ETF

By

Gerasimos G. Rompotis∗

Abstract

This paper constitutes a presentation of empirical research on Exchange Traded Funds. Using daily data for a sample of 30 American ETFs during the period between 4/3/2001 and 8/7/2002, we first investigate the price relation among ETFs and underlying indices, finding that these values are not equal. Further, we discover that ETFs are mainly traded in premium in regard to their Net Asset Values. Afterwards, we calculate the sample’s percentage return, which, on average, is negative but stands closely to zero, and standard deviation, which is low enough, indicating the great degree of ETFs portfolio’s diversification. Applying single regression estimations, we bear out that the falling of capital markets after the abnormal growth until latest’s 2000 affects ETFs to behave conservatively. Finally, we use three methods to measure the gap among ETFs and underlying indices return, the well known tracking error, finding that this difference is not much greater than zero, implying that ETFs’ performance moves closely to the tracking indices.

∗

Gerasimos G. Rompotis is a researcher in the Department of Economics of Athens University, Greece.

e-mail: grompotis@kpmg.gr

This paper is based on author’s master’s dissertation in Department of Economics, University of Athens, Greece, under the supervising of Professor Nikolaos. Th. Milonas.

1. Introduction

Exchange Traded Funds are a relatively new investment tool, which was based on the «portfolio trading» or “program trading” of latest 1970’s and early 1980’s.1 These proceedings contributed to the inspiration of trading electronically the components of a whole index through a single transaction. Officially, the Standard and Poor’s Depository Receipts (SPDRs) is considered to be the first ETF. It was created in 1993 and its return tries to replicate the performance of S&P 500 Index. Another familiar ETF is the QQQQ, which follows the return of Nasdaq 100 Index. ETFs faced a rapid growth during the subsequent years in consider of assets and total availability, rising to almost $85 billions under administration and over of 80 funds totally. The objectives of this investing product vary, since there are ETFs that invest to indexes of major capital markets, there are style and sector ETFs, as also international ETFs. As well, a mid-risky investor, either institutional or retail, has the ability to choose bond ETFs, which offer great range of bond’s price transparency. ETFs combine the principal characteristics of classic mutual funds and stocks. Like mutual funds, they offer great rate of portfolio’s diversification, since an investor is able to be posed in the stocks of an entire index by buying a share of ETFs. Otherwise, ETFs are more flexible than mutual funds, since they are continually traded during the entire day like stocks and, also, they are allowed to be traded in short. A significant advantage of ETFs is their tax efficiency, which derives from their creation and redemption mechanism. ETFs are created by the deposit of underlying stocks to a trustee and redeemed “in kind” by exchanging the portfolio’s assets, without any significant money transaction to occur and, consequently, without any tax effect.

ETFs are a cheap investment tool, under the consideration that their expense

ratios are significantly slight, as a result of their passive investing character. According to Morgan Stanley, the average expense ratio of ETFs was 0.42% until June 2002, whereas mutual funds have average expense ratio equal to 1.26%.2 However, ETFs have to pay commissions to brokerage companies, whereas conventional mutual funds do not and, also, they suffer from the bid/ask spread effect, contrary to open mutual funds, which do not.

ETFs constitute a competitor to the traditional index funds. They track the same indexes, but they usually follow more accurately the composition of the underlying indices, since they invest almost to the entirety of index components. In comparison to index funds, ETFs are in major preferred by risky stock investors. The investors on mutual funds seem to be conservative against to ETFs and to choose index funds. Rompotis (2006) provides an empirical comparison among ETFs and index funds, searching their performance, their tracking ability and the sources of their expenses.

At first, this paper describes the findings of previous literature, which concern

the characteristics and the returns of ETFs. Then, it concentrates to the relation among ETFs and indices’ values, as also to the premium or discount between trading and net asset values. In consequence, the study records the estimations of return and risk.

In the following step, the paper gives an appreciation about the aggressiveness of ETFs investing strategy, using the results of a single regressions analysis. A material issue of ETFs is the gap, which is usually observed, between the performance of ETFs

1

See Gary L. Gastineau (2001). 2

See John Spence (6/17/2002), Morgan Stanley Equity Research.

and the tracking indices. Such, we apply the three common methods the literature suggests, in order tracking error component of ETFs to be calculated. Finally, this study concludes, summarizing the main findings of the research.

2. Literature

Because of their brief history and despite their rapid growth and the spectacular acceptation by the investors, ETFs have not faced extended researching interest. The literature presents no sizeable records of studies related to this issue, particularly in empirical level. The most significant papers are introduced in this sector. Bernstein (2001) offers a primer on ETFs. Beyond the definition and description of ETFs, he demonstrates the tax and other certain advantages of ETFs in comparison to traditional mutual funds.

In parallel, Gastineau (2001) provides an introduction of ETFs, focusing on their

origin, describing their main types and the exchanges where they are (or were) traded, analyzing their characteristics and operating mechanism. He also indicates the benefits the participants of capital markets gain by ETFs’ existence.

