Tracking Performance of Leveraged and Regular Fixed Income ETFs

Transcription

1 Tracking Performance of Leveraged and Regular Fixed Income ETFs Hongfei Tang Stillman School of Business Seton Hall University South Orange, NJ 07079, USA Tel: (973) ; Fax: (973) Xiaoqing Eleanor Xu * Stillman School of Business Seton Hall University South Orange, NJ 07079, USA Tel: (973) ; Fax: (973) xuxe@shu.edu This version: June 2013 * We thank James Brotchie, Tong Yu, and session participants at the 2013 Midwest Finance Association Annual Meetings in Chicago for valuable comments and suggestions.

2 Tracking Performance of Leveraged and Regular Fixed Income ETFs Abstract This paper examines the tracking performance of regular and leveraged Fixed Income Exchange-traded Funds (FIETFs) on four major indices: medium-term Treasury, long-term Treasury, investment grade corporate, and high yield corporate bond indices. All sample LFIETFs display significant tracking errors, and these tracking errors are much larger for funds on the longer maturity bond index. In addition, funds tracking corporate bond indices show greater tracking errors than those on Treasury bond indices. Finally, tracking errors are larger for leveraged FIETFs than for regular FIETFs and increase as the magnitude of target leverage increases for bull/bear funds. These findings suggest that leveraged FIETFs carry substantial tracking risk in addition to the risk embedded in their benchmark returns. Furthermore, this tracking risk is associated with maturity and credit quality of the underlying index, as well as the magnitude of the fund s target leverage. The empirical evidence can help investors and portfolio managers understand the tracking performance of regular and leveraged FIETFs, and formulate strategic hedging and asset allocation strategies using FIETFs. Keywords: Leveraged Fixed Income Exchange-traded Fund; Tracking Performance; Treasury Index; and Corporate Bond Index JEL Classifications: G11, G12, G14

3 Tracking Performance of Leveraged and Regular Fixed Income ETFs 1. Introduction Fixed Income (FI) investments are different from equity investments in various aspects. 1 Most bonds are traded over-the-counter (OTC); consequently, it is challenging for retail investors to directly invest in FI securities. In addition, it can be difficult to short-sell even in the case of Treasury bonds. The FI sector s lack of market liquidity, price transparency, and trading flexibility has limited its accessibility to retail investors. The first batch of Fixed Income Exchange-traded Funds (FIETFs) were introduced to the U.S. markets in 2002, shortly after the reporting requirement of OTC bond transactions was implemented. 2 Since 2002, the introduction of FIETFs has facilitated retail investors participation in the FI market, as well institutional investors asset allocation in the FI sector. 3 For example, BlackRock reports that Inflows for the first half of 2012 were the largest ever for the global ETP Industry. 4 ETPs attracted net new assets of more than $100bn during the first half of Fixed income was the main driver of growth attracting 41% of all inflows. As of June 2012, the total assets under management (AUM) for global FIETFs passed $300 billion. 5 Beginning in 2008, Leveraged Fixed Income Exchange-traded Funds (LFIETFs) offered investors easily accessible vehicles to adjust their exposure to FI indices with limited liability. LFIETFs are 1 See Appendix Table A1 for detailed definitions of the main terms and variables used in this paper. 2 In particular, the Trade Reporting and Compliance Engine (TRACE) system started to operate on July 1, 2002 ( The first batch of FIETFs incepted on July 26, As argued by Guedj and Huang (2009), ETFs are more suitable for less liquid underlying indices than traditional open-ended mutual funds. ETFs combine the transparency of open-end mutual funds and the liquidity of close-end mutual funds. 4 In general, ETFs and Exchange-traded Notes are both referred to as Exchange-traded Products (ETPs). 5 Source: ETP Landscape - Industry Highlights June 2012 by BlackRock. 1

4 publicly-traded funds with a daily return objective of a constant leveraged multiple or inverse leveraged multiple, such as (3x) and (-3x) of the return on a fixed income index. Although FIETFs and LFIETFs have become more and more popular, there are only a few research papers in this area. For example, the important question as to how well these LFIETFs achieve their targets has not been explored yet. In addition, what factors influence their tracking performance? As such, we try to address these questions in this paper. To the best of our knowledge, this is the first academic study to address these questions and examine LFIETFs. Our findings are important to both academics and practitioners. We first find significant tracking errors associated with all sample LFIETFs in both daily and weekly horizons, indicating that daily investors take on further tracking risk in addition to the risk embedded in the benchmark returns of these funds. Therefore, when investors trade these funds, they cannot assume perfect tracking even in a daily horizon. A detailed analysis shows that general equity market volatility is positively associated with the tracking errors of LFIETFs on Treasury bond indices, suggesting that it is more difficult to track underlying indices when stock markets are volatile. For LFIETFs on corporate bond indices, the daily change and volatility of credit spread are positively associated with the tracking error. Comparing across the time to maturity of underlying Treasury bond indices, we find worse tracking performance for funds on the long-term (20+ years) Treasury index than those on the medium-term (7-10 years) Treasury index for both triple (3x) funds and inverse triple (-3x) funds. This finding is consistent with the interpretation that the returns of long maturity indices are more volatile than those of medium maturity. Consequently, the need to rebalance at the end of each trading day increases as the maturity increases, because the rebalancing need is proportional to the return of underlying index. In addition, as the volatility of the underlying 2

