 2001-May 2007. We do this for practical reasons. Since Datastream provides constituents list of the Stoxx from Dec 2001
onwards, data from the second period is complete. Datastream id-codes and information of the constituents from the first period had to be searched by hand and is therefore substantially less complete.
We construct fundamental indices on the bases of gross dividends, revenue, number of employees, book value of the assets and operating income. We also construct a composite index of the fundamentals excluding number of employees. To analyze the risk and return characteristics of the fundamental indices, we need to have a benchmark. Directly
comparing the returns of the fundamental indices to the returns of the Stoxx, as provided by the Dow Jones, could create a bias. There are two reasons for this. First, since market value and price data is not available for every stock, these stocks are excluded from our research. Second, since data on fundamentals is not available for every stock, these stocks are excluded from the fundamental index and should therefore also be removed from the benchmark of that particular fundamental index. For these reasons we reconstruct the Stoxx, we will refer to this benchmark index as the benchmark index throughout the paper.
We divide this subsection in two. Subsection 3.1.1 describes the reconstruction of the Stoxx, the benchmark index. Here, we also describe the checks we have performed on the data to verify if the data is correct and if the resulting benchmark index is still
representative of the Stoxx. Subsection 3.1.2 entails the description of constructing the fundamental indices and the adjustment of the benchmark index to create accurate
benchmarks for the fundamental indices. Here, we also present the summary of data used to construct the fundamental indices.
3.1.1 Construction of the benchmark index and data checks
Although we use total return prices (prices including the reinvestment of dividends paid) in the rest of our research, we use quoted prices (excluding the reinvestment of
dividends) to calculate the return of the benchmark index in first instance. The reason for this is that Datastream handles the reinvestment of dividends slightly different than the Dow Jones, which would make it more difficult to compare returns and thus to test whether the benchmark index is representative of the Stoxx. Sources of deviations in the total return prices of Datastream and the Dow Jones could stem from the ex-dividend date or the amount of dividends paid. To check the accuracy of our data, the market values that Datastream provides are compared to the market values as provided by the Dow Jones. The stocks that deviate more than 10% in market value are removed from the benchmark index. Since market value is the product of outstanding shares and price, this method automatically removes inaccurate prices from our dataset. The last two columns of Table 1 below present the yearly percentages of firms and market value of the Stoxx captured by our remaining data.
To construct the benchmark index, the constituents lists of the Stoxx from December of every year are used from the Dow Jones website. These constituents are held constant in the benchmark index throughout the year for practical reasons. The following step is weighting the constituents according to their market value in the benchmark index. Market value is defined as number of outstanding shares times price of the outstanding shares (and, from the year 1999 onwards, corrected for freefloat). The weight of any stock in the index is calculated as:
Wit = MVit/ TMVit
Where
Wit = The weight of stock i in the benchmark index on date t
MVit = The market value of stock i on date t.
TMVt = The total market value of all stocks in the index on date t
The return of a constituent on any day is calculated as follows Rit = (Pit/ Pi t-1)-1
Where
Rit = Return of stock i on date t
Pit = The price of stock i on date t
Pi t-1= The price of stock i on date t-1
The return of the benchmark index on a particular day is calculated as:
Rref it = ∑ (Wit * Rit)
Where
Tables 1, 2 and 3 below present a summary of the data that we have used. Table 1 shows the yearly and average returns of the Stoxx and our benchmark index. It also shows annualized standard deviations, the yearly correlation of daily returns and the yearly percentages of firms and market value of the Stoxx captured by the benchmark index. This information is given over the whole period under investigation. As can be seen from table one, although the percentage market capitalization is only 60% in 1993 (and ranges up to about 80% in 2001), the correlation of the return of our benchmark index with the real Stoxx is very high. Furthermore, the annualized standard deviations of the
benchmark index are very similar to the real Stoxx. We formally test whether the returns of our benchmark differ from the returns of the real Stoxx by performing a two-sided T-test on the paired daily returns. We find a T-statistic of -0.395 with a corresponding probability of 69.33% and conclude that the returns do not significantly differ at the 5% significance level.
Table 1. Yearly returns, yearly annualized standard deviations, yearly correlations and coverage of the Stoxx by the benchmark index. Yearly and average returns and annualized standard deviations of the Stoxx
600 and the benchmark index, the yearly and average correlation of daily returns of the Stoxx 600 and the reference index and the yearly and average percentages of firms and market value of the Stoxx 600 covered by
the benchmark index. The returns are calculated using prices excluding the reinvestment of dividends. Difference in daily returns are formally tested by performing a two-sided T-test on the paired daily returns of the
Stoxx and the benchmark. With a T-value of -0.395 and a probability of 69.33% the returns do not significantly differ at the 5% significance level.
Yearly return
Annualized standard deviation
Percentage covered by benchmark index
Year Stoxx Benchmark Stoxx Benchmark
Correlation in return
between Stoxx and
benchmark Firms Market Value
1993 34.23% 35.63% 9.43% 8.81% 0.935 61% 63% 1994 -10.13% -9.40% 11.22% 11.47% 0.979 63% 61% 1995 11.17% 13.30% 9.24% 9.55% 0.952 69% 67% 1996 26.33% 20.90% 9.12% 8.70% 0.941 72% 67% 1997 38.63% 37.64% 16.60% 16.73% 0.978 76% 72% 1998 15.59% 18.41% 23.66% 21.06% 0.988 77% 74% 1999 32.67% 35.92% 16.93% 16.00% 0.984 80% 76% 2000 -1.90% -5.19% 19.11% 18.04% 0.988 78% 75% 2001 -20.03% -19.69% 22.22% 22.15% 0.997 82% 81% 2002 -32.30% -32.47% 29.00% 28.52% 0.998 100% 100% 2003 12.76% 13.68% 21.59% 21.23% 0.999 100% 100% 2004 9.41% 9.51% 11.63% 11.51% 0.996 100% 100% 2005 23.07% 23.46% 9.55% 9.37% 0.997 100% 100% 2006 17.39% 17.81% 13.00% 12.70% 0.999 100% 100% 2007 6.82% 6.83% 13.11% 12.85% 0.999 100% 100% Mean 10.91% 11.09% 15.69% 15.25% 0.982 84% 82%
As mentioned in the introduction of this section, Datastream id-codes and information of the constituents from the first period had to be searched by hand and is therefore
over the countries and market sectors in tables 2 and 3. As can be seen when looking at the tables, the distributions of the benchmark index are very similar to the ones of the Stoxx. On the basis of these tables and table 1, we therefore conclude that the data we used to construct the benchmark index is representative of the Stoxx.
