The Performance of Market Indexed Exchange Traded Funds

The Performance of Market Indexed Exchange Traded Funds Rakesh Sah ETF have become popular in recent times. The purpose of this paper is to examine the reasons for the demand in these instruments. We find that the short levered ETF are in greater demand than long only ETF. Further, the lower multiple levered ones are more desired than the higher multiple ETF. We also find that the volume of trading in our sample ETF increases during greater market volatility. However, the tracking error of these funds is independent of market volatility, which makes them a desired hedging instrument. [Field of Research: Investments, Risk Management, Exchange Traded Funds] 1. Introduction Market Indexed Exchange Traded Funds (ETF), when first introduced, were designed to replicate the returns on some broad based market index. In the United States of America the early ETF that were popular at the start of the century were the SPDR (Ticker Symbol SPY) designed to replicate the returns on the S&P500 Index, the Diamond (Ticker Symbol DIA) designed to replicate the returns on the Dow Jones Industrial Average (DJIA) and the Triple Q (Ticker Symbol QQQQ) designed to replicate the NASDAQ Index. These ETF gave the investor, and also the speculator and the hedger, a simple instrument that could be traded like a stock but because it was backed by a basket of underlying securities, was well diversified and contained minimal market and firm specific risk. Investing in these ETF precluded the need to diversify into a basket of stocks with significant trading and other expenses and these soon became very popular. The second generation ETF first came to the scene in 2006 (Little 2009) and aimed to replicate twice the performance of the benchmark index. However, the uniqueness of these new ETF were that they also replicated twice the short position of the underlying index, so that if the underlying index had a daily return of 2%, the long ETF would ideally have a return of 4% while the short ETF would have a return of -4%. The early second generation entrants had the ticker symbols DDM that aimed to replicate 2xDJIA, and DXD aimed for the inverse of 2xDJIA; the SSO (2xS&P500) and the SDS(inverse of 2xS&P500); and the QLD and QID aimed for 2xNASDAQ and the Rakesh Sah, Ph.D., Associate Professor of Finance, College of Business, Montana State University, Billings, MT 59101, USA. rsah@msubillings.edu

inverse, respectively. The Third Generation ETF were more ambitious and were designed to replicate three times the market indices and their inverse, the UDOW and SDOW are the long and short ETF that try to replicate 3xDJIA and its inverse, the UPRO and SPXU are associated with 3xS&P500 and its inverse, and the TQQQ and the SQQQ with 3xNASDAQ and its inverse, respectively. The two hallmarks of the second and third generation ETF were the use of leverage and derivative products with daily rebalancing of their portfolios. In addition, to the broad market based indexes, some second and third generation ETF are more ambitious and were designed to replicate other not so common indices. There are ETF that try to replicate some multiple (and its inverse) of the crude oil index (UCO and SCO), the gold price index (UGL and GLL), the Real Estate Index (URE and SRS), the Energy price index (DIG, DOG, ERX and ERY), Natural gas price index, the Semi-Conductor price index (SOXL and SOXS), the Financial Index (UYG, SKF, FAS and FAZ), etc. There are also ETF on currencies like the US Dollar, the Euro, and the Yen, on the Treasury yield curve (UBT an d TBT), on market volatility (VXX and VXN), and also on countries like China (CZM and CZI), India (INDL and INDZ) and Brazil (BRIL and BRIS). There has been an explosion in the number and types of ETF now available to common investors. The purpose of this paper is to research the performance of the broad based market Index ETF related to the DJIA, the S&P500, Russell 1000, Russell 2000 and the NASDAQ Indices. The ETF that are considered have the ticker symbol DIA, DDM, DXD, UDOW, SDOW, SPY, SSO, SDS, UPRO, SPXU, QQQQ, QLD, QID, TQQQQ and SQQQQ, IWM, UWM, TWM, TNA, TZA, IWD, UVG, SJF, BGU and BGZ. These ETF are the only ones that are based on the broad market indices with a high frequency of trades. 2. Literature Review Little (2009) provides a concise introduction to ETF and the pitfalls in obtaining targeted returns on these instruments, especially in high volatility non trending markets. Little shows that outperformance in these ETF is extremely difficult given the high costs of trading. Charupat and Miu (2011) examine the characteristics of levered ETF. They find that daily rebalancing of these funds increases market volatility at the close of trading. They also find that daily tracking errors are very small. Lu, Wang and Zhang (2009) using data from 2006 to 2008 study the long term performance of leverage ETF and find that over short periods of time, these achieve the desired level of return, however for longer time frames there are substantial deviations in their performance. Avellaneda and Zhang (2009) provide a formula for linking the return of a leveraged fund with the corresponding multiple of the return of the unleveraged fund and its realized variance. They find that weekly rebalancing of leveraged EFT s also provides satisfactory performance. Johnson (2009) studies the tracking errors between foreign ETF and the underlying home index on a daily and monthly basis. Barnhart and Rosenstein (2010) show that the introduction of an ETF in an asset class similar to an existing Closed End Fund (CEF) results in a substitution effect that reduces the value of CEF shares relative to that of its underlying assets.

