Abnormal performance of US large-cap exchange-traded funds

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Abnormal performance of US large-cap exchange-traded

Funds

Bachelor Thesis

Abstract

This research paper investigates whether US large-cap exchange traded funds underperform compared to the market during the period 2012 until 2016. A sample of 33 large-cap US exchange-traded funds and 17 small-cap US exchange-exchange-traded funds is tested for negative alpha values. In addition two unweighted portfolios are formed respectively one for small-cap ETFs and one for large-cap ETFs. These portfolios are also tested for negative alpha values. The tests are performed by ordinary least squared regression analysis. The capital asset pricing model, Fama-French three-factor model and Carhart four-three-factor model are used as models in the regression estimation. The research shows that small-cap ETFs outperform large-cap ETFs. It also indicates that the unweighted portfolio of large-cap ETFs exhibits significant negative alpha values. The Carhart four-factor model had the highest explanatory power in this study compared to the other two asset pricing models.

Student: Richard Hartweck Student number: 10914129

Thesis supervisor: Dr. J. Ligterink

Specialisation: Economics & Finance Research field: Asset pricing

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impossible to beat the market and is consistent with the efficient market hypothesis. The efficient market hypothesis states that stock market prices reflect all information available and as a result no investor can outperform the market by buying undervalued assets or selling overvalued asset (Fama, 1965).

In subsequent research Fama and French (2010) indicated that US mutual fund managers underperform capital asset pricing, Fama-French three-factor and Carhart four-factor benchmarks when management fees and expense ratios are taken into account on an aggregate level. They write that US mutual fund managers rather outperform the market by luck than by skill. Past academic research deals with the performance of mutual funds compared to the market but there is to a lesser extent research on a related product namely the exchange-traded funds (ETFs).

Exchange-traded funds have been traded in US markets since 1993. Since 2004 assets invested in ETFs have been rising from under one trillion US Dollar to just over five trillion US Dollar in January 2018 (Fuhr, 2018). In addition, ETFs offer several advantages over the traditional mutual fund for example low expense ratios and lower capital gains contributions (Gastineau, 2001). When compared to a mutual fund an ETF does not need to finance investment inflows and outflows with the sale of their securities which results in less capital gains contributions for

investors. Poterba and Shoven (2002) also find that ETFs offer tax advantages and are tax efficient for taxable investors.

(Reinganum, 1981) showed that small-cap firms outperform large-cap firms. So it is only rational to expect that investors would choose to invest in small-cap ETFs rather than large-cap ETFs. Yet there are many investors that invest into US large-cap ETFs.

This leads to the research question of this paper: do US large-cap exchange-traded funds underperform in comparison to the market if management fees and other expenses are taken into account ? This paper will try to answer this question by testing 33 large-cap US exchange-traded funds for an alpha by the means of the Capital Asset Pricing Model, the Fama-French Three-Factor

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Model and the Carhart Four-Factor Model during the period from January 2012 until December 2016. Furthermore, 17 small-cap ETFs will be tested in order to see if they outperform the large-cap funds which would be in accordance with the work done by Reinganum in 1981.

In the next section the relevant literature is presented and discussed. The third section deals with the data collection and methodology. The results will be presented in the fourth section and the limitations of this research are discussed in the penultimate section. Finally, the paper will be concluded in the last section.

2. Literature review

This part examines the existing literature surrounding the research question. The first part establishes the concept of the efficient market hypothesis. The second section deals with the asset pricing models that are used to answer the research question. The underperformance of funds will be discussed in the fourth section and the last section reviews past academic research about exchange-traded funds.

2.1 Efficient market hypothesis

The efficient market hypothesis states that stock market prices reflect all accessible information and as a consequence investors cannot outperform the market by buying undervalued assets or selling overvalued assets (Fama, 1965).

Furthermore, Fama (1970) distinguishes three forms of the efficient market hypothesis each one subject to a different information set: weak-form efficiency, semi-strong-form efficiency and the strong form, all assuming that investors make rational decisions. He states that in the weak-form efficiency the market is efficient, mirroring all market data and that historical prices have no impact on future prices. Fama writes that in the semi-strong-form efficiency the market prices mirror all publicly accessible information while in the strong-form efficiency market prices mirror all accessible information public and private.

The efficient market hypothesis is a key pillar for the research in this paper because if it holds, exchange-traded funds should not be able to beat the market if management fees and other expenses are taken into account. Some investors and scholars argue that the efficient market hypothesis might not hold.

Grossman and Stieglitz (1976) argue that information is not publicly available and has to be retrieved at a cost. They say that stock prices do not entirely mirror all available information.

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way than the uninformed investor. Scholars from the field of behavioural finance disagree with the efficient market hypothesis since they believe that investors are not rational but have cognitive biases (Kahneman, 2012). Also, DeBondt and Thaler (1985) find that most people are likely to “overreact” to abrupt or unanticipated incidents and as a result causing inefficiencies in the market. Fama (1991) revised his initial work about the efficient market hypothesis and recognised that the costs of the informed investor incurred to get informed are offset and concludes that in that case markets are not fully efficient. Besides, empirical results generally tend to fail to support the strong-form efficiency (Rosenberg, 1985).

