The Impact of Leveraged and Inverse ETFs on Underlying Stock Returns

Transcription

1 The Impact of Leveraged and Inverse ETFs on Underlying Stock Returns Qing Bai, Shaun A. Bond, and Brian Hatch Department of Finance University of Cincinnati August 2012 Abstract Leveraged and inverse ETFs (LETFs) were introduced in 2006 and their popularity surged starting in As of the first quarter of 2012 there were over 200 such ETFs with over $30 billion in assets under management (AUM). By late 2008 there was concern about their late-day impact on stock prices and by 2009 they were accused of causing market-wide volatility. A vocal set of market participants insist that LETF-related trading causes excess volatility and manipulates prices while others insist that the AUM is too small to impact the market. The pitch of the rhetoric reached sufficient levels to motivate a Senate Banking Committee hearing in October We examine six such LETFs and their impact on the trading of 63 real estate sector stocks. We find that late-day LETF rebalancing activity significantly moves the price of component stocks, increases their volatility, and that some of this impact is reversed in the first hour of the next day. The impact is the greatest for smaller, less actively traded, more volatile stocks. Our evidence is also consistent with predatory trading by strategic investors exploiting the predictable late-day order flow. Key words: Leverage and Inverse exchange traded funds (ETFs), REITs, Financial Crisis, rebalancing demand JEL Codes: G1, G14, G17 Electronic copy available at:

2 1. Introduction During the financial crisis of , equity markets experienced a huge spike in volatility. Beginning in 2006, ETF managers began to market funds, leveraged and inverse ETFs (hereafter LETFs), that seek to return a multiple of the daily performance of the underlying index. The popularity of LETFs surged in late 2008 and continued to grow through Morningstar states that, as of December 2011, 245 LETFs traded in the US with $32 billion under management. 1 Many market participants came to the conclusion that the growth in LETF assets and increased market volatility were related. Because LETFs seek to return a multiple of the index return on a daily basis, the managers must lever their positions and manage their exposure on a daily basis. This rebalancing may be in the form of trading the target index component stocks or trading in futures or swaps. 2 As the AUM of LETFs grew, countless market participants, pundits, and bloggers fretted over the impact of rebalancing-related trades of LETFs on market volatility. 3 CNNMoney cites a study by Harold Bradley, the chief investment officer at the Ewing Marion Kauffman Foundation, which claims that the ETF market has caused massive dislocations and distortions of equity markets. 4 A CNBC report claims that levered ETFs create an artificial market for the stocks they own. 5 A New York Times story 1 Michael Rawson, Leveraged ETFs aren t the cause of increased market volatility, Morningstar ETF Specialist on Dec. 26, 2011 ( 2 Dave Nadig, Leveraged/Inverse ETFs: Not Wagging the Dog, IndexUniverse.com on October 17, 2011, indicates that the rebalancing by LETFs is typically in the form of adjusting their swap positions, but their swap counterparties need to hedge their resulting risk, and often do this in the last hour of the day through trading the underlying component stocks ( 3 T. Lauricella, Stocks swing in wild week, Wall Street Journal on Aug. 12, 2011 indicates that volatility increased late in the day due to trading by LETFs in the last 90 minutes of the day. 4 Maureen Farrell, What s behind that wild final hour of trading, CNNMoney, Nov. 8, 2011 ( 5 Herb Greenberg, Proof: ETFs a self-fulfilling prophecy, CNBC Market Insider, Oct. 14, 2011 ( 2 Electronic copy available at:

3 quotes Douglas A. Kass, the founder and president of Seabreeze Partners Management, that LETFs are the new weapons of mass destruction and They have turned the market into a casino on steroids. They accentuate the moves in every direction. 6 The rhetoric rose to such a high level that on October 19, 2011 the Senate Banking Committee invited representatives from the SEC, Nasdaq, BlackRock (whose ishares unit manages many ETFs), and the Ewing Marion Kauffman Foundation to testify at a hearing to explore whether ETFs are contributing to market volatility and if they present systemic risks to the financial system. 7 On May 7, 2012, ETFTrends.com reported that Senator Jack Reed, the chair of the Banking Committee, called for a second hearing and commented that LETFs may be affecting market structure, volatility and price discovery, and have the potential to harm investors. I think this market deserves more attention from both domestic and foreign regulators. While there was much rhetoric and anecdotal evidence in the financial press about LETFs causing market-wide volatility, there were also practitioner studies that provided counter evidence. The Credit Suisse Portfolio and Derivatives Strategy Group issued market commentary on October 13, 2011 in which they cite two factors to contradict the notion that LETFs cause late day volatility: 1) they estimate that rebalancing volume is too small to have a large impact (2% of dollar volume in the last 30 minutes of the day) and 2) in October and November 2008 (two very volatile months), the market reversed the intraday trend in the last hour 40% of the time. The opposite direction to the leveraged ETF trades. 8 ProShares, a purveyor of LETFs and thus a potentially biased source, provided similar arguments indicating that the lack of evidence of momentum in market returns in the final minutes of the trading day and the small 6 Andrew Ross Sorkin, Volatility, thy name is ETF, New York Times Dealbook, Oct. 10, 2011 ( 7 John Spence, Previewing the Senate subcommittee hearing on ETFs, ETFTrends.com, Oct. 18, 2011 ( 8 Credit Suisse Portfolio & Derivative Strategy Market Commentary, October 13, Dave Nadig writing at Index Universe on October 17, 2011 comes to similar conclusions. 3 Electronic copy available at:

4 relative size of the LETF market ($32 billion relative to the total ETF market of $1 trillion and the $11 trillion mutual fund market) suggests that LETFs have no impact on late day volatility. 9 While the Credit Suisse report discounts the possibility that LETFs cause market-wide volatility, it does concede that LETF rebalancing may impact smaller sectors and cites anecdotal evidence from the financials, energy, and real estate sectors. This fits with accounts in the financial press from market participants that believe the rebalancing done at the end of the day by LETF fund managers is harmful to component share prices. 10 Management of the component stock firms would allege that these trading tactics lead to inefficient pricing of their shares as much of the order flow is not based on company fundamentals, but on the needs of a LETF to rebalance their exposure at day end. This is particularly the case for LETFs written on smaller sectors such as the ProShares Ultra Real Estate long and short ETFs which are written to track the Dow Jones US Real Estate Index. The Wall Street Journal (WSJ hereafter) documents that in nearly 60% of the trading days in late 2008 the DJ Equity All REIT Index changed by more than 5%, compared to only 28% of such days for the S&P 500. Many REIT managers assert that this higher level of real estate sector volatility can be attributed to LETF-related trading. As cited in an interview with a REIT manager in the WSJ, the consequences of an increase in volatility is that it is more difficult for component firms to do deals, raise capital, attract institutional investors, and compensate employees The facts about geared ETFs and market volatility ( 10 Lauricella, Pulliam, and Gullapalli, Are ETFs driving late day turns? Leveraged vehicles seen magnifying other bets; Last hour volume surge, Wall Street Journal on Dec. 15, 2008 cite an example in which participants calculate that 52% of the volume in Equity Residential Shares on Dec. 1, 2008 was traded by ProShares leveraged short fund. They also quote market participants indicating that ETF trading activity reinforces a trend once it starts in motion. On the other hand, Michael Sapir, the CEO of ProShares claims that the idea that leveraged ETFs cause the end-ofday ups and downs is utter postulation. 11 Troianovski (2008) makes this claim in a December 26, 2008 article about REIT volatility. 4

