Evidence of Idiosyncratic Seasonality in Etfs Performance

n. 603 Apr 2018 ISSN: 0870-8541

Evidence of Idiosyncratic Seasonality in ETFs Performance

Carlos Francisco Alves 1,2 Duarte André de Castro Reis 1

1 FEP-UP, School of Economics and Management, University of Porto 2 CEF.UP, Research Center in Economics and Finance, University of Porto Evidence of Idiosyncratic Seasonality in ETFs Performance

Carlos Francisco Alves

Faculty of Economics, CEF.UP, University of Porto, 4200-464 Porto, Portugal. Email: [email protected]

Duarte André de Castro Reis

Faculty of Economics, University of Porto, 4200-464 Porto, Portugal.

Version: January 2018

______Abstract Studies of the seasonality of ETFs are relatively scarce compared with other financial assets. Moreover, most of the existing literature on ETFs did not assess the seasonality patterns of risk-adjusted returns and tracking error. This article seeks to suppress some of these gaps. The results provide evidence of a first-half of the year effect (higher returns), an outperformance of the second quarter and an underperformance of the fourth quarter compared with the remaining quarters, and higher (lower) returns in the first (third) month of the quarter vs the other months of the quarter. Furthermore, April exhibits a superior and December an inferior performance compared with the remaining months. Besides, higher (lower) returns on Wednesdays (Fridays) were observed compared with the other weekdays. Regarding the tracking error, some seasonal patterns are also reported. For example, the replication was more accurate in April than it was in remaining months and in the first month of each quarter. Finally, the effects detected in ETFs returns were not reflected in indices returns, with the exception of the April effect, indicating that the main seasonality patterns detected are caused by idiosyncratic ETFs factors and not to the constituents of the underlying indices.

Keywords: ETFs seasonality; indices seasonality; raw returns; risk-adjusted returns; tracking error; US equity. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

 The Research Center in Economics and Finance (CEF.UP) is supported by the Foundation for Science and Technology (FCT) through the Operational Program for Science, Technology and Innovation (POCTI) of the Community Support Framework (QCAIII), financed by the European Regional Development Fund (ERDF) and Portuguese funds. This project was specifically supported by FCT and by the Programa Operacional Temático Factores de Competitividade (COMPETE), supported by the European program FEDER. 1. Introduction

There is an ample literature that seeks to detect and explain the seasonal patterns of returns in stock markets (e.g., Keim, 1983; Jaffe and Westerfield, 1985; Reiganum, 1983; Damodaran, 1989; Kim and Park, 1994; Booth et al., 2001), as well as research that proceeds to a similar scrutiny of bonds (e.g., Jordan and Jordan, 1991; Dbouk et al., 2013), mutual funds (e.g., Gallagher and Pinnuck, 2006; Alves, 2014), and pension funds (e.g., Andreu et al., 2013). The effects documented in this literature include, among others, the January effect (e.g., Rozeff and Kinney, 1976; Gultekin and Gultekin, 1983; Nippani and Arize, 2008; Sikes, 2014), the pre-holiday effect (e.g., Cadsby and Ratner, 1992; Teng and Liu, 2016), turn of the month effect (e.g., Ariel, 1987; Ogden, 1990; Maher and Parikh, 2013), and the weekday effect (e.g., Cross, 1973; Chen and Singal, 2003; Lin and Chen, 2008). More recently, some studies have reported the disappearance and even the reversal of some of these phenomena in some periods of history.

This literature is important because it can allow the identification of arbitrage opportunities (and their disappearance), as well as symptoms of anomalies in asset valuation models that may derive from their inability to incorporate properly all the risk- generating factors, or from behavioral factors that are not considered determinant of the equilibrium returns. It is, therefore, important to detect these return patterns, and understand the reasons for their existence.

In the case of passive management funds, which simply try to replicate a benchmark index, knowing this reality is even more important, as eventual seasonality may be derived not from underlying asset market, but from idiosyncratic fund market factors. Therefore, it is crucial to know whether there are seasonal patterns in the returns of this type of funds, and, if seasonal patterns are detected, understand whether their origin is due to the assets in which the funds invested, the behavior of their managers, or other factors specific to the industry.

However, the published studies about seasonal patterns of the returns of passive funds are, in contrast to other financial instruments, scarce. Even the few that are known do not analyze or compare the returns among certain calendar periods. This article seeks to contribute to the suppression of these gaps by looking for seasonal patterns in the returns

2 of Exchange-Traded Funds (ETFs), as well as by seeking to understand whether these patterns are caused by the underlying asset market or to idiosyncratic factors. In particular, this work seeks to answer the following questions. 1) Is there evidence of seasonality in the returns and tracking error of ETFs? 2) Do the seasonal patterns in the return of ETFs differs from the underlying indices, indicating that this seasonality is due to idiosyncratic factors in the ETFs industry, or are they identical to the underlying indices, indicating that this seasonality is induced by the constituents of the underlying index?

This study uses a sample of 148 equity ETFs with a geographical focus in the US and traded in the NYSE Arca. Raw returns and risk-adjusted returns were calculated using the market model and the Carhart model (1997). The calculations of the returns and tracking error were performed based on the prices and NAV of the ETFs, and the seasonality of the benchmark indices was investigated. In terms of econometric models to test the seasonality, the models of Marquering et al.(2006) and Alves (2014) were used. The data were obtained mainly from Thomson Reuters Eikon databases (Datastream), but also from other databases (in particular additional information on benchmark indices).

Regarding the results obtained, there is evidence of higher returns in April (risk-adjusted and not-adjusted) and the first half of the year (risk-adjusted). December month is the month with the lowest risk-adjusted returns. Moreover, the ETFs have better performance (risk-adjusted returns) in the second trimester and worse performance in the fourth quarter. The first (third) month of each trimester exhibits higher (lower) risk-adjusted returns than the remaining months of that quarter. Friday (Wednesday) presents lower (higher) performance compared with other days regarding the risk-adjusted returns.

Finally, the seasonal patterns detected in ETFs are not reflected on the indices replicated, indicating that the seasonality patterns are due to idiosyncratic ETFs factors and not to the underlying asset market.

The remainder of the article is organized as follows. Section 2 reviews the previous literature on the seasonality of Stocks, Bonds, Funds, and ETFs, Section 3 describes data and the methodology used in this study, and Section 4 presents the empirical results. A conclusion is presented in Section 5.

