Research Paper on Classical Exchange-Traded Funds

Abstract

Exchange-Traded Funds (ETF's) have become widely held financial instruments among investors. Their popularity has produced an explosion in the number of different ETF's currently available in most financial markets. This revolution started in the early 90's with a single product which consisted of a basket of single securities that where part of (and therefore closely follow) the S&P 500 index (SPDR). The idea was to have a financial instrument that was less volatile than a single stock and yet could be traded as one thus avoiding the shortcomings of traditional mutual funds such as management fees, liquidity and tax disadvantages. The idea worked and currently there are nearly 1000 of such instruments. Our research empirically analyzes the idea that there is no need for so many of these products and therefore an investor could be better off by picking among a handful of them with each of them belonging to a statistically different cluster of such funds. To investigate this idea we randomly sampled 574 Exchange-Traded Funds (ETFs) and analyzed them using three multivariate methods: Cluster Analysis, Factor Analysis and Chernoff-Faces. For each fund, we recorded performance measures that included: Intraday, YTD, 3-Month, 1-Year and 3-Year returns . Utilizing a k-means clustering algorithm we obtained 5 clusters of the ETF's which produced (statistically) similarly behaving funds within each cluster and dissimilar ones between clusters. Factor Analysis and Chernoff-Faces were used to graphically depict the similarities of the ETF's belonging to each cluster. The analyses also showed surprising similarities for many ETF's that supposed to follow different stock indexes, thus questioning the value of diversification for investors trusting this strategy. On the other hand, the results of this study could provide investors to further diversify their holdings by choosing funds belonging to different clusters.

Is your time best spent reading someone else’s essay? Get a 100% original essay FROM A CERTIFIED WRITER!

Order now

Introduction

Classical Exchange-Traded Funds (ETF's) are tradeable securities which derive their value from a fixed basket of stocks that track a particular index. Because of this, ETF's derive their price (and volatility) from the market movements of the underlying stocks in the basket. Not to be confused with Index Mutual Funds which are managed by institutional managers and (at least at the onset of the purchase) are not as liquid as ETF's that can be traded as regular stocks. ETF's also provide investors with diversification and the added advantages of tax efficiencies and lower expenses as compared to traditional mutual funds. At their inception in the early 1990's with SPDR (hence their nickname "Spiders"), ETF's mostly target institutional investors but very quickly got the eye of everyday investors. As of late 2006, SPDR (which follows the S&P 500 index movements) had assets of $58 billion and accounted for 16% of all the ETF market share (WSJ, Nov. 10, 2006). Since the inception of SPDR the number of ETF's (iShares and the likes) have exploded to nearly 1000 different instruments currently available for trading (Morningstar, Apr. 2011). Comparisons between the advantages and disadvantages of ETF's vs Mutual funds have received wide attention in the finance literature (Gastineau, 2001, 2004; Brom and Gastineau, 2007, Blitz et.al. 2011; Aber et. al. 2009). In a nutshell, ETF's have less volatility than individual stocks, are more liquid, and in in the short run, can produce higher returns than traditional mutual funds. Many investment houses (notably Fidelity and Vanguard) offer brokerage-free ETF's that are mostly tied to their large mutual funds (and some to the various indexes). This paper is not about the advantages or disadvantages but rather about diversification of an ETF portfolio. Given the large quantity of instruments being offered we proposed a multivariate approach to select instruments that follow different behavior thus an investor confronted with a decision of buying several ETF's will not need to purchase a basket that moves similarly therefore protecting them from potentially adverse market movements.

Literature Review

While abundant literature exists about the performance of index mutual funds, ETF's have received less attention than this counterpart. Early studies on ETF's were focused on the characteristics of this innovative investment instrument (Gastineau, 2002, Mussavian and Hirsch, 2002). More recent studies (Rompotis, 2006) examine their return performance and trading characteristics. Seasonal returns and volatility have been also studied by Rompotis (2007) who found a significant November effect in the sample of ETF's under study. A handful of other studies have compare traditional mutual funds and ETF's (that track the same indexes) in terms of trading costs, return performance and risk. Dellva (2001) found that the ETF's had a significant cost advantage compared to the mutual funds in their study. At least two studies (Elton et. al., 2002 and Gastineau, 2004) found that mutual funds outperform the sample of ETF's in their study. This comparison was based on a ten year period 1992-2002 and the underperformance (pre-tax) of the ETF in Gastineau's study (SPY) was 119.52% vs 120.61% and 121.68% for the Vanguard 500 and S&P 500 benchmark indexes. In a more recent study, Rompotis (2005) analyzes the performance of 16 pairs of ETF's and mutual funds against their tracking indexes and found they substantially produced similar returns and tracking errors. Agapoga (2006) found that ETF's had a lower index tracking errors and lower expenses than their mutual fund counterparts. He also suggests that their substitutability is due to a "clientele effect". A more recent study by Aber et. al. (2009) analyzed the price volatility and tracking errors of ETF's vs similar tracking mutual funds. They found that ETF's had a smaller tracking error and outperformed the index mutual fund counterparts in intraday trading. Overall the empirical studies comparing ETF's and index mutual funds offer a different picture. In the long run ETF's underperform mutual funds while on intraday trading they are better off. Additionally, ETF's track their benchmark indexes closer and have lower management fees than their related index tracking mutual funds.