3. Methodology The data on the ETF under study, the VIX and the underlying benchmark indices were collected from Bloomberg. The period under study is March 2008 to March 2011 because the earlier studies have covered periods prior to these dates. Table 1 gives the list of all ETF and their benchmarks studied in this paper. The single and double levered funds have been in existence for the entire data collection period but the triple levered funds were started in 2009 and 2010, therefore we have limited data series on these funds. TABLE 1: LIST OF EXCHANGE TRADED FUNDS AND THEIR BENCHMARKS ETF (TICKER) MARKET INDEX BENCHMARK DIA DJIA 1xDJIA DDM DJIA 2xDJIA DXD DJIA INVERSE 2xDJIA UDOW DJIA 3xDJIA SDOW DJIA INVERSE 3xDJIA SPY S&P 500 S&P 500 SSO S&P 500 2x S&P 500 SDS S&P 500 INVERSE 2x S&P 500 UPRO S&P 500 3x S&P 500 SPXU S&P 500 INVERSE 3x S&P 500 QQQQ NASDAQ NASDAQ QLD NASDAQ 2xNASDAQ QID NASDAQ INVERSE 2xNASDAQ TQQQ NASDAQ 3xNASDAQ SQQQ NASDAQ INVERSE 3xNASDAQ IWM RUSSELL 2000 1xRUSSELL 1000 UWM RUSSELL 2000 2xRUSSELL 1000 TWM RUSSELL 2000 INVERSE 2xRUSSELL 2000 TNA RUSSELL 2000 3xRUSSELL 2000 TZA RUSSELL 2000 INVERSE 3xRUSSELL 2000 IWD RUSSELL 1000 RUSSELL 1000 UVG RUSSELL 1000 2xRUSSELL 1000 SJF RUSSELL 1000 INVERSE 2xRUSSELL 1000 BGU RUSSELL 1000 3xRUSSELL 1000 BGZ RUSSELL 1000 INVERSE 3xRUSSELL 1000 This paper tests three hypotheses:(1) The volume of trading of these ETF is proportional to the level of panic in the market (2) These funds can be used as hedging instruments, and (3) The tracking error of these funds is mean reverting.