5 index increases, it becomes more difficult to rebalance an LFIETF according to the exact closing price of the underlying index. Consistent with this interpretation, we also find that the tracking error difference between the two indices is positively associated with the change in term structure spread (as measured by the difference between the 10-year Treasury and 1-year Treasury yields). LFIETFs on corporate bond indices have worse tracking performance as compared to LFIETFs on Treasury bond indices. This finding is consistent with the interpretation that corporate bond indices have a larger magnitude of daily returns than Treasury bond indices and that corporate bonds are less liquid than Treasury bonds. The larger magnitude of corporate bond return increases the need to rebalance at the end of each trading day. Furthermore, the illiquidity of corporate bonds makes it difficult to rebalance LFIETFs at a fair price. Consistent with this interpretation, we find the tracking error difference increases as the change in and the volatility of credit yield spread (as measured by the yield difference between the Moody s Baa-rated corporate bonds and the 10-year Treasury bond) increases. Comparing across funds with different leveraged multiples, (-3x) funds have worse tracking performance than (-1x) funds, and (2x) funds have greater tracking errors than (1x) funds. These findings are consistent with the rebalancing need and financing costs/benefits interpretation. In particular, as the magnitude of leverage increases, for the same underlying index return, the need to rebalance increases. For bull (bear) funds, as leverage increases, the financing costs (benefits) increase. For example, for regular (1x) funds, there is no daily rebalancing need and no financing cost. Therefore, relative to its leveraged counterpart, it is much easier for a regular fund to track its benchmark. 3

6 These findings are robust to the use of two different tracking performance measures: tracking error and mean absolute daily benchmark-adjusted returns. They are also robust to the use of daily or weekly investment horizons, showing that investing in LFIETFs is associated with extra tracking risk even in a weekly holding period. The paper most closely related to ours is Drenovak, Urosevic, and Jelic (2012), which examines regular fixed income ETFs on European sovereign debt indices. In this study, we examine fixed income ETFs tracking Treasury and corporate bond indices in the U.S. 6 Our article also complements their work by including both leveraged fixed income ETFs and their regular counterparts. In addition, they do not carry out multivariate analysis of the determinants of tracking errors, which we do. As the properties of underlying indices and the leverage ratios are critical to a fund s tracking performance, we carefully control for these aspects across funds to ensure comparability in the hypothesis testing. The rest of this paper proceeds as follows. In Section 2, we develop main hypotheses and lay out the framework for our empirical tests. In Section 3, we describe the data collection and define the tracking performance measures. Section 4 provides the main empirical results. We conduct additional tests and robustness checking in Section 5. Finally, Section 6 draws the conclusions and discusses the implications. 2. Hypothesis Development and Empirical Design 2.1 Background information 6 We also compare LFIETFs on the Italian/German sovereign debt indices to those on U.S. Treasury bond indices. Due to space limitations, differences in product design, and the unavailability of NAVs for European LFIETFs, we do not report the results in this paper, but they are available upon request. 4

7 Unlike exchange-traded stocks, the majority of bonds, especially corporate bonds, are traded over-the-counter (OTC) with low transparency and poor liquidity. The OTC market is dominated by large institutional investors, making it difficult for retail investors to invest in the FI market directly. To increase debt market transparency, the National Association of Securities Dealers (NASD) launched the Trade Reporting and Compliance Engine (TRACE) system on July 1, All brokers are required to report eligible secondary market, OTC transactions in corporate bonds through TRACE. 7 The introduction of the TRACE system has lowered bond transaction costs (Edwards, Harris, and Piwowar, 2007). 8 Partly due to the enhanced transparency of TRACE, FIETFs were introduced to the U. S. markets on July 26, The liquidity and transparency of these FIETFs greatly improved the accessibility of FI investments to retail investors. ETFs are traded on the exchange like stocks. They can be traded as long as stock markets are open, and their prices are typically in small denomination. In addition, ETFs publicize their intraday NAVs frequently, generally every seconds. One of the most stylized characteristics of ETFs is their creation and redemption features. For ETFs with in-kind creation/redemption, when the market price of an ETF is much higher than its NAV, certain authorized participants can exchange the underlying assets for ETF shares from the fund provider and then sell the shares in the market. On the other hand, when the market price of an ETF is much lower than its NAV, the authorized participants can buy ETF shares from the market and exchange them for the underlying assets from the fund provider. 9 These creation and redemption features prevent the 7 Source: 8 In particular, Edwards, Harris, and Piwowar (2007) report that the public dissemination of bond transaction prices by the TRACE system lowers bond transaction costs. 9 The arbitrage for in-cash creation/redemption is even simpler. 5

