Investors seeking access to the bond

Bond ETF Arbitrage Strategies and Daily Cash Flow The Journal of Fixed Income 2017.27.1:49-65. Downloaded from www.iijournals.com by NEW YORK UNIVERSITY on 06/26/17. Jon A. Fulkerson is an assistant professor at the University of Dayton in Dayton, OH. jfulkerson1@udayton.edu Susan D. Jordan is an associate professor in the Gatton College of Business and Economics at the University of Kentucky in Lexington, KY. sjordan@uky.edu Denver H. Travis is an assistant professor in the Haub School of Business at Saint Joseph s University in Philadelphia, PA. denver.travis@sju.edu Jon A. Fulkerson, Susan D. Jordan, and Denver H. Travis Investors seeking access to the bond market frequently consider bond ETFs for their portfolios. Total net assets for bond ETFs have increased from $3.9 billion in 2002 to $340 billion in 2015, representing 16.2% of all ETF assets. 1 While most trading in ETF shares takes place in the secondary market on a public exchange, ETFs also create and redeem shares directly. Reported volumes normally focus on exchange transactions, yet daily trading occurs regularly 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 exclusively create or redeem shares in-kind, and many also serve as market makers for the ETF. Because share creation and redemption are generally in-kind, any primary market activity by the AP necessarily also involves trading in the markets for the underlying assets. For bond ETFs, this means the APs are key participants in the OTC bond trading. As of the end of 2014, the Investment Company Institute reported that a typical Bond ETF had 32 AP agreements in place. However, many of these APs were inactive, and most ETFs have three to five active APs. 2 A key role for APs is to enable arbitrage trading; if the secondary market price drifts too far from the portfolio s underlying value (NAV), buying and selling through the AP can earn arbitrage profits. With the AP mechanism in place, investors expect that the market price and the underlying asset value should deviate rarely. When they occur, these deviations should quickly disappear. In reality, deviations occur regularly for all types of ETFs (see, e.g., Petajisto [2017]; Fulkerson, Jordan, and Riley [2014]) and sometimes persist for days. For stock ETFs, a deviation is mostly corrected within five days (Fulkerson and Jordan [2013]). For bond ETFs, the deviations take much longer to dissipate, with premiums and discounts persisting for as long as 30 days (Fulkerson, Jordan, and Riley [2014]). Given that bond ETFs take so long to correct deviations, this study considers how transactions in the primary market for ETF shares affect the returns to ETF investors around premiums and discounts in the secondary market. We construct a sample of U.S.- domiciled bond ETFs with daily return and net cash flow data operating during the period 2007 to 2015. The net cash flow for the ETF represents the balance of redemptions and creations for a given day, and allows us to observe primary market activity around Summer 2017 The Journal of Fixed Income 49

The Journal of Fixed Income 2017.27.1:49-65. Downloaded from www.iijournals.com by NEW YORK UNIVERSITY on 06/26/17. discounts and premiums. We first confirm that discounts and premiums regularly occur for bond ETFs, ranging from a -0.45% discount relative to NAV at the 5th percentile to a 0.73% premium at the 95th percentile. These discounts and premiums should present arbitrage opportunities for anyone willing to trade both the underlying bonds and the ETF shares. Specifically, discounts should be followed by redemptions to receive the underlying bonds, while premiums should be followed by creations. We find that premium ETFs have more creations, and discount ETFs have more redemptions, consistent with arbitrage trading. Transactions average about 3% of assets. However, despite the arbitrage opportunity, most deviations do not lead to primary market transactions in the following trading days. Since most deviations do not precede primary market activity, we next compare the returns of funds with and without share creations and redemptions. Considering ETFs in the top 25% of the Price/NAV ratio in a given week (premium ETFs), we estimate the alphas for 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 whether or not there is creation activity 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 (an alpha of zero) and more for low liquidity ETFs (an alpha of 4%). We find similar results for the long-short strategy among the bottom 25% (discount) of ETFs. These results suggest that market prices converge toward NAV with primary market activity, but the deviations persist in the absence of these share transactions. If primary market activity appears highly correlated with profitable arbitrage activity, it is puzzling that bond ETFs so rarely have transactions in the days following a premium or a discount. In our final set of tests, we consider how secondary market factors influence future primary market activity. While premiums and discounts affect creations and redemptions, secondary market liquidity has a nontrivial effect. This suggests that liquidity costs on the exchanges create 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 arbitrageurs. BACKGROUND ETFs provide a benefit to investors by allowing them to trade a whole portfolio of assets quickly and cheaply. This convenience is even greater for bond ETFs, 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. 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 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 rises sufficiently above NAV, APs will buy the underlying securities in the portfolio, create new shares through the ETF, and sell the shares on the exchange. The AP earns an arbitrage profit on these trades for sufficiently high premiums. On the other hand, if the ETF share price falls sufficiently below the NAV, the AP will buy the ETF shares, redeem the share in-kind with the ETF, and sell the underlying securities, again for an arbitrage profit. This mechanism implies that deviations quickly disappear, and are meant to lead to a market equilibrium where prices rarely deviate from NAV. Unlike closed-end funds, in-kind transactions utilizing 50 Bond ETF Arbitrage Strategies and Daily Cash Flow Summer 2017