Despite the ambivalent academic opinions and empirical results the efficient market hypothesis is a very important theory in finance and is the theoretical fundament of the research of this paper.

2.2 Asset pricing models

This subsection examines the three asset pricing models that are used in this paper to answer the research question. First, the capital asset pricing model is introduced. An extension of the model is discussed in section 2.2.2. The third model adds a momentum factor to the model discussed in section 2.2.2.

2.2.1 Capital asset pricing model

The notion of the capital asset pricing model was introduced by Markowitz (1952). Later, further developed by Sharpe (1964) and Lintner (1965). The objective of the CAPM is to determine the cost of capital, which compensates investors for the time value of money and the risk of the investment for a given investment (Sharpe 1964; Lintner 1965). The formula for the CAPM is:

E(R)=Rf+β[E(RM)-Rf]

The risk-free interest rate (Rf) in this model compensates for the time value of money and underlies the assumptions that investors can purchase and sell securities at competitive market prices, can borrow and lend at the risk-free interest rate, that investors have homogeneous expectations and that investors only acquire efficient portfolios of traded securities (Sharpe 1964; Lintner 1965). E(R) describes the return of the security. [E(RM)-Rf] characterises the market risk premium. (Sharpe 1964; Lintner 1965) describes that idiosyncratic risk does not give a premium to investors since it is a diversifiable risk and essentially the Law of One Price holds. They explains that the risk premium of an asset depends on the market risk premium multiplied by the asset’s beta (β). Berk

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and DeMarzo (2014, p.337) state that “the beta of a security is the expected percentage change in its return given a 1% change in the return of the market portfolio”. It is a measure of the systematic risk, a risk that affects all firms in the market.

A rewritten form of the capital asset pricing model equation gives Jensen’s Alpha (Jensen, 1967). Jensen’s Alpha is a performance measure of a security and is given by the equation:

α= (R– Rf) – β(RM-Rf)

Where a positive alpha indicates an outperformance of an asset compared to the market and a negative alpha indicates an underperformance in respect to the market (Jensen, 1967).

Despite the fact that the capital asset pricing model is one of the most important models for the description of the relationship between risk and return, many scholars criticise the model. Black, Jensen and Scholes (1972); Blume and Friend (1973); Stambaugh (1982) discover that the empirical validity of the model is low. Fama and French (2004) later support their empirical tests and show that variables such as size, price ratios and momentum should be added to the model in order to have more empirical validity. Roll (1977) reprimands that the market portfolio proxies used to find the return of the market are not the minimum variance portfolios and therefore states that the capital asset pricing model is erroneous.

In contempt of the critique of the capital asset pricing model is still the only surviving theoretical model to explain asset prices and it will be used in this research to test for negative alpha values and is the foundation for the two following asset pricing models.

2.2.2 Fama-French three-factor model

Empirical results show that small firms tend to outperform large firms (Reinganum, 1981) and firms with high price/earnings ratios do worse than firms with low price/earnings ratios (Basu, 1977). To control for these two anomalies of the capital asset pricing theory two additional

independent variables were added to the original capital asset pricing formula (Fama&French, 1993).

This extended version of the capital asset pricing model is called the Fama-French three-factor model and is given by the equation:

E(R)=Rf+β[E(RM)-Rf] + β

2 (SMB) + β3(HML)

Where SMB stands for small minus big and accounts for the findings that small firms tend to outperform large firms. HML is an abbreviation for High minus low and controls for the findings of Basu in the model. β

2 and β3 are their respective coefficients. Since it is an extension of the capital asset pricing model, the remaining variables are the same as defined in section 2.2.1.

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Fama and French (1993) write that while the capital asset pricing model can explain 70% of the return of a diversified portfolio on average, the three-factor model is able to explain 90% on average. Critics of the model argue that it suffers under data dredging bias (Black, 1993).

More recent critics argue the opposite and state that the model is incomplete and more variable should be included. Titman, Wei and Xie (2004) argue that there is a negative relationship among capital investment and average return. Due to the high explanatory power of the three-factor model, it is still a good model to be used in this research paper in order to answer the research question. The equation to calculate an alpha is given by:

α_p,= (R

p, – Rf,) - β1(RM, – Rf,)- β2 (SMB) - β3(HML)

2.2.3 Carhart four-factor model

An extension of the Fama-French three-factor model is the Carhart four-factor model (Carhart, 1997). Jegadeesh and Titman (1993) found that securities that have performed well in the past tend to increase in price in the future and vice versa.

Carhart (1997) captures this effect by adding a momentum factor (MOM) to the three-factor model which is the subtraction of the weighted average of the worst performing stocks from the best performing stock trailing one month. The equation is given by:

E(R)=Rf+β[E(RM)-Rf] + β

2 (SMB) + β3(HML) + β4(MOM) and Jensen’s Alpha is given by:

α_p,= (R

p, – Rf,) -β1(RM, – Rf,)- β2 (SMB) – β3(HML) – β4(MOM)

Recent academic research is in favour of the momentum effect and regard it as a valuable extension of the three-factor model (Low & Tan, 2016).

