MSc. Finance thesis

MSc. Finance thesis

A Comparison of Smart Beta Strategies on the European Market:

Breaking the link between price and weight

By L.M.A. Coenen ABSTRACT

Performance of smart beta portfolios are compared with the performance of optimal Markowitz portfolios and with the traditional capitalization weighted portfolios. Smart beta strategies break the link between price and weight of an asset in the portfolio to earn excess returns. The smart beta portfolios are based on employees, revenue, dividend yield, cash flow and book value. The portfolios are built over a period from 1991 until 2014. The Markowitz portfolio is found to be the best performing portfolio over the whole period. The smart beta strategies outperformed the optimal Markowitz portfolio in three of the five periods namely in 1996-2000, 2006-2010 and in 2011-2014. The five smart beta portfolios are found to be better performing portfolios than the traditional capitalization weighted portfolio. Of all the smart beta strategies the dividend yield-portfolio was the best performing portfolio.

Keywords: Markowitz, smart beta, cap-weighted

JEL classification: G10, G11

Date and locations: 26 June 2015

Author: Ludovic Marc Albert Coenen

Mail: lmacoenen@gmail.com

Student number: 1891596

Introduction

Nowadays many people are investing part of their savings in stocks since the interest rates on bank deposits are low or to top up their pension. With the existence of several online investment platforms, investing in stocks is virtually possible for everybody. Besides this there are a lot of online platforms that give tips, make analysis and give recommendations about the strategy you should follow. The overall objective of every investor is to end up with more money than the initial amount invested and to do as least as good as the benchmark. However the way to reach your objective depends on the investment philosophy, which has to be determined before the investment (Minahan, 2006).

Since Markowitz, in 1952, laid the foundation for portfolio theory or analysis, many different investment strategies have been invented. Markowitz (1952) argues that an investor will choose, or should choose, the portfolio that maximizes the discounted value of the future returns. However there are still academics who argue that more straightforward strategies show the same performance and are easier to implement (Jobson and Korkie, 1980). Frankfurter, Phillips and Seagle (1971) found that portfolios selected according tot the Markowitz criterion are likely not more efficient than an equally weighted portfolio.

Markowitz portfolio and capitalization-weighted portfolio. Furthermore this research tries to answer the following questions:

“Does a smart beta strategy outperform the optimal Markowitz portfolio?” And

“Do the smart beta strategies outperform the market capitalization strategy?”

This paper is structured as follows. First this paper will give an overview of the existing literature with respect to the Markowitz portfolios as well as the smart beta or fundamental strategies. In the methodology section we will explain how the different portfolios are constructed and how returns are calculated. Furthermore the principles of the Sharpe ratio and the information ratio are explained in the performance measurement section. After this the data used in this paper will be evaluated. In part 6 of this paper the results will be presented. The last part will present the conclusion and discussion.

Literature

This section gives an overview of relevant literature for this paper. This part will be split in two subsections. In the first subsection I will refer to papers covering the Markowitz portfolios, both the positive side of the mean variance approach and the disadvantages. The second subsection is devoted to the smart beta strategies.

Optimal Markowitz portfolio

In 1952 Markowitz compared the expected return and volatility of the stocks to compute a portfolio with the lowest volatility for a given return. Markowitz argues that an investor will choose, or should choose, the portfolio that maximizes the discounted value of the future returns. Furthermore Markowitz assumes that an investor who cares only about the mean and variance of portfolio returns should hold a portfolio on the efficient frontier. To come to an optimal portfolio according to Markowitz one needs to know the expected return of the asset, the standard deviation of the return of the asset and the correlation between the returns of the assets used. Markowitz assumes that these variables are known however, in real life, investors have to estimate them. Although the theoretical acceptance of the Markowitz mean variance model, there are some drawbacks too. According to Burgess and Bey (1988) its applications has been limited for two reasons. These reasons are:

2. The model’s complexity and non-intuitive nature make it difficult to explain to the end user.

Others say that the composition of the optimal portfolios is very sensitive to changes in the expected returns, variances and covariances. Especially estimation errors in the expected returns have a strong impact on the asset allocation (Chopra and Ziemba, 1993). Best and Grauer (1991) determined the sensitivity of the results to the different input parameters. They conclude that the portfolio composition is extremely sensitive to changes in asset means.

Another problem that might occur is the presence of large short sale position to get an optimal portfolio. Obtaining portfolios with large short selling positions can be a problem since regulators often restrict short selling and investment policies of different funds prohibit taking any short positions.

This research uses long-positions portfolio only, so no short positions are allowed. Furthermore this research uses Matlab (R2015a) to determine the Markowitz portfolio. Matlab (R2015a) will maximise the Sharpe ratio to find the optimal or tangent portfolio, which will be used as one of the benchmarks.

Smart beta strategies

Most stocks market indexes worldwide are weighted in proportion of their market capitalization. This would be a rational decision when market cap reflects the true fundamental value of the company. However lots of empirical research suggests that market prices of stocks deviate temporarily form their intrinsic value. As a result, when stocks are mispriced, cap weighted indexes suffer from the fact that they overweight overvalued stocks and underweight undervalued stocks. This is where smart beta indexes claim to be ‘smarter’ then the traditional cap-weighted indexes. According to Arnott (2014) a smart beta strategy is described best as follows; ‘A category of valuation-indifferent strategies that consciously and deliberately break the

link between the price of an asset and its weight in the portfolio, seeking to earn excess returns over the cap-weighted benchmark by no longer weighting assets proportional to their popularity, while retaining most of the positive attributes of passive indexing’. The most important feature of a

able to beat the market consistently. Although fundamental indexation is a relatively new strategy it already has sparked a heated debate. Some authors see fundamental indexation as a new revolutionary strategy and as ‘the next wave of investing’ (Siegel, 2006) while others warn investors that they should approach the smart beta with extreme caution (Bogle and Malkiel, 2006).