The Journal of Fixed Income 2017.27.1:49-65. Downloaded from www.iijournals.com by NEW YORK UNIVERSITY on 06/26/17. the primary market 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 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. In addition, by convention, the NAV for a bond ETF is calculated using bid prices. Any strategy that involves buying the underlying bond portfolio would require a fuller understanding of the related dealer networks to assess the size of possible profits. The prior academic literature highlights that premiums and discounts occur regularly. For example, Petajisto [2017] 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] find that the average equity ETF appears to have exchange prices near NAV, but 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 The literature also considers what characteristics of ETFs affect the share creation/redemption process. Petajisto [2017] 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 f lows are consistent with the expected arbitrage strategies. Several market factors also affect the cash flows for equity ETFs, including volume, bid-ask spreads, volatility, and assets under management. Chen and Qin [2016] 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 2015. Daily flow data likely better capture the arbitrage activities, and 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. 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 2015. 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, we include only observations with a fund age of over six months and AUM of over $20 million. 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, we evaluate each ETF by hand to confirm that it follows a fixed income strategy and does not represent a leveraged ETF. Following these filters, we obtain a sample of 181 bond ETFs with 186,296 daily observations. 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. 5 We estimate daily fund flow as the return-adjusted change in total net assets, where daily total net assets is Summer 2017 The Journal of Fixed Income 51

E x h i b i t 1 Summary Statistics for Bond ETF Sample, January 2007 December 2015 The Journal of Fixed Income 2017.27.1:49-65. Downloaded from www.iijournals.com by NEW YORK UNIVERSITY on 06/26/17. Notes: Summary statistics are provided for the bond ETF sample for the period January 2007 to December 2015. The sample includes 181 bond ETFs with 186,296 daily observations. Shares outstanding data is collected from Morningstar Direct. All other data is from CRSP. Observations are included only when data are 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 fiveday 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 five-day period, shown in hundreds. Volume 5-day std. dev. is the standard deviation of daily volume over the prior five-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. estimated by multiplying the daily shares outstanding by the daily net asset value as follows: Flow t SOt NAVt SOt 1 NAVt 1 (1 + rt ) = SO NAV t 1 t 1 where SO is the daily shares outstanding from Morningstar Direct, NAV is the daily net asset value from (1) 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. 6 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 52 Bond ETF Arbitrage Strategies and Daily Cash Flow Summer 2017

E x h i b i t 2 Bond ETF Sample by Liquidity and Style Categories E x h i b i t 3 Dollar Volume and Dollar Flow for the Bond ETF Sample The Journal of Fixed Income 2017.27.1:49-65. Downloaded from www.iijournals.com by NEW YORK UNIVERSITY on 06/26/17. Notes: 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. the period, the average creation flow is larger than the average redemption flow at 0.29% versus 0.12% per day, respectively. 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 comprises 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 Notes: This table presents 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. sample, followed by Municipal bond ETFs, and then by U.S. Government Long & Intermediate Maturity bond ETFs. 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. 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 growth in 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, Summer 2017 The Journal of Fixed Income 53