2. Literature Review

Numerous studies have been published that identified behavioral patterns in the average returns of several financial assets, mainly stocks. Researchers show evidence of abnormal and persistent returns patterns according to calendar periods.

2.1 Seasonality in Stock Markets

(i) January Effect

The January effect is characterized by higher average returns in January compared with the remaining months. This phenomenon was documented by Rozeff and Kinney (1976) in a study that focused on several stock indices listed on New York Stock Exchange (NYSE) from 1904 to 1974. The results of that study were, however, highly sensitive to the index used (Ritter, 1988). However, further works confirmed the January effect and revealed that this is a phenomenon primarily affecting the small capitalization companies. Keim (1983) indicated that the average daily returns in January of companies listed in the NYSE and American Stock Exchange (AMEX) for 1963 to 1976 are higher than those of the remaining months, and that the first week and the first trading day are the periods that contribute most to the January effect. Additionally, the same study showed the existence of a negative relation between abnormal returns and size, which was more pronounced in January than in the other months.

In another article, Reinganum (1983) used data from the NYSE and AMEX from 1963 to 1980 and also found evidence of high returns in January relative to the remaining months of the year for companies with a small size, mostly in the first trading days. Similarly, Fama (1991) obtained results consistent with the January effect for the US market from 1941 to 1991.

The January effect has also been documented in international markets. Gultekin and Gultekin (1983), in an analysis of 17 of the most industrialized countries, found the presence of the January effect for most of those countries from 1959 to 1979.

The same effect was documented for Canada between 1950 and 1980 by Berges et al. (1984) and Tinic et al. (1987). Moreover, Corhay et al. (1987) documented the January effect for France and Belgium from 1968 to 1983. In the British market, Reinganum and

Shapiro (1987) found evidence of the same effect between 1955 and 1980.

In terms of explanations for the phenomenon, Reinganum (1983) suggests tax-loss-selling as a cause of the January effect. This hypothesis states that, at the end of the year, investors sell the stocks that have experienced a decline in price over the year, thus recording losses to reduce the amount of tax to pay. These transactions cause the decline of stock prices at the end of the year. In January, these stocks are repurchased at a lower price, which explains the abnormal returns at the beginning of the year.

There are, however, studies that contradict the tax-loss-selling hypothesis (Gultekin and Gultekin, 1983; Berges et al.,1984). For example, Gultekin and Gultekin (1983) studied the Australian market from 1959 to 1979. In Australia, the calendar year does not coincide with the tax year, the latter ending at the end of June. Although the tax year differs from the calendar year, the January effect is observed and evidence of an excessive return in July was not found, which contradicts the tax-loss-selling hypothesis.

Some authors suggest window dressing as an explanation for the January effect - “just prior to year-end, institutional investors buy stocks with positive priors returns (“winners”) and sell stocks with negative prior returns (“losers”) to present attractive year-end portfolio holdings to their clients” (Sikes, 2014, p.23).

Other theories are presented in the literature. For example, Anderson et al. (2007) refer to psychological factors, while Sun and Tong (2010) reexamine the risk argument, concluding that the January effect is not caused by the risk itself.

It should be noted that some recent studies support a decline of the January effect or even its disappearance. In fact, Gu (2003) found evidence of a pronounced declining trend of the January effect since 1988. Marquering et al. (2006) indicated the disappearance of the January effect in the US stock market after Rozeff and Kinney (1976) documented the January effect. Finally, Patel (2016) also found evidence that the January effect is no longer perceptible in stock markets for the period from January 1997 to December 2014.

(ii) Pre-Holiday Effect

The pre-holiday effect is also documented in the literature and consists in abnormal higher returns on the day preceding holidays. Cadsby and Ratner (1992) identified the pre- holiday effect in the US, Canada, Japan, Hong Kong, and Australia. This effect was

5 detected for the holidays of each place. Hong Kong also exhibited higher returns in the day prior to holidays in the US. In European countries studied, there was no pre-holiday effect. Kim and Park (1994) also reported the existence of abnormal returns for the US stock market on the day before holidays, from 1963 to 1986. Furthermore, there is evidence of the pre-holiday effect in the UK and Japan stock market for the period from July 1972 to June 1987. The pre-holiday effects found in these markets are independent of the pre-holiday effect of the US market, i.e., the US market effect is not transmitted to the UK and Japan market.

Despite the multiple studies that provide evidence of the pre-holiday effect, more recent studies have indicated the diminishing of this anomaly or even its disappearance.

In fact, the work of Marquering et al. (2006) supports, the contention that, after its documented by Lakonishok and Smidt (1988) the pre-holiday effect no longer exists for US market, while Chong et al. (2005), based on data from the US, the UK, and Hong Kong markets from January 1973 to July 2003, concluded that the three markets presented a decrease in the pre-holiday effect. However, this reduction was only significant for the US market until 1990. From 1991 to 1997, the average daily return in the day before holidays in the US market became negative, and from 1997 to 2003 the effect was eliminated.

As an explanation for this reversal effect, Chong et al. (2005) suggest that the market participants define trading strategies based on historical studies that do not reflect the current market patterns. Thus, when market participants try to exploit anomalies that no longer exist, they end up creating new patterns of seasonality.

In terms of explanations for the phenomenon, Teng and Liu (2016) defend a behavioral thesis, indicating that the investors exhibit signs of higher positivism and greater propensity to buy stocks on the day before holidays.

(iii) The Turn of the Month Effect

The turn of the month effect is associated with abnormal higher returns on the last days of trading of the month and in the first days of trading of the following month. In this context, Ariel (1987) analyzed the CRSP equally-weighted index and CRSP value- weighted index from 1963 to 1981 and obtained evidence of higher returns on the days

6 around the turn of the month. Lakonishok and Smidt (1988) also encountered abnormal higher returns at the turn of the month through the analysis of daily data of DJIA over 90 years (1897-1986).

Several studies focused on countries other than the US. For example, Cadsby and Ratner (1992) found evidence that the turn of the month effect is significant in Germany, Australia, Canada, the US, the UK, and Switzerland. Kunkel et al. (2003) reported the existence of higher returns at the turn of the month in 16 out of 19 markets analyzed for the period of 1988 to 2000.

