An evaluation of the effect of the liquidity premium on the excess return of Smart-Beta investment funds and ETFs.
Student: Daan van Egmond Student number: 5767857 Master: Business-Economics – Finance
Thesis supervisor: Patrick Tuijp November 2014
Introduction
Quite recent innovations in equity-asset management are the so-called smart beta or alternative beta strategies. These are also called alternative beta strategies and for the remainder of this thesis both definitions will be used interchangeably. Issuers of these funds/ETFs aim to provide outperformance over the traditional value weighted index, by arguing that the value weighted index falls short on diversification and risk-adjusted return (Amenc, Goltz, and Lodh, 2012). Melas, Briand and Urwin (2011) review the value weighted, risk weighted, equal weighted and minimum volatility strategies over the period 1988 to 2011. They find indeed higher returns and higher Sharpe ratios for these alternative beta strategies.
Many researchers, for example Blitz and Swinkels (2008) and Jun and Malkiel (2007), argue that the observed outperformance is due to tilts toward sources of return also called factor premiums, such as value, low-volatility, momentum and small-cap exposures. These are induced by the alternative weighting strategies. However, the existing literature which evaluates the performance of alternative-beta strategies, while controlling for several factor premiums, find better risk-adjusted returns (Sharpe-ratio) and alphas, but is inconclusive about alpha’s significance. (Kang, 2012; Hsu et al. 2011; Clare, Motson and Thomas, 2013 and Plyakha, Uppal and Vilkov, 2014).
A risk factor, which is not controlled for in the existing literature on smart-beta funds, is liquidity. Pastor and Staumbaugh (2001) show that liquidity is important for asset pricing, because investing in illiquid stocks requires a liquidity premium. They derive a liquidity factor that is priced in an Arbitrage Pricing Theory (APT) setting. Furthermore, they find that the returns of small stocks are more sensitive to illiquidity due to the flight to liquidity phenomenon in times of low liquidity. This means that small stocks are more exposed to the priced illiquidity risk and this should lead to a higher small stock illiquidity premium. Building on this finding, it is plausible that alternative weighted methods are more exposed to liquidity risk than the value weighted index. The value weighted index allocates stocks according to their market capitalization and is therefore typically concentrated in a very small effective number of large highly liquid stocks. A deviation in weighing could lead to more exposure to the illiquidity risk.
To illustrate: an equal-weighted ETF/fund has a larger exposure to small stocks, and therefore potentially a higher illiquidity risk exposure, compared to a value weighted fund. The situation regarding fundamental indexing, which has an exposure on value stocks, is quite similar. Value stocks in general have a lower price-to-earnings (P/E) ratio and price-to-book (P/B) ratio. Their market-capitalization is lower on average, which results in holding relatively more small stocks.
If smart beta funds are more exposed to liquidity risk, it is relevant to control for this risk to see whether the four-factor alpha of smart-beta funds is robust to inclusion of a liquidity factor. In other words, a part of the observed four-factor alpha, could actually be liquidity beta. Therefore, the main contribution of my thesis to the existing literature is to give a conclusive answer whether these strategies achieve alpha, by adding the Pastor and Staumbaugh (2003) liquidity factor to a multivariate regression when evaluating the performance of smart beta strategies. Hence, I will use a five-factor benchmark, which is the Carhart (1997) four-factor model with an additional liquidity factor. The Carhart (1997) four factor model is a standard tool in portfolio performance evaluation.
“The research question of this thesis is: “Does the liquidity premium of illiquid stocks contributes significantly to the excess return generated by smart-beta funds and indices?”
A second contribution of this thesis is the evaluation of existing commercially available smart-beta funds/ETFs. However, data availability is not sufficient for a small number of the commercially smart-beta funds/EFs due to recent inception. In this case, I choose to select the underlying benchmark. For example, the S&P 500 Low Volatility Portfolio exists since May 2011. This would result in 31 observations, which I consider a too small sample. For this reason I will obtain monthly returns from the underlying benchmark, the S&P 500 Low Volatility Index, which exists for more than 10 years. Working with commercial funds/ETFs is different from previous research. Kang (2012) for example only evaluates the underlying benchmark indices, such as the S&P 500 Equal Weighted Index and the Russell 1000 Equal Weighted index. Other existing literature constructs their own benchmarks from a chosen stock universe and back tests these strategies when evaluating alternative beta strategies. (Chow et al., and Clare, Motson and Thomas, 2013)
Although such back tests provide insight into the theoretical performance of smart beta strategies, transaction costs and tracking errors are not included in this analysis. Ang, Goetzmann and Schaefer (2011) confirms this by stating that back tests of investment
methods give limited direction to investors, because this method usually does not take into account transaction costs, fees, price impact and can involve data mining. Furthermore, commercially available strategies can be combinations of methodological choices and self-constructed indices are not realistic representations of commercially available strategies. I am mainly interested in the actual performance and hence us realized U.S. smart beta fund returns. My dataset can be divided in two samples. The first sample consists of funds and indices with then years of monthly returns from 31/12/2003 until 31/12/2013. The second sample includes funds and indices with five years of monthly returns from 31/12/2008 until 31/12/2013. The complete sample includes 39 alternative beta funds and 2 indices. Furthermore, I add three the same value-weighted funds to both samples for comparison.
The results of this thesis shows that three out of 39 funds/ETFs/Indices and indices earn alpha. Furthermore, the results indicate that the liquidity premium does have a significant effect of smart beta funds. However, it almost all four-factor alphas (except 1) appear to be robust to the addition of the liquidity factor.
The remainder of this thesis is structured as follows: Section 2 describes the existing literature about smart beta strategies and contains background information about the history of passive investing and the evolution of alternative beta strategies. Furthermore, background information about the liquidity factor is provided. Section 3 describes the data and methodology used to obtain the results. Section 4 presents the descriptive results. Section 5 describes the regression results and section 6 contains the conclusion.
2. Literature Review
The aim of this section is to provide a clear understanding of the theory behind smart beta investing and review the existing literature about the subject. I start with the theory behind value weighting, which is the Capital Asset Pricing Model (CAPM). After this, the inefficiency of the value weighted index is discussed. Then, the different smart beta weighting methods are reviewed and empirical results from existing literature. Finally, the impact of liquidity on stock returns is discussed.
2.1 Efficient Market Hypothesis and CAPM
For a better understanding of the theory behind smart beta investing, it is relevant to mention the difference between active and passive investing. Active investment management attempts to exploit mispriced assets and earn an excess return over the benchmark also called alpha, whereas passive investing or indexing attempts to replicate the performance of an index and aims for a market return or beta. (Ang, Goetzmann and Schaefer, 2011). The underlying theory of passive investing or indexing is the efficient market hypothesis (EMH). The EMH states that financial markets are efficient, meaning that all available information is fully reflected in asset prices and implies that fundamental- and technical analysts cannot ‘outperform’ the market in the long run. (Fama, 1965; 1970) Therefore it pays of more (according to the EMH), to mimic the performance of the market. In practice, all commercial available passive index funds and ETF’s (Exchange Traded Funds), which have the intention to hold the market portfolio choose an index as a proxy for the market. Currently, the value-weighted index is the dominant form of indexing, due to the CAPM model. (Kang, 2012; Goltz and Le Sourd, 2011)
Sharpe (1964) and Lintner (1965) developed the CAPM model which is built on strong assumptions, including homogeneity of investors’ expectations, which is also part of the EMH. A result of the model is that securities carry systematic risk and non-systematic risk. Systematic risk, also called market risk is indicated in the model as the beta of a security and is a result from factors that affect the whole market and this risk cannot be diversified away. Therefore, systematic risk is rewarded by a higher expected return. The asset-specific risk can be diversified away by holding the mean variance efficient value-weighted portfolio.
This means that according to the CAPM model, the value-weighted portfolio has the highest risk-adjusted return with the same amount of risk, or achieves the same return with lower risk.
2.2 Inefficiency of the value weighted index
The CAPM model and the resulting efficient mean-variance market portfolio is built on five assumptions, which have been widely criticized empirically and theoretically. I will discuss this briefly.
In the setting of this model, investors are rational, risk averse and seek to maximize their economic utilities. Several researchers disagreed about this assumption including Kahneman and Tversky (1992), which argued that the assumed investor’s behavior was not consistent with their prospect theory. Furthermore, the model says that there are no taxes and transaction costs. This is not true in the real world. Long (1977) showed that portfolio’s which are efficient when there are no taxes, become inefficient when taxes are introduced. Also, the model presumes the possibility for investors to lend and borrow unlimited amounts against the risk-free rate. Black (1972) showed that the CAPM market portfolio is still efficient when there is no possibility to borrow against a risk-free rate, but that the market portfolio becomes inefficient in the case of short-sell constraints. An additional assumption says that all assets are tradable, also including for example real estate, stamps collection and jewels. Goltz and Le Sourd (2011) argue that if not all assets are tradable (which is obvious in the real world), the market portfolio becomes inefficient. Finally, the model assumes that investors have the same expectations about the future. Several researchers investigated the consequences when this assumption would not hold. They concluded that the market portfolio would still be efficient. (For example: Lintner (1969) and Sun and Yang (2003)). However, Gressis, Philippatos, and Hayya (1976) argued that when investors have different investment-horizons, the market portfolio would become inefficient. Clearly, the CAPM model is built on very strong assumptions that are questionable in the real world.