8 large deviation between the market price and the concurrent NAV of an ETF. The liquidity, transparency, and pricing efficiency make ETFs suitable vehicles for the illiquid FI sector. 10 Exchange-traded Funds (ETFs, also often referred to as Exchange-traded Products or ETPs in general) have experienced tremendous growth since their introduction into the U. S. markets in According to BlackRock, as of June 2012, 4542 ETPs exist globally with total assets under management (AUM) of US$1,677 billion. The 10-year compound annual growth rate is 29.3%. As mentioned previously, FIETFs also experience exponential growth in recent years. As of June 2012, Fixed Income ETPs account for $303 billion or 18.1% of the total global ETP AUM. 11 The availability of Leveraged FIETFs further enhances retail investors opportunities to adjust their exposure to the FI sector with limited liability. Leveraged Exchange-traded Funds (LETFs) typically seek to achieve a multiple or inverse multiple of underlying index return on each trading day. Unique to LETFs, in order to achieve a constant daily multiple, an LETF has to adjust its exposure to the underlying index on a daily basis. This adjustment is often referred to as daily rebalancing. In particular, as shown in Cheng and Madhavan (2009), for a leveraged multiple of L, the rebalancing need at the end of a trading day is proportional to (L 2 -L) and to the return of underlying index within the day. 12 For example, all else being equal, the rebalancing need for the (-3x) fund is six times that for the (- 1x) fund at the end of each trading day. The rebalancing need in a day with 2% index return is two times that in a day with 1% index return. In addition to holding underlying assets, to achieve their target leveraged exposure, LETFs also utilize swaps, futures, and other financial derivatives. Intuitively, the leverage is associated with financing costs/benefits. For example, if a 10 For example, to replicate illiquid underlying indices, Guedj and Huang (2009) argue that ETFs are more suitable than open-end mutual funds. In addition, the pricing efficiency of ETFs is stronger than close-end mutual funds due to their creation/redemption features. 11 Source: ETP Landscape - Industry Highlights June 2012 by BlackRock. 12 These results hold for both bull and bear LETFs and for both positive and negative underlying index returns. 6

9 bull (bear) fund uses equity swap to obtain positive (inverse) exposure to the index, it needs to pay out (receive) an interest, such as a spread over LIBOR. 13 Partly due to the illiquidity of FI assets, the markets for FI derivatives are not as well developed as those for equity derivatives. The financing costs/benefits add further complication to the tracking ability of an LFIETF over its targets. We expect the tracking error of LFIETFs to be highly significant and related to factors such as maturity, credit risk exposure, and leverage. Since an LETF s tracking performance should be affected by the rebalancing needs and the cost for a fund to adjust its exposure to the underlying index, we examine it in detail along the following dimensions for fixed income LETFs: the time to maturity of bonds in the underlying index, corporate vs. Treasury bond indices, and the magnitude of leverage. 2.2 Time to maturity of the underlying index For a parallel shift in yield curve, it is intuitive to expect that bonds with longer time to maturity experience a larger magnitude of returns than those with shorter time to maturity. As mentioned, the rebalancing need of an LFIETF increases proportionally to the magnitude of the underlying index return. In addition, previous literature reports that market frictions and transaction costs, such as bid-ask spread, increase as time to maturity increases (Chakravarty and Sarkar, 2003; and Chen, Lesmond, and Wei, 2007). Based on these two reasons, for funds with the same leverage, the tracking performance should be worse for funds on longer-maturity indices than for those on shorter-maturity indices. This leads us to formulate the following hypothesis: 13 See Avellaneda and Zhang (2009), Cheng and Madhavan (2009), and Tang and Xu (2013) for details. 7

10 [H1] All else being equal, LFIETFs on shorter-maturity bond indices have better tracking performance than those on longer-maturity bond indices. To test this hypothesis, we compare LETFs that track a long-term maturity Treasury index to those that track a medium-term maturity Treasury index (NYSE 20yr+ Treasury Bond Index [AXT] vs. NYSE 7-10yr Treasury Bond Index [AXS]). 14 To make sure that we have an analogous comparison, we confine our tests to fund pairs with the same leverage. For example, we compare the tracking error of the (3x) AXT fund to that of the (3x) AXS fund. 16 Our matched-pair comparison method is also consistent with previous literature (see Helwege and Turner, 1999; and Huang and Zhang, 2008). 2.3 Corporate vs. Treasury bond indices All else being equal, corporate bonds generally provide higher yields than Treasury bonds, mainly due to the credit risk, illiquidity, and possible call features of corporate bonds (Merton, 1974; Huang and Huang, 2012). From the perspective of credit risk, a corporate bond can be seen as a default-free bond combined with a short position in a put option on the firm value (Merton, 1974; and Cremers, Driessen, and Maenhout, 2008). 17 Since the put option always has non-negative value, all else being equal, the yield of a corporate bond should be no less than that of a Treasury bond. Using the long-history data of , Giesecke, Longstaff, 14 In Appendix Table A2, we illustrate all hypotheses, their testing strategies, and the related predictions. We also confine our tests to Treasury indices. The maturity tests on corporate bond indices are very difficult, because it is extremely difficult to hold the credit quality of the component assets of two corporate indices constant. In the case of bond-to-bond comparison, a way to control for the credit quality is to use bonds issued by the same firm that are only different in terms of maturity (Helwege and Turner, 1999; and Huang and Zhang, 2008). This method of control is not available for our indices. 16 DIREXION offers LETFs with leverage of (-3x), (3x), and (-1x). Due to the much longer history of (-3x) and (3x) funds, we carry out our analysis on funds with these two leverage ratios. 17 Cremers, Driessen, and Maenhout (2008) show that the jump risk premium of the put option is in line with that of an equity index put option. 8