5 Because the rebalancing trades that need to be performed by these funds (or their swap counterparties) are predictable, they likely spur front running and predation by strategic traders which may magnify the impact of LETF rebalancing. 12 As defined by Brunnermeier and Pedersen (2005), predatory trading induces and/or exploits the need of other investors to reduce their positions. Predators trade in the same direction and in the same time period as those with the predictable demands and then unwind their positions by providing liquidity. In our setting, predatory traders might exploit the predictable rebalancing demands of LETFs late in the day exacerbating any price overshooting and volatility. However, as suggested by Bessembinder et al (2012) in the context of the rebalancing activity of crude oil tracking ETFs, it is also possible that additional liquidity is provided to buffer the impact of rebalancing activity because liquidity providers know these trades are not based on private information. Such liquidity provision fits the sunshine trading model of Admati and Pfleiderer (1991). If trading in LETFs does lead to price overshooting, excessive volatility, and inefficiently priced shares, then policy makers need to take a look at the impact of such products and whether the externalities they impose outweigh the benefits to their investors. We seek to provide evidence to help weigh these trade-offs. It is not clear from the extant literature, Senate Banking Committee testimony, or practitioner analysis that anyone has yet provided direct evidence of the impact of LETF-related trading on the pricing of individual stocks, particularly small- and mid-cap stocks. Using component stocks from the Dow Jones US Real Estate Index, which is the target of multiple LETFs, we find that relative to a set of control stocks, component stocks experience increased variance of returns, increased trading volume, and increased serial correlation in returns late in the day all consistent with claims about the impact of LETF rebalancing activity on component stock returns. When we use a regression to control for other factors that might be impacting late-day price movements 12 Lauricella, Eaglesham, and Dieterich in the Wall Street Journal on March 29, 2012, suggest that because TVIX, a leveraged ETN aiming to deliver 2x the change in the VIX daily, must rebalance at the close of trading, other traders would attempt to frontrun the ETN traders. 5

6 and we estimate the magnitude of the rebalancing demand by these LETFs, we find a direct relationship between our proxy for LETF-induced trading activity at the end of the day and end-of-day returns in the component stocks the greater the rebalancing activity the larger the price change in the component stock. Not surprisingly, we also find that the magnitude of the rebalancing demand is directly related to component stock volatility. The regression results also are consistent with the existence of predatory trading. The strong positive relation between rebalancing demand and last hour returns and the subsequent negative relation between rebalancing demand and returns in the first hour of the following day provide evidence consistent with price overshooting and subsequent correction. To be concise and specific, our evidence suggests that LETF-induced trading causes price overshooting and volatility late in the day for smaller, volatile, real estate sector stocks and this overshooting tends to be reversed in the first hour of the next day. On days in which real estate sector volatility is particularly high the magnitude of the impact on 3:00-4:00 returns in a typical stock is 183bp and can be as high as 329bp. Our paper is organized as follows. The next section describes the mechanics of LETFs and briefly reviews the literature on LETFs. Section 3 explains how rebalancing demand is created due to the requirements of funds to rebalance daily to maintain leverage targets. Following this we discuss our data and present descriptive statistics in Section 4. Section 5 presents the empirical approach and results and Section 6 concludes the paper. 2. Mechanics of a leveraged ETF and the resulting rebalancing activity LETFs differ from traditional index ETFs in that they attempt to obtain a multiple of the daily return of an underlying index. Typically leveraged funds seek to match returns of 2x, 3x, -1x, -2x or -3x the daily return of the specified underlying index. To achieve this leveraged result funds hold the underlying index constituents, in addition to cash with leverage added using a total-return swap contract or occasionally a futures contract in combination with the swap. 6

7 In order to match the promised leveraged return, funds must rebalance daily. Cheng and Madhavan (2009) and Avellaneda and Zhang (2009) document the necessity of daily rebalancing. It is easy to understand this with an example. Assume that a fund has $50 in equity which is used to purchase the underlying asset. At the same time the fund borrows an additional $50, to purchase more of the asset. The fund has a leverage ratio of two, and if the value of the asset increases by 10%, the equity component (or fund NAV) increases by 20%. Hence, the 2X target return is achieved. However, at the end of the period, unless the fund rebalances, the leverage ratio now stands at Should the asset value increase again by 10%, the return on equity in the second period will not match the promised 2X leverage. If instead the fund does rebalance and borrows an additional $10 at the end of the first period to purchase an additional $10 of the asset, the leverage ratio will be restored to 2X and the return on equity in the second period will match the promised leverage multiple. However, due to the effects of compounding on leveraged investments, the return on the investment held for two days will be 44% not 42% (2 x 21% compound gain of the index over two days) as might be assumed by some investors 13. It is this late day re-balancing that may lead to pressure on the prices of component stocks. This pressure can be significant because leveraged, inverse, and leveraged inverse ETFs all must re-balance in the same direction. As Cheng and Madhavan show, the re-balancing demand of an ETF that delivers - 200% of the index return is a multiple of six times the daily change in the NAV of the ETF. If an index increases (decreases) in value substantially on day t, all of the leveraged, inverse, and leveraged inverse ETFs that track that index must increase (decrease) their exposure to that index by some multiple of the return before the end of day t in order to have the appropriate leverage/exposure at the start of day t+1 in order to deliver their target return. Dave Nadig of Index Universe says that the funds themselves aren't 13 Concern about retail investors holding leveraged ETFs over periods of longer than one day was addressed in an alert notice by FINRA in June 2009 (see FINRA regulatory notice 9-31). Subsequently, a combined SEC and FINRA alert was issued on August 18, 2009 (see Further details of the effects of compounding can be found in Hill and Foster (2009). 7

8 buying or selling anything. All of the levered and inverse funds in the U.S. get their exposure through total return swaps. someone in this chain of counterparties will be hedging out their risk by putting trades into the actual securities in the market. 14 Based on conversations with market participants, Nadig asserts that it's clear they all begin their swap coverage negotiations at different times following 3:00 pm. Anecdotal evidence in the financial press indicates that other market participants, as you would expect, are aware of the re-balance requirements of such funds and attempt to exploit this opportunity by trading ahead of the ETFs. It is this combination of front running, predatory trading, and LETF rebalancing that is alleged to impart excessive late day volatility on component prices. Related literature Cheng and Madhavan (2009) is the paper most similar to ours in that it explicitly considers the impact of LETFs rebalancing activity on the dynamics of an underlying asset return series. Their paper, along with papers by Avellaneda and Zhang (2009), Hill and Foster (2009), Jarrow (2010), and Lu, Wang, and Zhang (2009) document the necessity of daily rebalancing (as explained in the section above) and show how fund performance deviates from the benchmark over longer holding periods. Cheng and Madhavan then show how to derive the daily rebalancing demand arising from price movements in the underlying assets. We will use this as a basis for the creation of a rebalancing demand variable in the next subsection. In an empirical test, Cheng and Madhavan regress the return of the last hour of the day for the S&P500 index on the close to close return of the S&P500 index and the rebalancing demand variable. They find a positive and statistically significant impact from the rebalancing variable. Their estimate 14 Dave Nadig, Leveraged/Inverse ETFs: Not Wagging the Dog, IndexUniverse.com on October 17, 2011 ( 8

9 implies that each $1billion of rebalancing impacts returns by.54%. To determine the impact of such ETFs on late-day volatility, Cheng and Madhavan estimate a similar model but use absolute returns, absolute rebalancing demand, and the VIX value. They find that rebalancing directly impacts the volatility of the last hour return. Charupat and Miu (2011) report that in September 2009 leveraged ETFs in Canada (the US) accounted for 67% (40%) of all ETF trading volume. Focusing on Canadian leveraged ETFs, they examine the pricing deviations from NAV of leveraged ETFs and correlate these deviations with performance of the underlying benchmark. Bull LETFs, those seeking a positive multiple of the index, tend to trade at small discounts or premiums to NAV while bear LETFs, those seeking a negative multiple, trade at a larger premium. Charupat and Miu interpret a negative (positive) correlation between the premiums of bull (bear) LETFs and their target index returns as evidence suggesting that end-of-day rebalancing demand increases index volatility. Tang and Xu (2012) identify the determinants of the deviation between LETF returns and the levered returns of the target index for holding periods beyond one day. They show that the deviation between the LETF return and the target index return can be attributed to daily rebalancing, errors in tracking the target index, and market frictions. Shum (2010) focuses on the efficacy of LETF managers in tracking their benchmark but goes beyond the compounding question, to also focus on the manager s replication strategy, cost of leverage, and the impact of trading premiums/discounts. She finds that tracking ability is highly dependent on market liquidity, which was a particular problem during the 2008 financial crisis. Shum concludes that inverse ETFs depart more quickly from their target than leveraged ETFs as the holding period increases. During the financial crisis tracking error increased noticeably. Also, for a small number of funds in her sample she finds that management factors had a greater impact on performance than compounding. In this study we do not consider the issue of fund performance or tracking error but we note the potential importance of these issues to investors in the ETF. 9