Even if the CAPM assumptions hold, it is impossible in practice to hold the market portfolio, which contains all existing investment opportunities weighted to their market capitalization. Roll (1977) criticized the assumed complete knowledge of all constituents of the market portfolio and argued that proxy’s for the market (such as the S&P 500) could not be mean-variance efficient, while the true market portfolio is inefficient or vice versa. The
problem is that is according to Roll (1977), it is unfeasible to test a portfolio which contains all possible investment possibilities. In other words, the CAPM model is not testable.
Empirical evidence rejecting the efficiency of the CAPM market portfolio is provided by Kandel and Staumbaugh (1987) who showed that other portfolios could achieve a higher Sharpe Ratio. Haugen and Baker (1991) argue that in the case of a situation where investors disagree about risk and expected return, the capitalization-weighted index is a suboptimal investment strategy. This is also the case when there are short-selling constraints, when dividends are taxed, when not all investment opportunities are included in the index or when foreign investors are in the domestic market. By using a simulation experiment over the period 1972-1989, Haugen and Baker (1991) show that a low-volatility portfolio achieves an equal or greater return than the market-capitalization portfolio.
The CAPM model has only one risk factor, the undiversifiable systematic or market risk. Ross (1976) argued that there could be more non-diversifiable risk factors than market risk and developed the Arbitrage Pricing Theory (APT) by which he extended the single factor CAPM model to a multi-factor model. The APT states that exposures to these sources or risk is compensated by factor-risk premiums. Moreover, the APT model does not identify the other risk factors.
Since the creation of the APT, researchers have been trying to identify the main risk factors in stock returns. Fama and French (1993) identify three systematic risk factors in the returns on stocks, namely the overall market factor from the CAPM model, a size factor and a book-to-equity factor. These factors became the standard in portfolio performance evaluation, since the explanatory power of stock returns improves by adding the size and book-to-equity factor. (Fama and French, 1993). The size factor stands for small firms earning an excess return over large firms and the book-to-equity factor stand for ‘value’ stocks earning a higher return than ‘growth’ stocks. Carhart (1997) constructed a four-factor model by adding the ‘momentum’ factor, which implicates that past winners (within three to twelve months) have a higher returns for the following 3-12 months. Moreover, the APT model does not reject the EMH but does state that the market-capitalization weighted portfolio is inefficient. The APT is has less restricting assumptions compared to the CAPM model.
Using the Fama-French/Carhart factors gives rise to the possibility of determining an ex-ante amount of exposure to the factor-premiums and implement this by using a passive investment strategy. As long as a fund-manager does not change his passive-strategy, the exposure to the factor loadings will remain the same. An investor does not need an active
manager to get factor-exposure and active managers should only be rewarded for excess returns when controlling for risk-factors.
Empirical studies confirm that active managers systematically tilt their portfolios towards these risk-factors in order to outperform the market-cap benchmark. Fama and French (2010) find that mutual fund managers underperform the Fama-French factors benchmark on average by the amount of management fees charged. Mok, Bender and Hammond (2013) show that 80% of the average CAPM alpha earned by US institutional fund returns can be explained by the Fama-French factors. These studies did not recognize the possibility of funds providing passive, rule-based factor exposure similar to that of active funds. This raises the question why you would pay active managers to achieve something you can achieve with passive investing?
2.3 Smart-Beta
A recent research of Ang (2009) revealed that the excess return of active investing can be attributed to risk factors. Alternative beta indices can potentially capture the risk premiums associated with these factors and deliver returns equal to the returns of active funds but with lower costs with transparent implementation choices. (Bender et all., 2013) To illustrate the influence of alternative-beta strategies: 90% of the respondents to the European Index Survey 2011 and to the North American Index Survey 2011 have an interest in new forms of indexation or have already adopted alternative weighting schemes and over 50% are unsatisfied with their cap-weighted indices. Overinvestment in overpriced stocks, poor diversification, size biases, sector biases and lack of representativeness of the economy are mentioned.
2.3.1 Different types of Smart-Beta strategies
Chow et al. (2011) classifies alternative-beta strategies into Heuristic-Based and Optimization-Based weighting strategies. The first are strategies based on a simple weighting rule, which is different from the market-cap weighting technique. Equal weighting, risk-cluster equal weighting, diversity weighting, inverse volatility or non-optimized volatility, fundamental and dividend weighting fall into this category. The latter are strategies where the constituent weights are based on a maximization or minimization of some mathematical
function, while taking into account certain constraints. The minimum-variance, maximum diversification and risk-efficient strategy fall into this category.
Kang (2012) uses a different approach and makes a distinction based on the different objectives of the strategies. Value strategies have the objective to tilt towards a value factor, low-volatility strategies attempt to reduce the volatility of the portfolio; diversification-strategies have the objective to reduce stock-specific risks and Momentum diversification-strategies are subject to momentum exposure. Melas, Briand and Urwin (2011) make a distinction between risk-based strategies and return based strategies.
2.3.1.2 Heuristic-Based Weighting Strategies
Equal Weighting
According to Kang (2012), equally weighted strategies fall into the category of diversification strategies which are designed to reduce stock-specific risks and are heuristic-based according to Chow et all. (2011). Heuristic means following a strategy heuristic-based on a simple rule, which applies obviously to equal weighting. Melas, Briand and Urwin (2011) see equally weighting as risk-based strategy in contrast to return-based strategies. The weight for
stock 𝑖𝑖 in the equal-weighted portfolio is given by
ℎ𝐸𝐸𝐸𝐸,𝑖𝑖∗ = 1𝑛𝑛 , (1)
where 𝑛𝑛 is the number of stocks in the portfolio.
Diversity Weighting
To avoid the problem of investing relatively large positions in less liquid stocks when applying the equal weighting strategy, one can put a cap on the market value of any stock in the market-cap index. (Thomas, Clare and Motson, 2013). Fernholz et al (1998) describe this
approach.The weights are given by
𝐷𝐷𝑝𝑝 = �� 𝑛𝑛𝑗𝑗𝑝𝑝 𝑛𝑛 𝑖𝑖=1 � 1/𝑝𝑝 , (2)
where p is a constant between 0 and 1. This parameter provides the desired level of tracking
error compared to the cap-weighted index. n is the number of constituents and 𝜋𝜋𝑖𝑖 ,…, 𝜋𝜋𝑛𝑛
represents the capitalization weights.
Risk clustering weighting
This methodology equally weights among ‘risk-clusters’ instead of individual stocks. Risk-clusters can be for example countries or industries. Risk-Risk-clusters are equally weighted in the total portfolio, but the risk-clusters themselves are market-capitalization weighted. (Chow et al., 2011)
Inverse volatility or non-optimized low volatility strategy
When the index or fund is rebalanced, the weight 𝑤𝑤 of each stock 𝑖𝑖 is equal to the inverted
standard deviation of the particular stock divided by sum of all inverted volatility. As a result, the stock with the lowest standard deviation has the highest weighting.
𝑤𝑤𝑖𝑖 = 1 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑖𝑖𝑣𝑣𝑖𝑖𝑣𝑣𝑣𝑣𝑖𝑖 ∑ 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑖𝑖𝑣𝑣𝑖𝑖𝑣𝑣𝑣𝑣1 𝑗𝑗 𝑛𝑛 𝑗𝑗=1 , (3)
where, 𝑁𝑁 is the number of constituents and volatility is the standard deviation of the stocks’
daily returns over the preceding one year of trading days
Fundamental weighting
Arnott et al. (2005) construct indices on company size measured by economic fundamental measures as gross revenue, equity book value, gross sales, gross dividends, cash flow, and total employment an alternative for market-capitalization. They argue that market capitalization is a volatile way of measuring a firm’s size and/or value.
2.3.1.2 Optimization-Based Weighting Strategies.
Minimum-variance strategies
This strategy comes from the idea that expected returns and covariance matrices of stocks are very hard to estimate. A possible solution for this is problem is to assume all stocks have the same expected return. In this case, the variance portfolio is the optimal minimum-variance portfolio. (Haugen and Baker, 1991).
The constituent weights can be estimated by solving the following optimization problem:
min𝑥𝑥 𝑥𝑥′Σ𝑥𝑥
𝑠𝑠. 𝑣𝑣. 𝑣𝑣 ≤ 𝑥𝑥𝑖𝑖 ≤ u, i = 1, … , n,
(4)
In this formula, Σ is the covariance of returns estimated using historical returns of the
portfolio’s stocks and x is the vector of portfolio weights. 𝑣𝑣 and 𝑢𝑢 be used to set a lower bound
and cap on particular stocks.
2.4 Empirical Results from existing literature
Although relatively new, smart beta funds have been evaluated before. Chow et al. (2011) review the methodologies behind the most popular alternative-beta strategies. Developed global- and U.S. smart-beta portfolios are constructed based on the largest 1000 stocks from the CRSP/Compustat Merged Database and Worldscope/Datastream Database. Thereafter, the strategies are back-tested while rebalancing annually and quarterly to observe the differences. The results show that the reviewed smart-beta strategies outperform (achieving alpha) the cap-weighted index unadjusted for risk factors. The results of applying the Carhart (1997) four-factor model show non-significant alphas for all smart-beta strategies. It appears that almost all strategies have a positive factor-exposure to value (HML) and small-cap (SMB).