Table 2. Yearly distribution of the constituents over the different countries of the Stoxx 600 and the benchmark index.
Country
Year Index Aus Bel Swiss Ger Dan Esp Fin Fra
1993 Stoxx 1.7% 3.2% 5.2% 10.9% 2.7% 4.5% 1.5% 17.2% Benchmark 1.9% 1.9% 3.8% 10.9% 2.5% 1.4% 0.3% 19.9% 1994 Stoxx 1.5% 3.4% 5.7% 10.9% 3.0% 4.9% 2.2% 16.4% Benchmark 2.1% 2.6% 4.0% 9.8% 2.6% 5.5% 0.8% 18.7% 1995 Stoxx 2.0% 4.0% 4.9% 8.4% 4.0% 4.5% 2.8% 15.7% Benchmark 2.9% 3.6% 2.9% 8.4% 3.6% 5.3% 2.4% 18.0% 1996 Stoxx 2.2% 4.2% 4.8% 8.0% 3.8% 4.5% 2.7% 15.3% Benchmark 2.8% 3.8% 3.3% 7.3% 3.5% 4.2% 2.3% 17.1% 1997 Stoxx 2.5% 3.7% 4.2% 7.5% 3.8% 5.2% 3.3% 15.3% Benchmark 2.8% 3.5% 3.1% 7.0% 3.5% 5.7% 3.9% 17.3% 1998 Stoxx 3.1% 4.3% 4.1% 7.0% 4.5% 5.0% 4.1% 14.2% Benchmark 3.6% 3.8% 3.8% 7.6% 4.2% 5.8% 3.8% 15.4% 1999 Stoxx 2.7% 3.8% 4.3% 7.0% 4.3% 4.7% 4.2% 13.8% Benchmark 2.9% 4.4% 4.0% 7.1% 4.0% 5.2% 4.4% 15.0% 2000 Stoxx 1.0% 3.2% 5.4% 9.6% 2.0% 4.9% 1.9% 13.3% Benchmark 1.1% 3.7% 3.7% 10.0% 2.2% 5.6% 2.4% 15.4% 2001 Stoxx 0.5% 2.2% 6.5% 9.7% 2.2% 4.7% 1.2% 13.3% Benchmark 0.4% 2.0% 6.1% 10.3% 2.4% 5.1% 1.4% 14.4% Country
Year Index UK Gr Ir It Hol Nor Por Swe
Table 3. Yearly distribution of the constituents over the different industry markets of the Stoxx 600 and the benchmark index. The companies are assigned to the different industry markets using the
classification system of the Dow Jones
Industry market
Year Index BI CCG En F I M NCCG T Tel U
1993 Stoxx 8.0% 16.2% 2.5% 24.4% 20.2% 2.7% 14.2% 5.2% 0.0% 6.5% Benchmark 6.8% 17.7% 2.5% 24.8% 21.5% 1.9% 15.5% 6.0% 0.0% 3.3% 1994 Stoxx 8.7% 15.6% 2.5% 24.3% 20.8% 3.0% 14.1% 4.7% 0.0% 6.4% Benchmark 7.7% 15.8% 2.6% 24.3% 21.1% 3.2% 14.8% 5.3% 0.0% 5.3% 1995 Stoxx 9.4% 14.9% 2.7% 24.5% 21.6% 3.5% 13.4% 4.0% 0.0% 6.0% Benchmark 8.4% 16.1% 2.9% 25.7% 21.6% 3.1% 13.4% 4.1% 0.0% 4.8% 1996 Stoxx 9.0% 14.8% 3.2% 24.5% 21.0% 3.5% 13.0% 4.7% 0.0% 6.3% Benchmark 8.7% 15.5% 3.1% 25.4% 20.7% 3.5% 13.6% 4.5% 0.0% 5.2% 1997 Stoxx 9.3% 15.8% 3.5% 23.7% 21.2% 3.0% 12.0% 4.7% 0.0% 6.8% Benchmark 8.8% 16.2% 3.3% 24.1% 21.7% 2.8% 12.7% 4.4% 0.0% 6.1% 1998 Stoxx 10.3% 16.6% 3.6% 22.1% 20.8% 3.3% 12.0% 0.0% 5.1% 6.2% Benchmark 10.7% 17.2% 3.3% 22.1% 20.5% 2.7% 12.5% 0.0% 4.7% 6.3% 1999 Stoxx 10.2% 15.5% 3.5% 21.3% 20.3% 3.2% 12.7% 6.2% 0.0% 7.2% Benchmark 11.0% 15.6% 3.1% 21.3% 20.0% 2.9% 12.3% 5.8% 0.0% 7.9% 2000 Stoxx 6.9% 16.7% 2.4% 25.1% 15.7% 2.9% 12.3% 8.4% 0.0% 9.6% Benchmark 7.4% 16.0% 2.2% 25.3% 15.6% 3.0% 12.6% 8.7% 0.0% 9.3% 2001 Stoxx 5.8% 19.7% 2.8% 22.3% 5.5% 18.8% 9.2% 5.5% 5.3% 5.0% Benchmark 6.3% 19.2% 2.4% 22.3% 5.7% 19.0% 9.3% 5.7% 4.5% 5.7%
BI=basic industry, CCG=Cyclical consumer goods, En=Energy, F=Financial, I=industry, M=materials, NCCG=Non cyclical consumer goods, T=Technology, Tel=Telecom, U=Utilities
3.1.2 Construction and data summary of the fundamental indices
As mentioned before, we construct fundamental indices on the bases of gross dividends, revenue, number of employees, book value of the assets and operating income. The composite index is constructed using the average weight of stocks in the fundamental indices excluding number of employees.