Burce and Levy (2014) see a smart beta strategy as a passive way of investing. This is because of the rules-based selection and weighting. However they also note that the decisions to identify the factors on which the portfolio is based are active. These findings are supported by Estrada (2008). When looking at Markowitz, diversification is used to lower the risk for a certain return, however smart beta strategies are not well diversified. The portfolio based on smart beta can hold a large number of stocks or securities, however all these stocks are selected based on the same criteria (Bruce and Levy, 2014).

third reason is the additional exposure to distress risk and at last it could be a combination of the three reasons mentioned above.

Estrada (2008) tries to answer several questions that came with the paper of Arnott et al. (2005). He states that smart beta strategies may be viewed as a strategy designed to overcome the shortcoming of one of the key recommendations of modern financial theory, that of buying and holding the market portfolio. The ultimate goal of Estrada’s research is to link the issues of the smart beta strategies and international diversification by evaluating whether capitalization, price-insensitive fundamentals or other measures are the best way to weight country benchmarks when building global portfolios. In theory the cap-weighted market portfolio offers the highest risk-adjusted return and investors can do no better than buying this portfolio and holding it. However Markowitz (2005) recently stated that once real-world constraints are taken into account the cap-weighted market portfolio is not efficient any more. Furthermore he stated that the inefficiency might be so substantial it cannot be arbitraged away. With this in mind we can indicate several advantages in favour of smart beta strategies. At first, smart beta strategies do not overweight overvalued stocks and do not underweight undervalued stocks as cap-weighted portfolios do. A second advantage is that smart beta strategies appear to have higher returns and lower volatility than the cap-weighted portfolios have. At last, stated by Arnott et al (2005), smart beta strategies have many benefits, which are the same as the cap-weighted portfolios. Estrada (2008) used data from 16 countries over a period form December 1973 to December 2005. In his research he used dividend per share to determine the smart beta portfolio. He concludes that the portfolio based on dividend per share outperformed the cap-weighted portfolio by 1,9% a year. Although the dividend-per-share-portfolio outperformed the cap-weighted portfolio, Estrada is concerned whether the smart beta strategy is the best way to achieve good international diversification.

Hemminki and Puttonen (2008) examine the benefits of using smart beta strategies using European data. The metrics used to determine the portfolios are book value of equity, total employment, sales, cash flow and dividend. They gathered data from January 1996 to December 2006 and used the Dow Jones Euro Stoxx 50. Hemminkie and Puttonen (2008) found that all portfolios based on the fundamental metrics were able to outperform the cap-weighted market index by an average of 1,76 pps a year.

construct their portfolios. Furthermore they found that the outperformance of the smart beta portfolio is largely explained by its inherent bias towards value stocks. This is supported by Arnott et al. (2005).

Chow et al. (2011) tried to produce an apples-to-apples comparison of the alternative beta strategies in a controlled back test environment with full disclosure. Chow et al. studied two kinds of strategies namely; heuristic-based weighting methodologies and optimization based weighting methodologies. According to Chow et al heuristic-based strategies are ad hoc weighting schemes established on simple and sensible rules. Optimization-based strategies are predicated on an exercise to maximise the portfolios ex ante Sharpe ratio. Chow et al. show four different heuristic-based strategies, namely:

- Equal weighting: here constituents are selected from the largest 1000 stocks sorted by descending market capitalization. The weight of each stock is in this case 1/1000. It is important to notice that the resulting portfolio risk-return characteristics are highly sensitive to the number of includes stocks.

- Risk-cluster equal weighting: here constituents are selected based on equally weighted risk-clusters. Most of the time risk-clusters are defined on the basis of country and sector. This results in a more robust portfolio relative to the equally weighting portfolio.

- Diversity weighting: this strategy is the solution to two other potential concerns with equal weighting. Namely the relatively high tracking error and excess portfolio turnover. In general this redistributed weights from the larger stocks to the smaller stocks in the portfolio.

- Fundamental weighting: this is the same as Arnott et al. (2005) did. Chow et al (2011) defined four accounting size metrics namely; average sales, - cash flow, - total dividend paid and past years book value. They constructed the portfolio following Arnott et al. (2005).

Besides the heuristic-based strategies given by Chow et al. the following optimization-based strategies were given:

- Minimum-variance strategies: here the portfolio is constructed by selecting the 1000 largest companies sorted by descending market capitalization. After this the covariance matrix is estimated by using monthly excess returns for the previous 60 month. All this is done on the assumption of Chorpra and Ziemba (1993) that all stocks have the same expected returns.

maximum ex ante Sharpe ratio. To improve this, Choueifaty and Coignard (2008) proposed a linear relationship between the expected premium of a stock and its return volatility. Using this relationship the weights in the portfolio can be calculated.

- Maximum Sharpe ratio II: Amenc et al. (2010) developed a portfolio approach that assumes that the expected returns of stocks are linearly related to its downside. One of the arguments for this is that they think that investors are more concerned with potential losses than with gains.

All the portfolios, with different strategies, in the study of Chow et al. (2011) produced meaningful higher returns than the cap-weighted benchmark portfolios. This is line with research of DeMiguel et al (2009). They found that the mean variance models do not outperform more simple strategies.

As showed above there is a lot of literature in favour of smart beta strategies or fundamental index portfolios. However the smart beta portfolios are not free from criticism. When looking from a theoretical point of view, these portfolios do not properly represent the investable opportunity set, do not reflect the returns of the average investor and are not market clearing portfolios (Estrada, 2008). These arguments might be important to academics however what is important for the general investor is whether the smart beta portfolios will outperform the traditional cap weighted portfolios in the future.