2.3. Underperformance of mutual funds

A study of 115 mutual funds during the period 1945-1964 found that mutual funds do not outperform the market and if management fees and expense ratios are taken into account even underperform (Jensen, 1967). This study uses Jensen’s Alpha as a performance measure and calculates asset prices by means of the capital asset pricing model (Jensen, 1967). Grinblatt and Titman (1989) later confirmed the notion that mutual funds underperform compared to the market by testing a sample of mutual funds during the period 1975-1984.

Malkiel (1995) also investigated the topic for the period 1971-1991. He finds that during the 1970s performance persistence existed, but on the other hand, he found no consistency in returns

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during the 1980s. Malkiel (1995) takes survivorship bias into account in his study and concludes survivorship bias is more critical than earlier research states. Wermers (2000) uses a unique dataset of the mutual fund industry performance and concludes that there is significant value in active mutual fund management. Cutherson, Nitsche and O’Sullivan (2008) test the UK market and find that abnormal mutual fund performance is not due to luck but rather skill. It is debatable whether their findings are applicable to this paper since this paper focuses on the US market. Kosowksi, Timmermann, Wermers and White (2006) uses a new multi-variate conditional regime-switching performance methodology and concludes that mutual funds tend to have positive alphas.

Most recent studies suggest that mutual funds tend to underperform in comparison to the market. Fama and French (2010) tested mutual funds in the US market between 1984 and 2006 with bootstrapped simulations and conclude that nonzero alpha values were found in the extreme tails of the distribution but overall conclude that mutual funds have alpha values of zero. These findings are also consistent with the findings of Glode (2011).

Since mutual funds and exchange-traded funds are a comparable investment vehicle, the aforementioned academic results might give a good indication of the performance of exchange-traded funds.

2.4. Exchange-traded funds

The US securities and exchange commission (2017) states that exchange-traded funds pool, just like mutual funds, the money of investors and invest on their behalf into assets. Gastineau (2001) further describes that exchange-traded funds have features of both mutual funds and closed-end funds. He writes that ETFs are valued like mutual funds at net asset value but have the

tradeability of closed-end funds and can be traded throughout the trading day.

Gastineau (2001) elaborates that ETFs have stock like features and can be sold short, bought on margin and investors can put stop-loss orders on them. In comparison to mutual funds,

exchange-traded funds offer several advantages over the traditional mutual fund, for example, low expense ratios and lower capital gains contributions (Gastineau, 2001). Poterba and Shoven (2002) also find that ETFs offer tax advantages and are tax efficient for taxable investors. ETFs can be categorised into small-cap, mid-cap and large-cap. (Reinganum, 1981) showed that small-cap firms outperform large-cap firms. So it is only rational to expect that investors would choose to invest in small-cap ETFs rather than large-cap ETFs.

This raises the question if large-cap ETFs are underperforming the market if management fees and other expenses are taken into account. More specifically this research will test if large-cap US exchange-traded funds have a negative alpha.

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3. Methodology and Data

To test for negative alpha values in the period from January 2012 until December 2016 (60 months) the following hypotheses are formulated:

H0: US large-cap exchange-traded funds have an alpha value of zero (α = 0) H1: US large-cap exchange-traded funds have a nonzero alpha value (α < 0)

To test for this hypothesis ordinary least squared (OLS) regression is performed on 33 US large-cap and 17 small-cap exchange-traded funds. This sample constitutes all style ETFs in the US of either large-cap or small-cap. All of the ETFs in this study are highly diversified. An ETF is classified as large-cap if its market capitalisation is 10 billion US Dollar or more and it is classified small-cap if its market capitalisation is between 300 million US Dollar and 2 billion US Dollar.

The regressions were run in Stata with robust standard errors to correct for possible serial correlation and heteroskedasticity. First, the data was tested in the context of the capital asset pricing model since it is one of the most important asset valuation models. Followed by the Fama-French three-factor model and by the Carhart four-factor model which are extensions of the model to take care of other factors that might explain the return of the ETFs. The coefficients of the various asset pricing models were estimated by the subsequent equations:

(Rp– Rf) = αp + β1 (RM – Rf) + ε p (Rp– Rf) = αp + β1 (RM – Rf) + β2 (SMB) + β3 (HML) + ε p (Rp– Rf) = αp + β1 (RM – Rf) + β2 (SMB) + β3 (HML) + β4 (MOM) + ε p

The error term ( ε

p ) measures the fluctuations relative to the best fitting line. It represents the

firm’s specific risk, which has already been diversified, therefore, it is assumed to be equal to zero. The literature says that the constant term in the regression equation should equal to zero if the asset pricing models hold and if the ETFs aren’t under- or outperforming the market.

First individual regressions were run for each exchange-traded fund for each capital asset pricing model. In a second step, two portfolios were formed. One unweighted portfolio of the large-cap ETFs and one portfolio of the small-cap ETFs. Regression analysis was performed on the unweighted portfolios by the means of the three asset pricing models, too. So in total 156 regressions are performed. If the regression constant is not significant we fail to reject the null hypothesis.