Simply re-weighting the Stoxx would create a double metric portfolio as pointed out by Arnott, Hsu and Moore (2004), concentrated heavily in stocks with the highest market values and highest fundamental measure. To avoid this, they take a universe of 1500 stocks and rank them on the bases of their fundamental value. Then the 1000 largest stocks are included in the fundamental index. In this way, however, the fundamental indices and market capitalization index all have different constituents. In this research, the aim is to analyze the performance of weighting stocks in the index by their
distinguish these benchmark indices from the initial benchmark index we will name them according to their fundamental metric, for example “benchmark book value index”. To summarize the fundamental data used for constructing the fundamental indices, we present the data in quartiles in the graphs 1 to 6 below. Each year, we rank the
constituents of the index from large to small according to their market value. Then we divide the constituents into quartiles. In this way, the graphs show what percentage of the total value of the fundamental of all constituents is held by the largest 25 percent of constituents (according to their market value), the second largest 25 percent, etcetera. For comparison, we also present this information for the market value used in the unadjusted benchmark index.
Distribution of market value
0% 20% 40% 60% 80% 100% 1992 1994 1996 1998 200 0 200 2 200 4 200 6 Time C u m u lat ive p er cen tag e o f to tal m ar ket val u e Largest quartile 2nd quartile 3rd quartile Smallest quartile
Graph 1. Distribution of market values. The constituents are ranked from large to small and divided in
Distribution of book value of assets 0% 20% 40% 60% 80% 100% 1992 1994 1996 1998 200 0 200 2 200 4 200 6 Time C u m u lat ive p er cen tag e o f to ta l b o o k v a lu e Largest quartile 2nd quartile 3rd quartile Smallest quartile
Graph 2. Distribution of book values of the assets. The constituents are ranked from large to small and
divided in quartiles. The graph shows the cumulative percentage of the book value of the assets held by the constituents in the different quartiles.
Distribution of dividends 0% 20% 40% 60% 80% 100% 1992 1994 1996 1998 200 0 200 2 200 4 200 6 Time C u m u lat ive p er cen tag e o f tota l di v id e nd s pa id Largest quartile 2nd quartile 3rd quartile Smallest quartile
Graph 3. Distribution of dividends. The constituents are ranked from large to small and divided in
Distribution of operating income 0% 20% 40% 60% 80% 100% 1992 1994 1996 1998 200 0 200 2 200 4 200 6 Time C u m u lat ive p er cen tag e o f to ta l o p e ra tin g in c o m e Largest quartile 2nd quartile 3rd quartile Smallest quartile
Graph 4. Distribution of operating income. The constituents are ranked from large to small and divided
in quartiles. The graph shows the cumulative percentage of the operating income generated by the constituents in the different quartiles.
Distribution of revenue 0% 20% 40% 60% 80% 100% 1992 1994 1996 1998 200 0 200 2 200 4 200 6 Time C u m u lat ive p er cen tag e o f to tal r even u e Largest quartile 2nd quartile 3rd quartile Smallest quartile
Graph 5. Distribution of revenue. The constituents are ranked from large to small and divided in
Distribution of number of employees 0% 20% 40% 60% 80% 100% 1992 1994 1996 1998 200 0 200 2 200 4 200 6 Time C u m u lat ive p er cen tag e o f to tal em p lo
yees Largest quartile
2nd quartile 3rd quartile Smallest quartile
Graph 6. Distribution of number of employees. The constituents are ranked from large to small and
divided in quartiles. The graph shows the cumulative percentage of the number of employees working at the constituents in the different quartiles.
What conclusions can we draw on the raw data used for constructing the indices from looking at these graphs? The first thing that that meets the eye is that the distribution of fundamental data over the quartiles (except for number of employees) strongly resembles the distribution of market value over the same quartiles.
Compared to the distribution of market value and the other fundamental values, the distribution of the number of employees over the four quartiles deviates. The number of employees is more evenly spread over the different quartiles.
An important point to note is that the distribution of fundamental values is less stable than the distribution of market value. Since the constituents are ranked by market value every year, large changes in market value result in a constituent moving from one quartile to another. If this change in market value is not followed by a change in the fundamental value, it results in a shift of the distribution of the fundamental value over the different quartiles. Over the year 1995, dividends and revenue of the constituents in the three smallest quartiles rise with 18 percent and 24 percent respectively at the cost of the largest quartile. A smaller rise can be seen in operating income of the second largest quartile over the year 1998 (about 5 percent), also at the expense of the largest quartile. These deviations in distribution of the fundamental values over the four quartiles result in a different weighting of the constituents in the index portfolio and thus in a different return.
Wit = FVit/ TFVit
Where
Wit = The weight of stock i in the fundamental index on date t
FVit = The value of the fundamental of stock i on date t.
TFVit = The value of the fundamental of all stocks in the index on date t
The weight of a constituent in the composite index is calculated by taking the average weight of that constituent in the book value index, the dividend index, the operating income index and the revenue index. When the weight of one of these fundamental indices is not available for a particular constituent, the average weight in the remaining fundamental indices is taken. The calculation of the weights in the operating income index requires further explanation. Since operating income can take on a negative value, we set it to zero when this happens. The alternative would be to allow short positions in the stocks of the constituents, which would be highly undesirable in an indexing strategy. The returns of the constituent stocks and the indices are calculated as in the benchmark index except for the fact that we now use prices including the reinvestment of dividends, so called total return prices. We use total return prices since we are interested in all wealth that flows to the investor using the presented indexing strategies.