10 Trainor (2010) draws a comparison between claims in the late 1980s that index futures increased market volatility with the notion that leveraged ETFs might be the culprit responsible for increased market volatility in late 2008 and early Trainor finds no support for the idea that LETFs rebalancing trades lead to increased S&P 500 volatility. He relies on the fact that abnormally high market volatility subsided in 2009 and 2010 while growth in LETFs continued, that the nature of the financial crisis would have caused increased volatility in itself, and that volatility at times of day not associated with rebalancing reflected a larger spike than end-of-day periods associated with rebalancing. Ben-David, Franzoni, and Moussawi (2012) examine the transmission of non-fundamental shocks to component stocks produced by arbitrage activity between ETFs and the underlying index. They show that this arbitrage activity propagates a liquidity shock that moves the stock price away from its equilibrium value. Because of this mechanism, they also determine that ETF ownership of stocks causes and increase in their daily volatility, more so for smaller stocks. In terms of ETF studies specifically focused on the real estate sector, Boney and Sirmans (2008) have studied REIT volatility following the introduction of ETFs on the REIT sector. Using data from 1999 to 2001, they estimate unconditional volatility measures and a GARCH model to capture conditional volatility dynamics in daily returns for the top seven REITs held in the ETF and a sub-sample of REITs not otherwise covered by derivative contracts. Boney and Sirmans find that REITs had lower volatility following the introduction of a REIT ETF. Also, volatility dynamics appears to have changed with the volatility of the S&P500 becoming a significant driver of REIT volatility in the post-etf period. However, the impact of volatility on returns was less clear-cut in their analysis. Their argument for the finding of lower volatility is that trading activity by Authorized Participants improved market efficiency and the speed of price adjustment in the REIT stocks. Curcio et al (2012) examine the impact of the initiation of traditional and leveraged ETFs on real estate stock prices. Using 64 days of daily data before and after the initiation of ETF trading, they find that the volatility of underlying real estate stocks increased dramatically with the largest increase 10

11 occurring around the initiation of trading of leveraged ETFs. Tang and Xu (2011) find that LETFs that track real estate indices show a greater tendency to deviate from target index returns than do LETFs that track broader indices. Many papers study strategies similar to that of predatory trading. Brunnermeier and Pedersen (2005) model predatory trading and find that predators will trade in the same direction at the same time as a large distressed liquidator causing prices to overshoot and then unwind by providing liquidity to the liquidator. If their model is relaxed to allow the strategic traders to trader earlier than the liquidator, they front run the liquidator and when the liquidator starts to sell, they buy back. Carlin, Lobo, and Viswanathan (2007) examine episodic liquidity and determine that under certain conditions cooperation among traders breaks down leading predators to race a distressed trader to short a position and then they later repurchase the position at the depressed price. Bessembinder et al (2012) examine a likely opportunity for predatory trading that is similar to ours. They examine ETFs that seek to track crude oil prices through investment in crude oil futures. Because of the expiration of the futures contracts, the ETFs need to rebalance their portfolio of futures periodically which leads to predictable order flow and thus an opportunity for predation. But Bessembinder et al make the point that this predictable, uninformed order flow may also attract greater liquidity provision per the theory of sunshine trading as modeled by Admati and Pfleiderer (1991). Bessembinder et al determine that the preponderance of the evidence supports the sunshine trading theory, i.e., the ETFs are not exploited through predation, but rather enjoy low liquidity costs because of increased liquidity provision at the time of their rebalancing trades. 3. Construction of the rebalancing variable As described above, in order to meet their objective of returning a multiple of the underlying index return on a daily basis, LETF managers must adjust their exposure to the index daily. This adjustment of their exposure must be done very late in the day (or perhaps very early the next day) so that 11

12 they achieve the proper exposure for the following day and do not adjust their exposure prematurely so as to miss their target for the current day. Adjustment of their exposure may be done through swaps, futures, and/or trading the underlying component stocks. Those entities that might serve as counterparties on the swaps will also have a need to trade the underlying components in order to manage their exposure as well. Some market participants have speculated that a majority of the trading in some component stocks is driven by either LETFs or others piggybacking on the ETF-induced activity. Cheng and Madhavan develop a model of the daily exposure required of a LETF. The changes in that daily exposure represent a proxy for the ETF-induced trading activity (or rebalancing) in the index. We write this rebalancing as: (1) Where IRD t is the index rebalancing demand at the end of day t, A t is the ETF assets under management (AUM or market capitalization) on day t, x represents the leverage factor, and r t, t-1 is the return on the index from the close of day t-1 to the close of day t. Since we are specifically interested in the impact of this rebalancing activity on component stocks, we adjust this measure to reflect an estimate of rebalancing-driven trading activity in the component stocks by simply multiplying by the weight of the stock in the index, wt j : (2) So the more AUM, the greater the weight on the component stock, the more levered the ETF, or greater the magnitude of the index return, the greater will be the ETF rebalancing-induced trading activity in the component stock. 4. Data and Descriptive Statistics We collect data for the stocks in the Dow Jones US Real Estate Index (DJUSRE). We chose this index for a few reasons. First, two articles in the WSJ in late 2008 conjecture that trading in the ProShares Ultra Real Estate ETF long (ticker: URE) and short (ticker: SRS) adversely impacted the 12

13 component stocks in the index that these ETFs track (DJUSRE). These ETFs seek to return 200% or - 200% of the daily return of this index. Second, URE and SRS are two of the first such ETFs to be heavily traded. The component stocks in DJUSRE are all also contained in the Dow Jones US Financials Index (DJUSFIN) and many are also in the Russell 1000 Financials Index and both of these indices are also tracked by popular leveraged and inverse ETFs (UYG and SKF track DJUSFIN and FAS and FAZ track the Russell index). Finally, we focus on real estate stocks because if LETFs do induce trading-related effects, it is most likely to be detected in sectors which have a higher percentage of smaller, less frequently traded stocks. Recall that Credit Suisse claims there is anecdotal evidence of an impact of LETFs in the real estate and financial sectors. It was the confluence of tremendous market volatility during the crisis and heavy volume in LETFs that brought financial press attention to this issue. These events coincided from late 2008 through late 2009, as a result we choose to examine August - December 2006 as our control period since no leveraged or inverse real estate or financial ETFs existed at that time, and the period from August 2008 through October 2010 as our relevant sample period. This sample period provides us with three distinct regimes: 1) a period with no crisis and no trading in LETFs (last quarter of 2006), 2) a period with heavy trading in LETFs during a crisis period (last quarter of 2008 through the last quarter of 2009), and 3) a period of trading in LETFs outside of a crisis period (March-October 2010). Figures 1A, 1B, and 1C characterize the trading activity and assets under management for the six LETFs that we track individually and in aggregate. As can be seen in these figures, aggregate dollar volume and market capitalization peaked in Feb. and May, 2009 respectively. Subsequently, dollar volume fell by 79% by the end of our sample in Oct. 2010, while market capitalization fell by a comparatively small 35%. For a stock to be included in our sample, it must be a continuous component of DJUSRE from June 2006 through October such stocks meet that criteria. We collect intraday trade and quote data from the NYSE s Trade and Quote (TAQ) database and daily volume, price, and shares outstanding data from the Center for Research on Security Prices (CRSP) files for this set of stocks. To determine if 13

14 trading in LETFs impacted the trading on these underlying component stocks, we construct a control group of stocks for comparison purposes. Control stocks were chosen that minimize the sum of the percentage squared differences in market capitalization and share trading volume as of the end of December Because there are such a large number of equity LETFs, it was impractical to eliminate from the universe of possible controls, all stocks that were included in an index that is tracked by a LETF. Therefore, the control stocks may also be subject to the influence of trading activity related to rebalancing of ETF portfolios, but we believe that influence will be less than for the sample stocks. As a result, if LETF-induced activity does impact price efficiency and volatility, the differences between our sample and control stocks will be a downward biased estimate of the true impact. The characteristics of the sample stocks and the control group are displayed in Table 1. To the extent that market capitalization and trading volume proxy for visibility, asymmetric information, trading activity, and liquidity, our sample and controls should be quite similar on these dimensions. We compare the average daily volume, market capitalization and share price of the sample stocks with the control stocks in five periods: Aug-Oct 2006, 2008, 2009, 2010, and Apr-Jun By holding the time of year constant (at least for four of the periods) we control for any seasonality. We include the period from April through June 2009 because it was during those three months that trading volume and assets under management peaked for the six LETFs that we examine (URE, SRS, UYG, SKF, FAS, and FAZ). Table 1A shows that during 2006 the average daily volume of the control stocks was 29% greater than that of the sample stocks; however, as the crisis hit, sample stock volume exploded to exceed control stock volume by 32%, 105%, and 42% in the subsequent three periods. After the crisis subsided in 2010, sample stock volume declined to only 8% greater than control stock volume. We don t see a similar pattern in market capitalization because of the extreme drop in share price for the sample stocks. In fact, the market cap of the control stocks exceeds that of the sample stocks in every period. Finally, share 14

