FUNDAMENTAL AND COLLAR WEIGHTING IN THE EUROPEAN STOCK MARKET

FUNDAMENTAL AND COLLAR WEIGHTING IN THE EUROPEAN STOCK MARKET

Niek M. Bijlefeld

Thesis MScBA Risk and Portfolio Management Faculty of Economics and Business

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Abstract

Fundamental weighting renders higher returns and lower risks than market capitalization weighting. It uses measures of company size that are indifferent of market capitalization. Using a combination of these two weighting methods provides mean-variance ratios that are higher than those of market capitalization weighted portfolios, but lower than those of fundamental weighted portfolios. None of the weighting methods provides a significant alpha. The return differences are significantly related to the value premium.

JEL classification codes: G11, G14.

1 Introduction

Sharpe (1964), Lintner (1964) and Black (1972) developed the Capital Asset Pricing Model (CAPM). According to CAPM a stock portfolio in which the invested amounts are allocated according to each stock’s market capitalization is mean-variance efficient. This form of efficiency means that the portfolio is optimal regarding its mean return and the variance of this return.

Even though CAPM is based on some assumptions that do not hold in the real world, market capitalization is widely accepted as the basis for stock indexes. Worldwide many companies and individuals invest in market capitalization weighted (cap weighted) portfolios believing they will get the best possible combination of risk and return. But is this believe correct? Shiller (1981) argues that stock prices are subject to large fluctuations without apparent changes in the underlying company’s value. Siegel (2006) attributes these fluctuations to noise.

Are cap weighted portfolios the best method for acquiring the optimal combination of return and variance of this return? Perhaps there are different methods for constructing portfolios that provide a better mean-variance combination.

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1.1 Noise

Stock prices seem to be fluctuating around the fair value of the company they represent. According to Shiller (1981) these temporary deviations are too large to be attributed to new information. Summers (1986), Black (1986) and Fama and French (1988) suggest that noise causes stock prices to deviate from their fair values.

I define noise as data that looks like information but actually is not. Noise traders trade on noise under the assumption that they are trading on information. This noise trading causes stock prices to reflect the information as well as the noise that traders trade on. Siegel (2006) refers to this market capitalization bias with the ‘noisy market hypothesis’, which is a variation on CAPM’s ‘efficient market hypothesis’. Following the noisy market hypothesis the market price of a stock at a certain moment in time is its fair value plus or minus the amount of noise at that specific moment.

According to Siegel (2006) noise may last for days or for years and its unpredictability makes is hard to design a trading strategy that consistently produces superior returns. I suggest it is better to compose stock portfolios based on factors that are not influenced by this unpredictable and seemingly irrational noise.

1.2 Cap weighting vs. non-cap weighting

Arnott et al. (2005) construct portfolios in the U.S. market based on measures of company size that are indifferent from market capitalization. Arnott et al. (2005) use revenue, equity book value, sales, dividends, cash flow, and employment as weight metrics and call their portfolios ‘fundamental indexes’. Over a time span of more than forty years these fundamental indexes outperform a cap weighted reference portfolio by an average of more than two percentage points per year. The volatility of the returns of the fundamental portfolio is approximately equal to those of the cap weighted reference portfolio.

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Fundamental weighting provides the capacity, liquidity, diversification and broad-market perception that Hsu and Campollo (2006) describe to be the most important benefits of traditional cap weighted indexes. In their research the fundamental weighted portfolios outperform cap weighted portfolios by 3.5 percent globally with a turnover that is only 4 percent higher.

Estrada (2006) finds that dividend weighted fundamental weighting substantially outperforms cap weighting by 1.9 percent per year. This research represents over 93 percent of the world market capitalization.

Treynor (2005) and Hsu (2006) show that cap weighted portfolios are less efficient than non-cap weighted portfolios when stock prices contain more noise. Arnott et al. (2008) consider high yield bonds and emerging market bonds to contain more noise and compare these with investment grade corporate indexes. They find a positive relationship between the outperformance of fundamental weighted bonds and the amount of noise in market prices from 1997 to 2007.