The level of panic is approximated by the measure of market volatility (VIX) and for the NASDAQ benchmarked ETF the VXN. The tracking error (TE) is defined as the difference between the daily return on the ETF and the benchmark. TE ETF = RETURN ETF - RETURN BENCHMARK The total volume of daily trading was calculated for the entire data and also for all funds benchmarked to an index. VIX the measure of market is universally accepted as an indicator of panic in the market. Market volatility was regressed against these to determine the effect of volatility on the volume of trading. The tracking error of each individual fund was calculated along with the standard error. To determine if the tracking errors were mean reverting, two tests were carried out. First, the autocorrelations of the tracking error of each of the funds were determined. If the sign on the correlation coefficients between adjacent periods is negative, the series would show mean reversion tendencies. The variance ratio is another test for determining mean reversion. If the variance of the entire data period is greater than the variance of the sub-periods the series would show signs of mean reversion. 4. Discussion An analysis of the trading data of DJIA indexed funds found that the DIA (1xDJIA) dominated the DDM (2xDJIA), DXD (-2xDJIA), UDOW (3xDJIA) and SDOW (-3xDJIA) in terms of the volume of trading for all days of the sample period. DDM (2xDJIA) and DXD (-2xDJIA) dominated the UDOW (3xDJIA) and the SDOW (-3xDJIA). The inverse funds dominated the long funds most of the time. The DXD dominated the DDM 98% of the time and the SDOW dominated the UDOW 88% of the time. Therefore, as the inverse funds dominate the long only funds and the lower multiples dominate the higher multiple funds we can conclude that a much larger proportion of the participants use these ETF for hedging rather than investing or speculative purposes. The S&P 500 family of funds accounted for 54% of the total trades, followed by the NASDAQ 100 which was 24% of the total. The DJIA family was only 5% of the trade while the RUSSELL family was 17% of the total trades. As the DJIA consists of only 30 stocks and if ETF are primarily used to hedge portfolios, then these results are not surprising. For the S&P500 indexed funds, too, the lower multiple funds dominate all the higher multiple funds but the SDS (-2xS&P500) dominates the SSO (2xS&P500) 97% of the time while the SPXU (-3xS&P500) dominates the UPRO (3xS&P500) 63% of the time. For the NASDAQ and the RUSSELL indexed fund the lower multiple funds dominate the higher multiple funds and the inverse funds generally dominating the long only funds in trading volume. The complete results are given in TABLE 2. TABLE 2: TRADING VOLUME CHARACTERISTICS OF ETF DOW FAMILY (PERCENT DOMINATION) DIA(x1) DDM(x2) DXD(x-2) UDOW(x3) SDOW(x-3)

DIA(x1) - 100 100 100 100 DDM(x2) 0-2 100 100 DXD(x-2) 0 98-100 100 UDOW(x3) 0 0 0-12 SDOW(x-3) 0 0 0 88 - S&P 500 FAMILY (PERCENT DOMINATION) SPY(x1) SSO(x2) SDS(x-2) UPRO(x3) SPXU(x-3) SPY(x1) - 100 100 100 100 SSO(x2) 0-3 100 100 SDS(x-2) 0 97-100 100 UPRO(x3) 0 0 0-37 SPXU(x-3) 0 0 0 63 - NASDAQ 100 (PERCENT DOMINATION) QQQQ(x1) QLD(x2) QID(x-2) TQQQQ(x3) SQQQ(x-3) QQQQ(x1) - 100 100 100 100 QLD(x2) 0-95 100 100 QID(x-2) 0 5-100 100 TQQQQ(x3) 0 0 0-73 SQQQ(x-3) 0 0 0 27 - RUSSELL 2000 FAMILY (PERCENT DOMINATION) IWM(x1) UWM(x2) TWM(x-2) TNA(x3) TZA(-3) IWM(x1) - 100 100 100 100 UWM(x2) 0-93 3 67 TWM(x-2) 0 7-0 35 TNA(x3) 0 97 100-93 TZA(-3) 0 33 65 7 - RUSSELL 1000 FAMILY (PERCENT DOMINATION) IWD(x1) UVG(x2) SJF(x-2) BGU(x3) BGZ(x-3) IWD(x1) - N/A N/A 17 71 UVG(x2) N/A - N/A N/A N/A SJF(x-2) N/A N/A - N/A N/A BGU(x3) 83 N/A N/A - 95 BGZ(x-3) 29 N/A N/A 5 - N/A= Negligible trading volume The daily total trading volume for each family of funds was very large and fluctuated widely. The natural logarithm of the total daily trading volumes was taken to smooth the data. The VIX at close of trading was regressed against the total trading volume for each of the family of funds except for the NASDAQ family which was regressed against the VXN, the volatility index associated with NASDAQ traded stocks. The results