E x h i b i t 4 Percent of Observations with Creations or Redemptions The Journal of Fixed Income 2017.27.1:49-65. Downloaded from www.iijournals.com by NEW YORK UNIVERSITY on 06/26/17. we provide all further results both for the full sample and for the individual liquidity groups. 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 [2017], 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. 7 For a given five-day period, we create sub-groups for different percentile groups based on prior five-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, among ETFs with an average five-day P/NAV ratio above the 99th percentile (high premium), about 27% had share creations two days 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 1st percentile 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. Surprisingly, the medium liquidity group (Panel C) has a much higher likelihood of creations in the top percentiles compared to both high and low liquidity. We speculate this anomaly occurs for two reasons. First, compared to the high liquidity group, the medium liquidity group has much higher premiums. The 95th percentile premium is 0.85% for the medium group, but only 0.27% for the high group. Thus, it is more profitable to arbitrage in the medium liquidity group than the high liquidity group. Second, the differences in the underlying asset liquidity, and the ease with which the underlying assets can be acquired to create shares, contribute to the anomaly. The premiums are roughly similar at the 95th percentile for the medium and low groups (0.85% and 0.90%, respectively), but creations are much more likely in the medium liquidity ETFs. Jointly, this supports the idea that the liquidity of the underlying bonds has a nontrivial impact on the likelihood of premiums and discounts occurring, and the ability of arbitrageurs to take advantage of the opportunity. 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 54 Bond ETF Arbitrage Strategies and Daily Cash Flow Summer 2017

The Journal of Fixed Income 2017.27.1:49-65. Downloaded from www.iijournals.com by NEW YORK UNIVERSITY on 06/26/17. for two reasons. First, in general, ETFs have become more popular. As more investors seek out these new investments, 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 lower NAV would provide better execution quality 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-price 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 E x h i b i t 5 Price to NAV Ratio Ranges and Flow subsequent returns are different when the ETF has had a creation or a redemption. We create a simple method for benchmarking each fund against itself. 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, and use the ratio of the 5-day average over the 20-day average to rank the funds. 8 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. 9 We then test for differences in excess returns on the typical ETF arbitrage strategy among the no flow group, the creations group, and the redemptions group. 10 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-ofday closing price and going long the underlying bonds (end-of-day NAV) for these premium P/NAV funds over the following five days. Column i of Panel A provides results 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 (continued) Summer 2017 The Journal of Fixed Income 55

E x h i b i t 5 (continued) Price to NAV Ratio Ranges and Flow The Journal of Fixed Income 2017.27.1:49-65. Downloaded from www.iijournals.com by NEW YORK UNIVERSITY on 06/26/17. Notes: Panel A: For the full sample, percentile ranges for the five-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 five-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 five-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. Panel B: For the high liquidity subsample, percentile ranges for the five-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 five-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 five-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. Panel C: For the medium liquidity subsample, percentile ranges for the five-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 five-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 five-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. Panel D: For the low liquidity subsample, percentile ranges for the five-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 five-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 five-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. 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 56 Bond ETF Arbitrage Strategies and Daily Cash Flow Summer 2017

The Journal of Fixed Income 2017.27.1:49-65. Downloaded from www.iijournals.com by NEW YORK UNIVERSITY on 06/26/17. 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. However, 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. In order to highlight the relative difference in magnitudes, Panel B displays the combined arbitrage excess returns. Columns v, vi, and vii display 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 E x h i b i t 6 Abnormal Returns Following a P/NAV Premium 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 than 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% 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 APs (i.e., creating and selling ETF shares while buying the underlying bonds) appear to occur more frequently when mispricing is corrected. The effects are most pronounced when the underlying bonds have lower liquidity. In Exhibit 7, we repeat the same tests for those bond ETFs that rank in the lowest quartile of P/NAV ratios. In Panel A, excess returns are calculated for buying the ETF at market prices and shorting the ETF at NAV (i.e., the appropriate arbitrage strategy when the ETF trades at a discount). In full sample, buying at the exchange price results in excess returns of -4.54% per year, while going short NAV results in a significant (continued) Summer 2017 The Journal of Fixed Income 57