According to Hsu (2006) cap weighting is sub-optimal in comparison with non-cap weighting since cap weighting assigns more weight to overvalued stocks than to undervalued stocks. Jun and Malkiel (2007) attribute the excellent performance of fundamental weighting to an increased exposure to stocks with low price-to-book value and small capitalization. Fama and French (1992) describe this advantage for non-cap weighting as the value premium and the higher expected stock return for smaller companies as the size premium. Stocks of companies with low book to market values and stocks of small companies are considered to be more risky. More risk implies a higher expected return. The noisy market hypothesis explains these size and value premiums. If the market price of a stock declines (increases) while its fair value remains unchanged it is likely that this stock will render above (below) normal returns in the future.

Though non-cap weighting seems to outperform cap weighting Amenc, Goltz, and Le Sourd (2008) find that none of these non-cap weighted portfolios outperform equal weighted portfolios. However, rebalancing a large equal weighted portfolio implies high turnover costs. Also small listed companies do not have enough capacity to provide their stocks to investors if equal weighting would be used on a large scale.

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fundamental weighting should not be called an indexation method. Arnott (2006) defines an index as an objective, rules-based, transparent, replicable and low turnover way to compose a portfolio.

I leave it up to the investment community to decide if and how fundamental weighting can be useful to them. Asness (2006) writes that if the fundamental weighting methodology will be used as an index by the general public the spreads between over- and undervalued stocks will narrow. If this will happen and the advantage of fundamental weighting is primarily caused by the value premium I agree that fundamental weighting will become less attractive.

Even if fundamental weighting becomes as widely used as currently cap weighting, I don’t see serious drawbacks. As long as fundamental weighted portfolios select and weight stocks by their fundamental values fundamental weighting will suffer less from the day by day whims of investors than cap weighting.

1.3 Collar weighting

According to Siegel (2006) noise is not directly observable. Cap weighting invests more money in overpriced and less in underpriced stocks. So, fundamental weighting has a small-cap market bias in comparison with cap weighting. Therefore Treynor (2005) argues that fundamental weighting still depends, inversely, on market values. Kaplan (2008) shows that fundamental values cannot be unbiased value estimators because their sources, risk and expected growth, are determinants of market values. While cap weighting contains noise, fundamental weighting ignores risk and expected growth.

Combining cap weighting and fundamental weighting seems like a good idea, since both methods contain useful information for investors. Arya and Kaplan (2006) present the collar weighting approach which combines the advantages of cap weighting and fundamental weighting while minimizing their disadvantages.

Collar weighting puts a collar around the fundamental values. Basically it selects and weights the stocks using market capitalization. However, when market values deviate too much from fundamental values, the weights of these stocks are linked to their fundamental values. In doing so a collar weighted portfolio weights some stocks using market capitalization and some stocks using the value of the upper or lower boundary of the collar around their fundamental values.

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portfolio is intermediate that of the cap weighted and fundamental weighted portfolio. Collar weighting avoids high stakes in overvalued stocks, which reduces volatility. Also, it decreases the small-cap bias and turnover costs.

1.4 Research Objective

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Table 1

Characteristics of empirical research concerning fundamental weighting

Author Region Fundamental weight metrics Period Results

Anott et al. [2005] U.S. book value, cash flow, revenue, 1962-2004 Fundamental weighting outperforms cap weighting gross sales, dividends, employment & equal weighting.

Hsu and Campollo [2006] U.S. & world ex-U.S. reproduction of Arnott et al. [2005] 1984-2004 Fundamental weighting outperforms MSCI cap weighting, & Tamura and Shimizu [2005] except during technology bubble (around 1999).

Arya & Kaplan [2006] 97% of U.S. market cap revenue, expected available 1997-2005 Collar weighting avoids exaggerated stakes in overvalued invested capital, dividends stocks & moderates the value-bias.

Estrada [2006] 16 countries representing dividends 1974-2005 Fundamental weighting outperforms cap weighting, but a

93% of world market cap value weighting strategy outperforms fundamental weighting.

Research Affiliates [2007] 23 developed countries book value, cash flow, revenue, 1993-2007 Fundamental weighting outperforms cap weighting gross sales, dividends, employment & equal weighting.