Dellva (2001) applies a cost comparison among the primary trackers of S&P 500 Index, comparing funds of ETFs and index mutual funds investing classes. He exhibits a significant benefit of ETFs in consider of annual expenses, even though they shoulder transaction costs and commissions that concern brokerage firms. This advantage becomes greater if an investor does not liquid his shares for a last time period.

Poterba and Shoven (2002) compare the pre-tax and after-tax returns of SPDRs and Vanguard index fund; both track S&P 500 Index, finding that they substantially present the same records of performance. They combine these findings with the tax efficiency of ETFs and they conclude that ETFs offer investors a less taxable method to invest in a broad market index and to achieve returns analogous to their index funds counterparts. Rompotis (2006), using a larger set of comparable ETFs and index funds, confirms their narrowly connected relationship of performance.

Elton, Gruber, Comer and Li (2002) also exam the characteristics and the

performance of SPDRs. They find that the net asset value of SPDRs moves closely to its market price, as a result of the “in kind” creation and redemption’s mechanism. Further, they show that SPDRs underperforms the S&P 500 Index and its low costs index funds counterparts. They attribute this underperformance to the lost income caused by the policy of not reinvesting the dividends received on the underlying assets and holding them in cash.

Kostovetsky (2003) compares ETFs and index funds, demonstrating that the

main differences among them are related to management expenses, transaction fees and tax efficiency. He also suggests that the tracking error’s comparison between ETFs and index funds is difficult because of the lack of a true benchmark for comparison.

Tse and Erenburg (2003) use as crucial date the July 31st of 2001, when the NYSE began trading QQQQ shares, in order to exam the impact of the NYSE’s participation to the competition for order flow, market quality and price discovery in QQQQ on the AMEX, the NYSE, ECNs (electronic communication networks) and regional exchanges. The NYSE contributed to a reduction of bid-ask spread and pricing error for all centers and resulted in a higher market quality.

Gastineau (2004) suggests that the pre-tax return of benchmark index ETFs generally display inferior records in comparison to index funds that use the same

indices, especially in the cases of most popular benchmark indices like Russell 2000 index for small-cap stocks and S&P 500 index for large-cap stocks. He partly connects this underperformance with the lack of aggressiveness for a portion of ETFs managers. In additional, the “in kind” process of ETFs creation and redemption restricts the ability of their managers to follow accurately and immediately the adjustments of tracking indices. Also, the delay in ETF’s portfolio adjustment may embodies some modest transaction expenses associated with bookkeeping entries or trading commissions. All the factors above affect the ability of ETFs to exactly replicate their benchmarks.

The performance and the trading characteristics of Australian ETFs are examined by Gallagher and Segara (2004). The authors find that classical ETFs closely track their respective indices, but they note that ETFs in Australia have not faced the same degree of acceptance in comparison to the reception of ETFs in other markets.

In a recent working paper, Boney, Doran and Peterson explore the magnitude of SPDRs’ influence on the cash flow towards S&P index fund trackers. They discover that SPDRs draw money from index funds, demonstrating a negative correlation between flows to ETFs and index funds.

3. Methodology

I) The first issue we investigate in this paper is the relationship between the values of ETFs and tracking benchmarks. We estimate a single regression model, using the trading value of ETFs at the end of the day as the dependent variable, though the price of underlying indices is the determinant factor of the model. The estimated equation has the following form:

ETFi = αi + βi BENCHMARKi + ei (1)

The price relationship is defined from equation’s beta. According to Nasdaq’s primer on ETFs, I expect a 1/40 relation between the prices of QQQQ and Nasdaq 100 Index, 1/10 for SPDRs and S&P 500 Index, 1/5 for mid-cap SPDRs and S&P 400 Index, 1/100 for DIAMANDS and Dow Jones Industrials Index and a variety about iShares’ values.

II) Contrary to closed-end mutual funds, which are usually traded in prices that are significantly different than their net asset values, ETFs quote trading values that closely fit to their net asset value. This is due to the conjunction of primary and secondary market, which enables the institutional investors to execute arbitrage strategies and to eliminate the premium or discounts in short time period. I compute the gap between ETFs’ trading and net asset values, by the application of model:

(Trading Value)i = αi + βi (Net Asset Value)i + ei (2)

The difference of regression’s beta than unity denotes the premium or the discount in trading values. Specifically, if beta is bigger than unity, we conclude that ETFs are traded in premium and if beta is less than unity, we note that they are traded in discount.

III) We calculate the daily percentage return of ETFs, using the formula:

i−TVi−1

Ri = TVTV∗100 (3) i−1TVi is the trading value on day i. We do not take into account the dividends that derive

from underlying stocks because of the fact that they are usually kept in cash. Elton, Cruber, and Li (2002) suggest that the above tactic negatively influences the replication

of an index performance. We calculate the standard deviation of returns by the following formulas:

σ2 =

∑(Αi−Α)2

i=1

Ν

Ν−1

(4) and σΑ= σΑ (5)

2

The σ2 denotes the variation of an ETF’s return round of the average returnΑ. The σΑ expresses the percentage risk of portfolio in terms of returns’ standard deviation.

