ESSAYS ON BOND EXCHANGE-TRADED FUNDS

by

Charles W. Evans

A Dissertation Submitted to the Faculty of

The College of Business in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

Florida Atlantic University

Boca Raton, Florida

August 2011 ESSAYS ON BOND EXCHANGE-TRADED FUNDS

by

Charles W. Evans

This dissertation was prepared under the direction of the candidate's dissertation advisor, Dr. Antoine Giannetti, Department of Finance, and has been approved by the members ofhis supervisory committee. It was submitted to the faculty of the College of Business and was accepted in partial fulfillment of the requirements for the degree of Doctor ofPhilosophy.

SUPERVISORY COMMTITEE: ~e~ Dissertation Advisor 1A0

Emilio Zarruk, Ph.D. hair epartrnent ance /

J. Dennis Coates, Ph.D. Dean, College of Business n--- B!71oSS:P~/??--- :J11¥l? ZJ, ?-P// Date Dean, Graduate College

u ii ACKNOWLEDGEMENTS

The author wishes to express his sincere thanks and love to his wife, Lina, for her support throughout the writing of this manuscript and the coursework that preceded it.

The author is thankful for the unwavering encouragement of his dissertation committee members, Dr. Anna Agapova, Dr. William R. McDaniel, Dr. Ariel Viale, and especially his dissertation chairman, Dr. Antoine Giannetti, whose efforts and inspiration have been instrumental in the completion of this dissertation. The author is grateful to the chairman, Dr. Emilio Zarruk, and secretaries, Joan Schlossberg, Eileen Schneider, and

Myrna Sotolongo, of the College of Business Department of Finance and Economics at

Florida Atlantic University for providing financial and technical support for the research and writing of this manuscript, and to Judith Benson and Dr. Jeff Madura for their help with navigating the program. A special debt of gratitude goes to Geoff Gitlen, Will

Johnson, and Steve Foerster for their camaraderie and commiseration.

iii ABSTRACT

Author: Charles W. Evans

Title: Essays on Bond Exchange-Traded Funds

Institution: Florida Atlantic University

Dissertation Advisor: Dr. Antoine Giannetti

Degree: Doctor of Philosophy

Year: 2011

This dissertation investigates two fundamental questions related to how well exchange-traded funds that hold portfolios of fixed-income assets (bond ETFs) proxy for their underlying portfolios. The first question involves price/net-asset-value (NAV) mean-reversion asymmetries and the effectiveness of the arbitrage mechanism of bond

ETFs. Methodologically, to answer the first question I focus on a time-series analysis.

The second question involves the degree to which average returns of bond ETF shares respond to changes in factors that have been found to drive average returns of bond portfolios. To answer this question I shift the focus of the analysis to a cross-section asset pricing test. In other words, do bond ETF share prices track the value of their underlying assets, and are they priced by investors like bonds in the cross-section?

The first essay concludes that bond ETF shares exhibit mean-reversion asymmetries when price and NAV diverge, along persistent small premiums. These premiums appear to reflect the added value that bond ETFs bring to the fixed-income

iv asset market through smaller trading increments, greater liquidity, and the ability to buy on margin and sell short.

The second essay concludes that market, bond-specific, and firm-specific risk factors can help to explain the variation in U.S. bond ETF average returns, but only size seems to be priced in the cross-section of expected returns. This is not surprising as the sample used in the asset pricing tests is limited to the period 2007-2010, which corresponds to the „great recession‟, and size has been interpreted in the asset pricing literature as a state variable that proxies for financial distress and is highly dependent on the phase of the real business cycle.