15 price data shows that the sample mean price fell from $51.10 in 2006 to $23.12 in mid-2009 and rebounded to $38.53 in late Control stock prices follow a similar, albeit less volatile, pattern. It may be the case that the surge in sample stock volume relative to control stock volume is simply due to the financial crisis being driven by finance and real estate companies and not necessarily by any trading activity related to LETF rebalancing. To address that, we examined the industry characteristics of our control stocks and examined the trading in these stocks by time of day. As shown in Table 1B, our control stocks come from many different industries; however, 27.7% are from the finance/real estate sector. With such a substantial percentage of finance/real estate control stocks, it is not surprising that the control average daily volume surged in 2008 and Figures 2 and 3 show the difference in sample and control volume and number of trades early and late in the day for October in and May Particularly in October 2008 and May 2009, sample stocks traded more often and in heavier volume than the controls in the first 30 minutes of the day. In the last ten minutes of the day in every month after 2007, sample stocks traded more heavily than control stocks with that difference being most dramatic in May These descriptive statistics provide some circumstantial evidence to suggest that LETF rebalancing activity might be quite large, particularly late in the day. It is common knowledge that overall market volatility increased tremendously during the crisis; however, if LETF-induced trading created additional volatility in component stocks, a first step to determining this would be to measure changes in volatility for both the control and sample stocks. Table 2 indicates that before the development of LETFs and before the financial crisis, our control stocks were significantly more volatile than the sample stocks. By late-2008, volatility in both sets of stocks had increased by at least a factor of five. In 2009 the sample stocks were significantly more volatile than were the controls, but by late-2010 we returned to the relation found in 2006 with control stocks demonstrating greater volatility. We recognize that because to some degree the financial crisis was a financial/real estate sector crisis, it is perhaps not surprising to find that the volatility of real estate-related stocks increased more 15

16 than the control stocks and therefore we cannot necessarily attribute this incremental gain in volatility to LETF-induced trading activity (although recall that 27.7% of the control group is from the finance/real estate sector). To address this issue, we use daily returns for 12 sectors as reported on Ken French s website to calculate the variance of these sectors during our sample periods. Table 2B shows that all sectors experience a huge increase in volatility in Aug-Oct 2008 and Apr-Jun 2009 relative to Aug-Oct In fact, six sectors were more volatile than the finance/real estate sector (labeled as Money in Table 2) and all but one sector was more volatile in the Aug-Oct 2009 and 2010 periods. This data suggests that maybe it was not the industry composition of our sample that caused the sample volatility to exceed the control volatility, but perhaps the LETF-related trading activity could be partially responsible for the increased volatility of our sample stocks. To investigate more carefully, we calculate sample and control stock volatility by time of day. We measure volatility using absolute returns and using a rangebased measure adopted by Pagano, Peng, and Schwartz (2008), Volatility = (P H P L )/P avg where P H is the highest price in the minute, P L is the lowest price in the minute, and P avg is the average price in the minute. We measure price two different ways, as the national best bid and offer (NBBO) midpoint and as the trade price. Figure 4 shows the volatility by time of day for sample and control stocks using the NBBO midpoints. Sample stock volatility seems to be higher at the beginning and end of the day in October 2008 and May Figure 5 plots sample volatility less control volatility for the range-based measure and confirms the higher volatility early and late in the day for the sample stocks. While not shown here, the volatility measures using trade prices provide similar results with even larger differences for sample and control stocks in October 2008 and May Finally, we calculate variance by time of day using one-minute returns where prices are the last NBBO midpoint observed before the end of each minute. For each stock we calculate the mean variance of returns in a time period, say the first hour of the day, during each sample period. We then report in Table 3 the median of the 63 stock mean variances for that sample period. We test for a difference in 16

17 median variance across sample periods to determine the impact of LETF-induced trading and finally test the difference in the change in volatility across sample and controls. The variance by time of day confirms the previous graphical evidence to the extent that volatility is highest in the first hour of the day for both sample and control stocks in every year. The data is also consistent with Table 2 in that control stock volatility is equal to or larger than sample stock volatility in 2006 and 2010, but in 2008 and 2009 sample stock volatility is significantly larger. What we are particularly interested in is whether the volatility of sample stocks increases more than that of control stocks as we go from a period with no LETF trading (2006) to periods of heavy LETF trading (2008 and 2009). The last three columns of Table 3 show the difference between the change in sample stock volatility and the change in control stock volatility between various sub-periods (Aug-Oct 2008 and 2006, Apr-Jun 2009 and 2006, and Aug-Oct 2010 and Apr-Jun 2009). The increase in sample stock volatility is much larger than the increase in control stock volatility from 2006 to 2008 and 2009, particularly early and late in the day. We will later test specifically the role of LETF rebalancing demand on this volatility. Based upon the anecdotes in the financial press about late day momentum and the trades of other institutions meant to frontrun ETF trades and the necessity for LETFs (or their counterparties) to rebalance near the end of the day to optimize their exposure for the next day, we examine intraday autocorrelation in returns to look for evidence of the impact of this trading activity in the data. Using NBBO midpoints we calculate one-minute and five-minute returns. From these returns we calculate our intraday autocorrelations. Table 4 summarizes the information on intraday autocorrelations. To the extent that LETF-induced trading activity would result in one-sided order flow in component stocks early and late in the day, we would expect to see more positive autocorrelation during periods of heavy LETF-induced activity. In particular, we would expect this to manifest itself in an increase in late-day autocorrelation of sample stocks. Using one-minute returns, from 2006 to 2008 and from 2006 to 2009, we see a significant increase in mid- and late- day autocorrelation for sample stocks and no change, or even a small decrease late in the day, for the control stocks. The last three columns of 17

18 Table 4 show that this increase in sample stock autocorrelation is significantly larger than the change in control stock autocorrelation. 5. Empirical Model and Results Our simple comparison of the intraday dynamics of the component stocks of the indexes tracked by six LETFs to a matched control group of stocks shows evidence of a significant change in trading patterns with the growing popularity of LETFs. However, we cannot say in any meaningful way that these changes have been caused by the creation of leveraged or inverse ETFs. It could have been that real estate stocks were somehow impacted in a different way from other stocks during the financial crisis because of the central role that real estate played in the crisis. To more specifically examine how the rebalancing of LETFs could impact component stocks, we consider now whether the rebalancing of the LETF has any explanatory power in predicting price changes and volatility of the component stocks during the last hour of the trading day and the first hour of the next day. The model we estimate is similar to Cheng and Madhavan (2009), except we focus specifically on the component stocks of DJUSRE while Cheng and Madhavan examine the impact of rebalancing on the S&P 500. Rebalancing Demand and Component Stock Returns Our sample period for the regression model covers two years from October 2008 through October Intraday returns for individual stocks and the S&P 500 (actually the SPY ETF) are calculated using bid-ask midpoints from 9:30am to 3pm and 3pm to 4pm. Recall that our estimate of rebalancing demand is: We construct the rebalancing demand generated by each of our six LETFs (URE, SRS, UYG, SKF, FAS, and FAZ) for stock i at the end of day t using the AUM for each of the LETFs at the close of day t-1, the weight of stock i in each of the respective indexes tracked by the ETF (the indexes are DJUSRE, DJUSFIN, and Russell 1000 Finance Index and the stock weightings are updated quarterly), the leverage factor for the ETF, and the close-to-close index return on day t. We then 18