Arnott et al. [2008] U.S. & sales, profits, book values, dividends 1997-2007 Fundamental weighting outperforms cap weighting.

emerging markets bonds Outperformance is higher in less efficient markets.

Amenc et al. [2008] U.S. 15 characteristics based portfolios 1962-2006 Characteristics weighting outperforms cap weighting.

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2 Methodology

2.1 Portfolio construction

I construct portfolios using the capitalization weighted, the fundamental weighted and the collar weighted methods. For all three weighting methods I create a 500-stock and a 1000-stock portfolio. I use all major securities with primary quotes on the European stock markets for which the data to create the cap weighted and the fundamental weighted portfolios are available on Thomson Datastream1. Most data is displayed in millions of units of local currency. In order to be able to compare these data I convert them to Euros using historical interbank exchange rates2. I compare the performance of each portfolio from January 1999 until June 2008. Alford et al. (1994) show that a significant number of companies are late to publish their reports. To increase data availability I construct and review the portfolios based on data as at the close of business on the last trading day of June. I implement changes that arise from this annual review after the close of business on the last trading day of December. Table 2 shows the number of companies each year for which enough data is available to calculate the fundamental and the capitalization weight metrics.

Table 2

Number of stocks with information to calculate portfolio weight metrics

Last trading day of 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 Cap values 3394 3990 4650 5200 5418 5539 5744 5987 6405 7052 Fund values 3642 4503 4245 4366 4595 4833 4972 5009 4940 4752

2.1.1 Cap weighted portfolio construction

I construct a 500-stock and a 1,000-stock cap weighted portfolio which I call Cap500 and Cap1000. By creating these cap weighted portfolios I can make a direct comparison with fundamental weighting and collar weighting without having to worry about possible differences other than the included stocks and their weights. ‘Market Value (Capital)’ is the data type I use for market capitalization. It equals the share price multiplied by the number of shares in issue. For companies with more than one class of equity capital ‘Market Value (Capital)’ is expressed according to the individual issue.

1_{See: http://www.datastream.com/} 2

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2.1.2 Fundamental weighted portfolio construction

The 500 and 1,000 companies with the largest fundamental values are included in a 500-stock and a 1,000-stock fundamental portfolio. I call these portfolios Fund500 and Fund1000. Based on the FTSE RAFI Index Series3 I use the following four fundamental weight metrics:

· Total cash dividends: (Trailing five-year average of the total distributed cash dividend)

· Free cash flow: (Trailing five-year average of the operational cash flow minus capital expenditures)

· Total sales: (Trailing five-year average of the net sales or revenues)

· Book equity value: (The value of the common stock divided by the value of the total assets.)

For each fundamental weight metric I calculate its weight in the sample in terms of percentage. I multiply the average of these four weights by 10,000 to get the fundamental value of each company. The 1,000 and 500 companies with the largest fundamental values constitute the Fund1000 and Fund500 portfolios. I use trailing averages except for the book equity value to prevent substantial volatility in the portfolio weights. Arnott (2005) argues that by using trailing averages rebalancing turnover is reduced while results are expected not to differ substantially from the single-year data. If less than 5 years of data is available I calculate the average of the available data.

Table 3 shows the description and codes to download the required information and calculate the value of the fundamental weight metrics.

Table 3

Fundamental value variables

Fundamental weight metric Datastream description Datastream code

Total cash dividends Cash dividends paid WC04551

Free cash flow Operational CF - Capital expenditures WC04860 - WC04601

Total sales Net sales or revenues WC01001

Book equity value Common stock / Total assets WC03480 / DWTA

3

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‘Cash dividends paid’ represents the total common and preferred dividends paid to the shareholders of the company. ‘Operational cash flow’ equals the net cash receipts and disbursements resulting from the operations of the company. ‘Capital expenditures’ represents the funds that are used to acquire fixed assets that are not associated with acquisitions. ‘Net sales or revenues’ represents operating revenue minus discounts, returns and allowances. ‘Common stock’ is the stated value of the issued common shares of a company. ‘Total assets’ is the sum of total current assets, long term receivables, investments in unconsolidated subsidiaries, other investments, net property, plant and equipment and other assets.