In their study of seasonality, Maher and Parikh (2013) found the presence of the turn of the month effect in the Indian market. This effect was significant during the rising, but not during the falling of the market. In addition, these authors propose the portfolio- rebalancing hypothesis as a cause of the higher returns observed at the turn of the month. According to this hypothesis, institutional investors structure their purchases at the end of the month with the aim of improving the performance indicators, given the fact that these are usually calculated based on end-of-the-month prices. This idea can be reinforced by the fact that institutional investors increase their trading volume at the end of the month, both for the International market and for the Indian market, and by the evidence reported by Maher and Parikh (2013) of the existence of a positive relationship between trading volume and return.

Alternatively, Ogden (1990) and Booth et al. (2001) suggest the liquidity hypothesis - the standardization of the payment system in the US stimulates an increase in demand for stocks around this time, as investors have more money, which results in an increase of stock returns in this period.

(iv) Weekday and Weekend Effects

The weekday effect or the weekend effect is characterized by the presence of abnormal returns on specific days of the week, and in particular by the fact that the stock markets present abnormally high average returns on Fridays and abnormally low average returns on Mondays (Jaffe and Westerfield, 1985).

Cross (1973) and Gibbons and Hessen (1981) found evidence of this anomaly in the US market between the 50s and the 70s. Still pertaining to the US market, Harris (1986)

7 indicated that, in the first 45 minutes after the market opens on Mondays, the prices tend to decline, while in the remaining days prices tend to increase. This study was performed using data of the NYSE from December 1981 to January 1983.

The weekday effect has been the subject of study in other markets. The weekend effect was documented by Jaffe and Westerfield (1985) for the US, the UK, Japan, Canada, and Australia. However, Australia and Japan exhibited a lower average return on Tuesdays and not on Mondays. In their study, Charles (2010) verified the existence of the weekday effect in the European indices of Athens (ATHEX), Paris (CAC 40), and Dublin (ISEQ).

Some studies have reported a decline or even the disappearance of this effect. Olson et al. (2015) examined some indices of the US stock market and concluded that, after 1973 the weekday effect declined, followed by a reappearance in later periods, and a subsequent reduction. Marquering et al. (2006) indicated that the weekend effect started to diminish after the study of Cross (1973), which documented this anomaly.

Short positions were one of the factors that were mentioned most often to explain the weekend effect – “the inability to trade over the weekend causes short sellers to close their speculative positions on Fridays and reestablish new short positions on Mondays, causing stock prices to rise on Fridays and fall on subsequent Mondays” (Gao et al., 2015, p. 86). Chen and Singal (2003) defended this hypothesis as a cause of the weekend effect through a study that was performed using data from the CRSP (1962 to 2002).

Another explanation that has been suggested for this effect is that of Damodaran (1989), who indicated that companies release bad news after the close on Friday or toward the weekend, thus leading to a higher probability of negative returns on the following Monday.

2.2 Seasonality in Bond Markets

Regarding the bond market, as for stocks, the literature reports some seasonal patterns in returns. In this context, Jordan and Jordan (1991) studied the Dow Jones Composite Bond Average (DJCBA) for the period of 1963 to 1986 and found evidence of the January effect, turn of the year effect, and distinct return patterns during the different weeks within

8 each month1. However, seasonal patterns were not detected on weekdays and at the turn of the month. Similarly, Nippani and Arize (2008) detected the presence of turn of the year and January effects for three bonds indices of US companies, and also verified the presence of the Monday effect.

Moreover, Dbouk et al. (2013) obtained results that show the presence of the January effect. The analysis was performed for the period from 1995 to 2010 based on daily prices of individual bonds of public firms from the industrial, financial, and utility sectors and were not based on indices. These authors mentioned that, despite the observation that this effect was statistically significant, it was not economically significant. For them, the main cause of the Bonds January effect is tax-loss-selling.

Finally, Hamid (2014) did not find month-based seasonal patterns in US bonds from 1926 to 2013.

2.3 Seasonality in Fund Performance

Studies of the seasonality of closed-end funds, mutual funds, and pension funds are relatively scarce compared with studies on stock markets.

For closed-end funds of municipal bonds, Starks et al. (2006) found, for the period of 1990 to 2000, evidence of the January effect and that this is mainly explained by the tax- loss-selling hypothesis. The seasonal pattern detected in funds price is not observed in the underlying assets, and is, therefore idiosyncratic, i.e., it has an origin in funds and not in the markets where they invest.

Regarding the equity mutual funds, the studies of Gallagher and Pinnuck (2006), Lin and Chen (2008) and Alves (2014) were found. The former is a study of the Australian active funds from January 1990 to December 1997 and concluded that the performance of the funds was higher during the months in which the results are announced and inferior in the months prior to the end of the tax year. Furthermore, the existence of abnormal returns in December was observed, which possibly could be related to the window dressing and to the effect of the Christmas holidays. Lin and Chen (2008) found evidence of negative returns on Mondays and positive returns on Fridays in the Taiwan funds from January

1 Higher returns in the second week and lower returns in forth week when compared with the remaining weeks.

1986 to June 2006. Finally, Alves (2014) focused on the European market for the period of 2003 to 2012 and showed that the first six months presented a superior performance compared with the last six months of each year. Although the causes of this seasonal pattern were not studied, Alves (2014) indicated that this pattern could be the result of funds with weak performance at the beginning of the year trying to change their portfolios (increasing risk), to obtain better results at the end of the year. Evidence that the funds presented inferior returns in the first month compared with the remaining months of the trimester was also obtained. This pattern could be explained by the postponement of losses for the following quarter (where there would still be time for a possible recovery) seeking to improve the performance of the current trimester (where there is not sufficient time for recovery).

Lastly, in terms of pension funds, Andreu et al. (2013) studied the seasonality of Spanish pension funds. The results indicated that the funds with outperformance from January to November were penalized in December. For the author, the most probable cause for the anomaly detected is the window dressing.

2.4 Seasonality in Exchange-Traded Funds

Regarding the seasonality of ETFs, there is a small number of studies available that attempted to determine if the seasonality patterns documented in the past for other assets exist in ETFs.

Among these studies, Mazumder et al. (2008) investigated the seasonality patterns on weekdays using 17 iShares2 (17 countries) and the Standard and Poor´s Depositary Receipts (SPDR) from March 1996 to December 2003. This study reported evidence of the Monday effect for 7 of the 17 iShares under scrutiny. Thursday exhibited negative returns in 16 of the 17 iShares, and this effect was also observed in the US market; however, the Monday effect was larger in magnitude than was the Thursday effect for 5 out of the 7 iShares that registered the two effects. The risk measured by the standard deviation was superior on Mondays in 8 of the 17 iShares and inferior on Fridays in 8 of the 17 iShares compared with the remaining days.