19 sum the rebalancing demand across the six ETFs to get the total rebalancing demand at the end of day t for stock i. 15 Using pooled data in each day of the sample, we estimate the following model: (3) Where: is the return in the last hour of each day (3-4pm) for component stock j on day t. is the rebalancing demand for component stock j on day t. is the intraday return from 9:30am to 3pm, on component stock j, on day t. is the intraday return from 9:30am to 3pm on the S&P500 index on day t. is a random error term. The results from this regression are presented in Table 5. The first column presents the results from estimation of the model across all sample stocks for the full sample. We interpret b 1 to represent the impact of ETF-induced rebalancing demand on stock returns in the last hour of the day after controlling for market returns and component returns to 3:00. The rebalancing coefficient is positive and statistically significant, as is the coefficient for intraday S&P500 returns and intraday component stock returns. This suggests that ETF-induced trading late in the day impacts the final hour returns in the component stocks. If the index increases (decreases) in value throughout the day, this will induce buying (selling) of component stocks, which causes higher (lower) returns than otherwise in those components in the last hour of the day. Based on the magnitude of RD, b 1 = means that $1 million of rebalancing demand moves the 3:00-4:00 return in the component stock by 10.1bp. Later we will stratify the sample 15 Our sample stocks are likely components of other indexes that are tracked by other LETFs meaning our RD is an underestimate of the true RD. For example, we know that Direxion Funds initiated trading in bull and bear ETFs, DRN and DRV with sought to return daily multiples of the MSCI US REIT Index starting in July

20 to identify days with high rebalancing demand and the types of stocks that are most sensitive to this type of trading to provide a more refined estimate of the economic impact of this rebalancing activity. In order to determine if the impact of rebalancing activity changes through time (since we know that trading volume and AUM does change quite a bit) we split the sample into four sub-periods. During the first two sub-periods (10/08-3/09 and 4/09-9/09) trading and AUM is at its greatest in these six ETFs. Trading activity and AUM starts to wane during period three (10/09-3/10) and is at its nadir in the last period (4/10-10/10). In every period, rebalancing demand impacts returns in the last hour of the day. The direction and strength of the impact of intraday stock and S&P 500 returns changes across sub-periods and the ability to forecast last hour returns decreases over time. Unreported results indicate that the impact of rebalancing demand on last hour returns is significantly stronger in the first sub-period than in the other three sub-periods. While trading activity is at its lowest in our last sub-period, the only variable that significantly explains last hour stock returns is the rebalancing demand generated by these LETFs. 16 We include a regression from the fourth quarter of 2006 before the existence of LETFs and find a much lower R 2. In order to assess whether the impact of rebalancing carries over to the following day, we repeat the regression in equation (3), except this time we replace the return in the last hour of the day with the returns from 9:30-10:30am, 10:30-11:30am, 11:30am to 12:30pm, and 12:30 to 1:30pm of the following day. The results are presented in Table 6. In this case the explanatory variables are the rebalancing from the previous day, the previous day return on the component stock, and the previous day return on the S&P500 index. If LETF-related trading causes an overreaction in stock price at the end of the day, then we might see a reversal early the next day. Consistent with that conjecture, we find a negative relation between rebalancing demand through the end of day t and the first hour of stock returns on day t+1. In 16 We also estimated the regressions without the S&P 500 returns. The coefficient estimates are nearly unchanged for the rebalancing demand in each sub-period as is the R 2. 20

21 fact, this negative relation persists for the first two hours of the day, but is strongest from 9:30 to 10:30 and exists in all four sub-periods. The larger is the rebalancing demand generated on day t, the more negative are returns early in day t+1. These results suggest that large positive rebalancing demand on day t pushes component stock prices higher during the last hour of trading, but in the first hour of trading on day t+1, these prices reverse to some degree. By 11:30-12:30 the impact of the previous day s rebalancing demand has diminished to near zero. Such price dynamics are consistent with predatory trading or lack of liquidity causing prices to overshoot late in the day and the mispricing is corrected early the next day. Rebalancing Demand and Volatility Many of the arguments in the financial press center around increased volatility due to LETFinduced trading. Recall also that Ben-David, Franzoni, and Moussawi (2012) show that through the arbitrage process, ETF ownership increases the volatility of component stocks, particularly smaller stocks. While it is doubtful that there is extensive arbitrage activity between LETFs and the underlying indexes as they examined; however, the necessary rebalancing activity of LETFs provides a similar venue to propagate non-fundamental demand shocks to the underlying stocks. Our descriptive statistics suggest a larger increase in volatility in our sample stocks than our controls as LETF-related trading activity increases, particularly at the end of the day. To more directly address the issue of volatility and rebalancing we regress absolute component stock returns over the last hour of the day on absolute rebalancing, absolute component returns from 9:30 to 3:00 and the VIX at the close of the day. Specifically: (4) 21

22 The results from this regression are in Table 7. Not surprisingly, there is a positive relation between overall market volatility as represented by the VIX and closing volatility in the component stocks (b 3 = ). Consistent with the conjecture about rebalancing, after controlling for market volatility and individual stock volatility, the absolute value of rebalancing still contributes to end of day volatility in the component stocks (b 1 = ). In every sub-period, greater absolute rebalancing demand is associated with greater last-hour volatility. Similarly, larger intraday absolute returns and larger VIX are also correlated with larger last-hour volatility. In Panel B we examine whether absolute rebalancing demand impacts volatility in the first hour of trading in the next day. The results are consistent in the full sample and across all four sub-periods, the greater is the LETF-induced trading activity on day t, the lower is the volatility in component stock returns on day t+1. Sensitivity to Rebalancing Demand We would suspect that there are differing levels of sensitivity to rebalancing demand among the stocks in our sample. This sensitivity is likely directly related to the proportion of stock trading volume that is due to rebalancing demand. Those stocks that are very actively traded and thus tend to trade in deep, liquid markets likely have less of their overall order flow determined by rebalancing demand. Similarly, the smaller the weight of the stock in the tracking index, the smaller the rebalancing demand generated. In order to address this issue, we estimate the following model: Where SRD j is the sensitivity to rebalancing demand for stock j as estimated by b 1 from a stock-by-stock estimation of:. (5) 22

23 is the variance of return for stock j. ADV j is the average daily volume in stock j in millions of shares. MC j is the market capitalization of stock j in billions of dollars. Because of a lack of resiliency in the markets for such stocks, we would expect that volatile, lightly traded, small cap stocks might be the most sensitive to rebalancing demand, even though they may have a small weight in the index. The results in Table 8 confirm this conjecture as variance has a significantly positive coefficient in three of the four subperiods while there is a significantly negative coefficient estimate in three of the four sub-periods for both ADV and market capitalization. So it is the smaller, less actively traded stocks that are most susceptible to LETF rebalancing-related trading activity leading to momentum and high volatility late in the day and price reversals early the next day. Magnitude of the Impact of Rebalancing Demand As we reviewed in the introduction, there is extensive practitioner analysis which makes the case that the circumstantial evidence is inconsistent with LETF-related trading causing market volatility; however, some of this same analysis suggests that the volatility in smaller sectors, and for smaller stocks, could be impacted. Our evidence suggests that LETF rebalancing does impact the late day volatility of real estate sector stocks. Now that we have established a clear link between LETF rebalancing-related demand and 3:00-4:00 returns in component stocks, we need to determine the magnitude of this impact. From Table 5 we know that the return sensitivity to rebalancing demand varies through time and from Table 8 we know that it varies by stock. It stands to reason that for some stock-days, e.g., large, actively traded stocks on days for which there is little volatility in the real estate sector, there will be inconsequential LETF-induced trading activity. However, there may be stock-days, and the REIT managers quoted in the WSJ in December 2008 would suggest there are many, that the LETF-related trading dramatically affects component stock returns. It stands to reason that the stock-days of greatest impact will be on days of large real estate sector-specific volatility and those stocks most affected will be 23