2.1.3 Collar weighted portfolio construction

I call the collar weighted portfolios Col500 and Col1000. Collar weighted portfolios weight stocks using cap weights unless these cap weights deviate too much from the fundamental weights. Multiplying a stock’s fundamental weight with the lower (upper) collar multiplier renders the minimum (maximum) collar weights in the portfolio. These minimum and maximum stock weights create a collar around the fundamental stock weights. Every stock with a cap weight that falls within the collars is weighted according to its cap weight. When a stock’s cap weight falls outside the collar, the stock will be weighted according to its minimum or maximum weight.

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Table 4

Final Collar multipliers

Year Low multiplier High multiplier

1999 0.79 5.97 2000 0.76 5.97 2001 0.78 5.97 2002 0.70 5.97 2003 0.72 5.97 2004 0.72 5.97 2005 0.72 5.97 2006 0.75 5.97 2007 0.73 5.97 2008 0.73 5.97

Using the notation as in Arya and Kaplan (2006), I use the following figures in the calculations:

N = number of stocks in the portfolio xi = cap weight

wi = fundamental weight

L = lower bound on the ratio of a stock’s collar weight to its fundamental weight. U = upper bound on the ratio of a stock’s collar weight to its fundamental weight. zi (L,U) = collar weight of stock i for given values of L and U as defined in equation 1. Z (L,U) = sum of the collar weights given values of L and U.

Where,

Lwi, if xi < Lwi

zi _{(L,U) = { x}i, if Lwi ≤ xi ≤ Uwi (1)

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2.2 Regression variables

I test if return differences between the cap weighted and the fundamental and collar weighted portfolios are explained by the value and size premium as described by Fama and French (1992). To create a proxy for the value premium I calculate the excess return of the MSCI Value over the MSCI Growth AC World Index. To proxy the size premium I use the excess return of the MSCI Small Cap over the MSCI Large Cap AC World index.

Chordia and Swaminathan (2000) suggest that differences in stock turnover between portfolios are related to differences in return. I calculate the stock turnover for the portfolio constituents and test whether there is a relation between the difference in turnover and the difference in return between the portfolios. Stock turnover is the monthly turnover by volume divided by the average total number of ordinary shares (in thousands) that represent the capital of the company (table 5).

Table 5

Stock turnover variables

Datastream description Datastream code

Turnover by volume VO

Number of shares in issue NOSH

The return on the Chicago Board Options Exchange (CBOE) Volatility Index (VIX) is added to the regression to test if the return differences can be explained by changes in expected stock market volatility. If investors expect prices to be volatile they are more eager to trade upon new information in order to benefit from this expected volatility. Following the definition of noise in paragraph 1.1 noise can be easily mistaken for information. As explained by Treynor (2005) and Hsu (20006) noise causes a return premium for fundamental weighting.

Using the Ordinary Least Squares method (OLS) equation (1) is:

, (4)

where

: The excess return of a fundamental or collar weighted portfolio over the return of a cap weighted portfolio on time t.

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: The excess return of the MSCI small cap over the MSCI large cap AC World index

on time t. (size premium)

: The excess return of the MSCI value over the MSCI growth AC World Index on time t (value premium)

: The excess stock turnover of a fundamental or collar weighted portfolio over the stock turnover of a cap weighted portfolio on time t.

: The return on the VIX on time t.

it

η

: Error term statistic

The equation is tested two sided on a 5% significance level using Eviews4 software. Before

analyzing the regression statistics the data is tested for several conditional assumptions of the OLS. I use White’s test to ascertain if the error term has a constant variance, which is called homoscedasticity. This is true if the observations of the error term are assumed to be drawn from identical distributions. If the test suggests heteroscedasticity the OLS equation will be adjusted following White (1980).

