Bond ETF Arbitrage Strategies and Daily Cash Flow

Transcription

1 Bond ETF Arbitrage Strategies and Daily Cash Flow Jon A. Fulkerson Sellinger School of Business and Management Loyola University Maryland Susan D. Jordan Gatton College of Business and Economics University of Kentucky Denver H. Travis* Haub School of Business Saint Joseph s University denver.travis@sju.edu January 15, 2017 * Contact author

2 Bond ETF Arbitrage Strategies and Daily Cash Flow Abstract We consider how cash flows relate to arbitrage strategies for bond ETFs. Bond ETFs trading at a premium (discount) to NAV experience more creations (redemptions) than those trading at parity. When these cash flows occur, subsequent returns partially offset the premium or discount. In the absence of cash flow, premiums and discounts persist. We consider what factors discourage transactions around these anomalies and find that poor secondary market liquidity discourages creations and redemptions. Our results suggest that these anomalies persist in part due to costs and uncertainty in the secondary market.

3 Introduction Transactions in ETF shares take place in both the primary and the secondary market. Most non-institutional trading in ETF shares takes place in the secondary market on a public exchange. Reported volumes normally focus on exchange transactions, yet some daily trading can occur through primary market transactions. The primary market activity is nontrivial for bond ETFs for our sample covering 2007 to 2015, we find that 27% of total volume (primary and secondary) comes from the creation or redemption of shares. The primary market depends entirely on Authorized Participants (APs) as intermediaries. These firms have an agreement with the fund sponsor allowing them to create or redeem shares in-kind. As of the end of 2014, the Investment Company Institute reports that a typical Bond ETF had 32 Authorized Participant agreements in place. However, most of these APs were inactive, with most ETFs having only three to five active APs. 2 A key role for APs is to facilitate arbitrage trading; if the secondary market price drifts too far from the portfolio s underlying value (NAV), investors can buy and sell through the AP to earn arbitrage profits. As seen in prior studies (Petajisto, 2016; Fulkerson, Jordan, and Riley, 2014), the market price for an ETF regularly deviates from the fund s NAV, resulting in either a premium or a discount market price. The unique selling point of ETFs are that these deviations should quickly disappear through the AP mechanism. The prior research on ETFs shows that premiums and discounts disappear through time. For stock ETFs, the deviation is mostly corrected with five days (Fulkerson and Jordan, 2013). For bond ETFs, the deviations take much longer to dissipate, with premiums and discounts persisting as long as 30 days (Fulkerson, Jordan, and Riley, 2013). 2 The data on the number of APs is take from The Role and Activities of Authorized Participants of Exchange- Traded Funds, Investment Company Institute, March 2015 ( The data was obtained through a confidential survey and, consequently, the underlying data is not available.

4 In this study, we consider the degree to which the returns around premiums and discounts change with primary market transactions. We begin with a sample of daily return and flow data for US-domiciled bond ETFs operating during the period 2007 to We first show that discounts and premiums regularly occur for bond ETFs. For a given week, ETF prices range from a -0.45% discount to NAV at the 5 th and to a 0.73% premium at the 95 th percentile. The intent of the ETF structure is for these premiums and discounts to lead to creations and redemptions, respectively, which, in turn, should eliminate the mispricing. We observe a tendency for premium ETFs to have more creations and discount ETFs to have more redemptions, and these transactions average approximately 3% of assets. Despite the arbitrage opportunity, most premiums and discounts do not lead to creations or redemptions. This suggests that markets do not respond completely to correct the apparent mispricing. We next consider how share creations and redemptions relate to the returns for premium and discount ETFs. Considering ETFs in the top 25% of the Price/NAV ratio in a given week (premium), we estimate the alphas to shorting on the secondary market and buying on the primary market over the next five days. On average, an investor would earn an annualized alpha of about 8% from the short position and lose about 7% from the long position, for a net alpha of 1.27%. However, this profit changes depending on if there is creation activity or not during those five days. Conditional on no creations occurring, the average alpha is economically and statistically zero. If creations do occur, the long-short strategy earns an alpha of 2%. Trading matters less for the high liquidity ETFs (alpha of zero) and more for low liquidity ETFs (alpha of 4%). We find similar results for the long-short strategy among the bottom 25% (discount) of

5 ETFs. These results suggest that premiums and discounts decrease when share creations and redemptions occur, but persist in the absence of these share transactions. Primary market activity appears highly correlated with profitable arbitrage activity. However, since most premiums and discounts do not result in a creation or redemption, there is a puzzle as to why some deviations result in trades and others do not. In our final set of tests, we consider factors that affect future primary market activity. While premiums and discounts matter, secondary market liquidity has a nontrivial effect. This suggests that liquidity costs on the exchanges creates a barrier to arbitrage that allows some premiums and discounts to persist for bond ETFs. Overall, our study finds that creations and redemptions by APs have a strong relation to the premium and discount phenomenon in bond ETFs. Primary and secondary market prices converge more rapidly when the primary market shows evidence of arbitrage trading. However, arbitrage trading is relatively rare even in scenarios where the profitability appears high, suggesting that several barriers exist for the typical arbitrageur. Background ETFs provide a benefit to investors by allowing them to trade a whole portfolio of assets quickly and cheaply. For bond ETFs, this convenience is even greater as the underlying bonds may be illiquid or, for retail investors, difficult to access directly. Combined with relatively cheap expense ratios, ETFs have rapidly increased in popularity. This section will outline relevant details of ETF operations and then consider two areas of prior research related to this study.