Asness (2006) questioned whether the smart beta strategies are really new strategies or just a cleverly repackaged version of the discipline known as value investing. Asness states that the overweighting and underweighting of a certain stock in the smart beta portfolio relative to the cap-weighted portfolio is exactly proportional to the metric you use of the stock relative to the metric of the market, is in fact the same as value investing.

Kaplan (2008) demonstrated that except in trivial cases, that the assumption that metrics used for fundamental indexation are independent of market values is inconsistent because the sources of the “errors” are also determinants of market values. Furthermore the article shows in which conditions the fundamental based portfolios are better and when they perform worse. This is done by focussing on the relationships between fair prices, pricing errors and market prices.

follows: start with the premise that the market errors in its pricing of individual stocks but that the pricing errors occur in a random fashion, so some stocks are overvalued while other are undervalued. Overvalued stocks have inflated market cap and will have lower future returns, undervalued stocks have depressed market cap and will have higher future returns. As a consequence the cap-weighted strategy will overinvest in overvalued stocks and underinvest in undervalued stocks. Perold (2007) concludes that holding a stock in proportion to its capitalization weight does not change the likelihood that the stocks is overvalued or not, so the notion that capitalization weighting imposes an intrinsic drag on the performance is, accordingly, false. Furthermore he states that fundamental indexing is a strategy of active security selection through investing in value stocks, where smart beta strategies are considered to be an passive way of investing. In fact this is the same conclusion as Asness (2006) and partly the same as Burce and Levy (2014).

As existing literature show, a smart-beta strategy or fundamental indexation is a name for calculating portfolio weights or constructing portfolios based on all things besides market capitalization or price related metrics. There is not one specific smart beta strategy. This research will follow the approach as Arnott et al. (2005) did as well as the approach used by Chow et al. (2011). The performance of portfolios based on the metrics, number of employees,

revenues, dividend yield, cash flow and book value will be compared with the optimal Markowitz

portfolio and the market capitalization portfolio.

Methodology

Seven different portfolios will be investigated in this paper, including the optimal Markowitz portfolio. The optimal Markowitz portfolio and the market capitalization portfolio will be the reference portfolios in this research. The remaining five portfolios are weighted according to the fundamental metrics used for this research. These metrics are, employees, revenues, dividend

yield, cash flow and book value. The portfolio weighted according their market cap is not a smart

beta strategy.

Markowitz portfolios

Matlab-script of Dan K. is used1_{. By using this script long-only portfolios are constructed. The}

script used for this research can be found in the appendix 1.

DataStream provides information about the stocks. Because DataStream did not provide returns of all the stocks during the research period, the stocks were checked on sufficient information. The information of the stocks is sufficient if there is more than two years of data available. Stocks without sufficient information were deleted from the sample to form the optimal Markowitz portfolio. Of course the check whether information is sufficient is conducted each year.

By using the daily log returns from year t-1 the composition of the portfolio t0 can be determined.

So by using the daily log returns of 1990 Matlab determines the composition of the Markowitz portfolio in 1991. After the returns are imported in Matlab, Matlab calculates the covariance matrix. Furthermore the daily standard deviation, the annual standard deviation and the annual returns are needed. To annualize the daily standard deviation the following formula are used:

𝐴𝑛𝑛𝑢𝑎𝑙 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛𝑖= 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛𝑖 × √𝑛

In this formula n represents the number of trading days in year t and standard deviationi

represents the daily standard deviation of stock i.

To annualize the daily returns the following formula is used:

𝐴𝑛𝑛𝑢𝑎𝑙 𝑟𝑒𝑡𝑢𝑟𝑛𝑖= (1 + 𝑟𝑖)𝑛− 1

Here ri represents the average daily return of a stock i during one year and n represents the

number of days this stock was traded during this given year.

Matlab gives the weights of all the stocks that are imported for a given year. When the weights are determined the returns of the stocks, for that given year, are used to calculate the return of the total optimal Markowitz portfolio. The returns of the individual stocks are calculated with the following formula.

𝑟𝑖=

𝑂𝑃𝑖𝑡

𝑂𝑃𝑖𝑡−1− 1

In this formula ri represents the returns on stock i, OPit the opening price of stock i on the last

trading day of year t and OPit-1 the opening price of stock i on the last trading day of year t-1. This

research used opening prices since DataStream would not provide closing prices that were sufficient enough to use.

This process is repeated for every year, starting with the returns of 1990 to determine the Markowitz portfolio of 1991 to end with using the returns of 2013 to determine the portfolio in 2014. This results in 24 portfolios from 1991 to 2014. Table 1 shows the number of stocks included in each optimal Markowitz portfolio per year.

Table 1: Number of stocks used to construct the optimal Markowitz portfolio per year.

Year Number of stocks Year Number of stocks Year Number of stocks 1991 4 1999 9 2007 9 1992 4 2000 8 2008 9 1993 8 2001 28 2009 1 1994 28 2002 13 2010 6 1995 6 2003 6 2011 5 1996 10 2004 6 2012 5 1997 30 2005 12 2013 12 1998 8 2006 14 2014 8

Table 1 shows the number of stocks included in the optimal Markowitz portfolio per year. As can be seen the 2009 portfolio is the smallest portfolio with one stocks included. The 1997 portfolio is the largest portfolio with 30 stocks included. The average number of stocks included in a portfolio over the years is 10 stocks.

Smart beta portfolios

For this research five different smart beta portfolios and the market-cap portfolio are constructed. These smart beta portfolios are based on, employees, revenues, dividend yield, cash

flow and book value. Each portfolio will consist 50 stocks in total. The market-cap portfolio is

explained in this section as well because the determination of the composition is the same as by the smart beta portfolios.

The market cap portfolio, as all other portfolios, will be re-weighted on the last trading day of each year according their market cap, or other metric. The portfolio remains the same during the year and will be rebalanced at the end of the year when the new constituents are chosen for the next year’s portfolio. This process will be the same for each metric used to build the smart beta portfolios. The determination for the portfolios is as follows.