Kang (2012) finds equivalent results by using a five-factor model of the Carhart (1997) factors and an additional volatility factor. Alphas are not significant. Tilts toward value and size are also observed but also significant tilts toward momentum factors. No explanation is given for this result. The authors emphasize that alternative beta strategies take
significant active risks driven by factor exposures. Factor returns can be volatile over time and this brings the risk of periods of significant underperformance relative to the cap-weighted benchmark. Furthermore, they believe combining smart-beta strategies can reduce the active risk and improve performance ratios, because equity risk factors do not have to be correlated.
Clare, Motson and Thomas (2013) back-test alternative beta strategies using stock returns from the largest 1000 U.S. companies over the period 1968-2011. Their results indicate that all smart-beta strategies achieved a higher Sharpe ratio. Furthermore, their findings show that all evaluated strategies are biased towards small stocks, especially the equal risk contribution, non-optimized low volatility and optimized strategies. and in a lesser extent to value stocks. Logically, the market-cap index has a tilt towards the largest, most liquid stocks.
Plyakha, Uppal and Vilkov (2014) find that with monthly rebalancing, an equal-weighted portfolio outperforms a value-equal-weighted portfolio in terms of total mean return, four-factor alpha, and Sharpe ratio. They mention that they extend the model by the Pastor and Stambaugh (2003) liquidity factor, but do not present the results. They do say that the liquidity factor does not significantly affect the models fit.
Arnott, Hsu and Moore (2005) construct fundamental indices with annually rebalancing using gross revenue, equity book value, gross sales, gross dividends, cash flow, and total employment as weights. They show that these fundamental weighted indices outperform the market-cap indices. The excess that they find are 2.15 percentage points higher than the reference market-cap portfolio. Moreover, the excess returns are significant with a 𝑣𝑣 statistic of about 3.09.
Melas, Briand and Urwin (2011) review the characteristics of several smart-beta strategies including value characteristics weighted, risk weighted, equal weighted and minimum volatility characteristics. Their data set covers MSCI world constituents over the period 1988-2011. They conclude that over this period, alternative-beta strategies achieve positive alphas with a higher Sharpe ratio.
2.5 Impact of Liquidity on stock returns
Amenc (2013) argue that portfolios which are less concentrated than the value-weighted index, which is typically concentrated in a very small effective number of highly liquid stocks, will lead to an increase in the exposure to less liquid stocks. Thomas, Clare and Motson (2013) confirm that all alternative-beta strategies underweight large cap stocks.
Asset liquidity is a priced and state variable shown by Pastor and Staumbaugh (2003). They find that expected stock returns are related cross-sectional to the sensitivities of returns to fluctuations in aggregate liquidity. They find that from 1966 through 1999, the average return on stocks with high sensitivities to liquidity exceeds that for stocks with low sensitivities by 7.5 percent per annum, where they control for exposure to the market return as well as size, value, and momentum factors. Investors seem to pay a premium for more liquid stocks. To illustrate: An investor who uses leverage faces a margin requirement. When his overall wealth decreases to a point that he has to fill up his margin account, he might have to liquidate assets to generate cash. When the investor holds stocks, which are more sensitive to liquidity, that is a higher sensitivity to aggregate liquidity and the aggregate liquidity is low at that point, liquidity is more costly (Pastor and Staumbaugh, 2003 and Brunnermeier and Pederson, 2009).
Pastor and Stambaugh (2001) find that over the period 1966-1999, the difference in returns between stocks which are in the highest decile of sensitivity to liquidity and stocks which are in the lowest decile are on average 7.5% annually. They also find that the illiquidity premium is higher for small stocks. This is while controlling for market risk, size, value and momentum. They develop a liquidity factor, which can be included for example in the Carhart (1997) four factor model to control for liquidity premium. However, the existing literature, which evaluates smart-beta strategies, does not control for liquidity. It is plausible that alternative weighing methods are more exposed to liquidity risk than the value weighted index, due to their higher percentage of small stock holdings. The purpose of this paper is evaluating the returns of U.S. smart-beta funds with the Carhart (1997) four factor model with an additional factor that controls for liquidity. This will give new insights in the returns of smart-beta funds and contribute to the existing literature. The reviewed literature about alternative beta funds lead to the following research question for this thesis:
The research question of this thesis is: “Does the liquidity premium of investing in illiquid stocks contributes significantly to the excess return generated by smart-beta funds?”
To help answering the research question, two hypotheses are constructed:
Hypothesis 1: Smart beta funds have a significant alpha, when controlling for Carhart (1997) four factors.
Hypothesis 2: Smart-Beta funds have a significant and positive exposure to the liquidity factor.
Data & Methodology 3.1 Data
Morningstar, Inc. (henceforth referred to as Morningstar) provided me with a list from their database of all U.S. based funds/ETFs and indices which they categorize as smart-beta. The list contains 1123 funds/ETFs which track 336 unique benchmark indices. As a result, there are more smart-beta funds/ETFs with longer track records. To illustrate: Exchange Traded Funds (ETFs), which most alternative beta vehicles are, started to show up in the U.S. in 1993 and it took six years for Asia to follow and eight years before the first ETF was spotted in Europe. (Gastineau, 2001). In order to obtain at least 60 monthly observations, I excluded funds/ETFs, which had their inception after 31/12/2008. Due to the large amount of funds/ETFs, I choose to exclude smart-beta funds/ETFs that focus on a segment such as agriculture, biotechnology etc. Furthermore, I excluded funds/ETFs that have foreign equity holdings in their portfolio and/or fixed income products. These are in the Morningstar list, because the fund/ETF is listed in American dollars ($). After this selection, there are 167 fund/ETFs left.
Morningstar divides the smart-beta funds/ETFs into return orientated, risk orientated and other fund/ETFs/indices. These three groups are again divided by their strategic beta attribute. Table 1 shows how Morningstar groups the smart-beta funds/ETFs.
Table 1. Morningstar methodology of grouping smart-beta funds
My objective is to have a representative sample of U.S. alternative-beta funds. Table 1 shows that there are no risk-orientated fund/ETFs which had their inception after 31/12/2008. Therefore, I add the MSCI USA Minimum Volatility Index and the S&P 500 Low Volatility index to my sample. The first is a minimum variance strategy (see formula 4) and the second is a non-optimized low volatility strategy (formula 3).
The smart-beta classification of Morningstar is rough, which means that there can be different smart-beta strategies within the Strategic Beta Attributes Groups. The methodology used is often mentioned in the name of the fund/ETF and can be recognized in this way. This can be illustrated with, for example, the Growth, Pure Growth, Value and Pure Value ETFs. Issuers of smart-beta ETFs/fund often divide benchmark indices (for example the S&P 500) into growth and value segments. The Guggenheim S&P 500 Value and the Guggenheim S&P 500 Growth have respectively 357 stocks and 284 stocks in their portfolios. This adds up to over 500 stocks, which means some stocks of the S&P 500 are represented in both ETFs. To overcome this issue, Guggenheim created the pure value and pure growth ETFs. These ETFs do not have overlap and include only stocks with distinct growth or value characteristics. Morningstar classifies Value and Pure value both as Value and Growth and Pure growth as growth. Therefore, I divide the Strategic Beta Attributes groups by methodology and segment (small-cap, mid-cap and large-cap), when the methodology and segment can be easily derived from the ETFs name. Within these groups I select the underlying benchmark
Strategic Beta Group Strategic Beta Attributes # funds
Return Orientated Value 55
Growth 51 Dividend Screened/Weighted 17 Fundamentals Weighted 11 Multi-Asset 1 Low/Minimum Volatility/Variance 1 Growth/Multi-Factor/Size 5 Earnings Weighted 4 Revenue Weighted 4 Quality 2 Momentum 3 Expected Returns 2
Buyback Shareholder Yield 1 Value/Multi-factor/Momentum 8
Other Equal-Weighted 2
which is tracked by the highest number of funds/ETFs. Then, if there is an fund/ETF following the selected benchmark with ten years of monthly observations, this one is selected in preference of funds/ETFs with five years of monthly observations. If none can provide ten years of monthly observations, I choose the ETF with the highest AUM (assets under management). Moreover, AUM should not say anything about methodology, performance, etc. In the end, I get two samples with this methodology. A sample with funds and ETFs with ten years of monthly data and a second sample with funds and ETFs with five years of monthly data. I put a cap of 40 funds/ETFs on my sample in order to keep my results clear and interpretable. For this reason I cannot select for each smart-beta category the small cap, midcap and large cap version. (for example: Russell 1000, 2000 and 3000). When I have to make a choice in this situation, I choose to select the small cap version and the large cap version. In this way, differences along the market-cap segment spectrum can be observed. Monthly price data is obtained from Thomson Reuters DataStream. If the fund/ETF cannot be found in DataStream, I deleted this fund/ETF from the sample and re-run the selection procedure. Appendix A contains all smart-beta funds/ETFs with their weighing methodologies and stock selection criteria. Table 2 summarises the selection criteria. DataStream keeps dad funds/ETFs in their database, which avoids survivorship bias. I select value-weighted funds/ETFs and indices to compare with the alternative-beta funds/indices.
Table 2. Selection Criteria
1) Fund/ETF must had its inception at or before 31/12/2008 2) Fund/ETF cannot have a segment focus
3) Fund/ETF cannot have foreign equity holdings and/or fixed income product
4) Morningstar Strategic Beta Attributes Groups are divided by methodology and segment when when the methodology and segment can be easily derived from the ETFs name.
5) The underlying benchmark is selected which is tracked by the highest number of funds/ETFs 6) The ETF/Fund which can provide ten years of monthly data is selected
7) If no ETF/fund in that category can provide ten years of monthly data, the ETF/fund with the hightst AUM is selected.