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The data for the monthly holding period returns of the ETFs during the period 2012 until 2016 (60 months) were downloaded from CRSP (Center for Research in Security Prices). This data is survivorship bias free. The data for the risk-free interest rate (Rf) is the one-month Treasury bill rate and was obtained from the Federal Reserve Bank of St. Louis. All variables were labelled with their corresponding abbreviation (Rm-Rf, SMB etc.) and the returns of the individual ETFs were labelled “largecap” or “smallcap” with numerical labelling from 1 to 33 and 1 to 17 respectively. The two unweighted portfolios were labelled “Plargecap” and “Psmallcap”. The website of

Kenneth R. French provides benchmark factors for the asset pricing models and the data for Rm-Rf, SMB, HML and MOM were directly retrieved from there.

The descriptive statistics are given in Table I. From there it can be seen that the average return in excess of the risk-free rate of the unweighted portfolio of large-cap ETFs is 1.58986% which is below the average excess market return of 1.186333%. That is in line with the alternative hypothesis. The average return in excess of the risk-free rate of the unweighted portfolio of small-cap ETFs is 1.1800111% which is closer to the average excess market return. The portfolio of small-cap ETFs exhibits higher returns than the large-cap portfolio on average and that is in line with what is expected from the literature.

4. Results

This section presents the results of the regression estimation of the three asset pricing models. First, the large-cap ETFs will be discussed with respect to the capital asset pricing model, Fama-French three-factor model and Carhart four-factor model in this particular order. Followed by the analysis of the small-cap ETFs. In the appendix, the tables with the individual regressions can be examined.

For the capital asset pricing model the beta coefficients of all 33 individual large-cap fund estimates are all significant at the 1% significance level. Table II shows that only one ETF has an alpha value statistically significantly smaller than zero at the 5% significance level. This ETF has a negative alpha value of -0.6612%. Using the capital asset pricing model the unweighted portfolio of the large-cap ETFs showed no significant alpha value as can be seen in Table V. Table II shows that average R-squared of the 33 individual ETFs was 0.9 which indicated a high explanatory power with a maximum value of 0.9887 and a minimum value of 0.4584. The regression results of the unweighted portfolio can be seen in the following table with a very high R-squared value of 0.9817.

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Table V. Results of two-sided regression analysis of unweighted portfolio of large-cap

ETFs

Model Alpha F-Value squared R-CAPM -0.0494** 3117.8** 0.9817 (0.377) (0.0000) FAMA -0.08845** 2024.16** 0.9909 (0.033) (0.0000) CARHART -0.09928** 1516.29** 0.991 (0.021) (0.0000)

** indicate 5% significance level

The high R-squared is not surprising since all of the selected ETFs are highly diversified and

therefore designed to track the market portfolio. In addition, all of the models have high explanatory power. Table I and II show that the F-values for the Capital asset pricing model are high and the p-values of the F-value are all below the 5% significance and even below the 1% significance level.

The regressions of the Fama-French three-factor model, which can be examined in table III, indicates that 8 out of the 33 large-cap ETFs exhibited a negative alpha value of -0.08845% at the 5% significance level. In addition, all beta one coefficients where significant at the 1% significance level but 11 ETFs had insignificant coefficients of either SMB, HML or both. The average R-squared was 0.9338 which is higher than the R-R-squared of the capital asset pricing model indicating higher explanatory power. The minimum and maximum values of the R-squared values were 0.537 and 0.9958 respectively. The results of the regression of the unweighted portfolio can be seen in

table V. The analysis of the unweighted portfolio showed that the coefficient of HML is not

significant while the portfolio has a significant negative alpha value at the 5% significance level. The R-squared of the unweighted portfolio is 0.9909 and indicates that 99.09% of the average excess return can be explained by the variables RmRf, SMB and HML. This is higher than the R-squared of the capital asset pricing model but not surprising since the literature already discusses that the three-factor model has higher explanatory power. The F-values of all 33 individual

regressions are statistically significant at the 5% significance level and 1% significance level. This means that the regression estimations are significant overall.

Finally, the estimation of the Carhart four-factor model showed that 9 out of 33 ETFs (27.27%) had a negative alpha value at the 5% significance level as can be seen in table IIII. Out of

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the 33 ETFs, 25 exhibited insignificant coefficients of SMB, HML, MOM or of a combination of those three coefficients. But all 33 F-values are statistically significant at the 5% significance level and 1% significance level. Confirming that the regression estimations are significant overall. When compared to the other asset pricing models the four-factor model had the highest explanatory power with an average R-squared of 0.9392 and a minimum and maximum value of 0.6328 and 0.9958 respectively as can be seen in table IIII. Table V displays that the unweighted portfolio had the highest R squared when compared to the other asset pricing models with a value of 0.9910. This comes to no surprise since the prior research says that the momentum factor has some explanatory power and it was expected that the Carhart models give the highest explanatory power. The analysis of the unweighted portfolio resulted in a significant negative alpha value of -0.09928% at the 5% significance level. One should note that the coefficients of HML and MOM were not significant but the overall F-value indicates that the regression estimation is significant at the 5% significance level and 1% significance level. Based on these results we reject the null hypothesis and accept the alternative hypothesis.