E x h i b i t 6 (continued) Abnormal Returns Following a P/NAV Premium The Journal of Fixed Income 2017.27.1:49-65. Downloaded from www.iijournals.com by NEW YORK UNIVERSITY on 06/26/17. Notes: Panel A: For each fund, a weekly ratio of the fund s 5-day average P/NAV over the fund s 20-day average P/NAV is calculated. Each week this 5-day over 20-day ratio is used to rank the funds. The results in this exhibit are obtained following those funds that rank in the top quartile. For each week, equally-weighted portfolios of those premium funds are formed for the funds prices and the funds NAV values over the next five days. In order to test for abnormal returns following a premium P/NAV ratio period, 5-day returns are calculated from going short the funds prices and from going long the funds NAV values. The return risk premiums of an equally-weighted portfolio of these ETFs are regressed on four bond index factors, specifically 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. The annualized excess return, or Alpha, is displayed along with its respective p-value. The number of observation weeks of available funds is provided below each scenario. Column i is for all funds in the group regardless of flow. Column ii is for only those funds that experienced no flow in the following five days. Column iii is for only those funds that experienced a net increase in flow, or net creations, in the following five days. Column iv is for only those funds that experienced a net decrease in flow, or net redemptions, in the following five days. Panel B: For each fund, a weekly ratio of the fund s 5-day average P/NAV over the fund s 20-day average P/NAV is calculated. Each week this 5-day over 20-day ratio is used to rank the funds. The results in this exhibit are obtained following those funds that rank in the top quartile. For each week, equally-weighted portfolios of those premium funds are formed for the funds prices and the funds NAV values over the next five days. In order to test for abnormal returns following a premium P/NAV ratio period, 5-day returns are calculated from going short the funds prices and from going long the funds NAV values. The return risk premiums of an equally-weighted portfolio of these ETFs are regressed on four bond index factors, specifically 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. The annualized excess return, or Alpha, is displayed along with its respective p-value. The number of observation weeks of available funds is provided below each scenario. Column v is the combination of going short price and long NAV for only those funds that experienced no flow in the following five days. Column vi is for only those funds that experienced a net increase in flow, or net creations, in the following five days. Column vii is for only those funds that experienced a net decrease in flow, or net redemptions, in the following five days. Column viii is the resulting difference in alphas between net creations funds and no flow funds. Column ix is the resulting difference in alphas between net redemptions funds and no flow funds. excess return of 6.22% per year. Results are similar for the medium and low liquidity subsample. Conditioning on flow, we again find that the arbitrage strategy for discounts performs well. For net redemptions, the 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. The other cases (no flow and creations) have results that are generally smaller in magnitude and statistically insignificant. 58 Bond ETF Arbitrage Strategies and Daily Cash Flow Summer 2017

The Journal of Fixed Income 2017.27.1:49-65. Downloaded from www.iijournals.com by NEW YORK UNIVERSITY on 06/26/17. We consider the relative profits of arbitrage trading on discounted bond ETFs in Panel B of Exhibit 7. Specifically, the panel shows the combined arbitrage excess returns (i.e., the combination of shorting the ETF NAV and going long the ETF price) earned from trading 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%. The expected arbitrage trade appears to be highly profitable. Column ix considers the difference in the arbitrage trade alpha between the net redemption funds and the no flow funds. The arbitrage returns for net redemption funds are significantly larger than those for no flow funds in the full sample (3.89% per year) and for the low liquidity group (5.42%). In summary, the arbitrage actions of the APs reduce the P/NAV premiums and discounts. The APs earn significant profits when they trade. The absence of E x h i b i t 7 Abnormal Returns Following a P/NAV Discount trades leads to no significant changes in returns in the following five days, and the premiums and discounts persist. Our results suggest that the arbitrage activities are an important factor in the resolution of the price discrepancies, and that the ETF mechanism works well when used. However, we also observe that only a minority of ETFs have creations and redemptions even for the highest premiums and discounts. In the next section, we consider market factors that create barriers to arbitrage. 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 AP s decision to either create or redeem bond ETF shares by controlling for market factors that would discourage AP activity. For our sample period, 89% of daily observations have no net creation or redemption activity. Because the (continued) Summer 2017 The Journal of Fixed Income 59