24 the smaller, less actively traded stocks. We take several approaches to estimate the magnitude of this impact. First, we stratify our sample into quintiles based on days of real estate sector-specific volatility as measured by absolute DJUSRE returns less absolute S&P 500 returns. Quintile five is filled with those days with the largest difference and thus are the days of greatest real estate sector-specific volatility. In Table 9 we present the results from estimating the same basic regression whose results were presented in Table 5, except we run this regression using dummy variables for each of the five quintiles interacted with rebalancing demand to determine if sensitivity to LETF-related trading is a function of real estate sectorspecific volatility and adjust for fixed effects across quintiles. The first column of results in Table 9 indicates that the sensitivity to rebalancing demand increases nearly monotonically with real estate sectorspecific volatility. The coefficient on RD is insignificant in quintile one, negative and marginally significant in quintile two and is largest and most significant in quintile five. The next column replicates the results from Panel A of Table 6 (the relation with next day returns) by quintile and does not produce as clean a story, but does show that the significant negative relation between next day returns and RD is confined to the most volatile three quintiles. The final column replicates Panel A of Table 7 (the volatility relation) by quintile and finds a mixed relation when conditioned on real estate sector volatility. To more carefully estimate the magnitude of the impact on those stock-days where the impact is likely to be largest, we use our period-specific stock-by-stock sensitivity to rebalancing demand measure, SRD from Table 8, and the 75 th percentile absolute rebalancing demand value for that stock from that period. The first sub-period has the greatest real estate sector volatility and thus tends to generate the largest rebalancing demand. Multiplying the SRD for each stock by the 75 th percentile RD for each stock in the first period, we find that the across-stock median impact on 3:00-4:00 returns is 262bp, the maximum impact is 457bp and the minimum is 150bp. Panel A of Table 10 shows that the median impact steadily decreases through time as the size of the median rebalancing demand decreases. By the fourth sub-period the median impact is 50bp. Whether it is during the relatively volatile first period 24

25 (median impact of 2.62%) or the more stable last period (median impact of 0.50%), these results indicate that on days of relatively high rebalancing demand (75 th percentile days), LETF-induced trading has an economically meaningful impact on last hour stock returns. Table 10 also presents results based on median and 90 th percentile absolute rebalancing demand. A similar approach is to use our volatility stratification and measure the impact by quintile. With this approach we estimate stock-by-stock sensitivity in each volatility quintile and multiply that by the median absolute rebalancing demand for that stock during that quintile. This approach provides an estimate of the typical impact of rebalancing demand on those days of high real estate sector-specific volatility. On the days of highest sector volatility (quintile 5), the across stock median absolute rebalancing demand generated by the six LETFs is $5,316,120 and the median impact on 3:00-4:00 returns is 183bp with a maximum of 329bp and a minimum of 50bp. You can see in Panel B of Table 10 that median rebalancing demand monotonically decreases across quintiles (because it is a function of DJUSRE return) as does the impact on late day returns. There is no question that a typical last-hour-ofthe-day impact of 1.83% on high real estate sector volatility days is economically meaningful. 5. Conclusions LETFs have grown tremendously as an asset class since early By the first quarter of 2012, 1,229 U.S. ETFs had $1.2 trillion under management with 245 of those being LETFs with $32 billion under management. As the assets under management and trading activity by these funds has grown, so has concern over the impact of the daily rebalancing activity of these funds on market volatility and on the underlying component stocks. Many market participants and chief executives believe LETF-related trading causes excess volatility and manipulates price. The concern is so widespread that the Senate Banking Committee held a hearing on the topic in October 2011 and has scheduled another hearing later in The confluence of heavy trading in real estate LETFs, the heightened volatility of the financial 25

26 crisis, and the small market caps and trading volume of many of the component stocks in the Dow Jones US Real Estate Index, magnified these concerns with respect to these component stocks. The hypothesized impact as originally expressed in the financial press is that the predictable lateday rebalancing by LETF managers and other market participants that attempt to frontrun this trading leads to excessive late day volatility and momentum. Our comparison of sample and control stocks and intraday patterns shows an increase in volatility, volume, number of trades, and serial correlation that is greater for sample than controls, primarily late in the day, and these changes occur during sample periods when trading volume and assets under management surged for the six LETFs that we examine. Using our estimate of late-day rebalancing demand as an explanatory variable, we show that after controlling for intraday market movements and changes in the component stock price, rebalancing demand is strongly, positively related to returns in the last hour of the day. The higher or more positive (lower or more negative) the rebalancing demand, the larger (lower) the component stock returns. This impact is greatest on days of high real estate sector volatility and is negligible on days of low volatility. The price patterns then partially reverse in the first two hours of the next day as rebalancing demand from day t is negatively related to component stock returns in the first two hours of day t+1. Similarly, absolute rebalancing demand explains late-day component volatility. Of these components, it is the smaller stocks that are less actively traded whose prices are most severely impacted by the LETF-induced rebalancing demand. The magnitude of this LETF-induced trading activity on last-hour stock returns is 183bp for the typical sample stock on days of relatively high real estate sector volatility. 26

27 References Admati, A. and P. Pfleiderer, 1991, Sunshine trading and financial market equilibrium, Review of Financial Studies 4, Avellaneda, M. and S.Zhang, 2009, Path-dependence of leveraged ETF returns, working paper, New York University. Ben-David, I., Franzoni, F., and R. Moussawi, 2012, ETFs, arbitrage, and contagion, working paper, Ohio State University. Bessembinder, H., Carrion, A., Tuttle, L., and K. Venkataraman, 2012, Predatory or sunshine trading? Evidence from crude oil ETF rolls, working paper, University of Utah. Boney, V. and G.S. Sirmans, 2008, REIT ETFs and underlying REIT volatility, Real Estate Research Institute, working paper. Brunnermeier, M. and L. Pedersen, 2005, Predatory trading, Journal of Finance 60, Carlin, B., Lobo, M., and S. Viswanathan, (2007), Episodic liquidity crises: Cooperative and predatory trading, Journal of Finance 62, Charaput, N. and P. Miu, 2011, The pricing and performance of leveraged exchanged-traded funds, Journal of Banking and Finance 35, Cheng, M. and A. Madhavan, 2009, The dynamics of leveraged and inverse exchange traded funds, Journal of Investment Management 7, Curcio, R., Anderson, R., Guirguis, H., and V. Boney, 2012, Have leveraged and traditional ETFs impacted the volatility of real estate stock prices? Applied Financial Economics 22, Hill, J. and G. Foster, 2009, Understanding returns of leverage and inverse funds, Journal of Indexes, Sept/Oct 2009, Jarrow, R., 2010, Understanding the risk of leveraged ETFs, Finance Research Letters 7, Lu, L., Wang, J., and G. Zhang, (2009), Long term performance of leveraged ETFs, working paper. Pagano, M., L. Peng, and R. Schwartz, 2010, The quality of market opening and closing prices: Evidence from the Nasdaq Stock Market, working paper. Shum, P.M. (2010) The long and short of leveraged ETFs: The financial crisis and performance attribution, working paper, Schulich School of Business, York University. Tang, H., and X. E. Xu, (2011), On the performance and return deviation of leveraged real estate ETFs, working paper, Seton Hall University. 27

28 Tang, H., and X. E. Xu, (2012), Solving the return deviation conundrum of leveraged Exchange Traded Funds, forthcoming Journal of Financial and Quantitative Analysis. Trainor, W., 2010, Do leveraged ETFs increase volatility, Technology and Investment, 1, Troianovski, A. (2008), REIT moves rub executives wrong way, Wall Street Journal, December 26,

29 Aggr. $ Volume Aggr. Mkt Cap Millions Billions in thousands Millions $1,000 $900 $800 $700 $600 $500 $400 $300 $200 $100 $0 Figure 1A Monthly Dollar Volume of Six LETFs SRS SKF URE UYG FAS FAZ $4,000,000 $3,500,000 $3,000,000 $2,500,000 $2,000,000 $1,500,000 $1,000,000 $500,000 $0 Figure 1B Market Capitalization of Six LETFs SRS SKF URE UYG FAS FAZ Figure 1C Aggregate Monthly Dollar Volume and Market Capitalization of Six LETFs Aggr. $ Vol Aggr Mkt Cap Using data from CRSP, these figures characterize the monthly dollar volume and assets under management for the six LETFS from the finance/real estate sector that we track during our sample period. 29

30 Figure 2A Sample-Control Share Volume :31 9:33 9:35 9:37 9:39 9:41 9:43 9:45 9:47 9:49 9:51 9:53 9:55 9:57 9:59 Oct-06 Oct-07 Oct-08 May-09 Oct-09 Oct-10 Figure 2B Sample-Control Share Volume Oct-06 Oct-07 Oct-08 May-09 Oct-09 Oct-10 Figure 2A displays sample stock mean share volume less control stock mean share volume by minute between 9:30 and 10:00 in October 2006, 2007, 2008, 2009, and 2010 and May 2009 while Figure 2B displays the volume difference from 3:00 to 4:00. 30