6 Like most ETFs, investors trade shares of bond ETFs that represent an underlying portfolio of assets. 3 Most volume occurs on the exchange, but the ETF structure also allows investors to create or redeem shares at NAV directly with the ETF like a traditional mutual fund. Unlike a mutual fund, however, creation and redemption is controlled by Authorized Participants (APs), who serve as intermediaries between investors and the ETF. A further difference is that the creations and redemptions are often in-kind, meaning many transactions involve the actual underlying portfolio rather than cash. The APs provide additional liquidity to the market by creating shares when demand is strong and their activities help to ensure that the secondary market price of the ETF shares does not deviate significantly from the share s NAV. If for example, the price of the ETF shares rise sufficiently above NAV, APs will step in and sell the ETF shares at the bid and buy the underlying securities in the portfolio at the ask. On the other hand, if the ETF share price falls sufficiently below the NAV, the AP will enter the primary market and buy the ETF shares at the ask and sell the underlying securities at the bid. This mechanism implies that arbitrage opportunities quickly disappear and are meant to lead to market equilibrium where prices rarely deviate from NAV. Unlike closed-end funds, the primary market can be utilized to guarantee that the secondary market price is close to net asset value. The process is slightly more complicated for bond ETFs compared to equity ETFs. Since the majority of bond trading is over the counter (OTC) and many bonds do not trade on any given day, there is no closing price; consequently, the fund sponsor must use a pricing agency to estimate the portfolio s value. Also, by convention, bond prices are quoted at the bid, and thus the NAV for a bond ETF is calculated using bid prices. Any strategy that involves buying the 3 Exchange Traded Notes would be an alternative to ETFs with similar investment outcomes, but are excluded from our study.

7 underlying bond portfolio would require ask quotes on the bonds which are not widely available to individual investors. One question in the literature focuses on those cases where prices do deviate from NAV. The academic literature highlights that differences occur regularly. For example, Petajisto (2016) examines equity ETF premiums/discounts and finds that they tend to increase during times of market stress or volatility. Both Engle and Sarkar (2006) and Fulkerson and Jordan (2013) consider the persistence of premiums and discounts in equity ETFs. While the average equity ETF appears to have exchange prices near NAV, many ETFs have nontrivial premiums and discounts. Fulkerson and Jordan (2013) report an average premium of 9 basis points (bps), but also find that several ETFs in a given day can have a premium or discount more than 1% of NAV. These deviations persist for up to five days, but mostly are corrected following a large overnight drop in price (closing price to opening price). In contrast, Fulkerson, Jordan, and Riley (2014) find that bond ETFs have considerably longer reversion periods. They attribute this difference to the relatively illiquid underlying bonds, which may be difficult to acquire or price. 4 A second question revolves around what characteristics of ETFs affect the share creation/redemption process. Petajisto (2016) finds higher share creation activity around premiums, but this activity explains only a small part of the subsequent price reversion. Clifford, Fulkerson, and Jordan (2014) find following month creations are higher for equity ETFs with premiums, while redemptions are higher for ETFs with discounts. These flows are consistent with the expected arbitrage strategies. More generally, several market factors affect the cash flows for equity ETFs, including volume, bid-ask spreads, volatility, and assets under management. However, the study also observes significant return chasing by investors a seemingly irrational decision given that most of the ETFs follow index strategies. Chen and Qin 4 Many bond ETFs will accept cash for creations, but charge the APs an additional fee in these cases.

8 (2012) and Fulkerson, Jordan, and Riley (2013) find similar results for bond mutual funds, while Fulkerson, Jordan, and Travis (2015) confirm the same trends for bond ETFs. Relative to this existing literature, we contribute on several points. We focus on daily premiums and discounts for bond ETFs over the period 2007 to In this context, we explore how frequently redemptions and creations occur in the days following an observed premium or discount. We then consider how subsequent returns change conditional on creations and redemptions occurring. We finally consider what factors influence the creation and redemption decision. We model these decisions jointly using a two-stage hurdle procedure similar to Cragg (1971). In all cases, we consider how the underlying portfolio s liquidity affects our results. Data and methods We collect daily ETF shares outstanding data from Morningstar Direct. We match those ETFs by ticker with the CRSP Databases for the period January 2007 to December Fund characteristic variables are obtained from the CRSP Survivor-Bias-Free Mutual Fund Database. Daily prices and returns are obtained from the CRSP Daily Stock Database. Like Fulkerson, Jordan, and Travis (2015), we filter the sample with several restrictions. First, to remove the unusual patterns of freshly issued ETFs, only observations with a fund age of over six months and AUM of over $20 million are included. Second, to be categorized as a bond ETF, each fund is required to have held at some point at least 80% bonds. Third, we exclude observations with abnormally large daily changes in return-adjusted total net assets (greater than 200% or less than -50%). Finally, each ETF is evaluated by hand to confirm that it follows a fixed income strategy. Following these filters, we obtain a sample of 181 bond ETFs with 186,296 daily observations.