Monthly returns are calculated using the following formula:
𝑟𝑟𝑡𝑡 =𝑝𝑝𝑡𝑡𝑝𝑝− 𝑝𝑝𝑡𝑡−1 𝑡𝑡−1
(5)
where, 𝑟𝑟𝑡𝑡 denotes the return in month 𝑣𝑣 and 𝑝𝑝𝑡𝑡 denotes the adjusted price, which incorporates
a stocks capital appreciation and paid out dividends.
To annualized standard deviation of monthly returns are calculated using the following formula:
𝑠𝑠𝑣𝑣𝑠𝑠 𝑠𝑠𝑑𝑑𝑣𝑣 (𝑣𝑣𝑛𝑛𝑛𝑛𝑢𝑢𝑣𝑣𝑣𝑣 𝑟𝑟𝑡𝑡) = √12 𝑠𝑠𝑣𝑣𝑠𝑠𝑑𝑑𝑣𝑣(𝑚𝑚𝑣𝑣𝑛𝑛𝑣𝑣ℎ𝑣𝑣𝑣𝑣 𝑟𝑟2) (6)
3.2 Methodology
Jensen’s alpha, Sharpe Ratio, Treynor Measure, Fama-French three factor model and the Carhart four-factor model are commonly used measures which I will use to evaluate the selected funds.
3.2.1 Sharpe Ratio
The Sharpe Ratio (Sharpe, 1964) measures the risk-adjusted return for an asset or portfolio. The formula is:
𝑅𝑅 − 𝑅𝑅𝑓𝑓
𝜎𝜎 , (7)
where, 𝑅𝑅 − 𝑅𝑅𝑓𝑓 is the excess return of the portfolio and 𝜎𝜎 is the standard deviation of the
3.2.2 Jensen’s alpha
The Jensen’s alpha (1968) measure is defined as:
𝑣𝑣𝑖𝑖 = 𝑅𝑅𝑖𝑖 − �𝑅𝑅𝑓𝑓+ 𝛽𝛽𝑖𝑖𝑖𝑖�𝑅𝑅𝑖𝑖− 𝑅𝑅𝑓𝑓��, (8)
where, 𝑣𝑣𝑗𝑗 is Jensen’s alpha or excess return, 𝑅𝑅𝑖𝑖 is portfolio return, 𝑅𝑅𝑓𝑓 is the risk-free rate, 𝛽𝛽𝑖𝑖𝑖𝑖
is the return on the portfolio and 𝑅𝑅𝑖𝑖 is the return on the market.
3.2.3 Fama-French Three-Factor model
Fama and French (1993) use three factors to explain returns. The model is defined as:
𝑅𝑅𝑝𝑝,𝑡𝑡 − 𝑅𝑅𝑓𝑓,𝑡𝑡 = 𝑣𝑣𝑡𝑡+ 𝛽𝛽𝑖𝑖𝑅𝑅𝑖𝑖,𝑡𝑡 − 𝑅𝑅𝑓𝑓+ 𝛽𝛽𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝑡𝑡+ 𝛽𝛽ℎ𝐻𝐻𝑆𝑆𝐿𝐿𝑡𝑡+ 𝜀𝜀𝑡𝑡, (9)
where, 𝑅𝑅𝑝𝑝,𝑡𝑡− 𝑅𝑅𝑓𝑓,𝑡𝑡 is the return of the portfolio in month 𝑣𝑣 minus the risk-free rate, 𝑣𝑣𝑡𝑡 is the
excess return, �𝑅𝑅𝑖𝑖,𝑡𝑡� is the market return minus the frisk free rate in month 𝑣𝑣, SMB is the
average return on the three small portfolio minus the average return on the three big portfolios, HML is the average return on the two value portfolios minus the average return on the two growth portfolios and 𝜀𝜀𝑡𝑡 is the error term.
3.2.3 Fama-French Three-Factor model
Fama and French (1993) use three factors to explain returns. The model is defined as:
𝑅𝑅𝑝𝑝,𝑡𝑡 − 𝑅𝑅𝑓𝑓,𝑡𝑡 = 𝑣𝑣𝑡𝑡+ 𝛽𝛽𝑖𝑖𝑅𝑅𝑖𝑖,𝑡𝑡 − 𝑅𝑅𝑓𝑓,𝑡𝑡+ 𝛽𝛽𝑆𝑆𝑆𝑆𝑆𝑆𝐵𝐵𝑡𝑡+ 𝛽𝛽ℎ𝐻𝐻𝑆𝑆𝐿𝐿𝑡𝑡+ 𝜀𝜀𝑡𝑡, (10)
where, 𝑅𝑅𝑝𝑝,𝑡𝑡− 𝑅𝑅𝑓𝑓,𝑡𝑡 is the return of the portfolio in month 𝑣𝑣 minus the risk-free rate, 𝑣𝑣𝑡𝑡 is the excess return, 𝑅𝑅𝑖𝑖,𝑡𝑡− 𝑅𝑅𝑓𝑓,𝑡𝑡 is the market return minus the frisk free rate in month 𝑣𝑣, SMB is the average return on the three small portfolio minus the average return on the three big
portfolios in month 𝑣𝑣, HML is the average return on the two value portfolios minus the
3.2.3 Carhart (1997) Four-Factor model
Carhart (1997) added the momentum factor to the Fama-French Three-Factor model. We get the following model:
𝑅𝑅𝑝𝑝,𝑡𝑡− 𝑅𝑅𝑓𝑓,𝑡𝑡 = 𝑣𝑣𝑡𝑡+ 𝛽𝛽𝑖𝑖∗ 𝑅𝑅𝑖𝑖,𝑡𝑡+ 𝛽𝛽𝑆𝑆∗ 𝑆𝑆𝑆𝑆𝐵𝐵𝑡𝑡+ 𝛽𝛽ℎ∗ 𝐻𝐻𝑆𝑆𝐿𝐿𝑡𝑡+ 𝛽𝛽𝑖𝑖∗ 𝑆𝑆𝑀𝑀𝑆𝑆𝑡𝑡+ 𝜀𝜀𝑡𝑡, (11)
where, 𝑆𝑆𝑀𝑀𝑆𝑆𝑡𝑡 is the average return the two high prior return portfolios minus the average
return the two low prior return portfolios in month 𝑣𝑣.
3.2.4 Carhart Four-Factor model plus a liquidity factor
I add two liquidity factor of Pastor and Stambaugh (2003). The following model is specified:
𝑅𝑅𝑝𝑝,𝑡𝑡− 𝑅𝑅𝑓𝑓,𝑡𝑡 = 𝑣𝑣𝑡𝑡+ 𝛽𝛽𝑖𝑖∗ 𝑅𝑅𝑖𝑖,𝑡𝑡+ 𝛽𝛽𝑆𝑆∗ 𝑆𝑆𝑆𝑆𝐵𝐵𝑡𝑡+ 𝛽𝛽ℎ∗ 𝐻𝐻𝑆𝑆𝐿𝐿𝑡𝑡+ 𝛽𝛽𝑖𝑖∗ 𝑆𝑆𝑀𝑀𝑆𝑆𝑡𝑡+ 𝛽𝛽𝑙𝑙∗ 𝐿𝐿 + 𝜀𝜀𝑡𝑡
(12)
4. Descriptive Statistics
In this section the descriptive statistics are presented for funds and indices with ten years and five years of monthly data. Value-weighted funds and ETFs are added for comparison. In my descriptive statistics I annualize the monthly returns, using the following formula:
𝐶𝐶𝑣𝑣𝑚𝑚𝑝𝑝𝑣𝑣𝑢𝑢𝑛𝑛𝑠𝑠 𝐴𝐴𝑛𝑛𝑛𝑛𝑢𝑢𝑣𝑣𝑣𝑣 𝐺𝐺𝑟𝑟𝑣𝑣𝑤𝑤𝑣𝑣ℎ 𝑅𝑅𝑣𝑣𝑣𝑣𝑑𝑑 (𝐶𝐶𝐴𝐴𝐺𝐺𝑅𝑅) = (𝑏𝑏𝑑𝑑𝑒𝑒𝑖𝑖𝑛𝑛𝑛𝑛𝑖𝑖𝑛𝑛𝑒𝑒 𝑣𝑣𝑣𝑣𝑣𝑣𝑢𝑢𝑑𝑑)𝑑𝑑𝑛𝑛𝑠𝑠𝑖𝑖𝑛𝑛𝑒𝑒 𝑣𝑣𝑣𝑣𝑣𝑣𝑢𝑢𝑑𝑑 1𝑡𝑡− 1 (13)
Where, 𝑑𝑑𝑛𝑛𝑠𝑠𝑖𝑖𝑛𝑛𝑒𝑒 𝑣𝑣𝑣𝑣𝑣𝑣𝑢𝑢𝑑𝑑 is the most recent last fund/ETF value in the sample and
𝑏𝑏𝑑𝑑𝑒𝑒𝑖𝑖𝑛𝑛𝑛𝑛𝑖𝑖𝑛𝑛𝑒𝑒 𝑣𝑣𝑣𝑣𝑣𝑣𝑢𝑢𝑑𝑑 is the first and oldest fund/ETF value of the sample.