The two essays together suggest that bond ETFs can be used in trading strategies based on taking long and short positions in fixed-income assets, especially when trading in portfolios of fixed-income assets directly is not feasible.

v ESSAYS ON BOND EXCHANGE-TRADED FUNDS

List of Tables viii

List of Figures ix

Chapter 1: Bond Exchange-Traded Funds 1

Background 3

Bond ETFs 6

ETFs vs CEFs, OEFs, and OTC 8

Comparison 8

Substitution Effects 10

Liquidity 12

Noise Traders 13

Bond ETF Trading Strategies 15

Chapter 2: Bond ETF Mean-Reversion Asymmetries 18

Introduction 19

Background 22

Empirical Framework 23

Data and Methodology 25

Data 25

Methodology 28

Test of the Law of One Price 28

vi Test of Mean-Reversion Asymmetries 29

Liquidity and Behavioral Explanatory Variables 31

Empirical Results 36

Law of One Price 36

Mean-Reversion Asymmetries 38

Expanded ECM 39

Expanded Rockets & Feathers 42

Conclusion 44

Chapter 3: Risk Factors in the Returns and Premiums of Bond ETFs 46

Introduction 47

Literature Review 50

Methodological Approach 56

Data 56

Asset Pricing Tests 57

Empirical Results 60

Stylized Time Series Properties of Bond ETF Excess Returns 60

Fama-MacBeth CSR Asset Pricing Test Results 63

Fixed Effects Static Panel Data Results 64

Concluding Remarks and Future Research 66

References 94

vii TABLES

1: Descriptive Statistics 68

2: ECM / Rockets & Feathers 71

3: Expanded ECM 73

4: Expanded Rockets & Feathers 75

5: Descriptive Statistics 77

6: Time Series: Bond Factors 79

7: Time Series: Stock and Market Factors 81

8: Time Series: Five-Factor Model 83

9: GLS 85

10: ICAPM 86

11: Panel Data 87

viii FIGURES

Fig. 1: Monthly Number of Shares Outstanding (HYG) 88

Fig. 2: Monthly Percentage Growth in Shares Outstanding (HYG) 89

Fig. 3: Daily Premium/Discount (HYG) 90

Fig. 4: Bond ETF Market Growth 91

Fig. 5: ETF, CEF, OEF, OTC Comparison 92

Fig. 6: Trading Strategies 93

ix CHAPTER 1

Bond Exchange-Traded Funds

Four core fixed-income exchange-traded funds (bond ETFs) were introduced in the United States in 2002 that focus on investment-grade government and corporate debt.

Two more were issued in 2003, and the entire bond ETF market consisted of these six until the end of 2006. Beginning in 2007, bond ETFs have been issued that hold emerging-market, municipal, high-yield corporate, government agency, and mortgage- backed debt, with a range of maturities and risk profiles within each category. Now, retail traders, who are unable to participate actively in the bond market, are able to trade a wide variety of bond portfolios intra-day, to short-sell, and to buy on margin at a price that is close to the net asset value (NAV) and in increments that are within the budgets of retail traders.

The law of one price – equating ETF share price with NAV – is expected to be enforced by the Authorized Participant (AP) arbitrage mechanism, through which large institutional investors that have entered into contractual arrangements with ETF issuers can create and redeem shares directly, in exchange for bundles of underlying assets, when price diverges from NAV. However, the magnitudes of bond ETF premiums and discounts often exceed daily bid-ask spreads in the short run, and shares exhibit small, persistent premiums, meaning that the price is more likely to exceed the reported NAV slightly than to be precisely equal to or less than NAV.

1 ETFs are designed to mimic their underlying portfolios and to trade on formal stock exchanges. However, the vast majority of the underlying assets of bond ETFs trade over the counter (OTC), which raises the question of how well bond ETFs have served as proxies for the categories of bonds in their underlying portfolios assets in these early days following their initial inception, both in terms of how well prices track corresponding NAVs and to what degree ETF share returns behave like bond returns in response to shocks in bond and stock markets.

This dissertation's major contribution is to address these questions and to show that, even though bond ETFs differ from their underlying assets, their share price and return behavior have been sufficiently similar for them to be used in trading strategies in which trading in fixed-income asset portfolios is not practical or even possible. This is remarkable, considering that this early period of their existence has coincided with major turmoil in both the debt and the equity markets.

Specifically, I identify persistent premiums, confirm price/NAV mean-reversion using a dynamic model, and analyze mean-reversion asymmetries that favor premiums over discounts. This last point is different from the case with closed-end funds, which tend to exhibit persistent and significant discounts, discussed in detail below. I also show that factors that have been shown in the financial literature to help to explain the cross-section of average bond returns also help to explain the cross-section of bond ETF average returns.