Additionally, the Modern Index Strategy Indices (MSCI) country indices returns were

2 iShares is a leading ETF provider managed by BlackRock.

10 used to understand if the effects reported for the iShares are similar to the underlying indices. Based on that analysis between ETFs and indices it can be concluded that the average returns and risk of most of iShares are higher than the average return and risk of the underlying indices. Furthermore, despite the similarity of registered effects between the two, the magnitude of the effects of the iShares was higher than that of the indices. This study supports the thesis of an idiosyncratic origin for the seasonality pattern and, in this regard, is consistent with the results of Starks et al. (2006).

The Turn of the Month effect was reported by Chen and Chua (2011) for SPDR ETF and S&P 500 from 1993 to 2010. In addition, Chen et al. (2015) extended the study of this effect to international ETFs (9 markets). The analysis focused first on the verification of the existence of the turn of the month effect in the returns of the indices and then in the returns of ETFs. The results indicate the existence of the turn of the month effect for 8 of the indices studied, with the exception of the Japanese market. With respect to ETFs, all studies point to the existence of the TOM effect.

In a study that used a broad scope relative to the type of financial instrument analyzed, Agrrawal and Skaves (2015) looked at four calendar effects - the January effect, the Halloween effect3, the Mark Twain effect4, and the Santa Claus rally effect5 - in US and international stocks, bonds, real estate, and gold bullion via ETFs. The results indicate the absence of the January effect, thus contradicting most of the literature about stocks, which demonstrated the existence of that effect. December, March, and April have higher and more consistent returns than January. Regarding the Halloween effect, the existence of a robust effect was verified, with the exception of the Long-Term US Treasuries (TLT) and the short-term US Treasuries (SHY). The December effect prevailed for the equity assets. Lastly, no evidence of the Mark Twain effect was reported.

In summary, the set of studies that analyzed seasonal patterns of ETFs is small. Table 1 lists a synthesis of these studies.

3 The November to April period had higher returns than did the November to October period. 4 This effect was characterized by significantly lower returns in October than in other months. 5 Positive average returns in December, coinciding with the holidays.

TABLE 1. SUMMARY OF THE PERFORMANCE SEASONALITY PATTERNS OF ETFS

DOCUMENTED IN THE LITERATURE

Nº of ETFs / Type of asset Geographic focus Author Main seasonality patterns detected Analysis period

US and International

(Australia, Austria, Belgium, Canada, 18 / March of France, Germany, Hong Mazumder Kong, Italy, Japan, 1996 to Equity ETFs et al. Monday effect and Thursday effect December of Malaysia, Mexico, (2008) Netherlands, Singapore, 2003 Spain, Sweden, Switzerland, and United Kingdom)

1 / January of Chen and Equity ETFs US 1993 to April of Chua Presence of the turn of the month on the SPY (SPDR ETF) 2010 (2011)

9 / March of International (Australia, 1996 to October Brazil, Canada, France, of 2012 and from Chen et Equity ETFs Germany, Hong Kong, Turn of the month effect for the ETFs under July of 2000 to al. (2015) analysis Japan, Sweden, and October of 2012 United Kingdom) for Brazil

Absence of the January and Mark Twain 10 / 2005 – 2014 Agrrawal Equity, bonds, real effects; presence of the Halloween effect, and 2001 – 2014 and estate and gold US and International with the exception of the TLT (long-term for SPY and Skaves U.S. Treasuries) and SHY (short-term U.S. bullion ETFs IWM (2015) Treasuries), and December effect for the equity assets.

This Table shows that, despite the existence of some seasonality patterns reported for the ETFs, the literature pertaining to that type of financial instrument remains scarce. For example, no analysis was found relative to the pre-holiday effect and to the seasonality patterns of semesters, quarters, and months of quarters. Furthermore, these studies did not assess the seasonality patterns of risk-adjusted returns or tracking error, despite their importance in ETFs. Therefore, this article aims to suppress some of the existing gaps in the study of the seasonality of ETFs, not only for adjusted and not-adjusted returns, but also regarding the tracking error. It also seeks to contribute to the understanding of whether the seasonality is due to the market of underlying assets, or if is created by the industry of funds.

3. Methodology and Data

3.1. Sample Selection and Databases

The ETFs that were the object of the study were selected among those listed in the Fund Screener (between April and May of 2016) tool available on the Thomson Reuters Eikon databases. ETFs selection was performed using the following criteria: listed on the NYSE Arca; classified by the Lipper Global as US equity; having a domicile and geographical focus in the US; registered for sale in the US; and having an index tracking strategy. The sample include active, liquidated, and merged funds. In total, 148 ETFs were included in this study.

The fact that the US ETFs market is the largest one justifies its selection here6. Within this market the passively managed ETFs (index tracking) are those that have achieved the highest level of success7. Furthermore, those are the most adequate funds to evaluate the seasonality of the tracking error and, the possible idiosyncratic nature of this seasonality. The utilization of the US equity ETFs in this study is explained by the fact that these ETFs represent the highest percentage of US ETFs8. The inclusion of liquidated and merged ETFs aimed to eliminate any problems of survivorship bias.

The NAVs and prices were obtained from the Thomson Reuters Eikon databases. Regarding the indices that the ETFs try to replicate, in addition to the Thomson Reuters Eikon databases , the Bloomberg database, Yahoo Finance, Google Finance, and the internet pages of NYSE Arca, ETFs, and indices were also used. The factors used in the one-factor model and four-factor models were obtained from the internet page of Professor Kenneth French.

The data were collected from 12/31/2004 to 12/31/2015.

6 In 2014, according to the 2015 Investment Company Fact Book of the Investment Company Institute, the US represented 73% of the ETFs world market. 7 NextShares Solutions LLC (2015). 8 The US Equity ETFs represent approximately 59% of 2015 US ETFs market, according to the 2016 Investment Company Fact Book of the Investment Company Institute.