4.1 Funds with 10 years of monthly data
Table 4 shows descriptive statistics for the sample of funds and ETFs for which I could obtain ten years of monthly data. I included two indices, because the underlying ETFs that track these indices had their inception beyond 31-12-2008. These are the MSCI USA Minimum Volatility Index and the S&P 500 Low Volatility Index. The first is a minimum variance strategy (see formula 4) and the second is a non-optimized low volatility strategy (formula 3). The average annual returns vary from 6.86% (SPDR S&P 500 Value ETF) to 10.30% (Vanguard Small Cap Growth Index Fund). Sharpe ratios differ between 0.42 (SPDR S&P 500 Value) and 0.76 (S&P 500 Low Volatility Index). Figure 1 displays the distribution of returns and Sharpe ratios per fund/ETF.
Six out of thirteen alternative beta funds/ETFs seem to achieve higher returns compared to their value-weighted benchmarks. Morningstar assigns a value-weighted benchmark to each smart-beta funds, based on the universe of stocks in which the fund/ETF invests.
The alternative beta fund/ETFs which outperform their value-weighted benchmarks are the First Trust Value Line® Dividend ETF (2.51%), the Guggenheim S&P 500® Equal Weight ETF (1.77%), the iShares Russell 2000 Growth ETF (0.30%),the SPDR S&P 500 Growth ETF (0.10%), the MSCI USA Minimum Volatility Index (0.85%) and the S&P 500 Low Volatility Index (1.61%). None of the value-weighted funds/ETFs realize a higher return than their value-weighted benchmark.
Overall, the smart-beta funds/ETFs achiever higher returns and Sharpe ratios than the value weighted ETFs. For example, the Guggenheim S&P 500 Equal Weights ETF achieves on average a 2% excess return per annum over the value-weighted SPDR S&P 500 ETF and Sharpe ratios are 0.50 and 0.45 respectively. Table 3 shows the average returns and Sharpe ratios per strategic beta attribute category. Non-Optimized Low Volatility (0.76) and Dividend Screened/Weighted (0.65) achieve the highest risk-adjusted return and Value Characteristics (0.45) and Momentum (0.29) have the lowest ratios. Value Weighted is
positioned as 8th out of 13. The differences between the returns of commercial funds/ETFs
and their benchmarks ranges from -0.87% to 0.05% due to transaction costs, management fees and tracking error. CAPM alphas range from -2.84% (p-value 0.38) to 3.41% (p-value 0.23). Only the S&P 500 Low Volatility index (3.41%, p-value 0.04) achieves a significant CAPM alpha. This means no commercial available ETF or fund shows a significant CAPM alpha. Betas differ between 0.81 and 1.26
Table 3. Average returns and Sharpe Ratios per Strategic Beta Attribute Category
Strategic Beta Attribute
Average Return Funds/Efs
Average Sharpe Ratio Fund/ETFs
Non-Optimized Low volatility 9.18% 0.76
Dividend Screened/Weighted 9.92% 0.65
Min. Variance Optimization 8.26% 0.61
Growth, Multi-Factor, Size 10.30% 0.51
Equal Weighted 9.84% 0.50
Growth 8.31% 0.46
Value-Weighted 8.02% 0.46
Value Characteristics 8.22% 0.45
Figure 1. Average Annual Returns and Sharpe Ratios for the sample of funds for which I could obtain ten years of monthly data from 31-12-2008 till 31-12-2013. For the calculation of the Sharpe Ratio see formula 7. For the calculation of the average annual returns see formula 13. The left axe corresponds to the average annual returns and the left axe to the Sharpe ratios.
Table 4. Descriptive Statistics sample funds/ETFs with ten years of available data from 31-12-2003 till 31-12-2013. Betas and Jensen’s alpha are calculated using the market returns obtained from Kenneth French’s website (2014) . # as of November 1, 204. * - means cannot be found in DataStream.
* significance at 10% level
** significance at 5 % level
*** significance at 1% level
Name Fund/ETF obs. Strategic Beta Attributes ann. Return
std. dev.
Return max. down max. up
ann.
Return-rf Beta assets in $ Benchmark
Return Benchmark
Value-Weighted Sharpe Ratio Jensen's alpha p-value
Smart-Beta Funds
First Trust Value Line® Dividend ETF 120 Dividend Screened/Weighted 9,92% 13,75% -13,92% 9,09% 8,26% 0,81 800.512.016 Value Line Dividend Index - 7,41% 0,65 2,83% 0,23 Guggenheim S&P 500® Equal Weight ETF 120 Equal Weighted 9,18% 17,63% -20,91% 18,69% 7,53% 1,15 7.509.929.055 S&P 500 Equal Weighted Index 9,84% 7,41% 0,50 0,15% 0,87 iShares Russell 1000 Growth ETF 120 Growth 7,63% 15,05% -17,73% 10,81% 6,00% 0,98 21.197.256.637 Russell 1000 Growth Index 7,83% 7,78% 0,46 -0,42% 0,70 iShares Russell 2000 Growth ETF 120 Growth 9,37% 20,15% -21,65% 15,97% 7,72% 1,26 5.325.576.993 Russell 2000 Growth Index 9,41% 9,07% 0,47 0,00% 1,00 SPDR S&P 500 Growth ETF 120 Growth 7,51% 15,06% -17,91% 11,70% 5,88% 0,97 385.486.538 S&P 500 Growth Index 7,69% 7,41% 0,46 -0,48% 0,71 Vanguard Small Cap Growth Index fund 120 Growth, Multi-Factor, Size 10,30% 20,26% -22,19% 16,66% 8,55% 1,27 12.136.416.315 MSCI US Small Cap Growth Index 11,18% 10,43% 0,51 0.94% 0,64 First Trust Value Line® 100 ETF ETF 120 Momentum 5,43% 19,84% -21,17% 18,94% 3,84% 1,15 47.582.019 Value Line 100 Index - 7,88% 0,29 -2,84% 0,38 iShares Russell 1000 Value ETF 120 Value 7,42% 15,45% -16,98% 11,45% 5,79% 1,00 19.869.340.088 Russell 1000 Value Index 7,58% 7,78% 0,44 -0,71% 0,57 iShares Russell 2000 Value ETF 120 Value 8,49% 19,62% -20,97% 15,35% 6,85% 1,21 4.814.389.925 Russell 2000 Value Index 8,61% 9,07% 0,44 -0,55% 0,83 SPDR S&P 500 Value ETF 120 Value 6,86% 15,00% -16,79% 12,53% 5,25% 0,97 185.491.453 S&P 500 Value Index 7,05% 7,41% 0,42 -1,03% 0,39 SPDR S&P Small-Cap 600 Value ETF 120 Value 10,10% 19,88% -20,20% 19,78% 8,12% 1.25 260.822.944 S&P SmallCap 600 Value Index 10,05% 10,43% 0,51 0.68% 0,73
MSCI USA Minimum Volatility Index 120 Min. Variance Optimization 8,26% 11,59% -14,53% 7,27% 6,62% 0.71 - MSCI US Index - 7,41% 0,61 1.78% 0,30 S&P 500 Low Volatility Index 120 Non-Optimized Low Volatiltiy 9,18% 10,32% -12,83% 5,95% 7,53% 0.62 - S&P 500 Index - 7,57% 0,76 3.41%** 0,04
Value-Weighted Funds
SPDR S&P 500 ETF 120 - 7,34% 14,56% -16,52% 10,91% 5,72% 0.97 198.039.206.000 S&P 500 Index 7,41% 7,41% 0,45 -0.66%* 0,10 Ishares Russell 1000 ETF 120 - 7,67% 14,81% -17.14% 10.97% 6.04% 0.99 10.532.975.000 Russell 1000 index 7,78% 7,78% 0,47 -0.45% 0,14 Ishares Russell 2000 ETF 120 - 9,06% 19,51% -20.96% 15.39% 7.41% 1.12 $27,547,034 Russell 2000 index 9,07% 9,07% 0.46 -0.20% 0,92
Smart-Beta Indices which have no commercial fund tracking them or the commercial funds trakcing them have a too recent inception
4.2 Funds with five years of monthly observations
Descriptive results for the funds of which I could obtain five years of monthly data are presented in table 6. The average annual returns vary from 16.59% (PowerShares Fundamental Pure Lg Core ETF) to 28,14% (Guggenheim S&P MidCap 400® Pure Gr ETF). Sharpe ratios differ between 0.83 for the Guggenheim S&P Small-Cap 600® Pure Gr ETF and 1.40 for the PowerShares Buyback Achievers ETF. Figure 2. Displays the distribution of returns and Sharpe ratios.
17 out of 26 alternative beta funds/ETFs outperform their value-weighted benchmark. Generally spoken, the smart-beta funds achieve higher returns than their value-weighted benchmarks. The largest difference is 9.89%, which is between the return of the Guggenheim S&P 500® Pure Value ETF and the S&P 500. However, this is not a significant outperformance due to the high beta (1.50) of the Guggenheim S&P 500® Pure Value ETF. The SPDR S&P Mid-Cap 400 Value underperforms the value-weighted benchmark (S&P 500) the most with -1.75% on average per annum. Looking at the Sharpe ratios, the alternative beta funds have a higher risk-adjusted return than the value-weighted funds.
Table 5 shows the average returns and Sharpe ratios per strategic beta attribute category. Buyback/Shareholder yield (1.40) and Equal Weighted (1.28) achieve the highest risk-adjusted return and Value Weighted and Revenue Weighted have the lowest ratios.
Value Weighted is positioned a shared 8th out of 13.