The determination of the weight of each stock in the portfolio can be calculated using the following formula:

𝑤𝑖,𝑎=

𝑣𝑖,𝑎

𝑣𝑡𝑜𝑡𝑎𝑙,𝑎

In here 𝑤_𝑖,𝑎 represents the weight of stocks i for metric a, 𝑣_𝑖,𝑎 represents the stock i’s value for metric a. At last 𝑣𝑡𝑜𝑡𝑎𝑙,𝑎 represents the sum of the 50 stocks metrics.

After the weights are determined, the weight of each stock is multiplied by the return each stock made during the year and the portfolios total return can be calculated.

The 1991-portfolio is the first portfolio built for this research. This portfolio is built using the metrics available at the last trading day of 1990. In total 24 different portfolios for each of the five metrics and 24 portfolios according to market cap will be constructed until the 2014-portfolio.

Performance measurement

When comparing the results of the portfolios we have constructed, it is important to look at more parameters than just the return per year or the average return over time. In this research other performance measures will be presented. They add different information to the results of the portfolio. Besides the returns of the portfolios over time, we will look at the Sharpe-ratio and the information-ratio.

Sharpe-ratio

The famous saying is ‘there is no such thing as a free lunch’, so in theory a portfolio with a higher expected return should bear higher risk. The Sharpe ratio measures excess return per unit of risk, where risk is measured by the standard deviation of the excess returns (Sharpe, 1994). It answers the question of how much an investor was compensated for investing in a risky asset. So a higher Sharpe-ratio means a higher return per unit of risk and thus this is preferred over investments with a lower Sharpe-ratio. According to Kidd (2011) the Sharpe-ratio is the industry standard for measuring risk-adjusted returns. The Sharpe-ratio is calculated as follows:

𝑆ℎ𝑎𝑟𝑝𝑒 𝑟𝑎𝑡𝑖𝑜 = 𝑅𝑝 𝜎𝑝

𝑆ℎ𝑎𝑟𝑝𝑒 𝑟𝑎𝑡𝑖𝑜 = 𝑅𝑝− 𝑟𝑓 𝜎𝑝

Where formula 𝑅_𝑝 is the return of the portfolio rf is the risk free rate and 𝜎_𝑝 the standard deviation of the portfolio. In this research the first way of calculating the Sharpe ratio is chosen because the script used, in Matlab, is programmed with the first formula as well.

Information-ratio

The Information-ratio measures the ability of the portfolio manager to generate excess returns relative to the benchmark. The higher the information-ratio is the better the manager is able to generate excess returns consistently. The Information ratio answers the question of how much reward a manager generated in relation to the risks the manager took deviating from the benchmark. According to Grinhold and Kahn (2000) top-quartile active managers generally have Information-ratios of 0,5 or above. In other research Grinhold and Kahn (1995) rated an ratio of 1,0 as ‘exceptional’, 0,75 as ‘very good’ and 0,5 as ‘good’. The Information-ratio is calculated with the following formula:

𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜 = 𝑅𝑝− 𝑅𝑏 𝜎𝑡𝑒

Where 𝑅_𝑝 is the return of the portfolio, 𝑅_𝑏 the return of the benchmark and 𝜎_𝑡𝑒 the tracking error. The tracking error can be calculated as follows:

𝜎𝑡𝑒= √ 1

𝑛∑(𝑅𝑝,𝑛− 𝑅𝑏,𝑛)2 𝑁

𝑛=1

Data

The data of this study consist of the constituents of the DAX, CAC40 and the AEX, the major main indices of Germany, France and The Netherlands respectively. This results in a total of 95 stocks to choose from. Of each stock the following metrics, from 1989 on daily basis, are retrieved from DataStream: market capitalization, employees, revenues, dividend yield, cash flow per share, book value per share. Although there are 95 different stocks listed on these three indices, not always all the 95 stocks were available for this research every year. The most important reason for the fact that not all the 95 stocks were available was due to the fact of missing data concerning the opening prices. Table 2 gives a clear overview of the total stocks available for the construction of the different smart beta portfolios as well as the market cap portfolio during the research period.

Table 2. Number of stocks available per year to construct the smart beta portfolios and the market cap portfolio.

Year Market _{Capitalization} Employees Revenue Dividend _yield Cash flow Book _value

As shown by table two there is only one metric when al the 95 stocks listed are also available for research namely the metric book value, for the years 2012 and 2013. The lowest number of stocks available for research is 56, for the metric dividend yield in 1992. It is important to note that for all the metrics the lowest number of stocks available for research is above 50, since all smart beta portfolios and the market capitalization portfolios are built with 50 stocks.

The time period is primarily chosen based on the fact that data availability was not sufficient enough when taking a longer period. As can be seen in the table 2 above, the minimal number of each metric available is sometimes a little over the 50 stocks required. When time passed by, the general trend is that the number of available metrics increases.

Table 3. Number of stocks deleted per metric, per year to create the smart beta portfolios each year. Year Market capitalization Employees Revenue Dividend yield Cash flow Book value

1991 3 13 12 1 7 7 1992 2 12 12 1 5 5 1993 2 10 13 1 6 6 1994 1 9 10 1 4 4 1995 1 8 9 1 2 2 1996 1 7 8 1 3 4 1997 1 7 8 1 6 6 1998 1 7 8 1 3 5 1999 0 5 7 0 2 3 2000 1 5 8 1 5 4 2001 0 2 3 1 1 1 2002 0 1 2 0 0 0 2003 0 1 2 0 0 0 2004 0 1 2 0 0 0 2005 0 1 2 0 2 2 2006 0 0 0 0 0 0 2007 0 0 0 0 0 0 2008 0 0 0 0 0 0 2009 0 1 0 0 1 0 2010 0 2 0 0 0 0 2011 0 2 0 0 0 0 2012 0 0 0 0 0 1 2013 0 1 1 0 0 1 2014 0 0 0 0 0 1

Besides the metric mentioned above the opening prices and common shares outstanding were retrieved from DataStream as well. To calculate the returns of each stock the opening prices were needed. Since DataStream could not provide us the total cash flow and total book value at once, the cash flow per share and book value per share were chosen to retrieve from DataStream. To calculate the total cash flow and total book value, the cash flow per share and book value per share were multiplied by the number of share outstanding.