2 1.1. Background

ETFs, like conventional open-end (OEF) and closed-end (CEF) funds, are vehicles for trading entire portfolios in single transactions. ETFs are structured to combine the best features of OEFs and CEFs. Similar to OEFs, which trade at NAV,

ETFs are designed to trade at or near net asset value (NAV), and like CEFs, to trade as shares on formal exchanges (Barnhart & Rosenstein, 2009; Gastineau, 2001).

Unique to the ETF market is the AP, a participant in the Depository Trust

Company (DTC) that enters into a formal AP agreement with the fund's issuer and the appropriate custodian bank. The AP arbitrage mechanism causes ETF shares to be created and liquidated through in-kind transfers of underlying assets. If the underlying assets are non-transferrable, as is the case with mortgage-backed securities and Treasury

Inflation-Protected Securities (TIPS), the cash equivalent is paid1. (Vanguard, 2009)

With OEFs, the size of the fund varies as investors buy (sell) shares directly from

(to) the issuer. With CEFs, the number of shares outstanding is fixed, and investors buy and sell shares on formal exchanges. With ETFs, the number of shares can vary as APs redeem and create shares, although individual and other non-AP investors buy and sell shares on formal exchanges.

ETF share creation and redemption occur in increments called Creation Units, which typically are on the order of 50,000 to 100,000 ETF shares or the equivalent value of underlying assets. Each creation or redemption carries a fee that has a fixed and a variable component. The fixed fee is most commonly on the order of $500, although for

1 For brevity, mortgage-backed and Treasury inflation-protected securities are referred to as 'bonds' below.

3 some funds – e.g., an emerging-market small-cap fund – it can run into the tens of thousands of dollars. The variable fee can be as low as twenty-five basis points to as high as three percent of the transaction amount, and issuers often waive the fees on funds that their managers are particularly keen to grow (Vanguard, 2009; Yones, 2010).

For thinly traded ETFs, the size of the Creation Unit can be equal to the average of volume of one or several trading days, and APs that attempt to take advantage of small divergences from price/NAV parity can move the market, thereby erasing relatively small arbitrage opportunities. Thus, although the number of shares in circulation expands and contracts in response to changes in premiums and discounts, the process is discrete and can result in significant short-term premiums and discounts, which can trigger substantial changes in the number of shares outstanding. By way of example, the iShares iBoxx $ Liquid High Yield Index ETF (HYG), saw dramatic activity during and immediately after the Lehman Brothers bankruptcy in September

2008.

Fig. 1 provides a bar chart illustrating the monthly level of HYG shares outstanding from its inception in 2007 through the middle of 2010, and Fig. 2 provides a bar chart illustrating the monthly percentage change in the number of shares outstanding over the same period.

The general trend is upward, with only a few months in which the number of shares fell, one of which was September 2008, when the number of shares fell by 3%, although by December 2008 demand increased and the number of shares increased by

4 56% within the month. Similarly dramatic is the record of premiums and discounts of price relative to NAV illustrated in Fig. 3.

Here, we see that daily discounts in September and October 2008 ran as low as -

7% to -9%, and daily premiums in December 2008 and January 2009 ran as high as

+10% to +12%.

Together, the number of shares outstanding and the level of premiums/discounts provides evidence of how the AP arbitrage mechanism works, and how large the disequilibrium can become in times of high volatility for ETFs that hold highly illiquid underlying assets.

In September 2008, the stock market crashed on the announcement of the

Lehman Brothers bankruptcy. In that same month, HYG discounts reached unprecedented lows, meaning that the share price had fallen substantially below its intrinsic value. This created an incentive for APs to purchase underpriced shares and to exchange them with the ETF issuer – in this case, iShares – for Creation Units of junk bonds. As one would expect, the removal of excess shares from the market coincided with share price and NAV moving closer to parity. Three months later premiums spiked in December, resulting in the opposite action, in which the number of shares increased dramatically, presumably – because ETF share creation and redemption is initiated by

APs – as APs exchanged Creation Units of junk bonds for relatively overpriced HYG shares that they then sold into the market.