Rit = (RIit / RIit-1)-1
Where
Rit = Return of stock i on date t
RIit = The total return price of stock i on date t
RIi t-1 = The total return price of stock i on date t-1
The return of a fundamental index on a particular day is calculated as:
Rfund it = ∑ (Wit * Rit)
The resulting weights are not held constant throughout the year because that would mean that the portfolio would have to be rebalanced every day. This would result in large turnover costs and little added return as Arnott, Hsu and Moore (2004) show in their research. Instead, the index portfolio is rebalanced once a year at the end of each year and is allowed to change with market value throughout the year.
As mentioned before, the benchmark index is adjusted according to the availability of data. This results in six different market capitalization weighted benchmark indices, one for each fundamental index and the composite index. To check whether these adjusted benchmark indices are still in line with the unadjusted benchmark index, we provide the yearly, average and full period returns of the unadjusted benchmark index and the adjusted benchmark indices in table 4. In table 5 we present yearly and average
indices with the unadjusted benchmark index. Both the standard deviations and the correlations are calculated using daily returns of the indices. Unlike the comparison of the unadjusted benchmark index with the Stoxx in subsection 3.1.1, we do not perform T-tests here. In our opinion tables 4, 5 and 6 are sufficient, since the adjusted benchmark indices are constructed in the same way as the unadjusted benchmark indices and the adjustments entail the exclusion of only a handful of companies each year.
Table 4. Yearly, average and full period returns of the unadjusted benchmark index and the adjusted benchmark indices over the period 1993-2007. Due to the unavailability on fundamental values of some
constituents, the initial benchmark index has to be adjusted to provide accurate benchmarks for the fundamental indices. This table is presented to show to which level the adjusted benchmark indices are still representative of the
unadjusted benchmark index after adjusting for missing data. (* = until may 15th)
Table 5. yearly and average annualized daily standard deviations of the unadjusted benchmark index and the adjusted benchmark indices over the period 1993-2007. The standard deviations are calculated using the
daily returns of the indices and then annualized by multiplying the resulting daily standard deviations by the square root of the number of trading days in a year (261^(1/2)). (* = until may 15th)
Index Year Unadjusted benchmark Index Book value benchmark index Operating income benchmark index Employee benchmark index Dividend benchmark index Revenue benchmark index Composite benchmark index 1993 7.94% 8.20% 8.39% 8.33% 8.26% 8.21% 8.20% 1994 11.14% 11.31% 11.42% 11.47% 11.52% 11.31% 11.14% 1995 8.65% 8.60% 8.36% 8.68% 8.66% 8.60% 8.60% 1996 8.08% 8.19% 8.10% 8.23% 8.35% 8.18% 8.19% 1997 15.89% 16.07% 15.97% 16.14% 15.70% 16.06% 16.07% 1998 21.08% 21.59% 21.49% 21.79% 21.68% 21.64% 21.59% 1999 15.54% 15.70% 15.07% 15.77% 15.84% 15.72% 15.70% 2000 17.54% 17.77% 12.38% 17.92% 18.22% 17.84% 17.77% 2001 26.07% 26.25% 23.71% 26.32% 26.58% 26.27% 26.23% 2002 27.76% 27.84% 27.24% 27.85% 27.80% 27.76% 27.83% 2003 19.91% 19.97% 19.91% 19.95% 20.13% 19.95% 19.97% 2004 11.13% 11.13% 10.52% 11.13% 11.25% 11.13% 11.13% 2005 8.84% 8.84% 9.01% 8.85% 8.83% 8.85% 8.84% 2006 12.85% 12.85% 12.96% 12.85% 12.94% 12.86% 12.85% 2007* 13.56% 13.55% 13.59% 13.56% 13.62% 13.57% 13.55% Mean 15.07% 15.19% 14.54% 15.26% 15.29% 15.20% 15.18%
Table 6. Yearly correlations of the returns of the adjusted benchmark indices with the returns of the unadjusted benchmark index over the period 1993-2007. The correlation is calculated using the daily returns
of the indices. This table is presented to show to which level the adjusted benchmark indices are still representative of the unadjusted benchmark index after adjusting for missing data. (* = until may 15th)
As can be seen from tables 4 and 5, yearly and average returns and standard deviations of the adjusted benchmark indices compared to the unadjusted benchmark index are slightly higher, but very much alike. The full period returns deviate more, but this can be
reasonably explained by the fact that small deviations in return are magnified as time passes. That the adjusted benchmark indices are in line with the unadjusted benchmark index is confirmed by the yearly correlations in table 6, which are very high. Overall, we conclude from these tables that the adjusted benchmark indices are in fact accurate benchmarks and representative of the unadjusted benchmark index. We go one step further and conclude that the adjusted benchmark indices are representative of the real Stoxx as well. We do this, since we have concluded that the unadjusted benchmark index is representative of the real Stoxx in the subsection on constructing the benchmark index. Tables 7 and 8 show the yearly, average and full period returns and standard deviations of the fundamental indices. We have included the unadjusted benchmark index in the table to give a first impression of the differences between the fundamental indices and the unadjusted benchmark index. For a more accurate comparison of the returns and standard deviations we refer to tables 4 and 5.