9 Summary statistics for the sample of daily bond ETF data for the period of January 2007 to December 2015 are displayed in Exhibit 1. In comparison to the sample of monthly bond ETF data for the 2008 to 2013 period in Fulkerson, Jordan, and Travis (2015), most fund variables, and market variables have similar summary statistics. Two variables that are unique in this study are creation unit size and daily flow. We estimate the creation unit size for each ETF by observing the minimum change in shares outstanding rounded to the nearest 25,000 units. The mean creation unit size is 82,662 shares with a median of 100,000 shares. 6 [Insert Exhibit 1 about here.] We estimate daily fund flow as the return-adjusted change in total net assets, where daily total net assets is estimated by multiplying the daily shares outstanding times the daily net asset value as follows: FFFFFFFF tt = SSSS tt NNNNNN tt SSSS tt 1 NNNNNN tt 1 (1+rr tt ) SSSS tt 1 NNNNNN tt 1 (1) where SO is the daily shares outstanding value from Morningstar Direct, NAV is the daily net asset value from CRSP, and r is the daily return value from CRSP. Positive values of flow are designated as net ETF share creations while negative values of flow are designated as net redemptions. 7 The average daily flow is very low at 0.17% of assets per day while the median is 0%. For the average bond ETF, most daily observations are zero flow days. With the growth of the ETF industry over the period, the average creation flow is larger than the average redemption flow at 0.29% versus 0.12% per day, respectively. 6 A creation unit ( CU ) is the minimum multiple of shares an AP can create or redeem with an ETF. These data are not reported in any of our databases, so we had to impute the results from the size of the flows. We hand verified many of the CU s we estimated and found no errors. While an ETF could hypothetically have any multiple, we found no example of an ETF that was not a multiple of 25,000, and the majority had CU s of 100, A number of flow calculations created non-zero flow when shares outstanding did not change, due to changes in returns; these observations were set to a flow value of zero. We acknowledge that on a given day a fund could have both redemptions and creations and that we only observe the net effect.

10 We form three liquidity subcategories based on the liquidity of the underlying portfolio using Lipper asset and class codes in CRSP. Exhibit 2 illustrates our breakdown of subcategories of bond ETFs. We categorize the high liquidity group as those ETFs that are U.S. Government bond funds, which includes U.S. Government Long & Intermediate Maturity, U.S. Government Short Maturity, and U.S. TIPS. The medium liquidity group is comprised of ETFs of Corporate Investment Grade bonds. The low liquidity group includes ETFs from the following Lipper categories: Municipal, International, General multi-category, and Corporate High Yield bonds. Corporate Investment Grade bond ETFs are the largest group in the sample, followed by Municipal bond ETFs, and then by U.S. Government Long & Intermediate Maturity bond ETFs. [Insert Exhibit 2 about here.] In order to provide some perspective on the relative size of the bond ETF primary market compared to the secondary market, Exhibit 3 provides summary statistics for dollar flow and dollar trading volume. Dollar flow is calculated using the numerator in Equation 1. Dollar volume is calculated by multiplying daily volume times the daily close price of the ETF. Total volume is the sum of dollar flow and dollar volume. For our sample period of 2007 to 2015, 72.8% of the total volume came from secondary market trading with the remainder from primary market fund flow volume. Thus, it appears that the majority of bond ETF investors gain access through the secondary market, but a nontrivial amount of trading occurs on the primary market. [Insert Exhibit 3 about here.] Exhibit 4 presents the percent of observations with creations and/or redemptions. We present this information for the full sample and for our liquidity subsamples. First, we note that creations are more common than redemptions. This is expected given the tremendous growth in

11 overall assets invested in ETFs during our sample period. We also form three subsamples of ETFs based on the liquidity of the bonds in the underlying portfolio. We find that only 18% of the observations for our low liquidity group have either a creation or redemption. This would seem consistent with the higher cost to the AP associated with transacting in the lower-liquidity bonds. Given the differences in frequency of AP activity, we provide all further results both for the full sample and for the individual liquidity groups. [Insert Exhibit 4 about here.] Flow and the price-to-nav ratio From prior research on ETFs, deviations of the ETF price-to-net asset value (P/NAV) ratio provide arbitrage opportunities for APs (see, e.g., Engle and Sarkar (2006), Fulkerson and Jordan (2013), Petajisto (2016), and Fulkerson, Jordan, and Riley (2014)). In this section, we consider how trading increases or decreases around premiums and discounts for bond ETFs. Exhibit 5 displays flow results following deviations of the P/NAV ratio for the sample period. 8 For a given 5-day period, we create sub-groups for different percentile groups based on prior 5- day average P/NAV ratio and then examine primary market trading in the subsequent two days. The table shows the likelihood and average size of creations and redemptions for various percentile P/NAV groups. Panel A provides the results for the full sample while Panels B, C, and D provide subsample results by liquidity group. In Panel A for example, ETFs with an average 5-day P/NAV ratio being above the 99 th percentile (high premium), 27.47% had share creations twodays later, while only 0.39% had redemptions. The average creation represented 3.16% of assets. Considering discount ETFs, creations happen very infrequently. An ETF at the 1 st percentile 8 In a few cases, the end-of-day price is not available. In these cases, we use the mid-point of the bid and ask prices. All of our results are robust to the exclusion of these observations.