5 Hypothetically, an AP could have earned a 20% return over the three months from September through December 2008 by acquiring assets at almost a 10% discount and reselling them for more than a 10% premium.

1.2. Bond ETFs

The first bond ETFs, designed to be core fixed-income Treasury and investment- grade holdings, began trading in the U.S. in July 2002, the same month that the NASD introduced the TRACE database that compiles data on all OTC trades in bonds issued by publicly traded corporations, creating a level of transparency that previously had not existed in the corporate bond market (Bessembinder & Maxwell, 2008; Edwards, Harris

& Piwowar, 2007; FINRA, 2002).

Each bond ETF tracks a specific bond index, selling underlying assets that cease to fit the portfolio profile and replacing them as required. This results in a duration that stays within predictable bounds that are described in each ETF's prospectus, relieving investors of the need to build and rebalance each portfolio. The bond index can be formal, like the Barclays Capital 20+ Year Treasury Index or the Barclays Capital U.S.

Aggregate Bond Index, or it can be unique to a specific bond ETF issuer if no formal index exists.

Coupon payments made by the underlying bonds pass through to the bond ETF shareholders, net of management fees, as unqualified dividends that are taxed at the shareholder's marginal tax rate (iShares, 2006).

Between 2002 and 2007, the bond ETF market remained relatively small, as SEC regulators enforced a trial period of bond ETFs that held conservative assets. The first

6 four bond ETFs were issued by iShares, holding Treasury notes, bills, and bonds

(hereinafter, 'Treasury bonds') with 1-3 year maturities (ticker: SHY), 7-10 year maturities (ticker: IEF), and 20+ year maturities (ticker: TLT); and investment-grade corporate bonds (ticker: LQD). These were followed in 2003 by the introduction of aggregate bond market (ticker: AGG) and Treasury Inflation-Protected Securities (ticker:

TIP) ETFs. In late 2006 the SEC granted iShares, ProShares, and Wisdom Tree permission to issue new categories of bond ETFs (SEC, 2006a, 2006b, 2006c), and in

2007 granted exemptive relief to bond ETF issuers in general, removing the need for an issuer to seek a waiver from existing regulations and opening the market to any issuer that met the SEC's standards (SEC, 2007). The number of bond ETFs issued rose from 6 to 47 between January and December 2007.

The total capitalization of the U.S. bond ETF market has increased at a rate of more than 50% per year since their introduction in 2002, from approximately $3 billion in July 2002 to more than $153 billion in May 2011, approximately 13.75% of the more than $1 trillion invested in all categories of ETFs. The number of bond ETFs issued rose at approximately the same rate from 4 to more than 150 over the same period (National

Stock Exchange, 2011).

Because ETFs do not have transfer agents to perform shareholder accounting at the fund level, unlike OEFs, and therefore do not have records of shareholders' identities

(Gastineau, 2001), it is difficult to determine who trades bond ETFs. However, one can infer from TAQ data on the size of trades whether a trade is initiated by an individual or

7 institutional investor, and industry participants believe that individual investors conduct the majority of bond ETF trades (Yones, 2010).

1.3. ETFs vs CEFs, OEFs, and OTC

Before 2002, individual investors who wanted to trade fixed-income assets were limited to over-the-counter (OTC) purchases through bond dealers, OEFs, and CEFs, each of which suffers from some inconvenience unique to its structure that ETFs are designed to avoid.

1.3.1. Comparison

OTC is the least convenient means for individual investors to trade bonds. The median increment for a specific municipal or corporate bond is approximately $10,000, making diversification difficult for an individual investor, and the median number of trades per day for corporate bonds is less than one, increasing bid-ask spreads and making rebalancing costly (Bessembinder & Maxwell, 2008; Edwards et al., 2007).

Trading directly with the U.S. Treasury through its Treasury Direct Program is relatively straightforward, since minimum transaction sizes were reduced from $1,000 to $100 in

April 2008 (US Treasury, 2008). However, intraday trading is not as convenient even with U.S. Treasury bonds as it is with assets that are traded continuously on formal exchanges, and retail traders cannot take short positions in bonds or – in spite of how inadvisable it might be – to buy them on margin.