Objective of the Study

This study differs from the others in the sense that we concentrate on the performance of ETF's among themselves (we don't compare them to index mutual funds or to any benchmark index). Our idea is that performance-wise most ETF's concentrate in a handful of clusters. Identifying these clusters could provide investors with a) an extra layer for diversification, or b) a way to improve performance by concentrating in ETF's that are part of a single cluster.

Methodology

A random sample of 574 ETF's was collected in early 2011 from Yahoo! Finance, (finance. yahoo.com). The ETF's in our sample are listed in Appendix A. Intraday, YTD, 3-Month, 1-Year and 3-Year returns were recorded. This 5-variable sample was clustered using a K-means clustering algorithm (Hartigan and Wong, 1979) which produced 5 clusters (Appendix B). Figure 1 shows the clusters in a 2 dimensional space where the axes correspond to the principal components of the 4 variables.

Note that the multi-dimensional scaling is based on the Factor loadings (80% of the variance of the 4 variables is explained by these two factors) and it was used only to be able to plot the clusters in a two dimensional space. In reality the 5 clusters do not overlap as shown in Figure 2 where the clusters are shown in a 3 dimensional space by adding a third factor to the plot above (the 3 factors now account for almost 90% of the variance of the 6 variables).

The k-means clustering algorithm adds membership to the clusters by minimizing the within clusters sums of squares (see Hartigan for more detail) and thus producing k-clusters of points that are as closed as possible to every point within their clusters. The center of the cluster therefore could be an observed point (in this case an ETF) or could be a point calculated by the algorithm. In Figure 3 we show the means of each cluster based on their variables (the performance measures). Notice how different the clusters are in terms of their variable means. Also note that the intraday return mean differences (although significantly different) are meaningless given an almost negligible intraday percent returns for the day the sample was taken. In particular Cluster 5 (the highest overall returns) and Cluster 4 (the lowest overall returns) are of interest. The cluster means returns show highly significant differences as shown in the ANOVA (Table 1).

Table 1: Analysis of Variance for Cluster Means

Table 2 shows the descriptive statistics for each of the clusters by variable (same data depicted in Figure 3). Highlighted clusters are the ones with the highest and lowest (overall) means (clusters 5 and 4 respectively).

Table 2: Cluster Means and Standard Deviations

Since the clusters are quite large, we proceeded to select the ETF's that where the closest to their cluster centroid and depict those funds by means of a Chernoff Face (Chernoff, 1973) just to see how different they looked (judging by their significantly different performance means). Figure 4 shows those ETF's (VTI, VGK, IPE, SJL, and IJT which were the funds closer to their centroids for clusters 1 through 5 respectively. Even though certain features of the faces are the same for all ETF's (eyes, eyebrows, mouth curvature and nose are the same) still we can discern differences in at least two of the faces, those corresponding to SJL and IJT (which belong to the most different clusters (4 and 5). In fact, we can almost be certain that the other 3 ETF's behave about the same in terms of these 6 performance measures. Again, this shouldn't be surprising since Figure 3 (in terms of the variable means) depicts the same as Figure 4. Again, Figures 3 and 4 complement each other, and not necessarily tell us the exact same story.

Discussion

This analysis takes advantage of well know multivariate statistical methods to a sample of 574 ETF's based on 6 performance measures (intraday, YTD, 3 month, 1-year, and 3-year returns. The basic idea was to break down the various ETF's into similar clusters based on these 6 performance measures. Principal Components analysis was then used to plot the clusters in 2 and 3 dimensional spaces based on the Factor coordinates. The ETF's closest to the cluster centroids where plotted using Chernoff faces to show the similarity/disparity of those ETF's which can be thought as representatives of the rest of their cluster constituents. The analysis of variance for the between cluster means of the 5 performance measures sh...