Table 7. Yearly, average and full period returns of the unadjusted benchmark index and the fundamental indices over the period 1993-2007. The benchmark index is included to give an impression of the differences
between the fundamental indices and the unadjusted benchmark index. For a more accurate comparison, we refer to the returns and standard deviations of the adjusted benchmark indices in tables 4 and 5. (* = until may 15th)
Index Year Benchmark Index Book value index Operating income index Employee
index Dividend index Revenue index Composite index
Table 8. yearly and average annualized daily standard deviations of the unadjusted benchmark index and the fundamental indices over the period 1993-2007. The standard deviations are calculated using the daily
returns of the indices and then annualized by multiplying the resulting daily standard deviations by the square root of the number of trading days in a year (261^(1/2)). (* = until may 15th)
Index Year Benchmark Index Book value index Operating income index Employee index Dividend index Revenue index Composite index 1993 7.94% 9.57% 8.39% 8.64% 8.15% 8.86% 8.57% 1994 11.14% 12.69% 11.42% 11.20% 11.22% 11.48% 11.57% 1995 8.65% 10.06% 8.36% 8.72% 8.38% 9.38% 8.94% 1996 8.08% 8.87% 8.10% 8.15% 8.04% 8.26% 8.20% 1997 15.89% 17.54% 15.97% 16.41% 14.73% 16.30% 15.99% 1998 21.08% 24.78% 21.49% 21.89% 19.67% 22.36% 21.92% 1999 15.54% 18.16% 15.07% 14.08% 14.26% 14.93% 15.36% 2000 17.54% 13.40% 12.38% 12.05% 12.88% 11.54% 12.03% 2001 26.07% 27.25% 23.71% 22.90% 22.74% 23.82% 24.16% 2002 27.76% 32.26% 27.24% 25.59% 25.88% 27.61% 28.08% 2003 19.91% 25.48% 19.91% 21.53% 20.63% 22.69% 22.10% 2004 11.13% 12.81% 10.52% 12.21% 10.15% 12.14% 11.29% 2005 8.84% 9.93% 9.01% 9.22% 8.63% 9.58% 9.20% 2006 12.85% 14.66% 12.96% 13.47% 12.30% 13.52% 13.29% 2007* 13.56% 15.33% 13.59% 13.96% 12.98% 14.07% 13.93% Mean 15.07% 16.85% 14.54% 14.67% 14.04% 15.10% 14.98%
When we compare tables 4 and 5 on the adjusted benchmark indices to tables 7 and 8 on the fundamental indices, we can see that the fundamental indices exhibit a larger mean return while the standard deviation stays equal (in most cases is even a little smaller). The book value index shows a higher mean standard deviation over the years, but also has the highest excess mean return (17.5 percent compared to 13.8% percent). The difference in returns of the fundamental indices is even more dramatic when we compare the full period returns of the fundamental indices to their benchmark counterparts. However, we cannot conclude anything from these tables yet, we have to conduct our analysis to see whether these differences are statistically significant. Also, we want to include more measures of risk in our research. In the next subsection we describe our methodology of analysis.
3.2 Methodology of analyses
In this subsection we present the methodology that we applied two answer our research question. We divide this section in three parts. Subsection 3.2.1 describes the
methodology used to analyze the difference in returns between the fundamental indices and the adjusted benchmark indices. In 3.2.2 we explain which risk factors we include in our analysis and how we analyze the risk that comes with fundamental indexing.
Subsection 3.2.3 deals with the way we analyze the costs of managing the fundamental indices compared to the adjusted benchmark indices.
3.2.1 Methodology of analysis on excess returns of the fundamental indices
First, we want to determine whether the differences in return between the fundamental indices and their adjusted benchmark benchmarks are significant.
We will perform two tests on the returns of the fundamental indices and their benchmark benchmarks. First, we will perform a t-test on the monthly returns of the fundamental indices and their adjusted benchmark indices. We test at the 5 percent significance level whether the mean return of the fundamental index is significantly higher than the mean return of its benchmark index. This test will be performed using the one sided “t-test: paired two sample for means” in Excel. Results of the t-test are biased, however, since our data violates a condition for applying this test, the samples of returns are not normally distributed. Using the natural logarithm of returns and using daily returns does not
normalize our data so we perform a second test. We perform a simple binomial sign test to the monthly excess returns of every fundamental index over its benchmark index. If differences in returns between the fundamental index and its benchmark index would be random, one would expect the fundamental index to have a positive excess return close to 50 percent of times. We will calculate the critical number of positive excess returns at the 5 percent significance level for which we can conclude that if the fundamental index exceeds this number of positive excess returns, it is unlikely that the excess return is random. This test has a drawback, however. It does not take into account the size of the excess returns. If the fundamental index outperformes its adjusted benchmark index 99 percent of the time, the test will reject the null-hypothesis that there is no difference in return. However, it is still possible that the positive excess return will be negated in the 1 percent of the times when it underperforms.
3.2.2 Methodology of analysis on the risk characteristics of the indices
Analysis of the risk exposure of the fundamental indices will be done by regressing the monthly returns of the indices to the monthly risk premiums of value and size identified by Fama & French (1993) and the CAPM market premium. We will refer to these premiums as the style premium, the size premium and the market premium respectively. Since the style premium and the size premium are not readily available, we have to derive them ourselves. We use a method that differs from the method we described in the
literature review of Fama and French (1993). Instead we use the returns of size and style indices and regress them to each other to make them independent. We will now give a more complete description of the method used.
The premiums are defined as:
Rstyle t = (Rvalue t – Rgrowth t)
Rsize t = (Rsmall t- Rbig t) and
Where
Rstyle t is the style premium in month t
Rvalue t is the return the MSCI Europe Value stocks index in month t
Rgrowth t is the return the MSCI Europe Growth stocks index in month
Rsize t is the size premium in month t
Rsmall t is the return of the Dow Jones Stoxx Europe Small stocks index in month t
Rbig t is the return of the Dow Jones Stoxx Europe Small stocks index in month t
Rmarket t is the market premium in month t
Rstoxx t is the return of the Dow Jones Stoxx 600 in month t
Rft is the risk free rate in month t
As the risk free rate we will use a synthetic Euribor over the period 1993-1998 and the Euribor over the period 1999-2007 as provided by Datastream. We use the synthetic Euribor until 1999 since the Euribor is not available until then. The synthetic Euribor is calculated by Datastream taking a weighted average of interbank rates of countries in the EU at that time.
It is very likely that the style premium and the size premium overlap since the indices used consist for a great deal of the same constituents. To test whether this is the case and to filter the size effect out of the style premium and the style effect out of the size
premium, we make use of the following regressions:
Rstyle t - Rft = α1 + β(Rsize t -Rft) + e1t
And
Rsize t - Rft = α2 + β(Rstyle t -Rft) + e2t
So that
Rstyle* t = (Rstyle t - Rft) - β(Rsize t - Rft) and Rsize* t = (Rsize t - Rft) - β(Rstyle t-Rft)
Where
Rstyle* t is the style premium, cleared of size effects
Rsize* t is the size premium, cleared of value effects
α1 is a constant in the regression of the style premium
α2 is a constant in the regression of the size premium
β is a factor coefficient
e1t is a residual in the regression of the style premium in month t
e2t is a residual in the regression of the size premium in month t
Table 9. Regressions of value and size premium. Regressions are performed on the uncorrected
monthly value and size premiums. The style premium is defined as Rstyle t = (Rvalue t – Rgrowth t) and the size
premium is defined as Rsize t = (Rsmall t- Rbig t).