IV) In this section, we exam the aggressiveness of ETFs managers, applying the single regression model:

Rpt = αi + βi Rbt + εpt (6)

where Rpt indicates the row return of ETFs and Rbt is the return of tracking indices. The alpha coefficient implies the return an ETF could achieve if there was not any connection between ETF and index. Practically, this is not the subject, so we expect alpha to be statistically insignificant. Beta accounts the level of the systematic risk, in which an ETF is exposed and reflects the aggressiveness of management strategy. If beta is bigger than unity, the ETF moves more aggressively in comparison to the market and if beta lies bellow unity, the ETF follows a conservative investing policy.

V) The previous literature about Indexing indicates the tracking error issue, which reflects the inequality of returns between the indices and the index trackers, as crucially significant.

Roll (1992) demonstrates that the major problem a portfolio’s manager faces is

the minimization of return’s volatility with respect to the volatility of benchmark’s return. Frino and Gallagher (2001) analyze the factors that strengthen the size of tracking error, focusing on managerial fees, transaction costs and brokerage commissions, portfolio’s rebalancing and capital flows. They also provide three methods for tracking error’s estimation.

The first one concerns the standard error’s residual of regression (6). The second

one computes the tracking error by calculating the average of absolute differences between the returns of ETFs and the corresponding indices. This estimation is expressed by the formula (7):

ΤΕ2.Ρ =

∑ep

t=1

n

n

(7)

where TE denotes the tracking error and eP is the absolute return differences. The last method computes the standard deviation of differences between ETFs and indices’ returns. It is the most commonly used method and, according to Pope and Yadav (1994), produces the same results in comparison to first method’s results only if equation’s (1) beta is equal to unity. The third method is presented by the formula bellow:

ΤΕ3,Ρ =

1n−1

∑(e

t=1

n

pt

−ep)2 (8)

where ept is the differences of returns and ep is the average return’s difference.

4. Data

The sample of this study includes 30 ETFs, which are listed on AMEX and NASDAQ exchanges, and their corresponding indices; 17 of them track broad indices of American capital markets and 3 follow the return of sector indices, while the rest 10 ETFs of the sample try to replicate the performance of international indices. As implied above, the sample comprises the most significant ETFs in account of assets and trading volume. These are QQQQ, SPDRs, mid-cap SPDRs, DIAMANDS and a variety of Barclays’ iShares, which follow the Nasdaq 100 Index, the S&P 500 Index, the S&P 400 Index, the Dow Jones Industrials Index and a set of Morgan Stanley’s international indices correspondingly. AMEX and NASDAQ’s web databases supplied this study with daily trading prices and Net Asset Values of ETFs. As well, the closing prices of underlying indices were collected from these databases, but also Frank Russell and Wilshire Groups supplied us with data for their own constructed and monitored indices. The values of international indices were gathered from Morgan Stanley’s webpage.

The time period of study exceeds from 4/3/2001 to 8/7/2002. The selected

period provide a number of 313 observations for the majority of sample’s ETFs, except iShare IWR (Russell MidCap Index), iShare IWS (Russell Mid Value Index), VTI (Wilshire 5000 Index) and iShare EZU (Index of European Monetary Union), which record 238, 236, 273 and 248 daily observations respectively. The usage of daily data was enforced in a way by the lack of extended historical records about ETFs.

5. Empirical Results

I) The results of regression’s (1) estimating during the period 4/3/2001-7/8/2002 are furnished on Table 1. The table exhibits the regression’s coefficients alpha and beta, the R-squared, the percentage relationship between ETFs and indices’ trading prices and the number of available observations for each sample’s ETF. The funds of sample are ranked in alphabetical order in each class of domestic broad markets, domestic sector and international capital markets. The alpha coefficient, which expresses the percentage of ETF’s assets that is allocated to a different than the specific tracking index,3 is mostly estimated statistically insignificant. The average value of alpha is equal to 0.272. The beta coefficient is statistically significant at 1% level in any case and its value is 0.084 on average.

The R-squared is extremely high and approximately equal to the unity, demonstrating that the applied regression efficiently illustrates the correlation of ETFs and indices’ trading values. The average percentage relationship is 8.4%, denoting that there is a huge gap between ETFs values and their tracking indices.

Appreciating the estimations on Table 1, we verify that the price relationship

between the DIAMONDS and Dow Jones Industrial is equal to 1% or 1/100; the trading value of QQQQ counts for 2.5% or 1/40 of Nasdaq 100 Index and SPDRs’ price is equivalent to the 10% or 1/10 of S&P 500 Index. In the case of Mid-Cap SPDRs, we trace a slight difference of estimated percentage in relevance to the expected value. Specifically we computed a percentage of 18.4%, since we expected 20%.