The analysis of small-cap ETFs indicates that no alpha significant different from zero is given within the framework of the capital asset pricing model and Fama-French three-factor model as can be seen in tables VII and VIII. Table VIIII shows that 4 out of 17 small-cap ETFs have a negative alpha value significant at the 5% significance level when estimated using the Carhart model. The F-values of the regressions run on the small-cap ETFs are significant at the 5% significance level and 1% significance level for all three models. Table VI gives the results of the regressions estimated on the unweighted portfolio of small-cap ETFs. From this table it can be seen that the portfolio has no significant alpha value different from zero at the 5% significance level for all three models. The respective R-squared values are 0.8038, 0.9752 and 0.9838. This is consistent with the findings of the analysis of the large-cap funds and what would be expected from the literature. When compared to large-cap ETFs the portfolio of small-cap ETFs outperformed the portfolio of large-cap ETFs when the three-factor model and Carhart model are used. This is what would be expected from the literature.

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Table VI. Results of two-sided regression analysis of unweighted portfolio of small-cap

ETFs

Model Alpha F-Value R-squared CAPM -0.1902** 237.55** 0.8038 (0.447) (0.0000) FAMA 0.036444** 733.9** 0.9752 (0.69) (0.0000) CARHART -0.07539** 835.87** 0.9838 (0.331) (0.0000) ** indicate 5% significance level

5. Conclusion and Discussion

The purpose of this research paper is to investigate whether large-cap US exchange-traded funds have abnormal returns. The research indicates that the returns of large-cap ETFs underperform the market when an unweighted portfolio of the ETFs is estimated by the means of the Three-factor model and Carhart model and therefore the null hypothesis is rejected and the alternative hypothesis accepted. This is in line with previous research on mutual funds done by Jensen (1967) and

Grinblatt and Titman (1989). In addition, this paper examined whether small-cap ETFs outperform large-cap ETFs. Indeed this paper confirms the notion of Reinganum (1981) that small-cap firms outperform large-cap firms. This would conclude that investors should rather invest into small-cap ETFs than large-cap ETFs.

The study also is in line with existing literature on the field of asset pricing models. The R-squared values indicate that every added variable adds explanatory power and hence the Carhart four-factor model has the highest explanatory power. Overall, the F-values of all models and estimations showed that the models are statically significant. The data fits the models really well since this paper examines the US market and most of the theories and research that have been performed in the past are based on the US market.

This research paper only examines the individual US small- and large-cap ETFs and their unweighted portfolios which is a limitation of this paper. Recommendations for further research would be to replicate the research with weighted portfolio and bootstrapped simulations similar to the research done by Fama and French (2010). It would also be interesting to examine ETFs issued in other markets of the world.

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7. Appendix

Table I. Descriptive statistics

Variable Mean Std. Dev. Min Max RmRf 1.186333 3.120473 -6.27 7.82 SMB -0.00267 2.15038 -4.64 4.78 HML 0.281667 2.535629 -4.77 9.19 MOM 0.159 3.338663 -7.92 10.29 Rf 0.0935 0.105169 0 0.49 largecap1 1.075835 3.038688 -6.1076 9.3559 largecap2 1.084198 3.076103 -6.0888 7.3475 largecap3 1.097315 3.008447 -6.1363 8.3814 largecap4 1.089517 3.065985 -6.4143 8.0199 largecap5 1.081152 3.157312 -6.1529 8.6083 largecap6 1.09277 3.070989 -5.8131 7.5343 largecap7 0.943552 2.685284 -5.0536 6.8008 largecap8 1.035612 2.743597 -5.3164 8.6922 largecap9 1.09722 3.016727 -6.1437 8.4091 largecap10 1.076912 3.089547 -6.1409 9.3827 largecap11 1.089545 3.094452 -6.6678 7.3083 largecap12 1.094283 3.051039 -5.9664 7.445 largecap13 1.076778 3.171356 -6.4742 8.6289 largecap14 1.091033 3.008192 -6.1516 8.0384 largecap15 1.090298 3.024165 -6.2024 8.2094 largecap16 1.065467 3.357164 -6.3389 8.904 largecap17 1.121693 2.976224 -5.9643 7.5782 largecap18 1.083103 2.855548 -4.9916 7.9184 largecap19 1.130748 3.122399 -6.2623 7.5527 largecap20 1.358823 4.157036 -9.1168 9.0377 largecap21 1.126353 3.524151 -7.5238 7.5175 largecap22 0.87044 2.774038 -5.867 6.6699 largecap23 0.990343 2.759794 -5.9415 8.0281 largecap24 0.963945 2.830934 -5.3382 8.7689 largecap25 0.377493 3.118501 -5.823 7.5928 largecap26 1.065613 2.777599 -5.6593 8.3418 largecap27 1.138025 3.385077 -6.7612 7.7646 largecap28 1.079093 3.311045 -6.5339 9.7422 largecap29 1.111445 2.940886 -6.0786 7.7323 largecap30 1.089843 3.020329 -6.3187 8.7535 largecap31 1.087073 3.00751 -6.1424 8.1031