CAPM alphas differ between 5.70% (Guggenheim S&P MidCap 400® Pure Gr ETF) and -2.51% (Ishares Russell 2000 ETF). The Powershares Buyback Achievers ETF has the only significant CAPM alpha (4.17%, p-value 0.01).
Table 5 Average returns and Sharpe Ratios per Strategic Beta Attribute Category.
Strategic Beta Attribute
Average Return Funds/Efs Average Sharpe Ratio Fund/ETFs Buyback/Shareholder Yield 23.01% 1.40 Equal Weighted 24.60% 1.28 Growth 25.98% 1.27 Expected Returns 26.21% 1.24 Multi-Asset 20.81% 1.13 Earnings Weighted 21.54% 1.12 Value; Multi-Factor; Momentum 22.07% 1.12
Value-Weighted 18,88% 1,09
Revenu Weighted 22.87% 1.09
Figure 2. Average Annual Returns and Sharpe Ratios for the sample of funds for which I could obtain five years of monthly data from 31-12-2008 till 31-12-2013. For the calculation of the Sharpe Ratio see formula 7. For the calculation of the average annual returns see formula 13. The left axe corresponds to the average annual returns and the left axe to the Sharpe ratios.
Table 6. Descriptive Statistics sample funds/ETFs with five years of available data from 31-12-2003 till 31-12-2013. Betas and Jensen’s alpha are calculated using the market returns obtained from Kenneth French’s website (2014) . # as of November 1, 204. * - means cannot be found in DataStream.
* significance at 10% level
** significance at 5 % level
*** significance at 1% level
Name Fund/ETF obs. Strategic Beta Attributes ann. Return
std. dev.
Return max. down max. up ann.
Return-rf Beta assets in $000# Benchmark
Return Benchmark
Return Value-Weighted
Benchmark Sharpe Ratio Jensen's alpha p-value
Smart-Beta Funds
PowerShares Buyback Achievers ETF 60 Buyback/Shareholder Yield 23.01% 15.76% -11.56% 13.33% 22.94% 0.95 2,154,302,599 NASDAQ US Buyback Achievers Index - 17.94% 1.40 4.17%** 0.01 Vanguard High Dividend Yield ETF 60 Dividend Screened/Weighted 16.74% 16.08% -13.64% 10.26% 16.67% 0.94 11,052,861,642 FTSE High Dividend Yield Index - 17.94% 1.05 -1.04% 0.79 WisdomTree Earnings 500 ETF 60 Earnings Weighted 17.77% 15.15% -10.52% 10.81% 17.70% 0.93 99,997,716 WisdomTree Earnings 500 TR USD 17.94% 1.16 -0.05% 0.96 WisdomTree SmallCap Earnings ETF 60 Earnings Weighted 25.31% 23.61% -13.37% 26.91% 25.24% 1.35 324,049,126 WisdomTree SmallCap Earnings Index - 21.37% 1.08 -0.15% 0.96 First Trust NASDAQ-100 Equal Wtd ETF 60 Equal Weighted 24.60% 18.68% -8.69% 14.62% 24.52% 1.09 402,602,473 NASDAQ 100 Equal Weighted Index 25.59% 25.56% 1.28 3.20% 0.43 Guggenheim Raymond James SB-1 Equity ETF 60 Expected Returns 26.21% 20.54% -10.99% 16.65% 26.13% 1.21 211,116,629 RaymondJames SB1 Equity Incorp Index - 17.94% 1.24 2.62% 0.45 PowerShares Fundamental Pure Lg Core ETF 60 Fundamentals Weighted 16.59% 14.23% -10.59% 8.96% 16.52% 0.85 33,453,893 RAFI Fundamental Large Core TR USD - 17.94% 1.15 0.35% 0.85 PowerShares Fundamental Pure Sm Core ETF 60 Fundamentals Weighted 16.78% 20.39% -14.94% 14.95% 16.71% 12,518,869 RAFI Fundamental Small Core TR USD - 17.94% 0.86 -4.66% 0.13 PowerShares FTSE RAFI US 1500 Sm-Mid ETF 60 Fundamentals Weighted 26.23% 24.31% -12.07% 27.16% 26.16% 1.39 828,221,086 FTSE RAFI US Mid Small 1500 Index 26.14% 20.08% 1.08 0.00% 0.98 PowerShares FTSE RAFI US 1000 ETF 60 Fundamentals Weighted 21.57% 19.41% -11.90% 18.97% 21.50% 1.15 3,379,376,784 FTSE RAFI US 1000 Index 22.07% 18.59% 1.11 -0.33% 0.85 Guggenheim S&P 500® Pure Growth ETF 60 Growth 25.69% 18.11% -9.55% 13.79% 25.62% 1.08 1,484,486,205 S&P 500 Pure Growth Index 28.65% 17.94% 1.36 4.26% 0.14 Guggenheim S&P MidCap 400® Pure Gr ETF 60 Growth 28.14% 19.86% -9.27% 19.37% 28.07% 1.12 596,782,561 S&P MidCap 400 Pure Growth Index 25.32% 21.89% 1.35 5.70% 0.13 Guggenheim S&P Small-Cap 600® Pure Gr ETF 60 Growth 24.73% 22.61% -12.84% 27.93% 24.66% 1.12 83,353,625 S&P SmallCap 600 Growth Index 28.17% 21.37% 1.09 1.24% 0.69 SPDR S&P Mid-Cap 400 Growth 60 Growth 24.87% 18.64% -9.78% 17.12% 24.80% 1.09 151,056,166 S&P MidCap 400 Growth Index 23.22% 21.89% 1.29 3.48% 0.34 SPDR S&P Small-Cap 600 Growth 60 Growth 26.48% 20.33% -9.87% 19.40% 26.40% 1.18 325,545,460 S&P SmallCap 600 Growth Index - 21.37% 1.26 3.34% 0.24 First Trust Capital Strength ETF 60 Low/Minimum Volatility/Variance 19.77% 18.84% -9.97% 14.45% 19.71% 1.10 65,917,330 Capital Strength Index - 17.94% 1.05 -0.99% 0.74 Guggenheim Multi-Asset Income ETF 60 Multi-Asset 20.81% 18.22% -14.86% 22.36% 20.74% 1.00 973,871,873 Zacks Multi-Asset Income Index - 17.94% 1.13 1.67% 0.65 PowerShares S&P 500 High Quality ETF 60 Quality 16.87% 13.36% -9.31% 10.27% 16.80% 0.76 365,083,650 S&P 500 High Quality Index 20.04% 17.94% 1.24 2.12% 0.31 RevenueShares Large Cap ETF 60 Revenue Weighted 19.87% 17.35% -12.06% 14.47% 19.81% 1.06 222,957,321 RevShares Large Cap Fund TR USD - 17.94% 1.13 -0.39% 0.72 RevenueShares Small Cap ETF 60 Revenue Weighted 25.87% 24.94% -14.10% 26.47% 25.79% 1.44 240,080,551 RevShares Small Cap Fund TR USD - 17.94% 1.05 -1.10% 0.72 Guggenheim S&P 500® Pure Value ETF 60 Value 27.83% 27.00% -19.80% 33.16% 27.76% 1.50 1,024,492,902 S&P 500 Pure Value Index 28.65% 17.94% 1.05 0.00% 0.98 Guggenheim S&P MidCap 400® Pure Val ETF 60 Value 24.80% 25.73% -15.70% 29.55% 24.72% 1.44 95,674,644 S&P MidCap 400 Pure Value Index 25.32% 21.89% 0.99 -1.75% 0.62 Guggenheim S&P SmallCap 600® PureVal ETF 60 Value 27.65% 37.10% -22.21% 51.47% 27.58% 1.93 138,624,586 S&P SmallCap 600 Pure Value Index 28.17% 21.37% 0.83 -5.45% 0.42 SPDR S&P Mid-Cap 400 Value 60 Value 20.14% 19.29% -12.99% 16.18% 20.07% 1.14 78,914,529 S&P MidCap 400 Value Index 20.58% 21.89% 1.05 -1.32% 0.58 First Trust Small Cap Core AlphaDEX® ETF 60 Value;Multi-Factor;Momentum; 23.47% 22.13% -13.51% 20.95% 23.40% 1.28 444,379,691 Defined Small Cap Core TR USD - 17.94% 1.07 -0.70% 0.78 First Trust Large Cap Core AlphaDEX® ETF 60 Value;Multi-Factor;Momentum; 20.68% 17.31% -10.76% 15.21% 20.61% 1.05 1,205,792,462 Defined Large Cap Core TR USD - 18.59% 1.18 0.38% 0.78
Value-Weighted Funds 1
SPDR S&P 500 ETF 60 - 17.85% 15.82% -10.74% 10.91% 17.78% 0.98 198,039,206,000 S&P 500 Index 17.94% 17.94% 1.12 -0.80% 0.27 Ishares Russell 1000 ETF 60 - 18.46% 15.95% -10.45% 10.97% 18.39% 0.99 10,532,975,000 Russell 1000 index 18.59% 18.59% 1.14 -0.44% 0.26 Ishares Russell 2000 ETF 60 - 20.33% 20.64% -11.98% 15.39% 20.26% 1.22 27,547,034 Russell 2000 index 20.08% 20.08% 1.00 -2.51% 0.28
Results
In this section, the results of the one, three, four and five-factor regressions are given separately for the two sample sizes (five and ten years). Hypotheses 1, 2 and 3 will be answered per category.