31 Figure 3A Sample-Control # of Trades Oct-06 Oct-07 Oct-08 May-09 Oct-09 Oct :31 9:33 9:35 9:37 9:39 9:41 9:43 9:45 9:47 9:49 9:51 9:53 9:55 9:57 9:59 Figure 3B Sample-Control # of Trades Oct-06 Oct-07 Oct-08 May-09 Oct-09 Oct Figure 3A displays sample stock mean number of trades less control stock mean number of trades by minute between 9:30 and 10:00 in October 2006, 2007, 2008, 2009, and 2010 and May 2009 while Figure 3B displays the number of trades difference from 3:00 to 4:00. 31

32 9:31 9:56 10:21 10:46 11:11 11:36 12:01 12:26 12:51 13:16 13:41 14:06 14:31 14:56 15:21 15:46 9:31 9:54 10:17 10:40 11:03 11:26 11:49 12:12 12:35 12:58 13:21 13:44 14:07 14:30 14:53 15:16 15:39 9:31 9:56 10:21 10:46 11:11 11:36 12:01 12:26 12:51 13:16 13:41 14:06 14:31 14:56 15:21 15:46 9:31 9:54 10:17 10:40 11:03 11:26 11:49 12:12 12:35 12:58 13:21 13:44 14:07 14:30 14:53 15:16 15:39 Figure 4A Sample Range Volatility Figure 4B Control Range Volatility Oct Oct Oct-07 Oct Oct-07 Oct May-09 Oct May-09 Oct-09 0 Oct-10 0 Oct-10 Figure 4C Sample Absolute Returns Figure 4D Control Absolute Returns Oct-06 Oct-07 Oct Oct-06 Oct-07 Oct May May Oct-09 Oct Oct-09 Oct-10 32

33 Figures 4A and B display the volatility of the sample and control stocks as measured by the price range each minute. More specifically, the measure of volatility is: (high price t low price t )/mean price t where prices are NBBO midpoints. Figures 4C and D demonstrate volatility as measured by absolute returns using NBBO midpoints. 33

34 15:01 15:04 15:07 15:10 15:13 15:16 15:19 15:22 15:25 15:28 15:31 15:34 15:37 15:40 15:43 15:46 15:49 15:52 15:55 15:58 Figure 5A Sample-Control Range Volatility Oct-06 Oct-07 Oct-08 May-09 Oct-09 Oct :31 9:33 9:35 9:37 9:39 9:41 9:43 9:45 9:47 9:49 9:51 9:53 9:55 9:57 9: Figure 5B Sample-Control Range Volatility Oct-06 Oct-07 Oct-08 May-09 Oct-09 Oct E Figure 5A shows the extent to which sample stock volatility exceeds control stock volatility from 9:30 to 10:00 where volatility is measured as (high price t low price t )/mean price t where prices are NBBO midpoints. Figure 5B displays this difference for the time period from 3:00 to 4:00. 34

35 Table 1A Characteristics of Sample Stocks and Matched Control Stocks Period Sample Control Sample Control Sample Control Aug-Oct Avg. Daily Volume Market Cap (000 s) Share Price , ,369 $4,489,268 $4,602,958 $51.10 $ ,061,268 1,555,924 3,889,906 4,105, * 3,873,743 1,887,960 2,461,826 3,018, ,452,419 1,727,167 3,353,325 3,622, ,579,085 1,468,056 4,697,941 3,808, The sample stocks are 63 constituent stocks of DJUSRE, which is the index tracked by the ProShares Ultra and UltraShort Real Estate ETFs (tickers: URE and SRS) all of which are also components of DJUSFN which is the index tracked by ProShares Ultra and UltraShort Financials (tickers: UYG and SKF) and most of which are components of the Russell 1000 Financial Services Index which is tracked by the Direxion Daily Financial Bull and Bear 3x Shares (tickers: FAS and FAZ). The controls are a selection of stocks randomly drawn from the CRSP database that minimize the squared sum of the difference in market capitalization and average daily share volume with the sample stocks as of December The table reports the mean daily trading volume, market capitalization, and share price of the sample and control stocks. Each sample period is August through October of the designated year with the exception of 2009* which is April through June and is included because it is during this three month period that trading volume and assets under management peaked in the six LETFs on which we focus. Table 1B Industry Composition of Control Stock Portfolio Industry % of Portfolio Industry % of Portfolio Non-Durable Goods 1.5% Telecom 0.0% Durable Goods 3.1 Utilities 9.2 Manufacturing 6.2 Shops 15.4 Energy 3.1 Healthcare 6.2 Chemicals 0.0 Finance 27.7 Business Equipment 9.2 Other 18.5 Our breakdown of the control stock portfolio is based on the 12 sectors as constructed on Ken French s website. 35

36 Table 2A Volatility of Sample and Control Stocks Period Sample Stocks Control Stocks Sample-Control Aug-Oct 25 th %ile Mean 75 th %ile 25 th %ile Mean 75 th %ile Difference in means *** * *** ** * Table 2A reports the distribution of the variance of daily returns of the sample stocks and their controls. Each sample period is August through October of the designated year with the exception of 2009* which is April through June and is included because it is during this three month period that trading volume and assets under management peaked in the six LETFs on which we focus. Statistical significance of the t-test statistics is denoted by ***, **, * for 0.001, 0.01, and 0.05 levels respectively. Table 2B Volatility of 12 Equal-weighted Sectors Period Dur NonDur Manuf Energy Chem BusEq Telcom Utils Shops Health Other Money * Table 2B uses the daily returns from Ken French s website to calculate the variance of returns in each sector for each sample period. 36

37 Table 3 Variance of Returns Sample Stocks Sample-Control Period * * * * * 9:30-10: *** *** *** ** *** *** 10:30-3: *** *** *** ** *** *** 3:00-4: *** *** *** *** *** *** Control Stocks 9:30-10: *** *** *** 10:30-3: *** *** *** 3:00-4: *** *** *** Sample Control 9:30-10: * ** *** *** * 10:30-3: ** * *** *** * 3:00-4: * *** *** *** Table 3 reports the median variance of one-minute returns for various portions of the day. Each sample period is August through October of the designated year with the exception of 2009* which is April through June and is included because it is during this three month period that trading volume and assets under management peaked in the six LETFs on which we focus. Statistical significance of the Wilcoxson test statistics is denoted by ***, **, * for 0.001, 0.01, and 0.05 levels respectively. 37

38 Panel A: One-minute returns Table 4 Intraday Return Autocorrelations Sample Stocks Sample-Control Period * * * * * 9:30-10: :30-3: *** *** *** *** *** :00-4: *** *** *** *** *** ** Control Stocks 9:30-10: ** :30-3: *** 3:00-4: ** *** *** Sample - Control 9:30-10: *** *** *** * *** 10:30-3: *** ** *** ** 3:00-4: *** *** ** ** Panel B: Five-minute returns Sample Stocks Sample-Control Period * * * * * 9:30-10: ** * ** 10:30-3: *** ** * 3:00-4: *** *** *** * Control Stocks 9:30-10: *** * 10:30-3: * *** 3:00-4: * ** * Sample - Control 9:30-10: ** * :30-3: * :00-4: *** ** Table 4 reports the mean intraday return autocorrelations for various portions of the day using one-minute (Panel A) and five-minute (Panel B) returns. Each sample period is August through October of the designated year with the exception of 2009* which is April through June and is included because it is during this three month period that trading volume and assets under management peaked in the six LETFs on which we focus. Statistical significance of the t-test statistics is denoted by ***, **, * for 0.001, 0.01, and 0.05 levels respectively. 38

39 Table 5 Rebalancing Demand Regression Results Variable Full Sample 10/08-3/09 4/09-9/09 10/09-3/10 4/10-10/10 4 th qtr 2006 Intercept *** *** *** * *** *** RD *** *** *** *** *** n/a r(9:30-3) *** * *** * *** S&P500 (9:30-3) ** *** ** ** Adj R Table 5 reports the estimation results from applying pooled regression techniques to the equation where the dependent variable,, is the return from 3pm to 4pm for stock j on day t, is the rebalancing demand variable for stock j on day t, is the intraday return from 9:30am to 3pm for stock j on day t, and is the 9:30am to 3pm return for the S&P 500 index on day t. The first column of results is for the full sample while the next four columns display sub-sample results. The last column presents results from the fourth quarter of 2006 before the existence of leveraged/inverse ETFs and thus there is no RD included in the regression. Statistical significance of the regression coefficients is denoted by ***, **, * for 0.001, 0.01, and 0.05 respectively. 39