A. Style premium (not corrected) B. Size premium (not corrected)
Factor
loading Probability Factor loading Probability
α1 0.002 33.2% α2 -0.006 0.3%
Size premium
(uncorrected) 0.219 0.1% Style premium (uncorrected) 0.301 0.1%
Adjusted
R-squared 6.0% Adjusted R-squared 6.0%
As can be seen from the factor loadings of the regressions, both the value and the size premium are partly explained by each other before they are corrected for overlap. The factors are significant at the 5 percent significance level and thus a correction should take place in the way that is explained above. Both regression formulas explain 6.0 percent of the premiums as can be seen from the adjusted R-squared value.
The regressions of the monthly returns of the fundamental indices and the adjusted benchmark indices on the three monthly risk premiums will have the following form:
Rfund t - Rft = γ0 + γ1(Rmarket t) + γ2(Rstyle* t) + γ3(Rsize* t) + eit
Where
Rfund t Is the return of a fundamental index in month t
γ0 Is the return of the fundamental index that cannot be explained by the
different risk factors, referred to as alpha in the rest of this paper
γ1 Is the factor loading of the fundamental index to the market premium
(CAPM Beta)
γ2 Is the factor loading of the fundamental index to the style premium
γ3 Is the factor loading of the fundamental index to the size premium
eit Is the residual value of the excess return of the adjusted benchmark index
over the risk free rate in month t
If these regressions show any positive monthly alpha (γ0), we are not there yet. We have
to take into account the costs of managing the fundamental indices.
3.2.3 Costs of managing the fundamental indices
This subsection identifies the main costs of managing the fundamental indices and describes how we take these costs into account in our analysis.
As mentioned in the subsection on constructing the fundamental indices, at the end of the year we recalculate the weights of the stocks in the fundamental indices and adjust our index portfolios accordingly. This involves trading percentages of our stock holdings on top of the normal trading due to emissions and omissions in the index. We define
rebalancing date and we define turnover costs as the brokerage fee that has to be paid as a result of turnover. We will present turnover costs as a percentage of the index portfolio as well. Turnover and turnover costs are calculated over the years 2002-2006. The reason for this is that before this period, availability of data on the constituents is rising. Because of this rising availability of data, constituents are added to the indices that where actually already in the index. This results in turnover that did not actually take place if data would have been available earlier.
Arnott, Hsu and Moore (2004) assume the cost of trading to be 1% for buying and selling. This is a very high rate that seems to be based on the reasoning of “better save than sorry”. We make a more realistic assumption based on the expertise of the index tracking team of Theodoor Gilissen Bankers N.V. and set the trading costs to be 0.20% for buying as well as selling. As a benchmark for the fundamental indices that represents a market capitalization weighted index we use the turnover of the MSCI Europe in 2003. This is the only available data on turnover we could find to use as a benchmark. The turnover of the MSCI Europe was 7.36 percent of the total portfolio in 2003.
Once we have calculated the turnover costs, we correct the alpha found (if any) in the regressions of the returns on the different risk factors. We do this by annualizing the alpha and subtracting it with the average annual turnover costs. The assumption here is that the average annual cost of turnover found is a good proxy of turnover costs that would be incurred when adopting fundamental indexing as an investment strategy. We refer to the resulting return as corrected alpha. The formula for corrected alpha is: αc = [(γ0 + 1)^12] – 1 – TCav
Where
αc Is alpha corrected for turnover costs
γ0 Is (as before) the return of the fundamental index that cannot be explained by the
different risk factors, referred to as alpha.
TCav Is the average cost of turnover found in our analysis.
4. RESULTS
The results are presented in three subsections in the same way as the subsection on methodology (3.2) was subdivided. First we show the results of the analysis we did on the differences in return between the fundamental indices and the adjusted benchmark indices (4.1). In the second section (4.2), we present our analysis of the risk
characteristics of the fundamental indices and the adjusted benchmark indices. The last section (4.3) shows the turnover costs associated with managing the fundamental indices. In this section we also correct the alpha found in the returns of the fundamental indices (if any) with the turnover costs.
4.1 Analysis of the excess returns of the fundamental indices
Table 10 shows the excess returns of the fundamental indices over their benchmark counterparts over the period under investigation. T-tests are performed on the paired monthly returns of the fundamental indices and the adjusted benchmark indices.
Table 10. Excess returns and corresponding T-tests. T-tests are performed on the monthly returns of the
fundamental indices and the corresponding adjusted benchmark indices over the period 1993-2007. Table 10 shows the T-values and the probability that the excess returns are significant. * means that the excess
return is significant at the 5% level.
Index Book* value index income index Operating* Employee index Dividend index Revenue* index Composite* index Excess
return 268.12% 192.39% 136.82% 152.67% 153.87% 194.79%
T-Statistic 1.873 2.598 1.533 1.612 1.777 2.308
Probability 3.1% 0.5% 6.4% 5.4% 3.9% 1.1%
As can be seen from the table, the excess returns are very high over the period 1993-2007 (195 percent for the composite). The excess return is significant at the 5 percent level for the book value index, the operating income index, the revenue index and the composite index. The book value index shows the highest excess return, followed by the composite index.
Table 11. Binomial test on signs of the excess returns. The critical number of positive excess returns at the 5
percent significance level is calculated for which can be concluded that if the fundamental index exceeds this number of positive excess returns, the excess return is significant. Since the test does not take the size of the excess returns into account, data on the range and means of the excess returns are provided for closer analysis.