11 Schaefer, and Strebulaev (2011) show that credit spread is about twice the default losses and averages 3 basis points. As previously mentioned, an LETF s daily rebalancing need increases proportionally as the magnitude of the underlying index s return increases. In addition, corporate bonds are often less liquid than Treasury bonds (Chakravarty and Sarkar, 2003; Houweling, Mentink, and Vorst 2005; and Chen, Lesmond, and Wei, 2007). 18 The illiquidity problem is even more serious for high yield corporate bonds (Levine, Drucker, and Rosenthal, 2010). Accordingly, for funds with the same leverage, the tracking performance should be worse for funds on corporate bond indices than for those on the Treasury bond indices. This leads us to formulate the following hypothesis: [H2] All else being equal, LETFs on Treasury bond indices have better tracking performance than those on corporate bond indices. To test this hypothesis, we compare LETFs that track corporate bond indices to those that track Treasury bond indices while controlling for the leverage ratio. In our sample, for the target leverage of (-1x), we examine the tracking performance of the LETFs on the iboxx $ Liquid High Yield Index and iboxx $ Liquid Investment Grade Index versus that of the LETFs on the NYSE 20yr+ Treasury Bond Index and NYSE 7-10yr Treasury Bond Index Tests across leverage 18 Amihud and Mendelson (1991) demonstrate that liquidity also affects yield of fixed income assets. 19 Theoretically, it would be ideal to control for other parameters, such as the maturity of the bonds. However, we are constrained by the availability of the underlying indices. To partly address this concern, we compare corporate indices with both the 20yr+ and the 7-10yr Treasury bond indices. 9

12 As discussed previously, for bull/bear LETFs tracking the same underlying index, the rebalancing need increases as the magnitude of leverage increases. In addition, the magnitude of financing costs (benefits) related to the leverage also increases with the leverage ratio of the bull (bear) funds. Due to these two reasons, for LETFs on the same underlying index, there should be worse tracking performance for FIETFs with larger magnitude of leverage for both bull and bear funds. This leads us to formulate the following hypothesis: [H3] All else being equal, tracking performance is worse for bull or bear FIETFs with larger leverage ratios. To test this hypothesis, we compare across bull (bear) FIETFs that track the same underlying index but have different magnitudes of leverage ratio. Our sample allows us to carry out this test over all four indices. In particular, our sample allows us to compare (-3x) with (-1x) bear funds on Treasury bond indices and compare (2x) with (1x) bull funds on corporate bond indices. 3. Data collection and tracking performance measures 3.1 Data collection To test these hypotheses, we start from all U.S.-listed LFIETFs that track U.S. fixed income indices and exclude those without underlying index return data from Bloomberg. For LFIETFs with available index return data from Bloomberg, we include all those tracking the same FI index and require a FI index to be tracked by at least two FIETFs (one of which may be 10

13 regular FIETF). Table 1 presents our final sample FIETFs sorted by their underlying indices and leverage ratios. As shown in Table 1, our final sample includes both Treasury bond indices and corporate bond indices, which allow for credit spread comparison. Our sample also includes both a longterm Treasury (20 year +) index and a medium-term Treasury (7-10 year) index, which allow for term structure spread comparison. In addition, we have two pairs of bear LFIETFs with different leveraged multiples of (-1x) and (-3x) for each of the two Treasury bond indices and two pairs of bull FIETFs with different multiples of (1x) and (2x) for each of the two corporate bond indices. For each FIETF, we obtain the daily market close price, Net Asset Value (NAV), total return (dividend inclusive), shares outstanding, volume, inception date, expense ratio, underlying index, and the return of underlying index from Bloomberg. Appendix Table A3 lists the characteristics of these FIETFs. As shown in the table, LFIETFs typically have high expense ratios (generally 0.95% per year), much higher than the regular (1x) investment grade FIETF which only has an expense ratio of 0.% per year. 20 The LFIETFs high expense ratios reflect their high operational rebalancing needs at the end of each trading day. In terms of AUM, LETFs on high yield and investment grade indices are much smaller in size than their regular unlevered funds, which eases the concern that daily rebalancing need will increase the volatility of the regular (1x) fund. These LFIETFs also have a higher turnover ratio than the (1x) funds, which is consistent with the uncertainty associated with the compounding 20 The (1x) high yield corporate bond fund has an expense ratio of 0.5% per year, likely due to the difficulty of tracking its benchmark. This is consistent with previous literature. Levine, Drucker, and Rosenthal (2010), document the problems and challenges of high yield bond benchmarking. 11

14 effect over long holding periods. 21 We also obtain the yield on Moody s Baa-rated corporate bonds from the Federal Reserve s website Tracking performance measures Tracking error The objective of an LFIETF is to achieve a target leveraged multiple of the underlying index return as accurately as possible. Consequently, LFIETFs belong to passive investment instruments. The most frequently used tracking performance measure for passive investments is the standard deviation of the difference between the actual return and its benchmark return. This difference is also referred to as the benchmark-adjusted return, out-performance, relative return, or active return (Drenovak, Urosevic, and Jelic, 2012; Alexander, 2008; and Bacon, 2008). Based on the objective of the LFIETF, we calculate the benchmark return as the product of the fund s stated leveraged multiple and the daily underlying index return. We define the standard deviation of the benchmark-adjusted return as the tracking error (TE). If an LFIETF tracks its benchmark perfectly, this measure will have a value of zero. As the most frequently used measure of tracking performance, this tracking error definition has various advantages. First, it includes both positive and negative deviations. For example, if a fund underperforms its benchmark by 100 basis points on a Monday and reverses back in the rest of the week. The average out-performance during the week is zero. However, for an investor with a horizon of one trading day, there is still some tracking risk, which is reflected in the daily tracking error measure within the week. Since our sample LFIETFs are designed to achieve a constant daily leveraged 21 In particular, an LFIETF holder is only willing to hold it for a short period to avoid the uncertainty of the compounding effect, especially when the market is volatile. This is true no matter the holder uses the LFIETF for hedging or speculation. 22 Source: 12