Hypothesis 1: Smart beta funds have a significant alpha, when controlling for the Carhart (1997) four factors
Hypothesis 2: Smart-Beta funds have a significant and positive exposure to the liquidity factor
Hypothesis 3: The liquidity factor explains a part of alpha
5.1 Funds and indices with ten years of monthly observations
Table 7 presents the results of the funds/ETFs for which I could obtain ten years of monthly data, including value-weighted funds for comparison. The explanatory power of the five factor regressions is high, ranging from 0.75 to 0.99. The latter is almost equal to 1, as it is
the 𝑅𝑅2of the value-weighted funds, which are effectively market-trackers. To analyze
whether liquidity is a significant factor in explaining alternative beta funds returns, monthly returns from December 2003 till December 2013 are regressed on three models. The first is a CAPM regression, the second a Carhart (1997) four factor model and last a Carhart (1997) four factor model plus an additional Pastor and Staumbaugh (2001) liquidity factor. In this way, I can observe what impact adding the LIQ factor has on the regressed fund’s returns, while controlling for 𝑅𝑅𝑖𝑖,𝑡𝑡−𝑟𝑟𝑓𝑓, 𝑆𝑆𝑆𝑆𝐵𝐵, 𝐻𝐻𝑆𝑆𝐿𝐿 𝑣𝑣𝑛𝑛𝑠𝑠 𝑆𝑆𝑀𝑀𝑆𝑆.
A result of my regressions is that some funds/ETFs/indices have a negative significant exposure to the liquidity factor. This is possible when the fund /ETF/Index invests in highly liquid stocks. For the 10 years sample these are the MSCI USA Minimum Volatility index and the SPDR S&P 500 ETF. This is not very surprising, low-volatility stocks can be very liquid and large stocks (in which the value-weighted SPDR ETF invests in) can also be highly liquid). As expected, there are some funds/ETFs/indices that have a positive significant exposure to the liquidity factor. These are the Guggenheim S&P 500 Equal Weighed ETF (0.03043, p-value 0.02), the First Trust Value Line 100 ETF (0.14682, p-value
0.00) and the Vanguard Small Cap Growth Index Fund (0.05342, p-value 0.03). This is not surprising, because they invest largely in small stocks. This is merely evidence in favor of
Hypothesis 2 for these fund/ETFs. Adding the liquidity factor, increases 𝑅𝑅2 in all cases.
These three do not have significant alphas in the four-factor model, so strictly spoken, Hypothesis 1 and 3 do not apply here (alphas do decrease when the liquidity factor is added but stay not significant). However, the situation of the First Trust Value Line 100 ETF is interesting. In the four-factor model, the ETF has a not significant estimated alpha coefficient of -0.00356 (p-value 0.11). This significant alpha is not robust to the addition of the liquidity factor. In contrast with the Carhart (1997) four-factor model, the five-factor model results in a significant alpha of -0.00417 (p-value 0.05). Controlling for liquidity in this situation is useful when evaluating its performance.
Not one commercial available fund/ETF achieves a significant positive five-factor alpha. So, for ten years sample, hypothesis 1 must be rejected. This means that hypothesis 3 does not apply. The S&P 500 Low Volatility Index does show a significant positive alpha of 0.00293 (p-value 0.04). This is 3.57% annually. I added this index, because the Powershares S&P 500 Low Volatility ETF has an inception after 31-12-2008. Two out of three value-weighted ETFs have significant negative five-factor alphas. For this period, smart-beta funds/ETFs are better investments than value-weighted funds/ETFS, despite that they do not earn alphas.
The growth ETFs have a significant negative exposure to the HML (return value portfolios – return growth portfolios) and SMB (return small stock portfolios – return large stock portfolios) factor, which is expected. The value ETFs have a positive significant negative exposure to the HML factor, which is expected and varying exposure to the SMB factor, depending on the underlying benchmark. The SPDR S&P 500 value ETF has a negative exposure to the SMB factor, but the iShares Russell 2000 value ETF a positive exposure. The small cap ETFs have positive exposures to the SMB factor and the opposite is true for the value-weighted ETFs except the iShares Russell 2000 ETF. This is expected, because the Ishares Russell 2000 ETF invests in the 2000 smallest stocks of the Russell 3000 (which consist of 4000 US stocks). P-values of the SMB and HML factors are largely significant at the 1% level.
The momentum factor is significant and negative for the equal weighted ETFs. This is expected, because equal weighted ETF is rebalanced quarterly, whereby all constituents get the same weighting again. The growth ETFs have a significant negative exposure to the
momentum factor and the value characteristics ETFs have a significant positive exposure to the momentum factor. This result is not expected, because growth tends to be positively correlated with momentum and value tends to be negatively correlated to momentum (Jiang, Sarah et al. and Asness, Moskowitz and Pedersen, 2013).
Table 7 Regression results funds and indices with ten years of data.
𝑅𝑅𝑝𝑝,𝑡𝑡− 𝑅𝑅𝑓𝑓,𝑡𝑡= 𝛼𝛼𝑡𝑡+ 𝛽𝛽𝑖𝑖𝑚𝑚𝑡𝑡−𝑟𝑟𝑓𝑓,𝑡𝑡+ 𝛽𝛽𝑆𝑆𝑖𝑖𝑆𝑆,𝑡𝑡+ 𝛽𝛽ℎ𝑖𝑖𝑙𝑙,𝑡𝑡+ 𝛽𝛽𝑖𝑖𝑚𝑚𝑖𝑖+ 𝛽𝛽𝑙𝑙𝑖𝑖𝑙𝑙+ 𝜖𝜖𝑡𝑡
Regressions are estimated using the Fama-French (1993) three factor model, the Carhart (1997) four factor model and the four factor model with an additional liquidity factor. 𝛼𝛼 is Jensen’s alpha, 𝑚𝑚𝑚𝑚𝑣𝑣 − 𝑟𝑟𝑟𝑟 is the excess return on the market, which is the value-weighted return on all NYSE, AMEX and NASDAQ stocks minus the one-month Treasury bill rate. ℎ𝑚𝑚𝑣𝑣 is the average return on two value portfolios minus the average return on two growth portfolios. 𝑠𝑠𝑚𝑚𝑏𝑏 is the average return on three small portfolios minus the average return on three big portfolios. 𝑚𝑚𝑣𝑣𝑚𝑚 is the average return on two high prior return portfolios minus the average return on the two low prior return portfolios. 𝑣𝑣𝑖𝑖𝑙𝑙 is the liquidity factor of Pastor and Stambaugh (2001).
* significance at 10% level ** significance at 5% level
*** significance at 10% level
weighing method obs. α ajd.