* means that the excess return is significant
Index
Book* value
index Employee index Dividend index
Operating* income
index Revenue* index Composite* index
Number of months with
positive excess return 96 93 93 113 102 105
Critical number of
months 96 96 96 96 96 96
Range of excess returns
fundamental index* (6.87%) - 7.81% (4.96%) - 4.36% (4.81%) - 6.78% (5.21%) - 3.45% (5.63%) - 3.96% (5.43%) - 3.63%
Mean negative excess
return -1.37% -0.92% -0.61% -0.59% -0.86% -0.71%
Mean positive excess
return 1.59% 1.05% 0.78% 0.57% 0.86% 0.76%
Table 11 leads us to the same conclusion on the significance of the excess returns as the T-tests do. Except for the employee index and the dividend index, the excess returns are significant. As already mentioned, however, this test has a drawback since it does not take the size of the excess returns into account. We therefore provide data on the range of the excess returns and means of the positive and negative excess returns. The numbers on the range of excess returns and means of the positive and negative excess returns lead to the belief that the positive excess returns are not lower than the negative.
Together, the two tests on the excess returns of the fundamental indices over their benchmark counterparts are reasonably convincing in their conclusion that the excess returns of the fundamental indices are significant for four of the six indices.
4.2 Analysis of the risk characteristics of the indices
Table 12 and 13 provide the results of the regressions we performed on the monthly returns of the adjusted benchmark indices and the fundamental indices for the analysis of the risk characteristics of the fundamental indices. Without repeating the details of the methodology, we give the regression formula again to make interpretation of the results easier.
Rfund t - Rft = γ0 + γ1(Rmarket t) + γ2(Rstyle* t) + γ3(Rsize* t) + eit
Where
Rfund t Is the return of a fundamental index in month t
Rstyle* t is the style premium, cleared of size effects in month t
Rsize* t is the size premium, cleared of value effects in month t
Rmarket t is the market premium in month t
Rft is the risk free rate in month t
γ0 Is the return of the fundamental index that cannot be explained by the
γ1 Is the factor loading of the fundamental index to the market premium
(CAPM Beta)
γ2 Is the factor loading of the fundamental index to the style premium
γ3 Is the factor loading of the fundamental index to the size premium
eit Is the residual value of the excess return of the adjusted benchmark index
over the risk free rate in month t
Table 12. Factor loadings, probabilities and adjusted R-squared values of the regressions on the adjusted benchmark indices. The monthly returns of the adjusted benchmark indices are regressed on the monthly market
premium, style and size premium. The regression formula is:
Rfund t - Rft = γ0 + γ1(Rmarket t) + γ2(Rstyle* t) + γ3(Rsize* t) + eit. * Means the factor loading is significant at the 5%
level. Index Variable Book value benchmark index Operating income benchmark index Employee benchmark index Dividend benchmark index Revenue benchmark index Composite benchmark index γ0 0.000 0.000 0.000 0.000 0.000 0.000 Probability 0.248 0.224 0.519 0.797 0.169 0.305 γ1 1.006* 1.005* 1.011* 1.018* 1.007* 1.004* Probability 0.000 0.000 0.000 0.000 0.000 0.000 γ2 0.009 0.007 0.005 -0.008 0.007 0.008 Probability 0.063 0.136 0.371 0.400 0.141 0.091 γ3 0.011* 0.012* 0.010* 0.021* 0.013* 0.009* Probability 0.004 0.004 0.030 0.011 0.002 0.021 Adjusted R-squared 0.999 0.999 0.999 0.997 0.999 0.999
Table 13. Factor loadings, probabilities and adjusted R-squared values of the regressions on the
fundamental indices. The monthly returns of the fundamental indices over the period 1993-2007 are regressed on
the monthly market premium, style and size premium. The regression formula is: Rfund t - Rft = γ0 + γ1(Rmarket t) +
γ2(Rstyle* t) + γ3(Rsize* t) + eit * Means the factor loading is significant at the 5% level.
Index Variable
Book value
index income index Operating Employee index Dividend index Revenue index Composite index
Looking at the adjusted R-squared values of the regressions applied, we can see that the regression model used explains a very large percentage of the excess returns of the fundamental indices and the capitalization weighted adjusted benchmark indices over the risk free rate. These adjusted R-squared values thus confirm that the model used for the explanation of the returns is fairly complete.
The tables tell us that the adjusted benchmark indices as well as the fundamental indices all have a CAPM Beta of approximately 1. According to the probability values, these values are significant at the 5 percent significance level.
Looking at this risk factor alone, we can thus conclude that the fundamental index does not exhibit higher risk.
This is not the case when we look into the factor loadings on the size and style premiums. For the adjusted benchmark indices, the factor loadings are either significant and very close to zero or they do not differ from zero significantly. The fundamental indices on the other hand, have high factor loadings on the style premium (ranging from around 0.30 to 0.60) that are significant. Also, the fundamental indices show factor loadings on the size premium and these loadings are also significant except for the book value index. If we follow the theory of Fama and French and accept the size and value effects as risk factors, we can conclude from this that the fundamental indices are riskier than the capitalization weighted benchmark indices.
Does fundamental indexing result in alpha? The answer is yes! The fundamental indices exhibit statistically significant alpha of 0.2 percent per month after correcting for the loadings on the size and value premiums. The alpha of the book value index is 0.1 percent per month but is statistically not different from zero.
4.3 Turnover costs and corrected alpha of the fundamental indices
We present the yearly turnover, the yearly turnover costs, alpha and corrected alpha in table 14. Remember that the benchmark turnover that represents a market capitalization weighted index, was the 7.36 percent turnover of the MSCI Europe in 2003.
Table 14 A and B. Yearly turnover, yearly turnover costs, alpha and corrected alpha of the fundamental indices over the years 2002-2006. Turnover is given in table 14 A as a percentage of the total portfolio. The
benchmark turnover that represents a market capitalization weighted index for the fundamental indices is 7.36%, as provided by the MSCI for the year 2003. Turnover costs in 14 B are calculated by multiplying the turnover with the assumed cost of trading, set to be 0.20%. The alpha is the annualized monthly alpha derived
from the regressions on the risk factors. The corrected alpha is calculated by subtracting the average yearly turnover costs of each fundamental index from alpha.