15 multiple, this daily tracking error measure is most appropriate. In addition, this tracking error measure penalizes large deviations from the mean. 23 Unfortunately, this measure has its own shortcomings. For example, this tracking error doesn t reflect the average deviation of an FIETF return from it benchmark, because standard deviation does not reflect the mean level of relative return. As an illustration, if an FIETF always underperforms by 10 basis points relative to its benchmark, then its active return is always -10 basis points every day, and consequently, this tracking error will give a value of zero, which is misleading. In addition, a number of observations are required to create an accurate measure. For example, for one trading day, it is impossible to calculate the TE measure using one daily return observation. To ensure that we have enough observations for our analysis, we focus on the tracking error measure within each week. More specifically, we calculate the standard deviation of daily benchmark-adjusted returns within each calendar week and generate only one observation for each week. We then analyze the weekly observations. 24,25 Mean absolute daily relative return To overcome the shortcomings of previous tracking error measures, we define a mean absolute daily relative return as the time-series average over the absolute value of daily benchmark-adjusted return (also referred to as mean absolute daily relative return or MADRR) See Drenovak, Urosevic, and Jelic (2012), Alexander (2008), and Bacon (2008) for details on this tracking error measure. 24 Consistent with our measure, Drenovak, Urosevic, and Jelic (2012) adopt tracking error measures within each three months using either monthly or daily data. Due to the short sample period that we have, we focus our analysis on weekly tracking performance measures using daily return data. As a robustness check, we also carry out analysis on monthly tracking performance measures and the results are consistent qualitatively. 25 Alternatively, we can also calculate this tracking error within the first five-day period starting from the first trading day and calculate the tracking error within the second five-day period during days 2-6. However this rolling tracking error measures are not independent from each other. For example, two consecutive 5-day periods share a large number of overlapping days. 26 This definition is consistent with the mean absolute deviation in Bacon (2008). 13

16 This definition can reflect any deviation between the two returns and can be applied to any number of observations. To be consistent with the weekly tracking error measure, we calculate an MADRR within each calendar week Main Empirical Results 4.1 Summary statistics of FIETF daily returns To empirically calculate the return of an FIETF, we can use its market prices or net assets values (NAVs). 28 Due to the small fund size and low trading volume of some of our LFIETFs, they may not have frequent transactions through the trading day. The daily market prices are based on the last transaction which could occur hours before the market close. There are also days when there are no transactions for some LFIETFs. Consequently, daily market prices may not reflect the true value of a fund at market close. Here is an illustration: Suppose the LFIETF s last transaction in a day occurs at 11:00 a.m. and the underlying index appreciates dramatically in the afternoon. The daily market price therefore does not fully reflect the underlying value at the end of the day. 29 However, the NAVs should reflect the actual values of the fund at market 27 As robustness check, we also calculate an MADRR within each calendar month and each calendar day and find qualitatively consistent results. See Section 5 for details. 28 Theoretically, we can also use bid-ask midquotes. However, the bid and ask prices are missing for many trading days. For example, there are only 6 daily observations for the ask price of (2x) HY fund. In addition, the bid (ask) prices at the market close may not reflect the actual prices that the marginal investors are willing to pay (accept). For example, the maximum ask price for our (3x) AXS is $9999, which is much higher than the average NAV of $ The minimum bid price for the same fund is $0.01, which doesn t make any sense either. Based on these reasons, we do not use the bid-ask midquotes. 29 This is referred to as non-synchronization between the closing prices of ETFs and the underlying index by Charupat and Miu (2011). They also show that large deviations between market price and NAV are more likely to happen in LETFs than in regular ETFs. 14

17 close. For this reason, we calculate the daily returns of our FIETFs using NAVs rather than market prices. 30 Table 2 shows summary statistics of FIETF daily raw returns (Panel A) and benchmarkadjusted returns (Panel B). We include the trading days from the inception date through June For the (3x) and (-3x) LFIETFs on the U.S. Treasury bond indices, there are 809 daily observations. For other LFIETFs, the number of observations ranges from 305 to 322. We observe that all indices experience an average positive return with a high standard deviation, showing highly volatile returns during our sample period. For example, the 7-10 year Treasury index experiences a daily average return of 2.9 basis points. 31 However, the standard deviation of this index is 47.6 basis points. Consistent with this pattern, as shown in Panel A, all bull (bear) FIETFs experience positive (negative) average daily returns. All sample FIETFs have large daily standard deviations. As previously mentioned, LFIETFs strive to achieve a constant leveraged multiple of the underlying index return. Therefore, we calculate the benchmark-adjusted return as the raw return less the product of leverage and index return. As shown in Panel B, except for the (2x) high yield fund, all FIETFs have negative average daily benchmark-adjusted returns. 32 Although this average daily relative return is informative, it doesn t fully reflect the ability of an LFIETF to 30 NAVs are also more appropriate to measure fund management s tracking performance, as they truly reflect a fund s fundamental value. In other words, the tests based on NAV returns are cleaner as they filter out the noise of the market price deviation, which doesn t reflect fund management s tracking ability. Nevertheless, we also examine tracking performance using market prices (available upon request) and find significant tracking errors in all sample FIETFs. 31 We report returns per trading day here, because our LFIETFs have a constant target multiple over each trading day. 32 In unreported analysis, we find that none of these benchmark-adjusted returns is statistically different from 0. We also examine the benchmark-adjusted return by taking expense ratio into consideration. The signs for the adjusted returns of LFIETFs are generally consistent with the reported results, although the underperformance is smaller in magnitude.