Rather than buy directly OTC, individual traders more commonly invest in bonds through either OEFs or CEFs.

8 As with OEFs, bond ETFs allow investors to diversify inexpensively while trading at or near NAV. However, OEFs do not allow intraday trading and impose penalties for 'excessive trading', defined as turnaround transactions made within a period of as long as 30 days, as is the case with Fidelity funds2.

As with CEFs, bond ETF shares are governed by the 1940 Investment Company

Act, which regulates the intraday and short-selling of investment fund shares on formal exchanges (Barnhart & Rosenstein, 2009). However, CEF share prices typically diverge substantially from their NAVs, as no mechanism exists to enforce convergence to NAV3.

ETFs combine the most desirable features of OEFs and CEFs, enabling active retail investors to trade – including intraday and short – diversified bond portfolios at or near NAV, because of the arbitrage mechanism that enables APs to create (redeem) ETF shares by paying in (receiving) underlying assets directly. Even though bond ETFs exhibit persistent premiums, those premiums tend to very small, and wide divergences from price/NAV parity are followed by mean-reversion within one or a couple days.

If shares trade at a premium (discount), APs can pay in (receive) underlying assets, exchanging relatively undervalued for relatively overvalued assets. The quantity of an ETF's shares is variable, as is the case with OEFs, and ETF issuers avoid flow- induced trading costs that OEFs incur, because creation and redemption generally is made in-kind rather in cash (Guedj & Huang, 2009), although cash settlement is the

2 http://personal.fidelity.com/products/trading/Trading_Platforms_Tools/excessive_trading_policies.shtml 3 See Boudreaux (1973), Anderson (1986), Lee, Shleifer, and Thaler (1991, 1990), Brauer (1993, 1988), Chen, Kan, and Miller (1993a, 1993b), Chopra, Lee, Shleifer, and Thaler (1993a, 1993b), Shleifer (2000), and Ross (2002) concerning the CEF Puzzle.

9 norm with with TIPS and mortgage-backed securities ETFs, and can be used in the event that assembling highly illiquid assets is prohibitively expensive (Yones, 2010).

To active traders, ETFs more closely resemble CEFs, with the distinction that the number of an ETF's shares is variable and a CEF's fixed, and that an ETF's premiums and discounts typically are within 1% of NAV, whereas a CEF's shares can trade at a persistent discount of as much as 10-20% of NAV (Cherkes, Sagi & Stanton, 2009;

Engle & Sarkar, 2006).

To passive investors, ETFs more closely resemble OEFs, except that ETF shareholders generally experience no direct tax obligations when the underlying portfolios rebalance. Similarly, OEFs must distribute net capital gains to shareholders at the end of each fiscal quarter, although bond ETF issuers typically pay dividends.

Additionally, retail traders must pay brokerage fees when buying and selling ETF shares, although issuers often waive creation and redemption fees for those ETFs that they want to promote, whereas OEF shareholders often can avoid brokerage fees if they transact directly with the issuers (Agapova, 2009; Guedj & Huang, 2009).

This combination of features can make bond ETFs more valuable to active retail traders than OEFs, CEFs, and bonds, which might explain their persistent, though small, premiums.

1.3.2. Substitution Effects

Given that ETFs appear to combine the advantages of CEFs and OEFs while avoiding the disadvantages of each, one might expect investors to view ETFs as substitutes for CEFs and OEFs and to crowd them out of the market.

10 Barnhart and Rosenstein (2009) find that CEFs experience wider discounts and reduced trading volumes immediately following the introduction of ETFs in similar asset classes, suggesting that demand for CEFs falls; and Agapova (2009) and Guedj and

Huang (2009) find evidence of similar substitution effects between ETFs and OEFs, although the effect is not perfect, indicating some segmentation and clientele effects.

Although studies that focus on similar asset classes, or even identical underlying portfolios, find evidence of substitution, ETFs appear to make the market more complete, rather than categorically crowd out either CEFs or OEFs. Although the delineation is blurred, the general tendency is for CEFs to hold illiquid assets (Cherkes, et al., 2009), whereas OEFs must be ready to convert assets into cash, and vice versa, in response to investment flows, and ETFs must be ready to transfer (receive) assets to

(from) APs. ETFs tend to hold narrower portfolios of less liquid assets than OEFs

(Guedj & Hunag, 2009), suggesting a market in which OEFs hold diverse and highly liquid assets, ETFs hold narrow and less liquid assets, and CEFs hold illiquid assets, with some overlap between categories. In other words, each is well suited to some category of assets for which the others are not as well suited.