E x h i b i t 7 (continued) Abnormal Returns Following a P/NAV Discount The Journal of Fixed Income 2017.27.1:49-65. Downloaded from www.iijournals.com by NEW YORK UNIVERSITY on 06/26/17. Notes: Panel A: For each fund, a weekly ratio of the fund s 5-day average P/NAV over the fund s 20-day average P/NAV is calculated. Each week this 5-day over 20-day ratio is used to rank the funds. The results in this exhibit are obtained following those funds that rank in the bottom quartile. For each week, equally-weighted portfolios of those premium funds are formed for the funds prices and the funds NAV values over the next five days. In order to test for abnormal returns following a discount P/NAV ratio period, 5-day returns are calculated from going long the funds prices and from going short the funds NAV values. The return risk premiums of an equally-weighted portfolio of these ETFs are regressed on four bond index factors, specifically 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. The annualized excess return, or Alpha, is displayed along with its respective p-value. The number of observation weeks of available funds is provided below each scenario. Column i is for all funds in the group regardless of flow. Column ii is for only those funds that experienced no flow in the following five days. Column iii is for only those funds that experienced a net increase in flow, or net creations, in the following five days. Column iv is for only those funds that experienced a net decrease in flow, or net redemptions, in the following five days. Panel B: For each fund, a weekly ratio of the fund s 5-day average P/NAV over the fund s 20-day average P/NAV is calculated. Each week this 5-day over 20-day ratio is used to rank the funds. The results in this exhibit are obtained following those funds that rank in the bottom quartile. For each week, equally-weighted portfolios of those premium funds are formed for the funds prices and the funds NAV values over the next five days. In order to test for abnormal returns following a discount P/NAV ratio period, 5-day returns are calculated from going long the funds prices and from going short the funds NAV values. The return risk premiums of an equally-weighted portfolio of these ETFs are regressed on four bond index factors, specifically 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. The annualized excess return, or Alpha, is displayed along with its respective p-value. The number of observation weeks of available funds is provided below each scenario. Column v is the combination of going long price and short NAV for only those funds that experienced no flow in the following five days. Column vi is for only those funds that experienced a net increase in flow, or net creations, in the following five days. Column vii is for only those funds that experienced a net decrease in flow, or net redemptions, in the following five days. Column viii is the resulting difference in alphas between net creations funds and no flow funds. Column ix is the resulting difference in alphas between net redemptions funds and no flow funds. data have such a large number of zeros, they are considered zero-inflated data, which suggests some empirical concerns. Furthermore, 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. This suggests that any model of the decision process should take into account the two stages in the process. We model the AP s decision with a two-stage hurdle model similar to Cragg [1971]. The hurdle model differs from other two-stage models in that two different equations can be used for the two stages. In this case, 60 Bond ETF Arbitrage Strategies and Daily Cash Flow Summer 2017

The Journal of Fixed Income 2017.27.1:49-65. Downloaded from www.iijournals.com by NEW YORK UNIVERSITY on 06/26/17. the first equation is a selection model that treats the AP s 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 AP s decision of how many shares to create (or redeem) 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: Decision = PNAV / + Volume + Age +ε it, it, 1 it, 1 it, 1 it, (2) where the Decision 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 the exchange price to the underlying NAV. A higher ratio 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 is the volume of trading. We anticipate that price might deviate from NAV on very light volume days, as the AP may wish to avoid entering a market with so little depth. We anticipate more creations and more redemptions when volume is relatively high. 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 agreements with a larger number of APs. 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 created (or redeemed): Quantity it, P = + Volume + Age + CU NAV it, 1 it, 1 it, 1 i + BAS + Return + STD( P/ NAV ) it, 1 it, 1 it, 1 + Controls + ε it, (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). 11 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. Therefore, higher flows follow higher returns, 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, and 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 address the fact that in-kind creation is more common for ETFs that have Treasuries and other liquid bonds in their portfolios. The cash-create process is more common for ETFs having lower liquidity bonds in their portfolios, such as high-yield corporate and municipal bonds. Our classifications are intended to capture the spread differentials in the underlying portfolios as well as the different creation options, but may also capture other factors, such as the difficulty to locate the assets. Therefore, we report results from the hurdle model separately for each group. Following the mutual fund and ETF literature, we also include a number of variables that have been found to be related to fund flows and that may affect the quantity created/redeemed. These additional control variables include: size, family size, expense ratio, turnover Summer 2017 The Journal of Fixed Income 61

The Journal of Fixed Income 2017.27.1:49-65. Downloaded from www.iijournals.com by NEW YORK UNIVERSITY on 06/26/17. ratio, standard deviation of bid-ask spread, share turnover, return squared, and standard deviation of return. The estimation outcomes for the hurdle model for the full sample and for each of the three liquidity groups are shown in Exhibit 8. 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. 12 For the full sample, a one-standard-deviation increase in the average P/NAV ratio over the past E x h i b i t 8 Hurdle Model Regression Results five days leads to a 5.854% increase in creations two days later, all else being equal. For the high liquidity group (U.S. government bond ETFs), this type of event leads to an 8.113% increase in creations. For the medium and low liquidity groups, higher P/NAV has a smaller impact on creations (5.298% and 5.281%, respectively). Creations increase when an ETF s volume has been high over the prior five days and when the ETF is older. Panel B contains the hurdle model results for redemptions. As predicted, higher P/NAV leads to fewer redemptions. Following a one-standard-deviation (continued) 62 Bond ETF Arbitrage Strategies and Daily Cash Flow Summer 2017