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largecap32 1.122213 3.293486 -7.2915 8.2133 largecap33 1.048792 2.956924 -5.9527 8.0917 smallcap1 1.274743 4.171614 -7.4127 13.3296 smallcap2 1.227213 3.880896 -7.2721 11.4413 smallcap3 1.251528 3.971076 -6.367 12.3775 smallcap4 1.08527 4.545879 -11.841 8.6003 smallcap5 1.12405 4.160107 -8.7302 10.6321 smallcap6 1.142685 4.160861 -8.0609 12.9545 smallcap7 1.133377 4.201872 -8.8275 10.6533 smallcap8 1.272037 3.947289 -6.4075 12.1121 smallcap9 1.159392 4.081115 -6.7978 12.7551 smallcap10 1.097788 4.473312 -10.847 8.484 smallcap11 1.286278 4.140115 -7.2253 12.9328 smallcap12 1.243898 3.904669 -6.6855 11.4217 smallcap13 0.992538 3.886789 -9.2339 7.5503 smallcap14 1.248473 3.754722 -6.6183 9.8013 smallcap15 1.136912 3.775658 -7.797 8.2646 smallcap16 1.222382 4.568752 -10.513 11.1775 smallcap17 1.163327 3.939003 -8.2465 9.2434 Plargecap 1.058986 2.942435 -5.8559 8.038615 Psmallcap 1.180111 4.020417 -8.0815 10.71661

Table II. Results of two-sided regression analysis of large-cap ETFs using CAPM

ETF Alpha F-Value R-squared largecap1 -0.02218** 542.3** 0.9034 (0.867) (0.0000) largecap2 -0.05176** 968.86** 0.9435 (0.614) (0.0000) largecap3 -0.03521** 2914.44** 0.9805 (0.55) (0.0000) largecap4 -0.06867** 4506.31** 0.9873 (0.16) (0.0000) largecap5 -0.07248** 701.99** 0.9237 (0.554) (0.0000) largecap6 -0.04619** 1142.33** 0.9517 (0.625) (0.0000) largecap7 0.252345** 49.09** 0.4584 (0.364) (0.0000) largecap8 0.087069** 277.24** 0.8270 (0.586) (0.0000) largecap9 -0.03827** 2874.33** 0.9802 (0.52) (0.0000) largecap10 -0.04246** 573.85** 0.9082 (0.746) (0.0000) largecap11 -0.05381** 987.76** 0.9445

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(0.599) (0.0000) largecap12 -0.03872** 1205.48** 0.9541 (0.673) (0.0000) largecap13 -0.08278** 714.99** 0.9250 (0.497) (0.0000) largecap14 -0.04612** 5062.35** 0.9887 (0.306) (0.0000) largecap15 -0.05166** 4253.2** 0.9865 (0.295) (0.0000) largecap16 -0.14459** 515.51** 0.8989 (0.335) (0.0000) largecap17 0.026856** 851.92** 0.9363 (0.799) (0.0000) largecap18 0.119275** 215.87** 0.7882 (0.518) (0.0000) largecap19 -0.0313** 1332.78** 0.9583 (0.726) (0.0000) largecap20 -0.10151** 338.75** 0.8538 (0.649) (0.0000) largecap21 -0.1155** 353.71** 0.8591 (0.534) (0.0000) largecap22 -0.11584** 404.5** 0.8746 (0.401) (0.0000) largecap23 0.000654** 468.12** 0.8898 (0.996) (0.0000) largecap24 0.005883** 221.41** 0.7924 (0.974) (0.0000) largecap25 -0.6612** 191.52** 0.7676 (0.003) (0.0000) largecap26 0.085843** 358.87** 0.8609 (0.555) (0.0000) largecap27 -0.10155** 744.84** 0.9278 (0.427) (0.0000) largecap28 -0.1137** 510.06** 0.8979 (0.444) (0.0000) largecap29 0.041478** 631.03** 0.9158 (0.729) (0.0000) largecap30 -0.04305** 2122.87** 0.9734 (0.533) (0.0000) largecap31 -0.04913** 4571.54** 0.9875 (0.3) (0.0000) largecap32 -0.0875** 813.13** 0.9334 (0.463) (0.0000) largecap33 -0.03442** 752.95** 0.9285 (0.756) (0.0000)

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Table III. Results of two-sided regression analysis of large-cap ETFs using Three-factor model