Consistent with this schema, OEFs trade at NAV, ETFs exhibit small premiums and discounts, and CEFs exhibit persistent and significant premiums and discounts.

Similarly, in international equity funds, OEF returns are NAV returns, ETF returns are influenced by the market in which ETF shares trade, and CEF returns diverge significantly from NAV returns (Hughen & Mathew, 2009; Delcoure & Zhong, 2007;

Engle & Sarkar, 2006; Pennathur, Delcoure & Anderson, 2002).

11 1.3.3. Liquidity

A particular challenge for corporate bond and municipal bond ETF investors is the calculation of NAV, due to the illiquidity of the underlying assets. Investment grade corporate bonds can trade once or twice per day, and junk bonds might go days between trades (Bessembinder & Maxwell, 2008; Edwards et al., 2007). Illiquidity is even more pronounced in the municipal bond market, where trading is highly irregular – as rare as six trades per year for some issues – and price and transaction transparency are lacking, as no equivalent of TRACE exists for municipal bonds (Harris & Piwowar, 2006).

Nonetheless, each bond ETF's NAV is published daily; and intraday, NYSE Alternext publishes an Intraday Indicative Value (IIV) estimate every 15 seconds of each ETF's underlying asset value (NYSE Euronext, 2009).

Even though a bond ETF might hold bonds from several hundred to more than

1,000 issuers, the infrequency of trading for each constituent bond could lead to misleading NAV and IIV estimates, because the market cannot know whether the value of a given bond is increasing or decreasing until the next trade is completed. Bearing these caveats in mind, one observes different levels of liquidity in bond ETF shares, as measured by the daily closing bid-ask spread, that conform to the finding of Chen,

Lesmond, and Wei (2007) that liquidity and yield spreads are negatively correlated.

Specifically, Treasury bond ETF closing bid-ask spreads are smaller than those of corporate bond ETFs, which are smaller than those of municipal bond ETFs.

Amihud and Mendelson (1986, 1988, 1991) demonstrate that the correlation between the expected holding period and liquidity of an asset is negative. The higher the

12 likelihood that the investor will hold an asset for a short period, the greater the liquidity the investor will demand, and the lower the overall demand for illiquid assets. However, if an investor expects to hold an asset for a long period, then the amortized cost of illiquidity is lower than it would be otherwise, and the difference in transaction costs between liquid and illiquid assets is asymptotically insignificant.

One would expect bond ETFs alleviate this concern, because they are highly liquid, although they hold often highly illiquid underlying assets. Nonetheless, even though it is as easy to sell a municipal bond ETF as it is to sell a Treasury bond ETF, we observe differences in the liquidity of bond ETFs, as measured by closing daily bid-ask spreads that correspond to differences in the liquidity of their underlying assets.

Gastineau (2001) identifies a tension between liquidity and holding period that exists between ETFs and OEFs. On the one hand, OEFs trade at NAV, suggesting that they should be popular among investors who plan to hold the assets for a very short time.

However, excessive trading restrictions prevent intraday or even intra-month trading.

Thus, even though the costs of entering and exiting an ETF are greater than those associated with OEFs, one expects active traders to prefer ETFs over OEFs.

1.3.4. Noise Traders

As it is a misnomer to say that ETFs trade like stocks in all but the most superficial way (Gastineau, 2010), it is equally plausible that bond ETFs do not behave in the short run like bonds. Even though bond ETF values are determined in the long run by the values of the fixed-income assets in their underlying portfolios, and their dividends are funded by the underlying bonds' coupon payments, net of management

13 fees, the presence of retail 'noise' traders in the bond ETF market, who are not represented in the bond market, might cause short-term violations of the law of one price that APs can exploit through the ETF arbitrage mechanism.