3.2. Returns and Tracking error

The raw returns were calculated based on Logarithms (continuous returns). Regarding the risk-adjusted returns, similarly to Alves (2014), the one-factor model (as a traditional measure) and the four-factor model of Carhart (1997) (as a multifactor model) were used; i.e., they were calculated based on models with the following specification:

푘 푅푝,푡 = 훼푝 + ∑푗=1 훽푝,푗 푟푗,푡 + 휇푝,푡 [1] where Rp,t is the excess return on ETFp over the risk-free asset on day t, αp is the performance measure of ETFp, Bp,j is the loading applied to factor j, and μp,t is the idiosyncratic risk of ETFp. For the one-factor model, k is equal to one and r1,t corresponds to market excess return over the risk-free asset. For the four-factor model, k equals 4 and

3 other factors are added to the first factor (r1,t): small-minus-big effect (SMB), high- minus-low effect (HML), and momentum effect (MOM). The SMB is the difference in returns between portfolios with small-capitalization and large-capitalization, the HML is the difference in returns between portfolios of stocks with high and low book-to-market ratios, and MOM is the difference in returns between stocks with best and worst recent- past performances.

The measure of performance αp is the risk-adjusted return measure, as it represents the

ETFs return given its exposure to the risk factors. Thus, it can be said that αp is a measure that indicates if the ETF can beat the market or not on a risk-adjusted base. In the case that it is positive and significantly different from zero, it can be said that the ETF presents an abnormal performance, based on the exposition to risk factors, this measure being obtained only for one factor in one case and in for four factors in the other.

The tracking error is the difference between the performance of an ETF and the underlying benchmark. In fact, Larsen and Resnick (1998) presented one measure of the tracking error that is based on the absolute difference between the return obtained by the ETF and the benchmark index. Its formula is as follows:

∑푛 |푒 | 푇퐸 = 푡=1 푗,푡 [2] 1 푛

푒푗,푡 = 푅푗,푡 − 푅푏,푡, where Rj,t is the return of ETFj in the period t, Rb,t is the return of the benchmark index in period t, and n is the number of observations.

Alternatively, Pope and Yadav (1994) used one measure of the tracking error that is based on the standard deviation of return differences between the ETF and the benchmark index. Its formula is as follows:

∑푛 (푒 −푒̅ )2 푇퐸 = √ 푡=1 푗,푡 푗,푡 [3] 2 푛−1 where 푒푗̅ ,푡 is the average difference of the return and n is the number of observations.

However, estimations based on equation [3] are generally biased for data with a high frequency. The annualized standard deviation of return differences measured over daily intervals will not be a good estimate of the expected standard deviation of longer-interval returns differences, because daily return differences will almost certainly be serially correlated (Pope and Yadav, 1994).

Thus, as the present study was based on daily returns, the measure of tracking error based on the absolute difference between the return of the fund and the index was used (equation [2]).

3.3. Econometric Model to Test Seasonality

This analysis aimed to verify the existence of patterns in months of the year, quarters of the year, semesters of the year, months of quarters, the day before holidays9, weekdays, and turn of the month (-1+3)10. For reasons of presentation simplification, X in equation

[4] is Rt (raw returns) or TEt (tracking error). The econometric model used to verify the existence of the seasonality patterns was the following:

푋푡 = 훽0 + 훽1퐷푚푡 + 휇푡 [4]

Where the dependent variable is the attribute (X - raw return or tracking error) in period t, β0 and β1 are the coefficients of the model to estimate, Dmt is the dummy variable, which assumes the value of 1 if X occurs in a specific period and 0 otherwise, and µt represents

9 The public holidays studied were the following: New Year’s Day, Martin Luther King Jr. Day, George Washington’s Birthday, Good Friday, Memorial Day, Independence Day, Labor Day, Thanksgiving Day, and Christmas Day. 10 According to Kunkel et al. (2003), the four-day turn of the month window was used – the last day of the month and the three first days of the new month.

15 the random error. The intention of this calculation is to determine if the estimated value for β1 is significantly distinct from zero.

Regarding the risk-adjusted returns, in an analysis using the one-factor model and four- factor model a dummy variable was added, similar to Alves (2014):

푘 푅푀푝,푡 = 훼0,푝 + 훼1,푝퐷푚푡 + ∑푗=1 훽푝,푗 푟푗,푡 + 휇푝,푡 [5]

Thus, when Dmt = 1, the performance of ETF p is the sum of α0,p and α1,p; and when Dmt

= 0, the performance is α0,p. Therefore, the incremental performance of fund p due to Dmt

= 1 is α1,p.

4. Empirical Results

This section provides a detailed analysis of the data collected by applying the econometric tests presented in the previous chapter and statistical tests, with the purpose of investigating the existence of seasonal patterns in ETFs raw returns, in risk-adjusted returns, and in tracking error. The effects detected in risk-adjusted and non-risk-adjusted ETFs returns are compared to those obtained by the indices, with the aim of verifying whether the seasonal patterns of ETFs are idiosyncratic to the funds or are induced by the underlying assets.

Table 2 reports the statistics of the raw returns of price, NAV (Panel A), and price minus NAV (Panel B) of an equally weighted average portfolio (EWAP) composed of all ETFs according to the total period (2005 to 2015), semester, quarter, month of the quarter, month of the year, turn of the month, day before holidays, and weekday.

The average raw returns of ETFs portfolios based on price and NAV, as shown in Panel A, are very similar, highlighting the role of the creation/redemption mechanism, which empowers the price to remain close to the NAV. The reduced average difference between the price - NAV returns of Panel B proves the similarity between the two raw returns.

As shown in Panel A, the price and NAV returns of the first month of the quarter exceeded those of the remaining months of the quarter. With respect to month of the year, April outperformed, and June underperformed the remaining months of the year regarding price and NAV. In terms of weekdays, Tuesday was the day with the highest and Monday was the day with the lowest average return for price and NAV. The day prior to holidays and June exhibited the biggest and the smallest price and NAV returns, respectively.

Despite the results exposed in the previous paragraph, the t-tests11 on the difference of means presented in Panel A of Table 2 revealed the inexistence of statistically significant differences. The same test was applied to price minus NAV returns and the outcomes indicate the absence of differences between the different periods.

11 The t-test requires the following conditions to be satisfied simultaneously: a) the dependent variable has a normal distribution; and b) the variance population is homogeneous. The first condition is assumed by the central limit theorem. The Levene test is used to determine if the second requirement is fulfilled. When the second condition is not met, Welch´s correction is applied to the t-test.