ETF Alpha F-Value

R-squared largecap1 -0.0544195** 637.02** 0.9715 (0.462) (0.0000) largecap2 -0.103656** 616.78** 0.9706 (0.176) (0.0000) largecap3 -0.0783957** 2778.38** 0.9933 (0.03) (0.0000) largecap4 -0.0963901** 3414.16** 0.9946 (0.004) (0.0000) largecap5 -0.0883114** 671.93** 0.973 (0.241) (0.0000) largecap6 -0.0870451** 608.47** 0.9702 (0.257) (0.0000) largecap7 0.2028762** 21.65** 0.537 (0.442) (0.0000) largecap8 -0.0116321** 144.85** 0.8858 (0.931) (0.0000) largecap9 -0.0804833** 2613.41** 0.9929 (0.031) (0.0000) largecap10 -0.0755616** 787.7** 0.9769 (0.267) (0.0000) largecap11 -0.107292** 722.24** 0.9748 (0.133) (0.0000) largecap12 -0.0746551** 677.13** 0.9732 (0.302) (0.0000) largecap13 -0.0941247** 674.53** 0.9731 (0.213) (0.0000) largecap14 -0.0672246** 3070.77** 0.994 (0.05) (0.0000) largecap15 -0.0840433** 4184.8** 0.9956 (0.005) (0.0000) largecap16 -0.1644256** 314.67** 0.944 (0.155) (0.0000) largecap17 -0.0381981** 516.66** 0.9651 (0.634) (0.0000) largecap18 0.1010139** 70.4** 0.7904 (0.592) (0.0000) largecap19 -0.0665685** 1065.82** 0.9828 (0.262) (0.0000) largecap20 -0.1248352** 205.06** 0.9166 (0.472) (0.0000) largecap21 -0.0496009** 191.96** 0.9114 (0.743) (0.0000) largecap22 -0.1676628** 170.88** 0.9015

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(0.185) (0.0000) largecap23 -0.0883483** 258.64** 0.9327 (0.393) (0.0000) largecap24 -0.0691521** 85.63** 0.821 (0.689) (0.0000) largecap25 -0.7327499** 78.55** 0.808 (0) (0.0000) largecap26 -0.0131563** 194.46** 0.9124 (0.912) (0.0000) largecap27 -0.0739708** 252.72** 0.9312 (0.564) (0.0000) largecap28 -0.1349989** 438.03** 0.9591 (0.165) (0.0000) largecap29 -0.0380751** 383.4** 0.9536 (0.677) (0.0000) largecap30 -0.0968893** 2339.97** 0.9921 (0.015) (0.0000) largecap31 -0.0795401** 4417.52** 0.9958 (0.006) (0.0000) largecap32 -0.0669654** 458.53** 0.9609 (0.477) (0.0000) largecap33 -0.114238** 446.13** 0.9598 (0.184) (0.0000)

** indicate 5% significance level

Table IIII. Results of two-sided regression analysis of large-cap ETFs using Carhart model ETF Alpha F-Value

R-squared largecap1 -0.06119** 470.17** 0.9716 (0.43) (0.0000) largecap2 -0.10915** 454.89** 0.9707 (0.174) (0.0000) largecap3 -0.08229** 2052.37** 0.9933 (0.03) (0.0000) largecap4 -0.09932** 2519.62** 0.9946 (0.005) (0.0000) largecap5 -0.04909** 529.52** 0.9747 (0.518) (0.0000) largecap6 -0.13176** 488.03** 0.9726 (0.09) (0.0000) largecap7 -0.04622** 23.7** 0.6328 (0.851) (0.0000) largecap8 -0.0575** 110.08** 0.889 (0.677) (0.0000) largecap9 -0.07912** 1925.68** 0.9929

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(0.043) (0.0000) largecap10 -0.0759** 580.23** 0.9769 (0.287) (0.0000) largecap11 -0.10623** 532.04** 0.9748 (0.156) (0.0000) largecap12 -0.10896** 527.18** 0.9746 (0.142) (0.0000) largecap13 -0.04697** 548.29** 0.9755 (0.531) (0.0000) largecap14 -0.05944** 2290.41** 0.994 (0.094) (0.0000) largecap15 -0.07972** 3098.54** 0.9956 (0.011) (0.0000) largecap16 -0.07975** 267.37** 0.9511 (0.478) (0.0000) largecap17 -0.08447** 413.58** 0.9678 (0.297) (0.0000) largecap18 0.0025** 56.29** 0.8037 (0.99) (0.0000) largecap19 -0.08839** 811.16** 0.9833 (0.15) (0.0000) largecap20 -0.01372** 168.43** 0.9245 (0.937) (0.0000) largecap21 -0.04889** 141.4** 0.9114 (0.758) (0.0000) largecap22 -0.23867** 137.05** 0.9088 (0.063) (0.0000) largecap23 -0.11506** 193.74** 0.9337 (0.286) (0.0000) largecap24 -0.03366** 63.84** 0.8228 (0.852) (0.0000) largecap25 -0.66937** 59.62** 0.8126 (0.002) (0.0000) largecap26 -0.05704** 148.39** 0.9152 (0.641) (0.0000) largecap27 -0.12559** 193.98** 0.9338 (0.342) (0.0000) largecap28 -0.09006** 340.44** 0.9612 (0.362) (0.0000) largecap29 -0.09085** 307.22** 0.9572 (0.325) (0.0000) largecap30 -0.10497** 1741.31** 0.9922 (0.012) (0.0000) largecap31 -0.07641** 3263.41** 0.9958 (0.012) (0.0000) largecap32 0.014189** 411.26** 0.9676 (0.874) (0.0000) largecap33 -0.18309** 389.25** 0.9659