It is common for iShares to invest a small amount of their assets in stocks, which belong to a different index than the main tracking index.

3

In regards to iShares, we observe a great fluctuation of their values in relation to

the prices of tracking indices. The iShare, which invests in the market of Hong Kong (EWH), records the minimum price and it is equal to 0.2% and the iShare, which is allocated on the index of European Monetary Union (EZU), has the maximum value, equal to 39.1% of underlying indexes’ value.

The findings of Table 1 confirm our expectations about a fractional correlation

between the trading prices of ETFs and their corresponding indices.

Table 1 The percentage relationship between the values of ETFs and tracking indices during the period 4/3/2001-7/8/2002

ETFs Percentage No of 2

beta RObs. Classes (Tracking indices) alpha relationship

Domestic DIA-D.J.Industrial 313 0.159 0.010* 0.999 1.000% Broad FFF-Fortune 500 313 -0.059 0.100* 0.998 10.000% Markets IWB-Russell 1000 313 10.00% 0.250 0.010* 0.999 ETFs

IWD-Russell1000 Value 313 16.200% -0.362 0.162* 0.999 IWF-Russell1000 Growth 313 15.100% -0.075 0.151* 0.999 IWM-Russell 2000 313 -0.210 0.199* 0.998 19.900% IWO-Russell2000 Growth 313 -1.067* 0.033* 0.998 3.300% IWV-Russell 3000 313 -0.217 0.101* 0.999 10.100% IWZ-Russell3000 Growth -0.248*** 0.021* 0.998 313 2.100%

IWR-Russell Mid Cap238 -0.068 0.039* 0.990 3.900%

IWS-Russell Mid Value236 -0.290 0.128* 0.996 12.800% IVV-S&P 500 313 0.177 0.100* 0.999 10.000% IJH-S&P Mid 400 313 20.000% 0.018 0.200* 0.999 MDY-S&P Mid 400 313 -0.157 0.184* 0.998 18.400% QQQ-Nasdaq 100 313 -0.020 0.025* 0.999 2.500% SPY- S&P 500 313 0.299 0.100* 0.999 10.000%

273 VTI-Wilshire5000-0.311 0.010* 0.999 1.000%

Domestic FEF-Fortune e-50 313 -0.099 0.100* 0.996 10.000% Sector ETFs IDU-D.J Utilities 313 4.435* 0.202* 0.998 20.200%

IBB-Nasdaq Biotech 313 -0.307* 0.101* 0.999 10.100%

313 International EWA-Australia -0.273 0.031* 0.974 3.101%

ETFsEWC-Canada 313 0.224 0.016* 0.969 1.627%

EZU-EMU248 4.049** 0.391* 0.983 39.100% EWG-Germany 313 0.330 0.013* 0.994 1.340% EWH-Hong Kong 313 -0.213 0.002* 0.979 0.200% EWI-Italy 313 0.066 0.051* 0.995 5.100% EWJ-Japan 313 -0.090 0.004* 0.993 0.400% EWD-Sweden 313 0.1 0.004* 0.984 0.400% EWL-Switzerland 313 0.269 0.006* 0.981 0.600% EWU-U.K 313 1.773* 0.014* 0.981 1.400%

Average 0.272 0.084 0.993 8.400% 303 Estimated Model: ETFi = αi + βi BENCHMARKi + ei (1)

*Significant in 1% level. ** Significant in 5% level. *** Significant in 10% level.

II) The results of model (2), in point of premium or discount trading values of ETFs, are introduced on Table 2. We record the estimations of alpha and beta coefficients, the R-squared and the number of

observations. Table also furnishes two columns, one of which concerns the premium in trading prices and the other one denotes the discount of net asset value. As mentioned above, the beta’s difference from the unity implies the premium or the discount in the trading prices.

Table 2 The deviation of ETFs trading values from net asset values during the period 4/3/2001-7/8/2002

Prem. ETFs No of Disc.

2

Classes (Tracking indices) alpha beta RObs. (%) (%) Domestic DIA-D.J.Industrial 313 0.027 0.999* 0.9 0.100 Broad FFF-Fortune 500 313 -0.037 1.000* 0.998 - - Markets IWB-Russell 1000 313 0.200 0.144 0.998* 0.999 ETFs

IWD-Russell1000 Value 313 -0.159 1.003* 0.999 0.300 IWF-Russell1000 Growth 313 0.007 1.001* 0.999 0.050 IWM-Russell 2000 313 -0.184 1.002* 0.998 0.200 IWO-Russell2000 Growth 313 -0.331** 1.006* 0.998 0.600 IWV-Russell 3000 313 -0.059 1.001* 0.999 0.100 IWZ-Russell3000 Growth 313 0.004 0.999* 0.997 0.100