12 rarely had creations (0.75%), but regularly had redemptions (7.09%). For both discount and premium ETFs, the creations and redemptions are consistent with arbitrage trading. Across liquidity groups, the apparent arbitrage trading still appears in Panels B, C, and D. However, the liquidity of the underlying assets does appear to effect the likelihood of trading occurring in the case of the medium liquidity group (Panel C), which is comprised of investment grade corporate bond ETFs. This group has a much higher likelihood of creations in the top 5% compared to both high and low liquidity. We speculate this anomaly occurs for two reasons. One, compared to the high liquidity group, the medium liquidity group has much higher premiums. The 95 th percentile premium is 0.85% for the medium group, but only 0.27% for the high group. This premium differential is not surprising since our high liquidity group is comprised of US Government securities for which there is an active market with greater price transparency. The greater frequency of creations for the medium liquidity group compared to the high liquidity group is because the larger premiums provide opportunities that are more profitable. The second reason likely is driven by the differences in the underlying asset liquidity and the ease with which the underlying assets can be acquired to create shares. The premiums are roughly similar at the 95 th percentile for the medium and low groups (0.85% and 0.90%, respectively), but creations are much more likely in the highest premium medium liquidity ETFs. Jointly, this supports the idea that the liquidity of the underlying bonds has a nontrivial impact on the likelihood and profitability of arbitrage trading related to premiums and discounts. [Insert Exhibit 5 about here.] One final trend we note is that the likelihood of creations for the premium ETFs is higher than the redemptions for the discount ETFs. We speculate that this occurs for two reasons. First, in general, ETFs have become more popular. As more investors seek out these new investments,

13 more shares are required to meet the demand, and thus we observe more share creation. An AP would be motivated to create shares around a premium even as an alternative to buying on the exchange because the NAV would be cheaper for the clients. A second reason comes from how bond ETFs measure NAV. As discussed earlier, the reported NAV is estimated at the bid price. A discount ETF would require transacting at the ask price, and we cannot observe the implied ask NAV for the portfolio. Hence, our identified population of discount ETFs is likely partly biased, though this does not change the fact that redemptions are in general less common than creations. Abnormal returns following a price-to-nav ratio premium or discount The prior section considers the likelihood of share creations or redemptions in bond ETFs conditional on the P/NAV ratio. We now consider if the subsequent returns are different when the ETF has had a creation or a redemption. We create a simple method for benchmarking each fund against its self. For each week (on Wednesdays), we calculate the rolling average P/NAV ratio over the prior 20 days and prior 5 days for each fund. The ratio of the 5-day average over the 20-day average is used to rank the funds each week. 9 Those funds that rank in the top and bottom quartiles (referred to as premium and discount hereafter) are examined for alphas conditional on flow over the five days following the ranking. 10 We then test for differences in 9 This measure adjusts for the fact that some categories of bond ETFs will naturally trade at larger premiums. This occurs because the NAV is based on the bid price of the underlying bonds. ETFs with less liquid bonds in the underlying portfolio should naturally trade at larger premiums. Thus, the measure captures differences in premium/discount from the norm or average over the prior 20 days. 10 Alpha is estimated from a regression of equally-weighted portfolio return risk premiums on four bond index factors, namely the Barclays U.S. Aggregate Bond Index less the U.S. Treasury Bill index, the Barclays U.S. Mortgage-Backed Security Index less the Intermediate U.S. Treasury index, the Barclays Global High Yield index less the Intermediate U.S. Treasury Index, and the Barclays U.S. Corporate High Yield Bond Index less the Intermediate U.S. Treasury index.

14 excess returns on the typical ETF arbitrage strategy between the no flow group, the creations group, and the redemptions group. 11 Exhibit 6 displays the results for the weekly premium (top quartile) funds. In Panel A of Exhibit 6, we present the alphas of going short the ETF end-of-day closing price and going long the underlying bonds (end-of-day NAV) for these premium P/NAV funds over the following five days. In column i of Panel A, results are provided for all premium funds in the sample regardless of flow. Shorting the ETF exchange price for this group results in a significant annualized excess return of 7.94% while going long the ETF NAV results in a significant excess return of 6.67%. These results are similar across liquidity subsamples. Results are presented for those ETFs that experienced no flow in the following five-day period (column ii), creations (column iii), or redemptions (column iv). While the trend of positive excess returns from shorting price and negative excess returns from going long NAV is consistent whether or not flow occurs, the relative magnitudes are quite different conditional on flow. The no flow and redemption funds have excess returns that approximately offset each other. Funds with creations show a lower return for the short position (7.02% compared to 7.94% for the full sample), and a higher return for the long position (-4.97% compared to -6.67%). The broad trend is consistent across the liquidity samples, though the difference is highest among the low liquidity ETFs. [Insert Exhibit 6 about here.] In Panel B, we explicitly examine the relative performance of the arbitrage scenarios (i.e., the combination of shorting the ETF price and buying at the ETF NAV to capitalize on the premium). In order to highlight the relative difference in magnitudes, the combined arbitrage 11 These tests require sufficient data every week to make the comparison. While our full sample has 463 weeks of data, individual tests may be for shorter periods.