To test for the presence of autocorrelation between the error terms over time the Breusch-Godfrey test is conducted. I use the Jarque-Bera test to test for the assumption of normality of the error term. To test for autoregressive conditional heteroscedasticity (ARCH) in the residuals I use the ARCH Lagrange multiplier (LM) test (Engle, 1982). If this test suggests the presence of ARCH in the residuals equation (1) is re-estimated using the GARCH(1,1) model.

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3 Data

3.1 Fundamental constituents

Summary statistics of the fundamental value variables are presented in table 6.

Table 6

Annual summary statistics of fundamental value variables (Jun’98-Jun’07)

Mean Median Minimum Maximum

Total cash dividends € 65,312 € 4,755 € 0 € 10,541,230

Free cash flow € 4,257 € 6 -€ 18,225,517 € 22,761,323

Total sales € 297,656 € 31,619 -€ 1,533,298 € 9,991,221

Book equity value € 0 € 0 -€ 1 € 411

trailing 5yr average:

Total cash dividends € 19,053 € 1,437 € 0 € 7,731,987

Free cash flow € 12,308 -€ 76 -€ 11,688,929 € 16,189,414 Total sales € 507,353 € 28,737 -€ 163,597 € 155,663,674

3.2 Regression variables

I use the returns of MSCI’s Value, Growth, Small Cap and Large Cap indexes to create proxies for the size and value premium. Return information for these indexes is available from 1999.

Table 7

Summary statistics of monthly return regression variables (Jan’99-Jun’08)

average median minimum maximum

Return MSCI-Small 0.5% 1.0% -13.1% 9.8%

Return MSCI-Large 0.0% 0.3% -11.8% 8.9%

Return MSCI-Value 0.1% 0.4% -12.9% 10.3%

Return MSCI-Growth 0.0% 0.1% -11.7% 12.1%

Return VIX 1.2% -0.2% -29.1% 48.0%

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4 Results

4.1 Return characteristics

Table 8 shows return characteristics of the portfolios. The mean-variance ratios of the fundamental weighted portfolios are higher than those of the cap weighted portfolios. Fundamental weighting performs better in both the mean return as the variance of their return. Also the collar weighted portfolios are more mean-variance efficient than the cap weighted portfolios. This higher efficiency level is attributed to the lower variances of the collar returns. The mean returns of the collar weighted portfolios are lower than the cap weighted mean returns. Tables 12 and 13 in the appendix present the monthly return and variance per year.

Table 8

Summary statistics of monthly portfolio returns (Jan’99-Jun’08)

Cap1000 Fund1000 Col1000 Cap500 Fund500 Col500

Mean 0.83% 1.02% 0.70% 0.83% 0.99% 0.69% Median 1.36% 1.65% 1.48% 1.35% 1.67% 1.26% Minimum -16.78% -18.34% -17.56% -16.82% -18.86% -18.09% Maximum 13.89% 12.83% 16.31% 14.02% 12.65% 15.36% Variance 0.29% 0.22% 0.23% 0.29% 0.23% 0.24% Mean/Variance ratio 2.85 4.71 3.03 2.82 4.40 2.91 Table 9

Differences in monthly portfolio returns (Jan’99-Jun’08)

Fund1000 Col1000 Fund500 Col500

minus Cap1000 minus Cap1000 minus Cap500 minus Cap500

Difference in means 0.19% -0.13% 0.16% -0.14%

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4.2 Fundamental and collar weighted return attribute statistics

Table 10 shows the regression statistics of equation (1). The p-values of the alpha coefficient in equation (1) range between 0.21 and 0.36 which does not suggest significant outperformance.

The coefficient in combination with the probability values of the value premium indicate a significant positive contribution of the value premium to the return attribute of the fundamental and the collar weighted portfolios. I find no evidence for the size premium. Also there is no evidence that the differences in stock turnover or changes in expected volatility influence the return differences.