IWR-Russell Mid Cap238 0.022 1.001* 0.990 0.100

IWS-Russell Mid Value236 -0.042 1.001* 0.997 0.100 IVV-S&P 500 313 -0.154 1.001* 0.999 0.100 IJH-S&P Mid 400 313 0.016 1.000* 0.999 - - MDY-S&P Mid 400 313 -0.341 1.004* 0.999 0.400 QQQ-Nasdaq 100 313 0.104*** 0.997* 0.999 0.300 SPY- S&P 500 313 0.160 0.998* 0.999 0.200

273 VTI-Wilshire50000.121 0.999* 0.999 0.100

Domestic FEF-Fortune e-50 313 0.400 -0.078 1.004* 0.996 Sector ETFs IDU-D.J Utilities 313 0.300 0.187*** 0.997* 0.999

313 IBB-Nasdaq Biotech 0.093 0.999* 0.999 0.100

313 International EWA-Australia -0.232** 1.027* 0.980 2.700

ETFsEWC-Canada 313 -0.601* 1.056* 0.972 5.600

EZU-EMU248 -1.256* 1.027* 0.986 2.700 EWG-Germany 313 -0.084 1.004* 0.996 0.400 EWH-Hong Kong 313 -0.003 1.002* 0.982 0.200 EWI-Italy 313 -0.171** 1.009* 0.997 0.900 EWJ-Japan 313 1.200 -0.094*** 1.012* 0.994 EWD-Sweden 313 -0.117 1.008* 0.986 0.800 EWL-Switzerland 313 -0.241** 1.020* 0.986 2.000 EWU-U.K 313 -0.062 1.007* 0.986 0.700

Average -0.112 1.006 0.994 0.978 0.175 303 Estimated Model: (Trading Value)i = αi + βi (Net Asset Value)i + ei (2) *Significant in 1% level. ** Significant in 5% level. *** Significant in 10% level.

Checking the estimations of Table 2, we observe the alpha coefficient mainly to

be statistically insignificant. In particular, 21 of 30 ETFs’ alphas have no any statistical significance. The average alpha is negative and equal to -0.112. Contrary, beta is significant at 1% level in any case. The average value of beta exceeds the unity,

indicating that the ETFs of our sample are on average traded in prices superior than their net asset values.

Especially, 20 ETFs are appeared to be traded in premium and 8 ETFs are

mercendised in discount. The average premium is 0.978% and the average discount is 0.175%. The minimum premium is 0.01% and refers to the iShare, which tracks the S&P MidCap 400 Index (IJH), though the higher premium is 5.6% and it concerns the iShare, which invests in Canadian capital market. Respectively, the DIAMONDS has the least discount equal to 0.01% and the QQQQ reveals the greater discount from net asset value. This discount counts to 0.3%. Finally, 2 of sample’s ETFs are traded in prices equal to their net asset value. These are the FFF (Fortune 500 Index) and the IJH (S&P MidCap 400 Index).

We conclude this section noting that the average percentages of premium and discount in the trading values of ETFs are considered to be low enough, reflecting the tight connection between the primary and secondary markets of ETFs. The low percentages also denote the efficient execution of arbitrage strategies by managers and investors.

III) The time between 4/3/2001 and 8/7/2002 generally represents a negative period for capital markets, since the most significant and influential stock indices were internationally declining, a fact that resulted an increase to uncertainty about the equity investments. As a consequence of the general hesitation towards stock markets and the observed portfolios’ liquidations, the return of ETFs felt. The negative percentage performance of ETFs is recorded on Table 3. The 8 of sample’s ETFs appear positive return, since the rest ETFs have negative estimations. The worst performer is the ETF, which is symbolized as IDU and invests on the stocks of Dow Jones Utilities. The best tracker is iShares EWA, which is allocated to Australian stocks. The average daily return of sample’s ETFs is negative and equal to -0.022%. Applying t-test, we conclude that this negative return is statistically different than zero, even though it is tenuous. Regarding the risk factor, we observe that the average standard deviation of ETFs’ returns is equal to approximately 1.6%. This percentage is deemed to be minor and it indicates the high degree of diversification of the ETFs’ portfolios. The less risky ETF is the IWS (Russell MidCap Value Index), whose standard deviation is 1.015%, since the most dangerous ETF is the FEF (Fortune e-50 Index), which has standard deviation equal to 3.083%. Ending this section, we note that we calculated the average return and standard deviation of tracking indices, which were -0.029% and 1.5% respectively. These percentages stand closely to their counterparts of ETFs. The similarity of ETFs and tracking indices’ return and risk levels reflects the strong connection among these investing components.

IV) In this section, we exam the aggressiveness of ETFs’ managers, presenting the results of regressing the daily returns of ETFs on benchmarks’ returns. The estimations are introduced on Table 4. The table contains the alpha and beta coefficients, the R-squared and the number of observations.

The average alpha, which expresses the performance a manager could achieve if there was not a relationship among ETFs and underlying indices, is positive but it does

not statistically differ from zero. Individually, any sample’s ETF exhibits statistically insignificant estimation for its alpha coefficient.