Table 4. Number of stocks available each year to construct the Markowitz portfolio and number of stocks selected to be part of the Markowitz portfolio per year.

Year Number of stocks available Number of stocks selected

1991 61 4 1992 62 4 1993 63 8 1994 64 28 1995 65 6 1996 68 10 1997 71 30 1998 73 8 1999 76 9 2000 78 8 2001 79 28 2002 83 13 2003 85 6 2004 85 16 2005 85 12 2006 86 14 2007 89 9 2008 90 9 2009 90 1 2010 90 6 2011 91 5 2012 91 5 2013 92 12 2014 92 8

Results

This research compares the optimal Markowitz portfolio and the market capitalization portfolio with several smart beta strategies. In this section the performance of the optimal Markowitz portfolio, the market cap portfolio and the smart beta portfolios will be presented. For each portfolio the returns per year will be presented first. Furthermore a table with the performance over the whole, 1991-2014 period and over five periods will be presented. These sub-periods are 1991-1995, 1996-2000, 2001-2005, 2006-2010 and 2011-2014. The stocks selected for the different portfolios are chosen from the German, French and Dutch indexes. To able the reader to put the returns of the portfolios in perspective table 5 gives an overview of the yearly returns of the indexes.

Table 5. Yearly returns of DAX, CAC and AEX. Returns are given over the whole period and over the five sub-periods.

Year 1991-2014 1991-1995 1996-2000 2001-2005 2006-2010 2011-2014

Germany (DAX) 8% 10% 23% -3% 5% 9%

France (CAC) 4% 4% 26% -4% -4% 3%

The Netherland (AEX) 6% 16% 24% -7% -4% 5%

Optimal Markowitz portfolio

In total 24 Markowitz portfolios are constructed. These portfolios are based on the returns available on the year before the portfolio’s year. Table 6, below, shows the returns of the Markowitz portfolios for each year in the research period. As can be seen in the table below the highest return made in the period 1991-2014 is 133,2% in 2004. In this year the Markowitz portfolio consisted of six different stocks. The worst performance in one year is a negative return of -52,6% in 2008. On average the Markowitz portfolios made a return of 20,8% per year.

Table 6. Returns, per year, for the constructed Markowitz Portfolios.

Year Return Year Return Year Return

1991 25,1% 1999 49,0% 2007 10,4% 1992 6,3% 2000 -24,4% 2008 -52,6% 1993 48,4% 2001 -4,0% 2009 6,2% 1994 2,4% 2002 -17,6% 2010 37,9% 1995 71,5% 2003 11,8% 2011 -10,1% 1996 57,2% 2004 133,2% 2012 11,6% 1997 31,4% 2005 19,8% 2013 11,7% 1998 30,1% 2006 46,6% 2014 -1,9%

over the periods 1991-1995, 1996-2000, 2001-2005, 2006-2010 and 2011-2014. Furthermore this table shows the standard deviation of the returns for these periods as well as the Sharpe ratios.

Table 7. The yearly returns made by the Markowitz portfolios, the standard deviation of the returns and the Sharpe ratio over the whole period 1991-2014 as well as over five sub-periods.

Year 1991-2014 1991-1995 1996-2000 2001-2005 2006-2010 2011-2014

Return 16% 28% 25% 20% 2% 2%

STD 36% 26% 28% 54% 35% 9%

Sharpe 0,4 1,1 0,9 0,4 0,1 0,3

As can be seen the Markowitz portfolios made a 16% yearly return over the period 1991-2014. When looking at the different periods, it is clear that the periods 2006-2010 and 2011-2014 were the ‘worst’ periods for the Markowitz portfolios with a yearly return of 2%. The 1991-1995 period is the best period for the Markowitz portfolios with a yearly return of 28%. Furthermore table 7 shows the Sharpe ratios of the whole research period as well as the different periods. As mentioned before a higher Sharpe ratio is preferred over a lower Sharp ratio since it shows that more return is made per unit of risk. The period 1991-1995 shows the highest Sharpe ratio of the periods investigated, with a ratio of 1,1.

Market capitalization portfolio

In this section an overview of the results of the market capitalization portfolio is given. The results of this portfolio are presented apart from the other portfolios because this is not a smart beta strategy.

Table 8 shows the returns made by the portfolios built based on the metric market capitalization per year. The average return made by the portfolios over the year is 8,2%. The 1997 portfolio made the highest return of all years, with a return of 41,4%. With a negative performance of -44,4%, 2008 was the worst year for the portfolios based on market capitalization.

Table 8. Returns, per year, of the portfolio constructed according to Market capitalization.

Year Return Year Return Year Return

Table 9 shows the returns made by the portfolio based on market capitalization in the five sub-periods between 1991-2014 and over the whole period. Besides the return, the standard deviation of the returns, the Sharpe ratios, tracking error and information ratio are displayed in table 9 as well. Here, the tracking error and information ratio are calculated relative to the Markowitz portfolios.