TABLE 2. RAW RETURNS

Panel B: price minus NAV Panel A: price and NAV returns returns

Standard Nº of Nº of Average Average Average (%) Maximum (%) Minimum (%) T-statistics T-statistics deviation (%) positives negatives differences (%) differences (%)

Price NAV Price NAV Price NAV Price NAV Price NAV Price NAV Price NAV Price NAV Total time analysis All Time 0,01 0,01 0,49 0,55 4,18 4,77 -3,81 -4,18 1 519 1 496 1 250 1 273 ------Half-year analysis 1st half of the year 0,01 0,01 0,43 0,47 2,65 2,88 -2,26 -2,38 751 739 618 630 0,00 0,00 -0,09 -0,08 0,00 0,00 2nd half of the year 0,01 0,01 0,54 0,62 4,18 4,77 -3,81 -4,18 768 757 632 643 0,00 0,00 0,09 0,08 0,00 0,00 Quarter analysis 1st quarter 0,01 0,01 0,45 0,50 2,65 2,88 -2,26 -2,38 362 369 311 304 0,00 0,00 0,07 0,10 0,00 -0,15 2nd quarter 0,01 0,01 0,41 0,45 1,71 1,92 -1,80 -1,95 389 370 307 326 0,00 0,00 -0,19 -0,20 0,00 0,16 3rd quarter 0,01 0,01 0,48 0,54 1,75 2,10 -3,03 -3,87 376 375 325 326 0,00 0,00 -0,19 -0,16 0,00 -0,03 4th quarter 0,01 0,01 0,60 0,69 4,18 4,77 -3,81 -4,18 392 382 307 317 0,01 0,01 0,25 0,22 0,00 0,02 Month of the quarter analysis Quarter 1st month 0,02 0,02 0,50 0,56 4,18 4,77 -3,81 -4,18 530 524 395 401 0,02 0,02 0,77 0,72 0,00 -0,22 Quarter 2nd month 0,00 0,00 0,50 0,56 3,07 2,97 -3,08 -3,09 498 499 412 411 -0,01 -0,01 -0,42 -0,32 0,00 -0,30 Quarter 3rd month 0,00 0,00 0,47 0,54 2,65 2,88 -3,32 -4,10 491 473 443 461 -0,01 -0,01 -0,35 -0,41 0,00 0,51 Month analysis January -0,02 -0,02 0,43 0,49 1,35 1,82 -2,05 -2,38 119 121 103 101 -0,03 -0,03 -0,89 -0,76 0,00 -0,17 February 0,02 0,02 0,42 0,46 1,44 1,72 -1,88 -2,07 120 123 91 88 0,01 0,01 0,29 0,27 0,00 0,19 March 0,03 0,03 0,49 0,54 2,65 2,88 -2,26 -2,24 123 125 117 115 0,02 0,02 0,70 0,66 0,00 -0,21 April 0,05 0,05 0,39 0,43 1,69 1,68 -1,80 -1,95 143 139 85 89 0,04 0,04 1,58 1,46 0,00 -0,08 May 0,00 0,00 0,41 0,45 1,71 1,92 -1,57 -1,74 126 120 106 112 -0,01 -0,01 -0,22 -0,20 0,00 0,01 June -0,03 -0,03 0,42 0,47 1,33 1,29 -1,42 -1,57 120 111 116 125 -0,04 -0,05 -1,32 -1,21 0,00 0,25 July 0,03 0,03 0,39 0,43 1,21 1,35 -1,16 -1,34 134 130 99 103 0,02 0,02 0,70 0,62 0,00 0,03 August -0,01 -0,01 0,51 0,58 1,62 2,07 -2,93 -3,09 122 128 121 115 -0,02 -0,02 -0,70 -0,56 0,00 -0,34 September 0,00 0,00 0,52 0,61 1,75 2,10 -3,03 -3,87 120 117 105 108 -0,01 -0,01 -0,29 -0,31 0,00 0,24 October 0,01 0,02 0,70 0,79 4,18 4,77 -3,81 -4,18 134 134 108 108 0,01 0,01 0,14 0,15 0,00 -0,14 November 0,01 0,01 0,62 0,71 3,07 2,97 -3,08 -3,08 130 128 94 96 0,00 0,00 -0,03 0,02 0,00 -0,21 December 0,02 0,01 0,46 0,53 1,96 2,23 -3,32 -4,10 128 120 105 113 0,01 0,01 0,29 0,16 0,00 0,54 Turn of the month 0,01 0,01 0,48 0,54 1,53 2,10 -3,32 -4,10 278 277 250 251 0,01 0,01 0,24 0,28 0,00 -0,40 Days analysis Pre-holiday 0,06 0,06 0,38 0,43 1,69 1,68 -1,16 -1,34 59 57 39 41 0,06 0,05 1,43 0,96 0,00 0,27 Monday -0,01 -0,02 0,56 0,62 4,18 4,77 -3,32 -4,10 269 257 251 263 -0,03 -0,03 -1,14 -1,30 0,01 1,59 Tuesday 0,03 0,03 0,49 0,56 3,05 4,14 -2,39 -2,57 304 303 263 264 0,02 0,03 0,97 1,18 -0,01 -1,74 Wednesday 0,02 0,01 0,48 0,54 1,53 1,82 -3,81 -4,18 321 318 249 252 0,01 0,01 0,49 0,26 0,00 0,99 Thursday 0,01 0,01 0,51 0,57 2,10 2,97 -3,08 -3,39 315 313 243 245 0,00 0,01 0,04 0,26 -0,01 -1,24 Friday 0,00 0,00 0,40 0,45 1,77 2,60 -1,42 -1,93 310 305 244 249 -0,01 -0,01 -0,46 -0,50 0,00 0,44 Notes: Panels A and B present statistics of daily returns for price and NAV and price minus NAV returns, respectively.

Table 3 presents dummy variable coefficients of the ETFs price and NAV for the raw returns model, the single-factor model, and four-factor model (Carhart (1997)) according to semester (Panel A), quarter (Panel B), month of the quarter (Panel C), month of the year (Panel D), turn of the month (Panel D), day before holidays (Panel E), and weekday (Panel E).

As shown in Panel A of Table 3, no seasonal patterns were detected for the price and NAV raw returns and for price factor models according to the semester of the year. In contrast, the NAV risk-adjusted returns for the first half of the year outperformed those of the second half of the year. The half-year effect was also reported by Alves (2014); however, it is necessary to consider that his study was about equity European mutual funds.

Panel B shows that the NAV half-year higher returns were mostly caused by the second and fourth quarters, which outperformed and underperformed the other quarters, respectively.