Table 3 The descriptive statistics of ETFs during the period 4/3/2001-7/8/2002 ETFs Average Standard Min

Classes (Tracking indices) return deviation Domestic DIA-D.J.Industrial -7.621 0.004 1.300 Broad FFF-Fortune 500 -0.028 -3.949 1.156 Markets IWB-Russell 1000 -0.029 -4.193 1.255 ETFs

IWD-Russell1000 Value -0.010 -3.974 1.017 IWF-Russell1000 Growth -5.183 -0.043 1.655 IWM-Russell 2000 0.016 -4.952 1.407 IWO-Russell2000 Growth -0.020 -5.346 1.792 IWV-Russell 3000 -0.025 -4.687 1.239 IWZ-Russell3000 Growth -5.494 -0.049 1.733

IWR-Russell Mid Cap-0.040 -7.636 1.244

IWS-Russell Mid Value0.006 -5.159 1.015 IVV-S&P 500 -0.030 -5.134 1.269 IJH-S&P Mid 400 0.033 -4.431 1.309 MDY-S&P Mid 400 0.032 -5.256 1.368 QQQ-Nasdaq 100 -0.058 -8.504 2.4 SPY- S&P 500 -0.030 -5.225 1.285

VTI-Wilshire5000-0.078 -4.748 1.214

Domestic FEF-Fortune e-50 -0.069 3.083 -10.410 Sector ETFs IDU-D.J Utilities -4.432 -0.110 1.257

IBB-Nasdaq Biotech -0.095 -9.039 2.715

International EWA-Australia 0.072 1.528 -11.400

ETFsEWC-Canada 0.013 -5.000 1.503

EZU-EMU-0.021 -5.188 1.4 EWG-Germany -0.013 -7.991 1.686 EWH-Hong Kong -0.021 -0.009 1.952 EWI-Italy -0.031 -7.740 1.579 EWJ-Japan -0.040 -3.851 1.660 EWD-Sweden -0.001 -8.219 2.446 EWL-Switzerland -6.695 0.018 1.456 EWU-U.K -0.013 -5.217 1.318

Average -0.022 -6.045 1.593

Average ETFs’ return is different from zero at 1% level. T-ratio is equal to -3.126.

Max 4.281 3.793 4.500 3.119 7.483 4.835 7.685 4.1 8.108 4.337 3.278 4.298 4.971 4.753 10.697 3.979 3.739 11.204 3.256 8.051 5.318 5.000 5.131 6.342 6.378 6.121 7.150 12.834 7.042 4.747 6.156

No of Obs. 313 313 313 313 313 313 313 313 313 238 236 313 313 313 313 313 273 313 313 313 313 313 248 313 313 313 313 313 313 313 303

The above finding accords to our expectations, because of strong dependence

ETFs have by their corresponding indices. The lack of a standard level of return that could be constantly achieved by ETFs’ managers makes difficult the formation of secure investing expectations and it reflects an inherent risk, which derives of ETFs’ structure and investing philosophy. In other words, the passive character of ETFs’ investing policy somehow restricts the ability of their managers to rebalance their allocations in order to produce superior performance. This disability is more substantial during declining periods.

The estimations of regression’s beta are highly statistically significant and approach the unity on average. The mean beta is equal to 0.921, a little below than the unity. The average inferiority of beta in relevance to the unity denotes that sample’s ETFs are less aggressive than their benchmarks. Especially, only 6 ETFs have beta bigger than 1. Further, the individual beta fluctuates from 0.75 of IWR (Russell Mid Cap Index) to 1.04 of IWO (Russell 2000 Growth Index).

Table 4 The performance of ETFs in regarding to the underlying indices 4/3/2001-7/8/2002

ETFs

Classes (Tracking indices) alpha beta Domestic DIA-D.J.Industrial 0.003** 1.004* Broad FFF-Fortune 500 -0.002** 0.905* Markets ETFs IWB-Russell 1000 0.001** 0.970*

IWD-Russell1000 Value 0.962* 0.002** IWF-Russell1000 Growth 0.000** 1.004* IWM-Russell 2000 1.018* 0.002** IWO-Russell2000 Growth 0.005** 1.040* IWV-Russell 3000 0.001** 0.972* IWZ-Russell3000 Growth -0.008** 0.980*

IWR-Russell Mid Cap-0.010** 0.750*

IWS-Russell Mid Value 0.001** 0.910* IVV-S&P 500 0.002** 0.981* IJH-S&P Mid 400 0.001** 0.979* MDY-S&P Mid 400 1.005* -0.001** QQQ-Nasdaq 100 0.002** 0.977* SPY- S&P 500 0.002** 0.987*

VTI-Wilshire5000 0.001** 1.007*

Domestic FEF-Fortune e-50 0.8* 0.003** Sector ETFs IDU-D.J Utilities -0.006** 0.914*