18 track its target, because positive and negative deviations can cancel out in this measure. 33 As discussed, the standard deviation of benchmark-adjusted return is most frequently used as a tracking performance measure of passive funds. As shown in Panel B, the standard deviation of these benchmark-adjusted return is actually sizable. For example, the standard deviation of daily adjusted return is 75.9 basis points for the (-3x) 7-10 year Treasury fund, which is dramatically larger than the size of its average relative return. The large size of standard deviation shows that one-day investors actually take some tracking risk by taking a long or short position in these LFIETFs. 34 Yet, how significant is this tracking risk for each LFIETF? To address this question and to test our hypotheses, we carry out formal analysis in the following subsection. 4.2 Tracking performance and hypothesis testing Table 3 tests the tracking performance of the (3x) and (-3x) Treasury bond LFIETFs and the difference in tracking performance between the LFIETFs on the two indices: NYSE 20yr+ Tsy Bd Index (AXT) versus NYSE 7-10yr Tsy Bd Index (AXS). As previously mentioned, we measure tracking performance using two measures: tracking error and mean absolute value of daily relative return. In particular, we calculate these measures for each week and use the weekly observations for the analysis. Panel A lists the summary statistics for these observations. 35 The average weekly tracking error for the (3x) AXT fund is 72 basis points, which is significantly 33 For instance, for an investor who uses LFIETFs to hedge his existing portfolio for a day, this average measure does not fully reflect the risk that he is taking. As an illustration, suppose that an LFIETF s daily return has 50% chance to deviate from its benchmark by +10% and 50% chance to deviate its benchmark by -10%. The average measure of 0% deviation does not reflect the significant risk taken for the holding day. 34 It is worth noting that this standard deviation of daily returns does not reflect the risk of a multiple-day horizon for two main reasons: first, a deviation within one day can be cancelled out in following days; second, there is an extra compounding effect with leveraged FIETFs as each LFIETF only targets a constant multiple within one trading day. We will return to this point in a later part of this paper. 35 As previously mentioned, Drenovak, Urosevic, and Jelic (2012) adopt a tracking error measure using monthly and daily returns within each three months. Due to the short sample period that we have, we focus our analysis on weekly tracking performance measures. As a robustness check, we also carry out analysis on monthly tracking performance measures. See Section 5 for details. 16

19 different from 0 at the 1% level as evidenced by a one-sample t-test. 36 This finding shows poor tracking performance of the (3x) AXT fund. This conclusion is further confirmed by the mean absolute daily relative return results. For the (3x) AXT fund, the MADRR is 0.54%, which is significantly different from 0 at the 1% level. In fact, as shown in Tables 3-5, all of our sample FIETFs have significant weekly tracking errors. To test hypothesis H1, we compare the LFIETFs on the long-maturity Treasury (AXT) index with those on the medium-maturity Treasury (AXS) index. The TE of the (3x) AXS is 0.24%, which is about one-third of the size of the (3x) AXT TE. The paired t-test between two samples shows a significant difference between the two funds. This significance is also confirmed by a zero p-value from a signed rank test. Consistent with H1, our results show that the (3x) AXT fund has a much higher TE than the (3x) AXS fund. This finding is further confirmed by the results using MADRR. In particular, the MADRR of the (3x) AXS fund is 0.19%, showing that, on average, the NAV return of this fund deviates from its target by 19 basis points in magnitude in a trading day. In contrast, the MADRR of the (3x) AXT is 0.54%, which is significantly higher as evidenced by a paired t-test and a signed rank test. Our results also show that the (-3x) AXT fund has significantly higher tracking error and MADRR than the (-3x) AXS fund. Overall, results from Panel A show that all sample triple and inverse triple U.S. Treasury LETFs have significant tracking errors and MADRRs and that tracking performance is worse for funds tracking longer time to maturity bond indices (referred to as maturity effect). What are the fundamental determinants of this difference in tracking performance? Panel B examines the determinants of the (3x) and (-3x) AXT/AXS LETFs tracking errors and the 36 The results from the one sample t-test for mean = 0 vs. mean > 0 are consistent as the p-value for this unidirectional test is half of the p-value for the unequal test. 17