Smart-Beta Funds
First Trust Value Line® Dividend ETF
120 0.00233 (0.00192) 0.81144*** (0.04718) 0.788543 0.00245 (0.00175) 0.78103*** (0.03957) -0.17166** (0.08072) 0.31734*** (0.10760) 0.09261 (0.06449) 0.816049 0.00262 (0.00168) 0.78451*** (0.03724) -0.16063* (0.08768) 0.29464** (0.11742) 0.09062 (0.06264) -0.04174 (0.04968) 0.816203
Guggenheim S&P 500® Equal Weight ETF Equal Weighted 120 0.00013 (0.00080) 1.15174*** (0.03782) 0.963606 0.00027 (0.00054) 1.04119*** (0.02782) 0.19194*** (0.02984) 0.09564** (0.03992) -0.08554*** (0.01951) 0.987054 0.00015 (0.00052) 1.03865*** (0.02438) 0.18390*** (0.03108) 0.11218*** (0.03660) -0.08409*** (0.01792) 0.03043** (0.01324) 0.987509
iShares Russell 1000 Growth ETF Growth 120 -0.00035 (0.00093) 0.98132*** (0.02470) 0.959408 -0.00019 (0.0055) 1.04835*** (0.01516) -0.01627 (0.02713) -0.35565*** (0.02996) 0.15400*** (0.01919) 0.981676 -0.00029 (0.00054) 1.04645*** (0.01541) -0.02229 (0.03514) -0.34325*** (0.02848) -0.15291*** (0.02241) 0.02281 (0.02036) 0.981954
iShares Russell 2000 Growth ETF Growth 120 0.00000 (0.00180) 1.25976*** (0.04596) 0.883064 -0.00092 (0.00064) 1.12245*** (0.02424) 0.88574*** (0.03979) -0.21977*** (0.03956) 0.01823 (0.02959) 0.982598 -0.00103 (0.0064) 1.11999*** (0.02297) 0.87828*** (0.04241) -0.20441*** (0.04429) 0.01958 (0.02975) 0.02825 (0.01717) 0.982821
SPDR S&P 500 Growth ETF Growth 120 -0.00041 (0.00108) 0.97413*** (0.03096) 0.944414 -0.00036 (0.00078) 1.01853*** (0.03089) 0.08739* (0.04929) -0.34608*** (0.04344) -0.13740*** (0.03503) 0.966697 -0.00042 (0.00382) 1.01729*** (0.02893) 0.08345* (0.04768) -0.33798*** (0.04750) -0.13669*** (0.03554) 0.01490 (0.02340) 0.966592
Vanguard Small Cap Growth Index fund 120 0.00078 (0.00350) 1.27455*** (0.18875) 0.901207 0.00018 (0.00353) 1.14532*** (0.19117) 0.80139*** (0.15742) -0.21475*** (0.14370) -0.01485 (0.11352) 0.980351 0.00006 (0.00382) 1.14088*** (0.17447) 0.78566*** (0.16582) -0.18592*** (0.15768) -0.01293 (0.1112) 0.05342** (0.12983) 0.981489
First Trust Value Line® 100 ETF Momentum 120 -0.00240 (0.00276) 1.14505*** (0.11120) 0.754728 -0.00356 (0.11) 1.20514*** (0.00) 0.48553*** (0.00) -0.31941*** (0.00) 0.20459*** (0.00) 0.863164 -0.00417** (0.00209) 1.19288*** (0.06116) 0.45673*** (0.07815) -0.23958** (0.10280) 0.21159*** (0.06006) 0.14682*** (0.04920) 0.872482
iShares Russell 1000 Value ETF Value Characteristics 120 -0.00037 (0.00106) 1.00223*** (0.03201) 0.951616 -0.00056 (0.00050) 0.95555*** (0.01412) -0.146944*** (0.02824) 0.40094*** (0.03185) 0.14142*** (0.02301) 0.984277 -0.00047 (0.00048) 0.95745*** (0.01235) -0.140922*** (0.02956) 0.38855*** (0.02974) 0.14043*** (0.02152) -0.02279 (0.01911) 0.984555
iShares Russell 2000 Value ETF Value Characteristics 120 -0.00047 (0.00213) 1.21325*** (0.04973) 0.945558 -0.00140 (0.00097)) 0.94981*** (0.03430) 0.73721*** (0.05230) 0.55347*** (0.06419) 0.28329*** (0.05829) 0.965561 -0.001202 (0.00092) 0.95381*** (0.02765) 0.74987*** (0.05460) 0.52742*** (0.05428) 0.28100*** (0.05334) -0.04792 (0.03550) 0.966401 Dividend Screened/Weighted
Growth, Multi-Factor, Size
𝛽𝛽_𝑚𝑚𝑚𝑚𝑣𝑣 𝛽𝛽_𝑠𝑠𝑚𝑚𝑏𝑏 𝛽𝛽_ℎ𝑚𝑚𝑣𝑣 𝛽𝛽_𝑚𝑚𝑣𝑣𝑚𝑚 𝛽𝛽_𝑣𝑣𝑖𝑖𝑙𝑙 𝑅𝑅^2 𝛽𝛽_𝑚𝑚𝑚𝑚𝑣𝑣 𝛽𝛽_𝑠𝑠𝑚𝑚𝑏𝑏 𝛽𝛽_ℎ𝑚𝑚𝑣𝑣 𝛽𝛽_𝑚𝑚𝑣𝑣𝑚𝑚 𝛽𝛽_𝑣𝑣𝑖𝑖𝑙𝑙
Table 7 continued
SPDR S&P 500 Value ETF Value Characteristics 120 -0.00086 (0.00100) 0.96664*** (0.02918) 0.939728 -0.00069 (0.00062) 0.96430*** (0.02244) -0.27882*** (0.03618) 0.32839*** (0.03264) 0.10744*** (0.02981) 0.975571 -0.00059 (0.00063) 0.96636*** (0.02074) -0.27230*** (0.03519) 0.31497*** (0.03349) 0.10626*** (0.02893) -0.02468 (0.01962) 0.975874
SPDR S&P Small-Cap 600 Value ETF Value Characteristics 120 0.00057 (0.00163) 1.24866*** (0.04507) 0.891163 0.0000 (0.00079) 0.99458*** (0.02144) 0.70099*** (0.03506) 0.35143*** (0.04185) 0.09907*** (0.03713) 0.972412 0.00012 (0.00078) 0.99703*** (0.02020) 0.70873*** (0.04348) 0.33551*** (0.03673) 0.09767*** (0.02014) -0.02928 (0.02014) 0.972585
MSCI USA Minimum Volatility Index Min. Variance Optimization 120 0.00148 (0.00141) 0.70783*** (0.04502) 0.839349 0.00162 (0.00131) 0.72420*** (0.04138) -0.204778*** (0.05607) 0.15772 (0.10471) 0.05180 (0.05829) 0.857830 0.00186 (0.00128) 0.72911*** (0.03633) -0.18922*** (0.05184) 0.12572 (0.09895) 0.04899 (0.05390) -0.05886* (0.03182) 0.861498
S&P 500 Low Volatility Index Non-Optimized Low Volatiltiy 120 0.00289*
(0.00145) 0.59050*** (0.03929) 0.731320 0.00287** (0.00140) 0.62179*** (0.03454) -0.20207*** (0.06224) 0.13295 (0.08618) 0.07169 (0.05283) 0.749699 0.00293** (0.00143) 0.62289*** (0.03307) -0.19858*** (0.06235) 0.12577 (0.08961) 0.07106 (0.05288) -0.01322 (0.04234) 0.747814 Value-Weighted Funds
SPDR S&P 500 ETF Value-Weighted 120 -0.00055*
(0.00033) 0.96883*** (0.00822) 0.992198 -0.00042** (0.00021) 0.98990*** (0.00531) -0.13041*** (0.01197) 0.02843 (0.01782) -0.00401 (0.00937) 0.996157 -0.00037* (0.00020) 0.99082*** (0.00531) -0.12749*** (0.01174) 0.02243 (0.01705) -0.00453 (0.00863) -0.01104*** (0.00445) 0.996232
Ishares Russell 1000 ETF Value-Weighted 120 -0.00037 (0.00025) 0.98700*** (0.00837) 0.994982 -0.00027 (0.00017) 0.99495*** (0.00630) -0.08093*** (0.01228) 0.02519** (0.01069) -0.00956 (0.00605) 0.996760 -0.00028 (0.00018) 0.99465*** (0.00610) -0.08189*** (0.01178) 0.02717** (0.01251) -0.00939 (0.00616) 0.00364 (0.00539) 0.996743
Ishares Russell 2000 ETF Value-Weighted 120 -0.00017 (0.00167) 1.23268*** (0.03619) 0.894433 -0.00113** (0.00054) 1.02818*** (0.01785) 0.84091*** (0.03430) 0.16435*** (0.04516) 0.15713*** (0.03695) 0.986366 -0.00111** (0.00054) 1.02863*** (0.01759) 0.84234*** (0.03530) 0.16141*** (0.04461) 0.15687*** (0.03681) -0.00541 (0.01103) 0.986261
Smart-Beta Indices which have no commercial fund tracking them or the commercial funds trakcing them have a too recent inception
5.2 Funds and indices with ten five years of monthly observations
Table 8 presents the results of the funds/ETFs for which I could obtain five years of monthly data, including value-weighted funds for comparison. The explanatory power of the five factor regressions is even higher than the 5 years sample, ranging from 0.90 to 0.99.
16 out of 26 smart-beta funds/ETFs have a significant exposure to the liquidity factor, from which nine are positive. This is evidence in favor of Hypothesis 2 for these funds/ETFs. The funds/ETFs with positive exposure includes, as expected, the First Trust NASDAQ-100 Equal Weighted ETF (0.08652, p-value 0.02). An explanation of the significant liquidity exposure of the First Trust Capital Strength ETF, The Guggenheim Raymond James SB-1 Equity, the First Trust Small Cap Core AlphaDEX® ETF and First Trust Large Cap Core AlphaDEX® ETF could also be their equal weighing. They fall into different smart-beta attribute groups, but give an equal weighting to their constituents.
Furthermore, three out of five growth ETFs have a positive exposure to the liquidity factor. An explanation could be that growth stocks are younger growing companies, which stocks are less liquid. It can be observed that three out of four value characteristics ETFs have a significant negative exposure to the liquidity factor. The Powershares BuyBack Achievers invests in companies that have effected a net reduction in shares outstanding of 5% or more in the trailing 12 months. This could lead to lower liquidity.
The Poweshares BuyBack Achievers ETF has a significant alpha of 0.00338 (p-value 0.02, 4.13% annually) in the four-factor regression. This is evidence in favor of hypothesis 1 for this ETF. Adding the liquidity factor gives a significant positive coefficient estimation of 0.05861 (p-value 0.04). This is evidence in favor of Hypothesis 2. In the five-factor regression, alpha increases and stays significant. Based on this result, I must reject hypothesis 3. The other fund/ETFs with positive exposures to the liquidity factor do not have significant alphas in the four-factor model, which makes that Hypothesis 1 and 3 do not apply here. The fund/ETFs with negative liquidity exposures also do not alter the (in)significance of alpha.
Two out of 25 alternative-beta funds have a significant alpha in the five factor
regression models. Besides the Powershares BuyBack Achievers ETF, this is the SPDR S&P Small Cap 600 growth with an estimated alpha coefficient of 0.00194 (p-value 0.00194, 2.35% annually). This is evidence in favor of Hypothesis 1.
The growth ETFs have as expected a positive exposure to the SMB factor and a negative exposure to the HML Factor. The value characteristics ETFs have as expected a positive exposure to the HML factor, but also positive exposures to the SMB factor. In general, it appears that smart-beta funds have a positive exposure to the SMB factor in contrast to the value-weighted funds/ETFs. It seems that a deviation from value-weighting leads to more small stock exposure, which was expected.
Regarding the momentum factor, the five years results show similarities to the ten years results. Growth ETFs have negative significant estimated coefficients to the momentum factor and value characteristics ETFs have positive significant coefficients. This contradicts with the existing literature (Jiang, Sarah et al., 2009 and Asness and Moskowitz and