IBB-Nasdaq Biotech -0.005** 0.950*

International EWA-Australia 0.026** 0.0*

ETFsEWC-Canada 0.017** 0.825*

EZU-EMU-0.002** 0.847* EWG-Germany 0.010** 0.924* EWH-Hong Kong 0.010** 0.756* EWI-Italy 0.010** 0.938* EWJ-Japan -0.005** 0.763* EWD-Sweden 0.020** 0.948* EWL-Switzerland -0.001** 0.944* EWU-U.K 0.006** 0.832*

Average 0.003 0.921 Estimated Model: Rpt = αi + βi Rbt + εpt (6) *Significant in 1% level. ** Insignificant in any level

during the period R0.952 0.1 0.949 0.955 0.968 0.930 0.921 0.967 0.830 0.524 0.783 0.938 0.947 0.913 0.958 0.929 0.978 0.706 0.855 0.955 0.517 0.361 0.728 0.750 0.331 0.768 0.497 0.632 0.568 0.549 0.743

2

No of Obs. 313 313 313 313 313 313 313 313 313 238 236 313 313 313 313 313 273 313 313 313 313 313 248 313 313 313 313 313 313 313 303

The finding of conservative investing policy by ETFs’ managers agrees to the

conclusion of Gastineau (2004), who suggests that the lack of management’s

aggressiveness negatively affect the effort of ETFs to accurately replicate the performance of tracking indices.

Table 5 The tracking error of ETFs during the period 4/3/2001-7/8/2002 ETFs Average No of

Classes (Tracking indices) Obs. ΤΕ1 ΤΕ2 ΤΕ3ΤΕ(1+2+3) Domestic DIA-D.J.Industrial 0.285 313 0.214 0.285 0.261 Broad FFF-Fortune 500 0.383 313 0.256 0.399 0.346 Markets ETFs IWB-Russell 1000 0.284 313 0.206 0.286 0.259

IWD-Russell1000 Value 0.217 313 0.166 0.220 0.201 IWF-Russell1000 Growth 0.297 313 0.226 0.297 0.273 IWM-Russell 2000 0.373 313 0.282 0.373 0.343 IWO-Russell2000 Growth 0.504 313 0.392 0.507 0.468 IWV-Russell 3000 0.226 313 0.172 0.228 0.209 IWZ-Russell3000 Growth 0.716 313 0.502 0.715 0.4

IWR-Russell Mid Cap0.860 238 0.557 0.908 0.775

IWS-Russell Mid Value0.474 236 0.303 0.481 0.419 IVV-S&P 500 0.316 313 0.217 0.316 0.283 IJH-S&P Mid 400 0.302 313 0.199 0.303 0.268 MDY-S&P Mid 400 0.404 313 0.292 0.404 0.367 QQQ-Nasdaq 100 0.596 313 0.445 0.598 0.546 SPY- S&P 500 0.348 313 0.242 0.348 0.313

273 VTI-Wilshire50000.181 0.133 0.181 0.165

Domestic FEF-Fortune e-50 1.674 313 1.240 1.702 1.539 Sector ETFs IDU-D.J Utilities 0.479 313 0.375 0.490 0.448

IBB-Nasdaq Biotech 0.577 313 0.395 0.592 0.521

313 International EWA-Australia 0.796 1.070 0.977 1.0

ETFsEWC-Canada 313 0.963 1.216 1.127 1.203

EZU-EMU0.765 248 0.630 0.796 0.730 EWG-Germany 0.844 313 0.658 0.851 0.784 EWH-Hong Kong 313 1.247 1.638 1.495 1.600 EWI-Italy 0.762 313 0.5 0.766 0.706 EWJ-Japan 313 0.972 1.232 1.128 1.179 EWD-Sweden 313 1.103 1.487 1.358 1.485 EWL-Switzerland 0.958 313 0.746 0.959 0.888 EWU-U.K 0.887 313 0.710 0.907 0.835 Average 0.675 0.508 303 0.685 0.623

ΤΕ1 is the standard errors of returns’ regression (6). ΤΕ2 is the average absolute difference in returns of ETFs and tracking indices. ΤΕ3 is the standard deviation of returns’ differences. ΤΕ(1+2+3) is the average of three methods.

V) The failure of index trackers to accurately replicate the performance of underlying indices has experienced a great interesting by literature. Many researchers tried to illustrate the sources of tracking error and to quantify its magnitude.4

See Roll (1992), Pope and Yadav (1994), Frino and Gallagher (2001), Gastineau (2004), Elton, Gruber, Comer and Li (2002).

4

In this section, we use the three methods that are suggested by Frino and Gallagher (2001) in order to estimate the tracking error of sample’s ETFs.

The results of tracking error’s calculation appear on Table 5. The column named

ΤΕ1 concerns the estimation of tracking error by the standard error’s residual of regression (6). The columns ΤΕ2 and ΤΕ3 are related to the calculation of mean absolute difference and the standard deviation of differences among ETFs and indices’ returns respectively. Finally, the column ΤΕ(1+2+3) represents the average tracking error after the combination of all three methods’ calculations.