15 excess returns are displayed in Panel B. Columns v, vi, and vii displays the arbitrage excess returns when no flow occurs, net creations occur, and net redemptions occur, respectively. In full sample, the net creations arbitrage excess return is 2.06% per year and highly significant; for the medium and low liquidity subsamples, the excess returns are 2.46% and 3.85%, respectively. Arbitrage excess returns are not significant for no flow or for net redemptions. This suggests that the premium is more likely to be corrected when trading occurs than when it does not. We test this explicitly in columns viii and ix by comparing the returns on a zero-cost portfolio that buys the creation (redemption) arbitrage strategy and shorts the no flow strategy. For the full sample, the arbitrage strategies for premium ETFs earned 1.74% more when there were creations compared to when there was no activity; for the medium and low liquidity subsamples, the differences are 2.96% and 5.95%, respectively. The same strategies lost 3.14% more when there were net redemptions. In summary, those ETFs that experience creations following a P/NAV premium exhibit significant excess arbitrage returns. The arbitrage seeking actions of Authorized Participants (i.e., creating and selling ETF shares while buying the underlying bonds) appear to occur more frequently when mispricing is corrected, especially for medium and low liquidity bond ETFs. In Exhibit 7, we repeat the same tests for those bond ETFs that rank in the lower quartile of P/NAV ratios. In Panel A, excess returns are calculated for going long the ETF prices and shorting the ETF NAV (i.e., the appropriate arbitrage strategy when the ETF trades at a discount). In full sample, going long the exchange price results in a significant excess return of 4.54% per year while going short NAV results in a significant excess return of 6.22% per year. Results are similar for the medium and low liquidity subsample, though excess returns are not significant in the high liquidity subsample. For no flow funds, the excess price returns lack

16 significance except for the medium liquidity subsample, while NAV excess returns are similar but smaller in magnitude compared to those in column i. For net creations in all but the high liquidity subsample, excess returns for price are larger in magnitude than excess returns for NAV; losses from buying the ETF shares are larger than the gains from going short the NAV. For net redemptions, excess returns for shorting NAV are larger in magnitude than the excess returns for going long the ETF shares; gains from shorting NAV are larger than the losses from buying the ETF shares. This is consistent with arbitrageurs earning a profit by redeeming shares trading at a discount to NAV. [Insert Exhibit 7 about here.] We consider the relative profits of arbitrage trading conditional on flow in Panel B of Exhibit 7. We present the combined arbitrage excess returns (i.e., the combination of shorting the ETF NAV and going long the ETF price) in order to capitalize on the discounted P/NAV ratio. For the no flow funds, only the medium liquidity subsample produces a significant excess return of 2.35%. For net creations funds, arbitrage excess returns are insignificant across subsamples. However, for the net redemption funds, excess returns are significant for all but the high liquidity subsample; the largest arbitrage excess return comes from the low liquidity subsample with an annualized value of 8.60%. Column ix provides the difference in alphas between the net redemption funds and the no flow funds when matched weeks are available. The arbitrage returns for net redemption funds are significantly larger than those for no flow funds in full sample and for the low liquidity group. The difference is 3.89% per year in full sample and 5.42% per year in the low liquidity group. In summary, the arbitrage actions of the Authorized Participants to eliminate the P/NAV discount (buying and redeeming ETF shares while selling the underlying bonds at NAV) appear to coincide with greater profits.

17 Factors affecting creations and redemptions Our analysis in the prior section shows that creation and redemption activity increases for premium and discount ETFs. However, we do not observe that every premium is followed by share creation 100% of the time, nor do we find that discounts always lead to redemptions. In this section, we further analyze the mechanism behind the APs decision to either create or redeem bond ETF shares by controlling for factors that would discourage AP activity. For our sample period, 89% of daily observations have no net creation or redemption activity. Because the data have such a large number of zeros, it is considered zero-inflated data, which suggests some empirical concerns. Arbitrageurs likely consider several factors before deciding to create or redeem shares. Having made that decision, they then face the question of how many shares to create or redeem. In prior economics research, the double hurdle model has frequently been employed to handle zero-inflated data; and we feel that the model is uniquely suited to model the decision of the AP. There are two components to the model: the first is a binary choice decision on whether to enter the primary market and create or redeem shares, and the second decision is the quantity of shares to create or redeem once the initial hurdle is cleared. We consider several factors that could affect these decisions. We model the AP s decision with a two-stage hurdle model similar to Cragg (1971). The hurdle model differs from a tobit model in that two different equations can be used for the two stages. In this case, the first equation is a selection model that treats the APs decision to create (or redeem) shares as a binomial event, bounded by zero. If the AP decides to create (or redeem) shares, that decision has cleared the hurdle, and is the first stage in the model. The second equation, known as an outcome or quantity model, is conditional on clearing the first hurdle. We model the APs

18 decision of how many shares to create (or redeem) shares in this second stage. For each stage, we include month and year dummy variables to control for time period effects. Standard errors are clustered by fund. We model the first equation in our hurdle model as: CCCCCCCCCCCC (rrrrrrrrrrrr)dddddddddddddddd ii,tt = PP/NNNNNN ii,tt 1 + VVVVVVVVVVVV ii,tt 1 + AAAAAA ii,tt 1 + εε ii,tt (2) where the decision to create (or redeem) is a binary choice variable. On a given day t, the AP either creates (or redeems) shares for fund i (1), or the AP does not create shares (0). We anticipate that a major factor affecting the AP s decision to enter the primary market will be the ratio of P/NAV. A larger value should lead to more creations and thus we expect a positive relationship between creations and P/NAV. On the other hand, if the ETF s price is lower than NAV this should lead to redemptions; so we expect a negative relationship between P/NAV and redemptions. A second key variable for the AP s decision to create/redeem shares is the volume of trading. We anticipate that price might deviate from NAV on very light volume days without the AP entering the market since they must transact in a large block (the creation unit) of shares. Thus, we anticipate seeing more creations/redemptions when volume is relatively high; there should be a positive relationship between both creations and redemptions and volume. A third variable that affects the decision to create/redeem is the age of the fund. We anticipate that older, more mature ETFs will have a larger number of APs with agreements with the fund. We expect a positive relationship between both creations and redemptions and the age of the fund. The second equation in our hurdle model is the quantity that is created (or redeemed):