20 tracking error difference between the AXT and AXS LETFs. Column (1) examines the potential factors associated with the tracking error of (3x) AXT fund. Since the volatility of entire equity market is likely to affect the return of the AXT index 37 and consequently impact the rebalancing ability and TE of the (3x) AXT, we include average VIX as an independent variable. As the AXT index represents the long-term maturity Treasury, we also include the standard deviation and average daily change of the term structure spread (computed as the difference between the ten-year and one-year Treasury yields) as two possible determinants. Due to the unit root concern, we include the average daily change in the spread rather than the spread itself. 38 Since the 3-month T-bill rate is generally considered as the risk-free rate in the fixed income market, we also control for the average daily change and standard deviation of this rate. For the constant term to be economically meaningful, we use median adjusted measures for all of our independent variables (also referred to as de-medianed variables). As shown in column (1), the VIX measure is positively associated with the tracking error. Economically, an increase of two standard deviations in VIX is associated with an increase of 99 basis points in the (3x) AXT tracking error. The average daily change in the term spread is also significantly associated with the tracking error, suggesting that an increase in the term spread makes it more difficult to track the fund s benchmark. Among other variables, standard deviation of the 3- month T-bill rate is positively associated with the tracking error. After controlling for these demedianed independent variables, the constant term is still significantly different from zero. 37 In our sample, the correlation between AXT index daily returns and S&P 500 index returns is From unreported Augmented Dickey-Fuller tests, we cannot reject the unit root hypothesis in the average daily term structure yield spread. After take a difference, we can reject the hypothesis at the 1% level in the daily changes. We therefore adopt the change measure of this term spread in our regression analysis. For the same reason, we also use the change of 3-month Treasury bill rate. 18

21 Economically, when all independent variables are at sample median level, there is a tracking error of 42.5 basis points. Collectively, all independent variables can explain 22% of the variation in tracking error, as evidenced by the R-squared in column (1). As shown in column (2), VIX is also positively associated with this tracking error. None of the other independent variables are significant. In summary, columns (1) (2) show that the tracking errors of the triple long-term and medium-term Treasury LETFs are both significant and positively driven by the general equity market s volatility. The average daily change in the term spread and the standard deviation of the 3-month T-bill rate affect the tracking error of the long-term maturity Treasury triple LETF, but not that of the medium-term maturity Treasury triple LETF. Column (3) examines the determinants of the tracking error difference between triple LETFs on the long-term and medium-term Treasury bond indices. The results show that the VIX, change in term spread, and volatility of the 3-month T-bill rate are positively associated with this TE difference. The constant of column (3) suggests that the tracking error difference is 20 basis points if all the independent variables are at their median. Columns (4)-(6) present the tracking error analysis results for the (-3x) funds. Consistent with those of the (3x) funds, the tracking errors for both the (-3x) AXT and AXS funds are highly significant. While both tracking errors are positively driven by the VIX, change in term spread, and volatility of the 3-month T-bill rate, the effects of these factors are much stronger on the (-3x) AXT than the (-3x) AXS. These findings are further confirmed by column (6), which shows that the TE difference between the (-3x) AXT and AXS funds is positively affected by the VIX, change in term spread, and volatility of the 3-month T-bill rate. As shown in column (6), if all independent variables are at their median level, the tracking error difference between the (-3x) AXT and (-3x) AXS is 17 basis points. 19

22 Overall, results in Panel B confirm the significance of tracking errors for all sample triple and inverse triple Treasury bond LETFs and the significance of the tracking error difference between the long-maturity and medium maturity LFIETFs. In addition, general equity market volatility, change in term spread, and volatility of the 3-month T-bill rate are positively associated with this difference. These findings show that it is more difficult for the LETFs to track long-term bond indices than to track medium-term ones. The multivariate results are consistent with the interpretation that tracking is more challenging when the general equity market is more volatile, when the term spread widens, and when the 3-month T-bill rate is more volatile. Table 4 examines the tracking performance of LETFs on corporate bond indices and compares it to the tracking performance of their counterparts on Treasury bond indices. As shown in Panel A, tracking errors and MADRRs of all sample LETFs are different from 0 at the 1% level based on the one-sample t-tests. The average weekly tracking error of (-1x) high-yield index (HY) is 49 basis points. In contrast, the average tracking error of (-1x) AXS is only 6 basis points. The difference between these two tracking errors is highly significant based on a paired t- test and a signed-rank test. Similarly, the tracking error of (-1x) HY is higher than that of (-1x) AXT and the tracking error of (-1x) investment-grade (IG) index is higher than that of (-1x) AXS/AXT. These findings are consistent with hypothesis H2, which predicts a larger tracking error for LETFs on corporate bond indices than those on Treasury bond indices. Panel B carries out regression analysis to examine the determinants of the tracking error of (-1x) corporate bond indices and the tracking error difference between the corporate bond LETFs and the Treasury LETFs. In addition to the independent variables in Table 3, we add the average daily change and standard deviation of the credit spread (computed as the yield 20

23 difference between Moody s Baa-rated corporate bonds and the 10-year Treasury bond). We expect the level and volatility of this credit spread to be positively associated with the tracking error of corporate bond LETFs. As shown in column (1), the volatility of this credit spread is positively associated with the tracking error of the (-1x) HY fund. All other independent variables are either insignificant or marginally significant at the 10% level. The R-squared shows that these independent variables can explain 73.5% of the variation in (-1x) HY tracking error. At the median level for all independent variables, there is a tracking error of 35.6 basis points. As shown in column (2), change in credit spread, volatility of credit spread, and volatility of term spread, are all positively associated with the tracking error of the (-1x) IG fund. Similarly, independent variables can explain more than half of the variation in tracking error. As shown in columns (3)-(6), tracking error difference between corporate bond indices and Treasury bond indices is highly significant. Both the change and the volatility of credit spread, as well as the volatility of term spread, are positively associated with the tracking error difference. In addition, our independent variables can explain more than half of this difference. These findings suggest that it is more difficult to track corporate bond indices than to track Treasury bond indices, especially when credit spread increases and when credit and term spreads are volatile. Table 5 examines the tracking performance across the magnitude of leverage for both bull and bear funds. As shown in Panel A, the tracking error of the (-3x) AXS fund is significantly different from that of the (-1x) AXS fund during the same sample period. Similar results hold for the MADRR measure and for the AXT index. For the two bull funds of HY, the (2x) fund has a much higher tracking error than the (1x) fund (134 vs. 2 basis points). This dramatic difference is in line with the rebalancing needs of leveraged funds as compared to 21