Table 9. Yearly returns made by the market capitalization portfolios, the standard deviation of the returns and the Sharpe ratio over the whole research period as well as the sub-periods investigated. Year 1991-2014 1991-1995 1996-2000 2001-2005 2006-2010 2011-2014

Return 6% 11% 24% -5% -2% 4%

STD 21% 14% 15% 22% 24% 13%

Sharpe 0,3 0,8 1,5 -0,2 -0,1 0,3

Table 9 shows that the portfolio based on the market capitalization made a yearly return over the whole period of 6%. The best period for the market capitalization portfolio is 1996-2000. During this period the portfolio made a yearly return of 24%. The worst period for the portfolio was 2001-2005, with a negative yearly return of -5%. Furthermore table 9 shows the Sharpe ratios over the periods. It shows that the period with the highest return has the highest Sharpe ratio as well.

Smart beta strategies

In this section the five different smart beta portfolios’ results will be explained. These portfolios are based on the metrics, employees, revenue, dividend yield, cash flow and book value.

The first real smart beta portfolio is the portfolio based on the metric employees. Table 10 shows the returns made by the portfolios for each year. As can be seen in the table below the worst year for the portfolio based on employees was 2008. This year the portfolio made a negative return of -50,2%. The best year, between 1991-2014, was 1999. In this year the portfolio made a return of 43,4%. The average return over the years is 10,9%.

Table 10. Returns, per year, of the portfolio constructed according to number of employees.

Year Return Year Return Year Return

To elaborate more on the performance of the smart beta portfolio based on employees table 11 gives the overall period return as well as the standard deviation of the returns, the Sharpe ratio, tracking error and information ratio over the sub-periods. The tracking error and information ratio are calculated relative to both ‘benchmark’ portfolios, the optimal Markowitz portfolio and the market capitalization portfolios.

Table 11.

Year 1991-2014 1991-1995 1996-2000 2001-2005 2006-2010 2011-2014 Return 8% 11% 25% -3% 2% 5% STD 24% 16% 17% 24% 31% 23% Sharpe 0,3 0,7 1,4 -0,1 0,1 0,2 TEMarkowitz 0,3 0,3 0,2 0,6 0,2 0,1 IRMarkowtiz -0,2 -0,6 0,0 -0,4 0,0 0,2 TEMarket cap 0,1 0,0 0,0 0,1 0,1 0,1 IRMarket cap 0,3 0,0 0,4 0,5 0,4 0,0

The portfolios based on the metric employees made a yearly return of 8% over the whole period as can be seen in the table above. The worst period for the employees portfolio is 2001-2005, with a negative yearly return of -3%. The best years for the portfolios are the period 1996-2000. During these years the portfolios yearly return was 25%. Like the highest return has been made during the period 1996-2000 the Sharpe ratio has the highest value in this period as well. The information ratios of the employees portfolio relative to the optimal Markowitz portfolio shows that the manager of the portfolio was able to generate excess returns during the periods 1996-2000, 2006-2010 and 2011-2014. The excess returns in 1996-2000 and in 2006-2010 are small, this resulted in the information ratios of 0,0 for these periods. Besides this the information ratios of the portfolio relative to the market capitalization portfolio are all positive. This indicates that the manager of the employees portfolio was able to outperform the market cap portfolio in all periods. Only during the period 1991-1995 both portfolios made the same yearly return of 11%, which leads to an information ratio of 0,0.

Table 12. Returns, per year, of the portfolio constructed according to revenue.

Year Return Year Return Year Return

1991 18,2% 1999 37,3% 2007 12,6% 1992 2,5% 2000 1,9% 2008 -48,7% 1993 43,0% 2001 -15,7% 2009 31,3% 1994 -8,6% 2002 -36,4% 2010 7,0% 1995 8,7% 2003 22,3% 2011 -21,2% 1996 25,1% 2004 4,7% 2012 15,1% 1997 44,7% 2005 25,1% 2013 24,7% 1998 21,7% 2006 19,4% 2014 0,9%

The yearly return over the whole research period is shown in table 13 below. Besides the overall yearly return the standard deviation of the return and Sharpe ratio are given. Furthermore the tracking error and information ratio over the different periods relative to the optimal Markowitz portfolio and market capitalization portfolios are displayed as well.

Table 13. Yearly returns made by the revenue portfolios, the standard deviation of the returns and Sharpe ratio, both for the whole period as for the sub-periods. Tracking error and information ratio over the whole research period as well as the different periods investigated relative to the Markowitz portfolio and the market capitalization portfolio.

Year 1991-2014 1991-1995 1996-2000 2001-2005 2006-2010 2011-2014 Return 7% 11% 25% -3% -1% 3% STD 23% 17% 15% 23% 28% 17% Sharpe 0,3 0,7 1,7 -0,1 0,0 0,2 TEMarkowitz 0,3 0,3 0,2 0,6 0,2 0,1 IRMarkowitz -0,3 -0,6 0,0 -0,4 -0,1 0,1 TEMarket cap 0,0 0,0 0,0 0,0 0,1 0,0 IRMarket cap 0,3 0,2 0,6 0,6 0,3 -0,2

The returns made by the dividend yield portfolio are displayed in table 14 below.

Table 14. Returns, per year, of the portfolio constructed according to dividend yield.

Year Return Year Return Year Return

1991 17,9% 1999 45,3% 2007 6,8% 1992 -0,7% 2000 12,6% 2008 -45,7% 1993 49,9% 2001 -10,8% 2009 47,2% 1994 -4,4% 2002 -30,0% 2010 8,1% 1995 6,4% 2003 28,6% 2011 -20,1% 1996 25,1% 2004 15,7% 2012 12,2% 1997 35,9% 2005 30,4% 2013 26,2% 1998 19,7% 2006 24,9% 2014 5,9%

Table 14 shows that the best year for the dividend yield portfolio is 1993, were the portfolio managed to get a return of 49,9%. 2008 is the year where the portfolio had its worst performance with a negative return of -45,7%. On average the dividend yield portfolios had a return of 12,8% between 1991 and 2014.