As shown for the Panels analyzed above, the Panel C (month of the quarter analysis) does not exhibit raw returns seasonality. Quarter initial month (higher performance) and quarter final month (lower performance) effects were detected through the price and NAV factor models.

Regarding the months of the year, Panel D provides evidence that April had a superior price and NAV risk-adjusted and NAV non-risk-adjusted returns. Conversely, December had an inferior performance (NAV risk-adjusted return). Agrrawal and Skaves (2015) reported higher raw returns in December, although this study did not find evidence of the same effect.

Similar to that reported by Agrrawal and Skaves (2015), our results demonstrate the inexistence of the well-known January effect.

Panels D and E also indicate the absence of turn of the month and pre-holiday effects. The turn of the month effect was documented for ETFs raw returns by Chen and Chua (2011) and Chen et al. (2015).

Panel E exhibits a higher price risk-adjusted return on Wednesday and a lower NAV risk- adjusted return on Friday, which contrast with the Friday effect reported in the literature.

There was no evidence of the Monday and Thursday effects reported by Mazumder et al. (2008).

TABLE 3. ETFS PERFORMANCE

Raw Return Single factor Model Carhart 4 factor Model

Additional Beta Additional Alpha Additional Alpha

Price NAV Price NAV Price NAV Panel A: half-year analysis 1st half of the year -0,002 -0,002 0,003 0,003** 0,003 0,004** 2nd half of the year 0,002 0,002 -0,003 -0,003** -0,003 -0,004** Panel B: quarter analysis 1st quarter 0,002 0,002 0,000 0,001 0,001 0,001 2nd quarter -0,004 -0,004 0,003 0,004** 0,003 0,004** 3rd quarter -0,004 -0,004 -0,001 0,000 -0,001 -0,001 4th quarter 0,006 0,006 -0,003 -0,004** -0,002 -0,004* Panel C: month of the quarter analysis Quarter 1st month 0,015 0,016 0,007** 0,006*** 0,006* 0,006*** Quarter 2nd month -0,008 -0,007 0,000 0,003* 0,000 0,003* Quarter 3rd month -0,007 -0,009 -0,007*** -0,009*** -0,006** -0,008*** Panel D: month analysis January -0,031 -0,030 0,001 0,006** 0,000 0,006*** February 0,010 0,009 0,004 0,002 0,005 0,002 March 0,023 0,025 -0,003 -0,005** -0,003 -0,005* April 0,044 0,044* 0,015*** 0,011*** 0,013*** 0,010*** May -0,008 -0,008 0,002 0,004* 0,002 0,004* June -0,044 -0,046 -0,009** -0,005*** -0,007* -0,004** July 0,023 0,023 0,005 0,003 0,005 0,002 August -0,023 -0,021 -0,002 0,003 -0,003 0,003 September -0,010 -0,012 -0,005 -0,006** -0,005 -0,007** October 0,007 0,008 -0,001 -0,001 -0,002 -0,001 November -0,001 0,001 -0,003 -0,001 -0,002 -0,001 December 0,010 0,006 -0,003 -0,009*** -0,004 -0,008*** Turn of the month 0,006 0,008 0,001 0,002 0,000 0,001 Panel E: day analysis Pre-holiday 0,057 0,054 0,007 -0,002 0,007 -0,002 Monday -0,027 -0,035 0,004 0,000 0,004 0,000 Tuesday 0,022 0,031 -0,004 0,001 -0,004 0,001 Wednesday 0,011 0,007 0,007* 0,002 0,007* 0,002 Thursday 0,001 0,007 -0,005 0,000 -0,005 0,000 Friday -0,009 -0,011 -0,002 -0,003* -0,002 -0,003* Notes: the results reported in Panels A, B, C, D, and E are the estimated dummy variable coefficients of equations 2.7 (raw returns) and 2.8 (single-factor and four-factor models). The dummy variables take the value of 1 for the period indicated in the first column. ***, **, and * indicate statistical significance at the 1%, 5 %, and 10% level, respectively.

Table 4 shows the average raw return data of indices and the estimated dummy variable coefficients of raw returns, the single-factor and four-factors models of indices. With the aim of comparing the raw returns differences between indices and ETFs, this Table also presents the excess returns and the dummy variable coefficients of the tracking error.

Regarding the half-year, the raw returns reported in Panel A are similar between the two periods, as observed for price and NAV ETFs returns. The excess returns were low, although the first semester achieved a better replication of the indices compared with the second semester, as shown by a significant negative additional Beta price tracking error.

In contrast to the ETFs NAV half-year effect, the indices did not display any seasonal pattern, indicating that the higher NAV risk-adjusted returns were due to idiosyncratic factors of the ETFs.

Panels B and C show the presence of seasonal patterns for price and NAV tracking error in the second quarter and for NAV tracking error in the first month of the quarter (accurate replication of the indices), respectively.

Regarding the month of the year (Panel D), April was the month with the greatest and June was the month with the lowest average raw returns, although the t-tests on differences of means revealed the inexistence of statistically significant differences12. These findings are in line with the results obtained for price and NAV average raw returns. April exhibited a significant negative coefficient dummy variable for price and NAV tracking error, indicating a rigorous replication of the indices in that period.

Index raw returns and factor models showed a better performance in April. These outcomes are consistent with price13 and the NAV ETFs April effect, which demonstrate that this effect is induced by the constituents of the indices. Similar to that observed for price and NAV ETFs, a January effect did not occur for indices.

As shown in Panels D and E, the turn of the month and pre-holiday effects were not observed, which contrasts with most of the findings reported in the literature. In relation to the tracking error, no seasonal pattern was detected.

12 The t-tests indices outcomes are not present in this work. 13 The April ETF price effect was only visible for the single- and four-factor models.

In contrast with the Wednesday price and Friday NAV effects, there was no evidence of these effects on the indices. These results indicate that the seasonal pattern is idiosyncratic to the ETFs. The tracking error presented a significant coefficient for Wednesday and Friday NAV, allowing a better replication and a worse replication, respectively.