19 PP QQQQQQQQQQQQQQQQ cccccccccccccc (oooo rrrrrrrrrrrrrrrr) ii,tt = + VVVVVVVVVVVV ii,tt 1 + AAAAAA ii,tt 1 + CCCC ii + BBBBBB ii,tt 1 + NNNNNNii,tt 1 RRRRRRuuuuuu ii,tt 1 + SSSSSS(PP NNNNNN) ii,tt 1 + CCCCCCCCCCCCCCCC + εε ii,tt (3) In addition to the factors that determine the AP s decision to enter the primary market to create or redeem, we utilize a number of additional variables in our quantity equation. A key variable for the quantity created/redeemed once the hurdle is cleared is the creation unit size (CU). 13 We expect a positive relationship between the quantity created (or redeemed) and the creation unit size. We also include the bid-ask spread (BAS) of the ETF in our quantity equation. We expect to see a larger quantity created/redeemed when the spread is small; thus, we anticipate a negative relationship between spread and quantity created or redeemed. Prior research shows that investors tend to chase returns in mutual funds. Thus, higher flows (demand) follows high return and negative flows follow lower/negative returns. We hypothesize that higher investor demand following high returns will lead to a larger quantity being created. Lower demand following low returns predicts a negative relationship between returns and quantity redeemed. Another variable in the quantity equation is the standard deviation of the P/NAV ratio. Fulkerson, Jordan, Riley (2014) found that deviations from NAV could persist for bond ETFs. We hypothesize that the lower the standard deviation of the P/NAV, or the more persistent the deviation, the greater is the quantity of shares that the AP will create or redeem. Finally, the decision to enter the primary market likely also depends on the spread of the underlying portfolio. We do not have a direct measure of this spread; consequently, we use our three liquidity groups to control for differences in the spread of the bonds underlying the ETF portfolio. Our liquidity groups also addresses the fact that in-kind creation is more common for 13 We estimate the creation unit size for each ETF as the minimum of the absolute value of the daily change in shares outstanding for each fund.

20 ETFs with Treasuries and other liquid bonds in their portfolios. The cash-create process is more common for ETFs having lower liquidity bonds in their portfolio; e.g., high yield corporate and municipal bonds. Thus our classifications are intended to capture the spread differentials in the underlying portfolios as well as the different creation options; therefore, we report results from the hurdle model separately for each group. Following the mutual fund literature, we also include a number of variables that have been found to be related to mutual fund flows and, thus, may impact the quantity created/redeemed. These additional control variables include: size, family size, expense ratio, turnover ratio, standard deviation of bid-ask spread, share turnover, return squared, and standard deviation of return. The estimation outcomes for the hurdle model are shown in Exhibit 8 for the full sample and for each of the three liquidity groups. For ease of interpretation, we only report the marginal effects. Panel A displays the results for bond ETF creations and Panel B displays the results for bond ETF redemptions. In each stage, the independent variables are converted to z-scores to aid in coefficient interpretation. 14 For the full sample, a one-standard deviation increase in the average P/NAV ratio over the past five days leads to a 5.854% increase in creations two-days later. For the high liquidity group (US government bond ETFs), this type of event leads to an 8.113% increase in creations. For the medium liquidity group (corporate investment grade bond ETFs), the result is a 5.298% increase in creations. The low liquidity group displays the smallest creations impact from an increase in the P/NAV average with a 5.281% increase. The other two selection model variables generally show that creations increase when an ETF s volume has been 14 For each independent variable, we subtract the full sample mean and divide by the full sample standard deviation. It has no impact on statistical significance, but makes the interpretation of the marginal effects as the one standard deviation change in the independent variable.

21 high over the prior five days and when the ETF is older (with age serving as a proxy for the number of APs). [Insert Exhibit 8 about here.] Panel B contains the hurdle model results for redemptions. Following a one-standard deviation increase in the P/NAV ratio over the prior five days, redemptions decreased by 2.792% in full sample, decreased by 7.525% for the high liquidity group, decreased by 5.442% for the medium liquidity group, and decreased by 1.975% for the low liquidity group. Similar to creations, redemptions are more likely when the fund volume has been high and the fund is older. In terms of the second stage model, the quantity of both creations and redemptions increase, as expected, with the size of the creation unit of the ETF. Creations and redemptions both generally decrease with the size of the fund. However, creations and redemptions both generally increase with the fund family size. Expense ratio and turnover ratio serve as fund control variables and show minimal influence only in the low liquidity group. The standard deviation of trading volume results in minimal impact in the redemption model. The mean and standard deviation of bid-ask spread displayed minor influence in some subsamples. The standard deviation of the P/NAV ratio shows a minor impact on the high liquidity subsample. The effect of past average returns appears only in the low liquidity group for creations; redemptions generally increase following a decrease in past returns. 15 Conclusion 15 In unreported results, we try multiple specifications of the first stage of the model. Our second stage results were qualitatively the same. We also run the hurdle model on the more well-populated period and find similar results.