24 regular funds. The results from the IG index are consistent. These findings support hypothesis H3, which suggests a larger tracking error associated with higher magnitude of leverage for either bull or bear FIETFs. Panel B examines the tracking error difference between two leverages of the same underlying index. The results from columns (1) and (2) show that VIX is positively associated with the tracking error difference between the larger and smaller leverages on the same Treasury index. The results from columns (3) and (4) show that the volatility of term and credit spreads are also positively associated with the tracking error difference between the larger and smaller leverages of the same corporate bond index 39. These findings are consistent with the interpretation that it is more difficult to track a levered benchmark, especially so when the term and credit spreads are volatile. In summary, Tables 3-5 show that all sample LFIETFs have significant weekly tracking errors and our empirical results are generally consistent with the three hypotheses put forth in this paper. 5. Additional tests 5.1 Absolute daily benchmark-adjusted return Thus far, our results are primarily based on weekly tracking performance measures. As a robustness check, we also adopt a daily tracking performance measure in Table 6. Since it is impossible to generate our tracking error measure within each trading day, we only focus on the 39 It is somewhat surprising to find a negative coefficient on VIX in column (4). In unreported analysis, we find that this VIX is positively correlated with volatility of credit spread (correlation = 0.45). To avoid the potential multicollinearity concern, we try a set of regressions by including only one independent variable at a time, the coefficient on VIX and on the volatility of credit spread is positive. 22

25 absolute value of daily benchmark-adjusted return (also referred to as absolute daily relative return or ADRR). As shown in the table, because we use daily observations, the sample size is large, which increases the statistical power of our tests. Consistent with our previous results, we find that this ADRR is highly significant for all sample FIETFs. Furthermore, all of our paired comparisons in tracking performance are highly significant and consistent with our weekly tracking performance results. 5.2 Monthly tracking performance measures As a robustness check, we also adopt monthly tracking performance measures in Table 7. In particular, we use the standard deviation of the daily benchmark-adjusted return within each month as the tracking error of that month and calculate the average absolute daily benchmarkadjusted return as MADRR of that month. As shown in Table 7, the monthly results are generally consistent with our previous weekly results. The only exception is that tracking performance measures of (1x) IG are no longer significant in the one-sample t-tests, mainly due to the small sample size of. 40 The tracking performance measures of all other funds are significantly different from 0. More importantly, all paired t-tests and signed rank tests for the three hypotheses are significant. 5.3 Cumulative weekly relative returns So far, our analysis has focused on the perspective of LFIETF tracking performance for investors with a one-day holding period. It is possible that the tracking error within a trading day 40 The one-sample t-tests are for mean = 0 vs. mean!= 0. When the tests are for mean = 0 vs. mean > 0, the tracking performance measures for (1x) IG are marginally significant at the 10% level. 23

26 can be reversed in the subsequent days, and consequently, tracking performance may improve if the investment horizon is longer. However, when the investment horizon is longer than one trading day, unique to LETFs, there is a compounding effect due to the fact that our LFIETFs have a target multiple only over one trading day. 41 To examine the tracking performance of our LFIETFs over an investment horizon of one week, we examine the absolute cumulative benchmark-adjusted returns within each week (also referred to as absolute weekly relative return or AWRR), which is defined as the absolute value of difference between cumulative NAV return of an LFIETF and the product of leverage and cumulative index return within a week. 42 As shown in Table 8, this cumulative benchmark-adjusted return is different from 0 for all sample FIETFs. In addition, the paired t-tests and signed-rank tests are consistent with our previous findings and further confirm the three hypotheses. 5.4 Leverage Deviation If an investor uses an LFIETF to hedge his existing portfolio, he will be interested in the actual leverage of an LFIETF and the closeness between the actual leverage and its target. There are different methods of estimating the actual leverage. One method is to divide the daily actual return of an FIETF by that of its underlying index. This way can create a leverage measure for each trading day. However, this calculation is not accurate if the index return is close to zero. An alternative method is to carry out a regression of actual FIETF daily returns over index returns. The coefficient on the underlying index return is defined as the actual leverage. To measure the 41 The compounding effect reflects the return deviation due to the daily rebalancing nature of LETFs. In Tang and Xu (2013), the compounding effect is defined as the deviation of the cumulative target return of an LETF from the naïve expected return. The naïve expected return is calculated as the product between the daily multiple of an LETF and the cumulative return of the underlying index. Compounding deviation occurs only when investors hold an LETF for more than one trading day. 42 It is worth noting that the product of leverage and cumulative index return within a week actually is not the target return of the fund in the week. Because the product of leverage and cumulative index return is important from a hedging perspective, we use this product as the benchmark for the week. 24