Table 10

Regression statistics equation (1) (Jan’99 – Jun’08)

Fund1000 Col1000 Fund500 Col500

-Cap1000 -Cap1000 -Cap500 -Cap500

ß0t (alpha) 0.001 0.002 0.001 0.008 P-value (0.719) (0.753) (0.832) (0.832) ß1t (size premium) -0.071 -0.012 -0.118 -0.011 P-value (0.478) (0.903) (0.250) (0.911) ß2t (value premium) 0.189 0.250 0.185 0.274 P-value (0.027) (0.001) (0.044) (0.000) ß3t (stock turnover) -0.065 -0.135 -0.051 -0.134 P-value (0.704) (0.458) (0.774) (0.517) ß4t (expected volatility) 0.012 0.001 0.008 -0.002 P-value (0.365) (0.936) (0.525) (0.843) R2 0.096 0.113 0.093 0.113 Observations 114 114 114 114

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Graph 1

Proportion of cap weighted and fundamental weighted stocks in the Col1000 portfolio

Graph 2

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4.3 Error term test statistics

Table 11

Error term statistics (jan’99-Jun’08)

Fund1000 Col1000 Fund500 Col500

-Cap1000 -Cap1000 -Cap500 -Cap500

Jarque-Bera's test 5.393 1.063 5.712 2.026 P-value (0.067) (0.588) (0.057) (0.363) White's test 22.139 27.702 21.367 32.380 P-value (0.079) (0.016) (0.093) (0.004) Breusch-Godfrey's test 5.570 3.856 5.450 4.230 P-value (0.062) (0.145) (0.066) (0.117) ARCH test 3.700 4.209 3.630 3.946 P-value (0.055) (0.040) (0.057) (0.047)

The error term statistics are shown in table 11 The Jarque-Bera test statistic does not suggest non-normality in the error term distributions. White’s test statistic show that the error terms for the equations with the fundamental weighted return premium are homoscedastic and independent of the regressors. For the equations with the collar weighted return premium the probability values of White’s test statistic suggest heteroscedasticity of the error terms.

The non significant probability values of the Breusch-Godfrey test statistic do not indicate the presence of serial correlation in the residuals. The results of the ARCH LM test do not suggest the presence of ARCH in the residuals for the equations with the fundamental weighted return premium. In the equations with the collar weighted return premium the ARCH LM test results suggest the presence of ARCH in de residuals.

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5 Conclusion

In this paper I find evidence that the value premium is significantly related to return differences between cap weighting and fundamental and collar weighting. These return differences are not statistically significant. Collar weighting is designed to get the best of both cap weighting and fundamental weighting. Just like Arya & Kaplan (2006) my results show that collar weighting reduces high stakes in overvalued stocks. Even though collar weighting renders lower returns its mean-variance ratio is still higher than with capitalization weighting.

Collar weighting avoids a part of the risk of cap weighting. However it does not capture the return benefits of fundamental weighting. Fundamental weighting creates much higher returns than cap weighting while its risk is comparable to the risk of collar weighting. The advantage of selecting stocks by their fundamental values should be further investigated when looking for new alternatives to portfolio weighting. Perhaps higher returns can be generated through collar weighting when a narrower collar is used.

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Appendix 1: Monthly return characteristics per year (Jan’99-Dec’07)

Table 12

Monthly return & variance of the 1,000-stock portfolios (Jan’99-Dec’07)

Cap1000 Fund1000 Col1000

Year Return Variance Return Variance Return Variance

1999 2.92% 0.20% 2.56% 0.08% 2.20% 0.09% 2000 -0.11% 0.19% 0.87% 0.10% 0.58% 0.09% 2001 -0.95% 0.60% -1.05% 0.28% -1.11% 0.31% 2002 -1.91% 0.68% -1.99% 0.67% -2.08% 0.63% 2003 1.97% 0.22% 2.17% 0.21% 2.22% 0.35% 2004 2.25% 0.03% 1.79% 0.05% 1.49% 0.04% 2005 2.71% 0.16% 3.61% 0.06% 2.40% 0.08% 2006 1.74% 0.11% 2.22% 0.05% 1.83% 0.06% 2007 0.65% 0.09% 0.55% 0.07% 0.46% 0.07% Average 1.03% 0.25% 1.19% 0.18% 0.89% 0.19% Table 13

Monthly return & variance of the 500-stock portfolios (Jan’99-Dec’07)

Cap500 Fund500 Col500

Year Return Variance Return Variance Return Variance