22 This paper contributes to existing literature on ETF fund flows by examining flow activity around premiums and discounts for bond ETFs. Premium ETFs with creation activity have a near-term correction in returns that decreases the size of the premium. Likewise, discount ETFs with redemption activity also see subsequent decreases in the size of the discount. In the absence of these flows, premiums and discounts largely stay the same. This suggests that the primary market has a significant impact on the secondary market prices. Despite this impact, most bond ETFs do not have share creation/redemption activity, even when there is a nontrivial premium or discount. We use a two-stage hurdle model to examine the factors that may affect the likelihood of these trades occurring, and find that among other factors secondary market liquidity plays an important role. Despite the high liquidity of bond ETFs relative to their underlying assets, typical exchange liquidity factors play a role in determining how easily a premium or discount is arbitraged away. ETFs with low volume or high spreads create a risk for the potential arbitrageur, and we find that these funds are the least likely to have flows. Our results suggest that large premiums or discounts can persist in part due to costs and uncertainty in the secondary market. Thus, one broader contribution of our study is to suggest that the current arbitrage mechanism works in many cases, but that barriers to arbitrage exist, including uncertainty regarding the pricing of the underlying bonds, the spreads, and other costs of trading less liquid bonds, that allow bond ETF premiums and discounts to persist.

23 References Chen, Yong, and Nan Qin, 2016, The behavior of investor flows in corporate bond mutual funds, Forthcoming Management Science. Clifford, Christopher, Jon Fulkerson, and Bradford Jordan, 2014, What drives ETF flows?, Financial Review 49, Cragg, John, 1971, Some statistical models for limited dependent variables with application to the demand for durable goods, Econometrica 39, Engle, Robert, and Debojyoti Sarkar, 2006, Premiums-discounts and exchange traded funds, Journal of Derivatives 13, Fulkerson, Jon, and Bradford Jordan, 2013, Reading tomorrow s newspaper: Predictability in ETF returns, Journal of Index Investing 4, Fulkerson, Jon, Bradford Jordan, and Timothy Riley, 2013, Return chasing in bond funds, Journal of Fixed Income 22, Fulkerson, Jon, Susan Jordan, and Timothy Riley, 2014, Predictability in bond ETF returns, Journal of Fixed Income 23, Fulkerson, Jon, Susan Jordan, and Denver Travis, 2015, Are bond ETF investors smart?, Journal of Fixed Income 24, Petajisto, Antti, 2016, Inefficiencies in the pricing of exchange-traded funds, Financial Analyst Journal, forthcoming.

24 Exhibit 1 Summary Statistics for Bond ETF Sample, January 2007 December 2015 Summary statistics are provided for the bond ETF sample for the period January 2007 to December The sample includes 181 bond ETFs with 186,296 daily observations. Shares outstanding data is collected from Morningstar Direct. All other data is either from CRSP. Observations are included only when data is complete. Percentage in bonds is the bond holding percentage reported. TNA is the total net assets reported in millions of dollars. Age for an observation, in years, is the difference between the observation date and the fund first offer date. Expense ratio is the total annual management fee. Portfolio turnover ratio is the portion of the fund reported bought or sold in the prior year. Family fund count is the number of ETFs in our sample that is managed by the same firm, matched by the family fund code in CRSP. Family size is the total TNA, shown in millions, managed by the same firm. Creation unit size is estimated by observing the smallest change in shares outstanding for the ETF rounded to the nearest 25,000 units. Average 1-day return is the average return over the prior one-day period, annualized. Average 5-day return is the average return over the prior five-day period, annualized. Std. dev. 5-day return is the standard deviation of daily returns over the prior five-day period, annualized. Shares outstanding is shown in billions. Volume 5-day average is the average daily volume over the prior 5-day period, shown in hundreds. Volume 5-day std. dev. is the standard deviation of daily volume over the prior 5-day period, shown in hundreds. Share turnover 5-day is the total volume over the prior five days divided by shares outstanding from the beginning of that five day period. Spread 5-day average and Spread 5-day std. dev. are calculated from the prior five day period daily bid-ask spread scaled by the midpoint of the bid-ask spread. P-NAV ratio 1-day average, P-NAV ratio 5-day average, and P-NAV ratio 5-day std. dev. are calculated from prior daily P-NAV ratio data, where P-NAV ratio is calculated by the bid-ask midpoint divided by the NAV ratio. Flow is calculated as the return adjusted daily percent change in TNA, as shown in Equation 1. Flow creations-only is the flow from only increases in shares outstanding. Flow redemptions-only is the flow from only decreases in shares outstanding. Flow from redemptions naturally creates negative flow values; Flow redemptions-only is displayed here in absolute value. Category Variable Mean Median Std. Dev. Fund Characteristics Percentage in bonds TNA Age Expense ratio Portfolio turnover ratio Family fund count Family size 48,669 24,200 55,741 Creation unit size 82, ,000 31,997 Returns Average 1-day return Average 5-day return Std. dev. 5-day return Market variables Shares outstanding Volume 5-day average 364,535 55,620 1,126,067 Volume 5-day std. dev. 176,721 29, ,634 Share turnover 5-day Spread 5-day average Spread 5-day std. dev P/NAV ratio 1-day average P/NAV ratio 5-day average P/NAV ratio 5-day std. dev Daily flow Flow Flow, creations-only Flow, redemptions-only