Table 15. Yearly returns made by the dividend yield portfolios, the standard deviation of the returns and Sharpe ratio, both for the whole period as for the sub-periods. Tracking error and information ratio over the whole research period as well as the different periods investigated relative to the Markowitz portfolio and the market capitalization portfolio.

Year 1991-2014 1991-1995 1996-2000 2001-2005 2006-2010 2011-2014 Return 10% 12% 27% 4% 3% 5% STD 23% 20% 12% 24% 31% 17% Sharpe 0,4 0,6 2,3 0,2 0,1 0,3 TEMarkowitz 0,3 0,3 0,2 0,5 0,2 0,1 IRMarkowitz -0,2 -0,5 0,1 -0,3 0,0 0,2 TEMarket cap 0,1 0,1 0,1 0,1 0,1 0,1 IRMarket cap 0,5 0,2 0,4 1,0 0,4 0,0

Table 16 shows the returns per year of the cash flow portfolio during the research period. The table shows that the highest return, of 44%, has been made in 1993. The worst performance of the cash flow portfolios was in 2008 with a negative return of -46,6%. Over the years the average return of the cash flow portfolios was 10,2%.

Table 16. Returns, per year, of the portfolio constructed according to cash flow.

Year Return Year Return Year Return

1991 13,5% 1999 34,9% 2007 9,9% 1992 4,4% 2000 2,2% 2008 -46,6% 1993 44,0% 2001 -17,3% 2009 30,7% 1994 -9,1% 2002 -34,3% 2010 3,2% 1995 12,6% 2003 22,0% 2011 -21,9% 1996 26,2% 2004 6,5% 2012 17,2% 1997 43,8% 2005 24,4% 2013 25,0% 1998 33,7% 2006 17,6% 2014 2,0%

Table 17.

Year 1991-2014 1991-1995 1996-2000 2001-2005 2006-2010 2011-2014 Return 7% 12% 27% -3% -1% 4% STD 23% 17% 14% 23% 26% 18% Sharpe 0,3 0,7 1,9 -0,1 -0,1 0,2 TEMarkowitz 0,3 0,3 0,2 0,6 0,2 0,1 IRMarkowitz -0,2 -0,6 0,1 -0,4 -0,2 0,2 TEMarket cap 0,0 0,0 0,1 0,0 0,0 0,1 IRMarket cap 0,3 0,2 0,6 0,8 0,2 -0,1

Furthermore the 1996-2000 period displays the highest Sharpe ratio of all periods in combination with the highest return. The cash flow portfolio outperformed the Markowitz portfolio during the 1996-2000 and 2011-2014 periods that leads to positive information ratios. Besides this the cash flow portfolio outperformed the market capitalization portfolios in all periods except form the last period, 2011-2014. As a result the information ratios are positive in the periods 1991-1995, 1996-2000, 2001-2005 and 2006-2010.

The last smart beta portfolio is the book value portfolio. Table 18 displays the returns of each year generated by the book value portfolios.

Table 18. Returns, per year, of the portfolio constructed according to book value.

Year Return Year Return Year Return

1991 17,6% 1999 46,3% 2007 10,1% 1992 3,2% 2000 1,5% 2008 -47,2% 1993 39,0% 2001 -19,4% 2009 32,5% 1994 -8,3% 2002 -36,6% 2010 3,1% 1995 9,2% 2003 25,1% 2011 -22,0% 1996 24,5% 2004 5,5% 2012 17,6% 1997 40,3% 2005 25,1% 2013 21,4% 1998 20,3% 2006 15,7% 2014 -0,3%

The table above shows that the highest return is 46,3% has been made in 1999. The worst performance of the book value portfolios is a negative return of -47,2% during 2008. On average the book value portfolios managed to get a return of 9,3%

portfolios. The tracking error and information ratio are calculated both relative to the optimal Markowitz portfolios as well as relative to the market cap portfolio.

Table 19. Yearly returns made by the book value portfolios, the standard deviation of the returns and Sharpe ratio, both for the whole period as for the sub-periods. Tracking error and information ratio over the whole research period as well as the different periods investigated relative to the Markowitz portfolio and the market capitalization portfolio.

Year 1991-2014 1991-1995 1996-2000 2001-2005 2006-2010 2011-2014 Return 6% 11% 26% -3% -2% 3% STD 23% 16% 16% 25% 27% 17% Sharpe 0,3 0,7 1,6 -0,1 -0,1 0,2 TEMarkowitz 0,3 0,3 0,2 0,6 0,2 0,1 IRMarkowitz -0,3 -0,6 0,0 -0,4 -0,2 0,0 TEMarket cap 0,0 0,0 0,0 0,0 0,0 0,0 IRMarket cap 0,2 0,1 0,4 0,5 0,1 -0,4

Table 19 above shows that the overall yearly return of the book value portfolios is 6%. Period 2001-2005 is the worst period for the book value portfolios with a negative yearly return of -3%. As indicated the 1996-2000 period is the best period with a yearly return of 26%. Looking het the Sharpe ratios, table 18 indicates that the 1996-2000 has the highest ratio of all periods. Since the book value portfolios outperformed the optimal Markowitz portfolio two times, the table above displays two positive values of the information ratio. These values are both 0,0 since the outperformance is minimal. The book value portfolios did outperform the market cap portfolios all periods except from the last one. Because of this the information ratios relative to the market cap portfolios are all positive for the first four periods as well as for the whole period.

Table 20, below, compares the overall yearly returns as well as the yearly returns per 5-year period of all the portfolios used in this research. As can be seen in table 20, the optimal Markowitz portfolios outperformed the other portfolios two times, out of the five sub-periods. Besides this the optimal Markowitz portfolio managed to outperform the other portfolios from 1991 to 2014 as well. In the last two sub-periods and the 1996-2000 period the optimal Markowitz portfolio did not outperform the other portfolios. In the 1996-2000 period the

dividend yield portfolio, the cash flow portfolio and the book value portfolio outperformed the

optimal Markowitz portfolio. During the 2006-2010 period the employees portfolio and the

dividend yield portfolio outperformed the Markowitz portfolio. During the 2006-2010 period the dividend yield portfolio managed to achieve the highest yearly return, a yearly return of 3% and

during this period. In the last period all the smart beta portfolios outperformed the Markowitz portfolio.