TABLE 4. RAW RETURNS, EXCESS RETURN, TRACKING ERROR, AND RAW RETURN SINGLE-

FACTOR AND FOUR-FACTOR MODELS OF INDICES

Benchmark Benchmark Benchmark Index Index Excess Return Index Raw Benchmark Tracking Error (ETF Raw Return - Return Carhart 4- Index Raw Single- Benchmark Raw factor Return Additional Beta factor Return) Additional Model Additional Beta Additional Alpha Alpha Price NAV Price NAV

Panel A – half-year analysis 1st half of the year 0,010% -0,003% -0,003% -0,024** -0,006 -0,002 0,003 0,003 2nd half of the year 0,013% -0,004% -0,004% 0,024** 0,006 0,002 -0,003 -0,003 Panel B - quarter analysis 1st quarter 0,013% -0,004% -0,003% -0,013 0,002 0,002 0,001 0,001 2nd quarter 0,008% -0,002% -0,03% -0,019** -0,010** -0,005 0,003 0,003 3rd quarter 0,008% -0,003% -0,003% 0,008 0,004 -0,005 -0,001 -0,002 4th quarter 0,017% -0,004% -0,005% 0,024 0,003 0,008 -0,003 -0,002 Panel C – month of the quarter analysis Quarter 1st month 0,019% -0,001% 0,000% -0,011 -0,010** 0,012 0,002 0,002 Quarter 2nd month 0,004% -0,001% 0,000% 0,001 0,001 -0,012 -0,002 -0,002 Quarter 3rd month 0,012% -0,008% -0,009% 0,010 0,009* 0,000 0,000 0,001 Panel D – month analysis January -0,019% 0,000% 0,000% -0,023 -0,008 -0,034 0,001 0,001 February 0,017% 0,001% 0,000% -0,018 -0,003 0,005 -0,002 -0,001 March 0,041% -0,011% -0,010% 0,006 0,015 0,032 0,003 0,003 April 0,049% -0,001% 0,000% -0,028*** -0,012*** 0,041* 0,009*** 0,007*** May 0,002% 0,000% 0,000% -0,019* -0,011** -0,011 -0,003 -0,002 June -0,026% -0,006% -0,007% 0,000 -0,001 -0,041 -0,002 -0,001 July 0,031% -0,001% -0,001% -0,019** -0,009* 0,021 0,001 0,000 August -0,011% -0,002% 0,000% 0,019 0,013 -0,024 -0,001 -0,002 September 0,005% -0,006% -0,008% 0,020 0,006 -0,007 -0,002 -0,002 October 0,016% -0,002% -0,001% 0,037 0,000 0,005 -0,004 -0,004 November 0,009% -0,002% 0,000% 0,019 0,003 -0,003 -0,004 -0,004 December 0,026% -0,009% -0,013% 0,002 0,005 0,016 0,001 0,002 Turn of the month 0,011% 0,001% 0,003% 0,005 0,002 0,000 -0,006 -0,006 Panel E – day analysis Pre-holiday 0,042% 0,021% 0,018% 0,011 0,024 0,032 -0,023 -0,023 Monday -0,013% -0,001% -0,007% 0,000 0,001 -0,030 0,004 0,003 Tuesday 0,034% -0,008% -0,001% -0,003 -0,003 0,028 -0,001 -0,001 Wednesday 0,013% 0,004% 0,000% -0,004 -0,005* 0,002 -0,002 -0,002 Thursday 0,019% -0,010% -0,006% 0,001 0,000 0,009 0,003 0,003 Friday 0,003% -0,002% -0,004% 0,005 0,007* -0,011 -0,003 -0,002 Notes: the additional beta and alpha represent the dummy variable coefficients of equations 2.7 (raw returns) and 2.8 (single-factor and four-factor models). The dummy variables assume the value of 1 for the period indicated in the first column. ***, **, and * indicate statistical significance at the 1%, 5 %, and 10% level, respectively.

5. Conclusion

This study analyzed the behavior of the US equity ETFs traded on the NYSE Arca and of the indices that the ETFs seek to replicate across the calendar year for the period of 2005 to 2015, with the aim of verifying the presence of seasonal patterns. The tracking error was also an object of the study.

In particular, this article attempted to answer the following questions. 1) Is there evidence of seasonality in the returns and tracking error of ETFs? 2) Do the seasonal patterns in the return of ETFs differ from the underlying indices, indicating that this seasonality is due to idiosyncratic factors in the ETFs industry, or it is identical to underlying indices, indicating that this seasonality is induced by the constituents of the underlying index?

Regarding the first question, we found evidence of seasonality patterns in the ETFs returns and in tracking error. The first-half of the year NAV risk-adjusted return outperformed the second half-year one. Moreover, a better replication of the indices was achieved in the first semester, as shown by the tracking error based on price. The ETFs NAV first-half of the year effect was essentially due to the second (high performance) and fourth (low performance) quarters. Moreover, a seasonal pattern for price and NAV tracking error was detected in the second quarter (superior replication).

The first (third) month of trimesters exhibited a higher (lower) price and NAV risk- adjusted returns compared with the remaining months of the quarter. The replication of the indices was more accurate in the first month of the quarter.

The ETFs performance was higher in April (price and NAV risk-adjusted and NAV raw returns) and lower in December (NAV risk-adjusted return) compared with the remaining months of the year. Moreover, the results indicate a rigorous replication of the ETFs (price and NAV) in April. The current study also showed the presence of a Wednesday effect (higher price risk-adjusted returns) and a Friday effect (lower NAV risk-adjusted returns). Furthermore, seasonality in NAV tracking error was detected on Wednesday (better replication) and Friday (worst replication).

With respect to the second question, the seasonal patterns detected in the ETFs returns were not reflected in indices, with the exception of the April effect. Thus, the first half of

23 the year, the second quarter, the fourth quarter, the first month of the quarter, the third month of the quarter, Wednesday, and Friday effects were due to the idiosyncratic factors (behavior of the managers or other factors specific to the ETFs industry), while the April effect was induced by the constituents of the underlying indices. The seasonality caused by the ETFs idiosyncratic factors are consistent with the results of Starks et al. (2006) and Mazumder et al. (2008).

This work contributes to the suppression of some existing gaps on the study of seasonality in risk-adjusted and non-risk-adjusted returns and in tracking error of ETFs, because to the best of our knowledge, there are no reports on the pre-holiday, quarter and month of the quarter periods. Moreover, this work aimed to determine if the effects detected are due to the underlying asset market or to idiosyncratic factors of the ETFs.

Further research should be conducted on the seasonality in the returns and tracking errors of ETFs, mainly regarding the identification of the causes of the results of the current work (reported calendar effects). Moreover, a performed analysis should be applied to other markets, such as the European market. Finally, it would be interesting to investigate if the seasonality of ETFs returns and tracking errors differ in the bull and bear market phases (during rising and declining markets).

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