14A. Turnover (in % of index portfolio) Index
Rebalancing date
Book value
index Operating income index Employee index Dividend index Revenue index Composite index
Dec-02 55.17% 46.62% 65.33% 54.42% 63.21% 50.89%
Dec-03 30.82% 37.66% 34.39% 47.35% 32.38% 33.64%
Dec-04 20.23% 34.14% 28.58% 34.43% 22.26% 23.22%
Dec-05 22.21% 30.72% 25.89% 33.13% 25.22% 24.94%
14B. Two way turnover costs (in % of index portfolio) Index
Rebalancing date
Book value
index Operating income index Employee index Dividend index Revenue index Composite index
Dec-02 0.11% 0.09% 0.13% 0.11% 0.13% 0.10% Dec-03 0.06% 0.08% 0.07% 0.09% 0.06% 0.07% Dec-04 0.04% 0.07% 0.06% 0.07% 0.04% 0.05% Dec-05 0.04% 0.06% 0.05% 0.07% 0.05% 0.05% Dec-06 0.05% 0.06% 0.05% 0.08% 0.05% 0.05% Mean 0.06% 0.07% 0.07% 0.08% 0.07% 0.06% Alpha 0% 2.43% 2.63% 2.25% 2.19% 2.17% Corrected alpha -0.06% 2.36% 2.56% 2.17% 2.12% 2.10%
The table shows that the turnover of the fundamental indices is much higher than the 7.36 percent turnover of the MSCI Europe index. Especially in December 2002, when
5. CONCLUSIONS AND RECOMMENTDATIONS FOR FURTHER RESEARCH
We present the conclusions and recommendations for further research into two
subsections below, one for the conclusions and one for the recommendations for further research.
5.1 Conclusions
The efficiency of weighting stocks in stock indices has come under debate in academic society. The reasoning behind this is that if there are overpriced and underpriced stocks in the market, market capitalization weighting will overweight the overvalued stocks and underweight the undervalued stocks. This supposedly causes a performance drag.
Treynor (2005) mathematically derives this performance drag and Hsu (2004) concludes that when prices do not reflect the fundamental values of a company, market
capitalization weighting is suboptimal.
As an alternative to market capitalization weighting, Arnott, Hsu and Moore (2004) propose weighting based on fundamental values. They find these fundamental indices to outperform market capitalization weighted indices by an average of 2.13 percent a year. They conclude that the fundamental indices are of lower risk in terms of CAPM Beta and standard deviation.
In this research we investigate the performance (in terms of return) of weighting a broad European index (the Dow Jones Stoxx 600) on the basis of fundamental values. We make fundamental indices on the basis of book value of the assets, gross dividends, number of employees, revenue, operating income and a composite of four of these five values. The period under investigation is December 1992- May 2007. We use a broader definition of risk than Arnott, Hsu and Moore (2004) by analyzing the risk characteristics of the fundamental indices using the three factor model of Fama and French. We also
incorporate the cost of managing the fundamental indices in our research. To summarize the results of this research we repeat our research question here.
Does the fundamental index show any excess return compared to its benchmark market capitalization weighted index when we correct for Fama and French (1993) risk factors, CAPM Beta and portfolio management costs?
From our analysis on the excess returns of the fundamental indices, we conclude that the fundamental indices show large excess returns over the period 1993-2007. The excess returns range from 136.82 percent for the dividend index to 268.12 percent of the book value index. The composite index shows an excess return of 194.79 percent. By
performing a T-test on the returns of the fundamental indices, we find that the excess returns are significant except for the employee index and the dividend index. Since we violate the condition that the samples should be normally distributed, we also perform a binomial sign test, with the same results.
that the fundamental indices have higher loadings on the Fama and French risk factors value and size than the market capitalization weighted adjusted benchmark indices. The CAPM beta of the fundamental indices is the same (around 1) as is the standard deviation of these indices. Taking these risk factors into account the fundamental indices still show a positive monthly alpha of 0.2 percent that is significantly different from zero at the 5 percent level, except for the book value index.
The yearly turnover of the fundamental indices over the period 2002-2006 is much higher than that of the MSCI Europe in 2003. The turnover ranges from around 25 percent of the index portfolio in 2006 to around 55 percent in 2002 compared to the benchmark of 7.36 percent. Although this results in higher turnover costs ranging from an average of 0.06 percent to 0.08 percent of the portfolio, there remains a large corrected annualized alpha for the fundamental indices. The corrected alphas range from 2.10 percent of the
composite index to 2.56 percent of the employee index.
The overall conclusion of this research is that the fundamental indexing strategy generates an excess return (corrected alpha in our analysis) after correcting for the risk factors CAPM Beta, value and size and turnover costs. As already mentioned in the literature review, whether the size and value factors are in fact risk factors is heavily debated. We do not take a stance in this matter, but note that if one would see them as anomalies in the stock market, the excess return of the fundamental indexing strategy is even higher than the corrected alpha that we find.
5.2 Recommendations for further research
In our analysis of the risk factors, we have used an unorthodox method for deriving the premiums on size en style. Although theoretically viable, this method has not been tested yet. It would be interesting to see whether there are differences in the premiums derived this way and the premiums derived using the conventional Fama and French (1993) method.
Although we take the three factor model of Fama and French (1993) for the analysis of the risk characteristics, more factors could be added to analyze excess returns of the fundamental indices over the risk free rate. As a suggestion we recommend incorporating the momentum factor. Also, a more fundamental approach could be applied to analyze the risks of the fundamental indexing strategy. For example, one could do an analysis of the firms that actually fell into demise and find out whether the fundamental indices place more weight into the stocks of these firms.
In our research, we restrict our analysis of the costs of managing the index portfolios to turnover costs. It is quite possible that other costs associated to the management of the indices exists, for example liquidity costs. We leave it up to further research to identify and quantify these costs.
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