When the smart beta portfolios are compared with the market capitalization portfolio, table 20 shows that the market cap portfolio outperformed only two smart beta portfolios and only in the last period. During the last period the market capitalization portfolio outperformed the revenue portfolio and the book value portfolio. Indeed the market cap portfolios performed the worst of all portfolios when comparing the market cap with the smart beta portfolios.

Table 20. Yearly returns of the Markowitz portfolio, market capitalization portfolio, employees portfolio, dividend yield portfolio, cash flow portfolio and book value portfolio over the whole period as well as the five sub-periods

Yearly return Markowitz

Market

capitalization Employees Revenue

Dividend yield

Cash

flow Book value

Overall 16%* 6% 8% 7% 10% 7% 6% 1991-1995 28%* 11% 11% 11% 12% 12% 11% 1996-2000 25% 24% 25% 25% 27%* 27% 26% 2001-2005 20%* -5% -3% -3% 4% -3% -3% 2006-2010 2% -2% 2% -1% 3%* -1% -2% 2011-2014 2% 4% 5% 3% 5%* 4% 3%

* Highest return of all portfolios during a period

When comparing the smart beta portfolios, table 20 indicates that the portfolio based on the dividend yield metric shows outperformance in almost every period. In the overall period the dividend yield portfolio managed to make a yearly return of 10%. The second best smart beta portfolio for the overall period is the employees portfolio with a yearly return of 8%.

Conclusion and discussion

In this research the optimal Markowitz portfolio and the market capitalization portfolios are compared with five different smart beta portfolios. These portfolios are based on the following metrics; employees, revenues, dividend yield, cash flow and book value. The aim of this research is to answer the following questions. Frist of all this research tries to find an answer on the question whether the more easy strategies, the smart beta portfolios, are able to outperform the more sophisticated optimal Markowitz portfolios. Secondly this research tries to answer the question whether the smart beta strategies are able to outperform the traditional portfolio based on market capitalization.

Markowitz portfolios were outperformed. The optimal Markowitz portfolio in the 1996-2000 period was outperformed by the dividend yield portfolio, the Cash flow portfolio and the book

value portfolio. The other two smart beta portfolios made a return equal to the optimal

Markowitz portfolio. In the 2006-2010 period the dividend yield portfolio outperformed the optimal Markowitz portfolio with 1 pps. During the 2011-2014 period all the smart beta portfolios outperformed the optimal Markowitz portfolio. The results largely in line with the literature found. Chow et al (2011) and DeMiguel (2009) found that the more simple smart beta strategies outperform the more sophisticated Markowitz portfolio. This research found that this is the case for three of the five periods used in this research.

Besides this, this research shows that the smart beta portfolios are able to outperform the traditional market capitalization portfolio. This is fully in line with the existing literature. Arnott et al. (2005) showed that the smart beta strategies are able to outperform the traditional market cap portfolios. Furthermore Estrada (2008) concluded that the portfolio based on dividend was able to outperform the traditional market cap. In this research the dividend yield portfolio performed best of all the smart beta portfolios, overall from 1991-2014 and in the five 5-years periods as well. Hemminki and Puttonen (2008) conducted research relating European stocks. They show that the smart beta portfolios outperform the market cap portfolio. This is also shown by Mar et al. (2009) but related to Australian stocks.

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Appendix

1. Script used in Matlab (R2015a) to determine the optimal Markowitz portfolios. nt in lines 24 and 25 represents the number of trading days in year t. st in line 41 represents number of stocks used in year t and ot in lines 41 and 71 represents the number of output columns are needed in year t.

1. tic 2.

3. nAssets = numel(P1Ret); 4. Aineq = - P1Ret’;

5. r = 0.0000001:0.00001 : 0.1; 6. Aeq = ones(1, nAssets); 7. Beq = 1;

8. lb = zeros(nAssets,1); 9. ub = ones(nAssets,1); 10. c = zeros(nAssets,1);

11. options = optimset(‘Algerithm’, ‘interior-point-convex’); 12. options = optimset(options, ‘Display’,’iter’,’Tolfun’,1e-10); 13. x0 = Aeq/nAssets;

14.

15. for i = 1:1:100000 16.

48. pSharpe = 0; 49. 50. continue; 51. 52. else 53. 54. break; 55. 56. end 57. end 58. 59. maxpSharpe = max(Output(5,:));

60. [row col] = find(maxpSharpe == Output); 61. optiDailyRet = Output(1,col); 62. optiDailyVar = Output(3,col); 63. optiYearlyRet = Output(2,col); 64. optiYearlyVar = Output(4,col); 65. 66. OptiAllocation = [optiDailyRet 67. optiDailyVar 68. optiYearlyRet 69. optiYearlyVar 70. maxpSharpe 71. Output(7,col) 72. Output(8,col) 73. Output(9,col) 74. Output(10,col) 75. Output(11,col) 76. Output(12,col) 77. . 78. . 79. Output(ot,col) 80. 81. 82. ] 83. 84. hold

85. plot (Output(4,:), Output(2,:)) 86. title(‘Efficient Frontier’); 87. xlabel(‘Portfolio Risk’); 88. ylabel(‘Portfolio Return’)

89. plot (optiAllocation(4,1),optiAllocation(3,1),’o’); 90. print(‘-dpng’, ‘-r300’, ‘Efficient Frontier’); 91. plot(P1StdAnn,P1RetAnn,’x’);

92. axis(‘on’); 93.