The mean ΤΕ1 is equal to 0.675, ΤΕ2 counts to 0.508, ΤΕ3 stands 10 basic points

above than ΤΕ1, since the average of three methods is 0.623. According to three methods’ average, the best index tracker is the VTI (Wilshire 5000 Index), which has mean tracking error equal to 0.165. Contrary, FEF’s return (Fortune e-50 Index) deviates from the performance of its corresponding index more than anyone else’s.

Table 6 The appreciation of tracking error estimation convergence Coefficients ΤΕ1- ΤΕ2 ΤΕ1-ΤΕ3 α 0,029 0,004

(2.036)** (1.341)

β 1.272 0,980 (53.042)* (172.560)* 2 R0,990 0,999 No of obs. 30 30 Estimated Model: TEi = αi + βi TEj + ei (9) The value in parentheses denotes the t-ratio

*Significant in 1% level. ** Significant in 10% level.

In the final step, we investigate the similarity of tracking error’s calculations

respectively to three different methods. We perform this investigation by applying the following single regression model:

ΤΕ2-ΤΕ3 -0.015 (-1.273) 0.763 (51.987)* 0.9 30 TEi = αi + βi TEj + ei (9)

TE symbol denotes the tracking error’s estimations, while the subscripts i and j indicate the particular method that are regressed each time. We use the beta of regression as an indicator of estimations’ convergence. The equalization of beta to unity implies that the tracking error’ calculations by each two successive methods are substantially identical.

The regression’s results are recorded on Table 6. The table includes the alpha and beta coefficients, as such the R-squared. The beta of regression between calculations of method 1 and their respective computations of method 2 sufficiently exceeds than unity. This fact is repeated when we regress the method 2 on method 3. So we could conclude that these methods derive unequal estimations.

In contrast, according to the findings of Table 6, the methods 1 and 3 substantially demonstrate the same results for tracking error. The regression’s beta approximates the unity, indicating the high correlation among these methods. This is not a surprising conclusion, since the average systematic risk of ETFs (beta of regression (6)) is nearby enough to unity.

6. Conclusions

In this paper, we empirically investigated the trading characteristics and performance of Exchange Traded Funds, an investing product that has been recently appeared in US market. The previous research about ETFs is mainly concentrated to the studying of SPDRs, one of the most significant and tradeable ETFs which is supposed to be the ETF

that was initially issued. The literature exams the performance of SPDRs in comparison to traditional index funds that also track the S&P 500 Index.

We expand the existing literature in the way that we use a broader sample of

ETFs, which is comprised from the most tradeable and sizeable ETFs listed on AMEX and NASDAQ’s exchanges. The sample’s ETFs track some of the most significant and representative indices of international capital markets.

In the first step, we viewed on the percentage correlation between the trading

prices of ETFs in the secondary market and the values of underlying indices. We ascertained that a gap exists among ETFs and indices’ values in any case. This gap spans from 0.2% to 39.1%.

Afterwards, we looked into the issue of trading values’ declination from net

asset values. We demonstrated that the majority of sample’s ETFs is traded in premium and only few of them perform in discount. The average premium and discount does not exceed the 10 basic points, a fact that indicates the efficient arbitrage’s execution by institutional investors.

We calculated the percentage rates of ETFs’ performance and risk. Accordingly

to the studied period’s general investing environment, ETFs recorded negative mean percentage return. However, the negative ETFs’ performance did not stand far from zero. Otherwise, the risk of ETFs was held in low levels, indicating the great diversification of risk that is in general achieved by ETF, as a result of their structure and the passive character of their investing philosophy. We added that the return and the standard deviation of tracking indices mainly stood closely to their associates of ETFs.

The last issue we inspected was the observed deviation among returns of ETFs and indices. Applying three methods, we saw that the average tracking error fluctuated from approximately 0.51% to 0.69%. Comparing the results of three methods, we concluded that the method, which concerns the tracking error’s estimation by standard error’s residuals of returns regression, and the method, which calculates the magnitude of tracking error by computing the standard deviation of return’s difference, substantially produce the same results. This similarity is justified by the convergence of systematic risk (beta of returns’ regression) to unity.

This deviation reflects the inherent frictions ETFs face, like administrative expenses, transaction costs and commissions, the delay between the index and ETF’s portfolios rebalancing, the underinvested dividends. In contrast, the indices do not face any of the above troubles. In addition, the passive character of ETFs’ strategy also restricts in a way the ability of administrators to actively manage their portfolios in order to improve the performance. Concluding this paper, we note that Exchange Traded Funds represent an issue of great investing and researching interesting, since they are an effective substitute to traditional investments in stocks and mutual funds. In a next paper, a further research could be concentrated on the impact of expenses to ETFs’ returns, the relation between the fore passed returns and the current asset flows to ETFs, the comparison among passively and actively managed ETFs.

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