25 Exhibit 2 Bond ETF Sample by Liquidity and Style Categories We categorize the bond ETF sample by bond investment or holdings style and then by liquidity group. The U.S. Government Long & Intermediate Maturity style includes bond funds of U.S. Treasuries, U.S. Government bonds, and U.S. Mortgages. The U.S. Government Short Maturity style includes U.S. Treasuries and U.S. Government bonds. The U.S. TIPS style includes only U.S. Treasury Inflation-Protected Securities. The Corporate Investment Grade style includes long and short maturity corporate bonds rated as investment grade. The Municipal style includes only municipal bonds. The International style includes international government and corporate bonds. The Corporate High Yield style includes corporate bonds rated as high yield. The General style includes funds with a blend of bond holdings and investment styles. We categorize the High Liquidity group as the three U.S. Government bonds styles, the Medium Liquidity group as the Corporate Investment Grade style, and the Low Liquidity group as the four remaining styles. Liquidity and Style Categories % of Obs. % of Obs. By Liquidity By Style High Liquidity 32.0% U.S. Government Long & Intermediate Maturity 15.7% U.S. Government Short Maturity 7.7% U.S. TIPS 8.6% Medium Liquidity 28.5% Corporate Investment Grade 28.5% Low Liquidity 39.5% Municipal 17.2% International 10.8% Corporate High Yield 7.8% General 3.8%

26 Exhibit 3 Dollar Volume and Dollar Flow for the Bond ETF Sample In this table, we present summary statistics on the dollar volume and dollar flow of the bond ETF sample. Dollar volume, i.e. secondary market volume, is calculated daily by multiplying the volume of shares traded times closing price. Dollar flow, i.e. primary market volume, is calculated by the return adjusted change in total net assets (TNA), where TNA is estimated daily by multiplying shares outstanding times NAV. Total volume is the sum of dollar volume and dollar flow. Variable Mean Median Std. Dev. Dollar Volume $28,400,000 $2,320,000 $117,000,000 Dollar Flow $8,260,000 $406,000 $39,200,000 Total Volume $36,700,000 $3,370,000 $134,000,000 Dollar / Total Volume 72.8% 81.3% 25.6% Total Volume / TNA 1.96% 0.88% 6.96%

27 Exhibit 4 Percent of Observations with Creations or Redemptions Percent of Observations with Creation or Redemption 25.00% 20.00% 15.00% 10.00% 5.00% 0.00% Full Sample High Liquidity Medium Liquidity Low Liqudity Total Creations Redemptions

28 Exhibit 5 Price to NAV Ratio Ranges and Flow Panel A: Full Sample For the full sample, percentile ranges for the 5-day prior average Price to NAV ratio (P/NAV) were calculated as displayed below. % Creations 2-days later represents the portion of observations that were ETF creation events following the 5-day Average P/NAV ratio being observed in the respective percentile range two days prior. Average size of Creations 2-days later represents the average creation flow size, where flow is the return-adjusted daily percent change in TNA. % Redemptions 2-days later represents the portion of observations that were ETF redemption events following the 5-day Average P/NAV ratio being observed in the respective percentile range two days prior. Average size of Redemptions 2-days later represents the average redemption flow size, where flow is the return-adjusted daily percent change in TNA. 5-day Average P/NAV Percentile Range Average size of Redemptions 2-days later 5-day Average P/NAV range % Creations 2-days later Average size of Creations 2-days later % Redemptions 2-days later >99% > % 3.16% 0.39% 3.31% >95%, <=99% > , <= % 3.42% 0.83% 3.45% >75%, <=95% > , <= % 2.06% 2.02% 1.91% >50%, <=75% > , <= % 1.44% 5.10% 1.54% >25%, <=50% > , <= % 1.95% 9.16% 1.94% >5%, <=25% > , <= % 2.41% 9.03% 2.11% >1%, <=5% > , <= % 2.62% 9.04% 2.59% <=1% <= % 6.76% 7.09% 3.59%

29 Exhibit 5 Price to NAV Ratio Ranges, Flow, and Excess Returns Panel B: High Liquidity Subsample For the high liquidity subsample, percentile ranges for the 5-day prior average Price to NAV ratio (P/NAV) were calculated as displayed below. % Creations 2-days later represents the portion of observations that were ETF creation events following the 5-day Average P/NAV ratio being observed in the respective percentile range two days prior. Average size of Creations 2-days later represents the average creation flow size, where flow is the returnadjusted daily percent change in TNA. % Redemptions 2-days later represents the portion of observations that were ETF redemption events following the 5-day Average P/NAV ratio being observed in the respective percentile range two days prior. Average size of Redemptions 2-days later represents the average redemption flow size, where flow is the return-adjusted daily percent change in TNA. 5-day Average P/NAV Percentile Range Average size of Redemptions 2-days later 5-day Average P/NAV range % Creations 2-days later Average size of Creations 2-days later % Redemptions 2-days later >99% > % 4.53% 0.47% 7.23% >95%, <=99% > , <= % 2.72% 2.18% 3.70% >75%, <=95% > , <= % 2.44% 5.60% 2.73% >50%, <=75% > , <= % 2.23% 7.48% 2.17% >25%, <=50% > , <= % 2.39% 12.50% 2.19% >5%, <=25% > , <= % 3.66% 11.40% 2.62% >1%, <=5% > , <= % 8.26% 9.19% 3.65% <=1% <= % 4.53% 5.20% 3.39%