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(0.03) (0.0000) ** indicate 5% significance level

Table VII. Results of two-sided regression analysis of small-cap ETFs using CAPM

ETF Alpha F-Value

R-squared smallcap1 -0.1163326** 193.46** 0.7693 (0.679) (0.0000) smallcap2 -0.0545732** 178.48** 0.7547 (0.839) (0.0000) smallcap3 -0.0739225** 195.05** 0.7708 (0.781) (0.0000) smallcap4 -0.4349087** 198.31** 0.7737 (0.155) (0.0000) smallcap5 -0.2763894** 210.59** 0.7841 (0.31) (0.0000) smallcap6 -0.2308316** 177.7** 0.7539 (0.426) (0.0000) smallcap7 -0.2816368** 211.3** 0.7846 (0.305) (0.0000) smallcap8 -0.0416234** 190.18** 0.7663 (0.876) (0.0000) smallcap9 -0.1668012** 157.3** 0.7306 (0.574) (0.0000) smallcap10 -0.3991118** 199.48** 0.7747 (0.183) (0.0000) smallcap11 -0.0859854** 183.78** 0.7601 (0.762) (0.0000) smallcap12 -0.027619** 159.78** 0.7337 (0.922) (0.0000) smallcap13 -0.3559745** 288.95** 0.8328 (0.114) (0.0000) smallcap14 -0.0749568** 354.97** 0.8596 (0.704) (0.0000) smallcap15 -0.1976144** 369.61** 0.8644 (0.312) (0.0000) smallcap16 -0.1998017** 117.98** 0.6704 (0.587) (0.0000) smallcap17 -0.2153621** 322.56** 0.8476 (0.319) (0.0000)

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Table VIII. Results of two-sided regression analysis of small-cap ETFs using Three-factor

model

ETF Alpha F-Value R-squared smallcap1 0.076473** 351.23** 0.9495 (0.572) (0.0000) smallcap2 0.176332** 215.28** 0.9202 (0.267) (0.0000) smallcap3 0.130478** 294.28** 0.9404 (0.352) (0.0000) smallcap4 -0.11726** 724.64** 0.9749 (0.261) (0.0000) smallcap5 -0.02392** 689.36** 0.9736 (0.806) (0.0000) smallcap6 -0.03631** 335.89** 0.9474 (0.792) (0.0000) smallcap7 -0.02816** 656.92** 0.9724 (0.78) (0.0000) smallcap8 0.169804** 326.72** 0.946 (0.202) (0.0000) smallcap9 0.033102** 331.5** 0.9467 (0.807) (0.0000) smallcap10 -0.087** 737.06** 0.9753 (0.392) (0.0000) smallcap11 0.103232** 333.56** 0.947 (0.453) (0.0000) smallcap12 0.206286** 190.7** 0.9108 (0.223) (0.0000) smallcap13 -0.13327** 531.92** 0.9661 (0.2) (0.0000) smallcap14 0.0506** 446.2** 0.9598 (0.641) (0.0000) smallcap15 -0.01923** 660.84** 0.9725 (0.831) (0.0000) smallcap16 0.132481** 362.54** 0.951 (0.365) (0.0000) smallcap17 -0.01408** 911.76** 0.9799 (0.861) (0.0000)

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Table VIIII. Results of two-sided regression analysis of small-cap ETFs using Carhart model ETF Alpha F-Value

R-squared smallcap1 0.0172453** 271.41** 0.95180 (0.901) (0.0000) smallcap2 -0.0141191** 245.88** 0.94700 (0.917) (0.0000) smallcap3 -0.0167669** 296.42** 0.95570 (0.894) (0.0000) smallcap4 -0.2026031** 635.26** 0.97880 (0.046) (0.0000) smallcap5 -0.1472472** 815.9** 0.98340 (0.073) (0.0000) smallcap6 -0.1808917** 337.05** 0.96080 (0.15) (0.0000) smallcap7 -0.1581268** 796.46** 0.98300 (0.06) (0.0000) smallcap8 0.0348137** 321.49** 0.95900 (0.773) (0.0000) smallcap9 -0.1169602** 345.78** 0.96180 (0.334) (0.0000) smallcap10 -0.1861327** 701.32** 0.98080 (0.051) (0.0000) smallcap11 0.0361106** 260.87** 0.94990 (0.796) (0.0000) smallcap12 -0.0016852** 225.17** 0.94240 (0.99) (0.0000) smallcap13 -0.1478076** 393.68** 0.96630 (0.174) (0.0000) smallcap14 -0.0258071** 373.12** 0.96450 (0.809) (0.0000) smallcap15 -0.0852688** 557.66** 0.97590 (0.337) (0.0000) smallcap16 0.0058019** 326.58** 0.95960 (0.967) (0.0000) smallcap17 -0.092149** 862.82** 0.98430 (0.219) (0.0000)

Abnormal performance of US large-cap exchange-traded funds