indicate a significant positive relationship between the volume of trading and the level of panic in the market for all family of funds and also for aggregate funds in the sample. The DOW family funds, both lever and unlevered, had the highest coefficient of determination (R 2 =0.63), with the t-statistic=35.98. This is to be expected as the DJIA consists of firms that are industry leaders and expected to be more responsive to market conditions. The results are similar for a sample consisting of only the levered DOW funds and these have a R 2 =0.52, with a t-statistic= 17.29. The NASDAQ family had a R 2 =0.47 and a t-statistic= 26.30. For the RUSSELL 2000 family of funds the R 2 = 0.45 with a t-statistic= 14.47. This relation was much weaker for the RUSSELL 1000 family which had a R 2 =0.21 with a t-statistic= 14.33. These results show that at times of increased investor fear, market players resort to hedging strategies using Exchange traded funds. For the RUSSELL family of funds the relationship is weaker because the associated ETF have a relatively lower trading volume. Further, the DOW and S&P shares being more popular are more widely held in portfolios that need to be hedged in times of market uncertainty. The complete results are given in TABLE 3. TABLE 3: RESULTS OF REGRESSION OF VIX (VXN) ON ETF ETF FAMILIES Coefficient of Determination (R 2 ) t-statistic DOW 0.63 35.98 LEVERED DOW ONLY 0.52 17.29 S&P 500 0.55 30.64 LEVERED S&P 500 ONLY 0.49 20.52 NASDAQ (with VXN) 0.47 26.30 RUSSELL 2000 0.45 14.47 RUSSELL 100 0.21 14.33 ETF seem to be primarily used for hedging purposes, but do they provide a stable hedge. The tracking error of these funds seems not to be affected by market volatility. When tracking errors of these funds are regressed on VIX, there seems to be no connection between the two series for any of the funds. Both the coefficients and the t- statistics for the regression equations are almost negligible and not significant at any level. Therefore, ETF have a steady performance relative to their benchmark regardless of volatility. The results can be seen in TABLE 4. Mean Reversion of the tracking errors were tested using 100 sample points because the Dickey Fuller test reports only 10% critical values for 100 data points, though there were no significant differences in using shorter time periods. The results of the test are reproduced in TABLE 5. The results clearly show that the tracking errors are mean reverting. However, the raw ETF price series fail to show mean reversion even for the Dickey Fuller test with a constant and trend. This is similar to the findings of Lu, Wang and Zhang (2009) who found substantial deviations in performance as the sample period got longer and with Charupat and Miu (2011).

TABLE 4: RESULT OF THE REGRESSION OF TRACKING ERROR ON VIX ETF Coefficient t-statistic DIA 0.001 0.414 DDM 0.001 0.070 DXD 0.001 0.048 UDOW 0.001 0.340 SDOW 0.002 0.620 SPY 0.001 0.520 SSO 0.001 0.110 SDS 0.001 0.220 UPRO 0.001 0.210 SPXU 0.001 0.320 TABLE 5: RESULTS OF DICKEY FULLER TEST FOR MEAN REVERSION ETF Test Statistic Critical Value DIA -8.55-2.58 DDM -7.16-2.58 DXD -7.16-2.58 UDOW -8.15-2.58 SDOW -7.39-2.58 SPY -10.29-2.58 SSO -12.89-2.58 SDS -8.94-2.58 UPRO -11.30-2.58 SPXU -9.32-2.58 5. Conclusion The paper finds that ETF are not all uniformly popular. The lower multiple and the short levered funds had larger trading volumes over the course of the sample period. Further, the trading volume seemed to increase in times of market volatility when investors seem to want an instrument to hedge their risk. As the lower multiple ETF and those that were short are in greater demand, it appears that these instruments are used primarily for hedging purposes rather than speculation or as an investment. Further, the broader indices responded more to market volatility than the more specialized ETF. The daily tracking errors for the sample ETF did not display any relation with market volatility and thus seem to be used for hedging purposes. The tracking errors were mean reverting but the returns on the ETFs were non stationary. Therefore, the ETFs would provide a tool for hedging purposes only for a short duration else there would be a divergence between actual and desired returns. This is perhaps what accounts for the large trading volume of these instruments.

6. References Avellaneda, Marco and Zhang, Stanley 2009, Path-dependence of Leveraged ETF returns, working paper series. Barnhart, Scott W. and Rosenstein, Stuart 2010, Exchange-Traded Fund Introductions and Closed-End Fund Discounts and Volume, The Financial Review, 45.4, November. Charupat, Narat, and Miu, Peter 2011, The pricing and performance of leveraged exchange-traded funds, Journal of Banking and Finance, 35.4, April, p966(12). Johnson, William F. 2009, Tracking errors of exchange traded funds, Journal of Asset Management, 10.4, October, p253. Little, Pat 2009, Inverse and Levered ETF: Not your father s ETFs, Research Note, Merrill Lynch. Lu, Lei, Wang, Jun and Zhang, Ze 2009, Long Term Performance of Leveraged ETF working paper series.