40 Table 6 Impact of Rebalancing Demand on Next Day Returns Panel A: Dependent variable is 9:30-10:30 next day return Variable Full Sample 10/08-3/09 4/09-9/09 10/09-3/10 4/10-10/10 4 th qtr 2006 Intercept *** *** *** ** RD *** ** *** *** * n/a r(j,t) ** *** *** *** SP500 (t) *** ** *** *** * *** Adj R Panel B: Dependent variable is 10:30-11:30 next day return Variable Full Sample 10/08-3/09 4/09-9/09 10/09-3/10 4/10-10/10 4 th qtr 2006 Intercept *** * *** *** *** RD *** *** *** *** *** n/a r(j,t) *** *** *** SP500 (t) *** *** *** *** *** Adj R Panel C: Dependent variable is 11:30-12:30 next day return Variable Full Sample 10/08-3/09 4/09-9/09 10/09-3/10 4/10-10/10 4 th qtr 2006 Intercept *** *** *** *** RD *** * n/a r(j,t) *** *** *** SP500 (t) *** *** *** *** *** Adj R Panel D: Dependent variable is 12:30-1:30 next day return Variable Full Sample 10/08-3/09 4/09-9/09 10/09-3/10 4/10-10/10 4 th qtr 2006 Intercept ** *** *** *** RD *** ** ** n/a r(j,t) SP500 (t) *** *** *** *** *** Adj R Table 6 reports the estimation results from applying pooled regression techniques to the equation where the dependent variable,, is the stock j return on day t+1 from one of the following intervals h: 9:30am- 10:30am, 10:30-11:30, 11:30-12:30, or 12:30-1:30, is the rebalancing demand variable for stock j on day t, is the return for stock j on day t, and is the return for the S&P 500 index on day t. The first column of results is for the full sample while the next four columns display sub-sample results. The last column presents results from the fourth quarter of 2006 before the existence of leveraged/inverse ETFs and thus there is no RD included in the regression. Statistical significance of the regression coefficients is denoted by ***, **, * for 0.001, 0.01, and 0.05 respectively. 40

41 Table 7 The impact of rebalancing demand on volatility Panel A: Dependent variable is 3:00-4:00 absolute return on day t Variable Full Sample 10/08-3/09 4/09-9/09 10/09-3/10 4/10-10/10 Intercept *** *** *** *** *** RD *** *** *** *** *** r(j,9:30-3) *** *** *** *** * VIX *** *** *** *** *** Adj. R Panel B: Dependent variable is 9:30-10:30 absolute return on day t+1 Variable Full Sample 10/08-3/09 4/09-9/09 10/09-3/10 4/10-10/10 Intercept *** ** *** ** RD *** * *** *** r(j,9:30-4) *** *** *** *** VIX *** *** *** *** ** Adj. R Table 7 report the estimation results from applying pooled regression techniques to the equation where the dependent variable, 9:30am to 10:30am on day t+1 in Panel B, is the absolute return from 3pm to 4pm in stock j on day t in Panel A and, is the absolute value of the rebalancing demand for stock j on day t, is the absolute return from 9:30am to 3pm for stock j on day t, and VIX t is the value of the VIX on day t. In Panel B when the dependent variable is the absolute return from 9:30 to 10:30 on day t+1, we use the full day t absolute return as the independent variable rather than the return to 3:00. Statistical significance of the regression coefficients is denoted by ***, **, * for 0.001, 0.01, and 0.05 respectively. 41

42 Table 8 Factors that determine stock return sensitivity to rebalancing demand Variable 10/08-3/09 4/09-9/09 10/09-3/10 4/10-10/10 Intercept *** *** *** Variance of ret *** *** ** ADV (in mil) ** ** Size (in $bn) ** * * ** Adj R Table 8 reports the estimate results from applying pooled regression techniques to the equation where SRD j is the sensitivity to rebalancing demand of stock j estimated from the regression equation in which is SRD j.. is the variance of return for stock j. ADV j is the average daily volume in stock j in millions of shares. MC j is the market capitalization of stock j in billions of dollars. Statistical significance of the regression coefficients is denoted by ***, **, * for 0.001, 0.01, and 0.05 respectively. 42

43 Table 9 Rebalancing Demand Regression Results Stratified by Real Estate Sector Volatility Dependent Variables Variable ret (3:00-4:00) ret(9:30-10:30) Abs ret(3:00-4:00) ret(9:30-3) *** ** *** S&P500 (9:30-3) or VIX *** *** *** Q 1 (RD) * *** Q 2 (RD) ** Q 3 (RD) *** *** *** Q 4 (RD) *** *** *** Q 5 (RD) *** *** *** Adj R Table 9 reports the estimation results from applying pooled regression techniques to the equations where the dependent variable,, is the return from 3pm to 4pm for stock j on day t, is the rebalancing demand variable for stock j on day t, Q i is an indicator variable that is 1 if real estate sector volatility as measured by ( ) on day t is ranked in quintile i of the daily volatility calculated from 10/08 to 10/10, is the intraday return from 9:30am to 3pm for stock j on day t, and is the 9:30am to 3pm return for the S&P 500 index on day t. Quintile 5 has the greatest real estate sector volatility. The intercept estimates are not reported here. The column headings indicate the dependent variable for different regressions. When the dependent variable is the return from 9:30 to 10:30 on day t+1, we use the full day S&P 500 return. When the dependent variable is the absolute return from 3:00 to 4:00, the S&P 500 return is replaced by the VIX and we use the absolute values of stock return and of rebalancing demand. Statistical significance of the regression coefficients is denoted by ***, **, * for 0.001, 0.01, and 0.05 respectively. 43

44 Table 10 Economic Impact of Rebalancing Demand on 3:00-4:00 Stock Returns Panel A: Magnitude and Impact of Rebalancing Demand by Period Impact from 50 th %ile RD (basis points) Impact from 75 th %ile RD Impact from 90 th %ile RD Period $RD Min Median Mean Max $RD Min Median Mean Max $RD Min Median Mean Max In Panel A, the respective periods are 10/08-3/09, 4/09-9/09, 10/09-3/10, and 4/10-10/10. $RD is millions of dollars of rebalancing demand. Min, median, mean, and max column headings signify the number of basis points the 3:00-4:00 returns were impacted by the daily rebalancing demand as determined by multiplying the stock sensitivity to rebalancing demand (SRD) for each stock in a period by the size of the rebalancing demand. Impact from the X th %ile RD represents the impact on 3:00-4:00 returns of the X th percentile daily absolute rebalancing demand for that period measured across the 63 stocks in the sample. For example, in period 1, the across-stock median rebalancing demand was $4,040,000 while the across-stock 90 th percentile rebalancing demand was $11,920,000. The median impact of the median rebalancing demand in period 1 was bp. This impact is determined by multiplying the median absolute rebalancing demand across all the days in period 1 for stock A by the sensitivity to rebalancing demand for stock A in period 1, then repeating this calculation for all 63 stocks, and then finding the median impact across these 63 products. For example, in period 2, the across-stock 90 th percentile rebalancing demand in period 2 was $5,070,000 and the maximum impact of a 90 th percentile rebalancing demand for any of the 63 stocks was bp. Panel B: Magnitude and Impact of Rebalancing Demand by Real Estate Sector Volatility Quintile Quintile Median RD ($mn) Min impact (bp) Median impact (bp) Mean impact (bp) Max impact (bp) In Panel B, quintile 5 represents those days with the highest real estate sector-specific volatility. Within each quintile of days we determine the median absolute rebalancing demand for each stock and calculate a sensitivity to rebalancing demand (SRD) for each stock. To determine the impact of rebalancing demand on 3:00-4:00 stock returns, we multiply a stock s SRD by the median absolute rebalancing demand for that quintile of days. What is reported in Panel B is the across-stock minimum, median, mean, and maximum impact in each quintile. For example, on those days with the greatest real estate sector-specific volatility, the median absolute rebalancing demand across all stocks is $5,320,000 and the average impact on 3:00-4:00 stock returns is bp. 44