As Friedman (1953) noted, “To say that arbitrage is destabilizing is equivalent to saying that arbitrageurs lose money on average,” or in this case that APs should lose money on average, which is counterintuitive. Contrary to the argument that arbitrageurs will trade against irrational investors in an efficient market, thereby rendering irrational investors unable to affect prices significantly (Fama, 1965), De Long, Shleifer,

Summers, and Waldmann (1990) argue that noise traders indeed can affect prices when their misperceptions are correlated. Barber (1994) finds evidence of such 'herding' behavior in his study of two categories of derivative securities that were traded predominantly by individual investors during the 1980s.

Black (1986) points out that liquidity and noise are inseparable, because noise traders increase volatility as a direct consequence of their increasing of liquidity in the form of transaction volume. Although information traders have an incentive to exploit the arbitrage opportunities created by noise traders as prices diverge from fundamental value, they often cannot do so quickly, thereby allowing the false signal to persist. This is less of an issue with Treasury bond ETFs, the underlying assets of which trade in small increments and are very actively traded (US Treasury, 2008), but it is substantial issue with corporate bonds, which might trade as infrequently as once every few days, and especially with municipal bonds, which might trade only a handful of times per year

14 with a median increment of approximately $10,000 (Bessembinder & Maxwell, 2008;

Edwards, et al., 2007).

1.3.4. Bond ETF Trading Strategies

Bond ETFs exist that hold portfolios respectively of municipal, corporate, government agency, sovereign, or international corporate bonds, enabling individual investors to follow strategies that 'ride the yield curve' (Pelaez, 1997), or trade risk classes against each other (e.g., junk vs investment-grade), corporate vs Treasury, domestic vs global, etc., if they mimic their underlying portfolios sufficiently well.

Figure 6 provides plots of daily returns for four two-ETF combinations that illustrate some of the possible pairs trading strategies that investors could pursue – including yield curve (TLT vs SHY), Treasury vs corporate debt (IEF vs LQD), investment-grade vs low-grade (LQD vs HYG), and corporate debt vs equity (LQD vs

SPY) – in which one could go long on the 'overpriced' asset and short on the

'underpriced' asset (Gatev, Goetzman, and Rouwenhorst, 2006).

Beginning in 2008, issuers started offering leveraged, inverse, and inverse leveraged bond ETFs that are designed to enable investors to seek returns that are a stated multiple (2x, 3x, etc.) of a category of fixed-income assets, the opposite return

(e.g., a 1% increase when the underlying fund realizes a 1% decrease, and vice versa), or a stated multiple of the opposite return (e.g., a 2% increase when the underlying fund realizes a 1% decrease, and vice versa). These more exotic ETFs are beyond the scope of these essays, which focus on plain vanilla U.S. domestic bond ETFs.

15 Because bond ETFs can be sold short, bought on margin, and traded intraday, if they proxy sufficiently well for the categories of assets that they hold, then they can be used in trading strategies that focus on changes in the level, slope, and curvature of the

Treasury yield curve, the corporate yield curve, Treasury/corporate credit spreads, investment-grade/high-yield credit spreads, etc., which would enable investment opportunities that have not existed before, because of the inaccessibility of the bond market to retail traders, the inability of traders to take short-sell bonds the way that one can short-sell stocks, and the difficulty of investors to trade bonds intraday.

The remainder of this dissertation proceeds as follows:

In Chapter 1 “Bond ETF Mean-Reversion Asymmetries” I investigate the time series behavior of bond ETF premiums and discounts. I find that daily changes in net asset value (NAV) explain most of the changes in U.S. Treasury bond ETFs prices, but substantially less of corporate and municipal bond ETFs' variability. When the frequency is lengthened to weekly observations, the explanatory power of NAV increases substantially, suggesting that short-term disequilibria resolve within one to several days.

Additionally, I find evidence of asymmetric price/NAV dynamics, indicating that bond ETF premiums tend to be persistent and discounts tend to be short-lived, perhaps because investors value bond ETFs in excess of NAV for the ability to trade intraday, short-sell, and buy on margin. When I expand the model to include liquidity, behavioral, and market variables the explanatory power of the models improve dramatically for the bond ETFs that hold illiquid assets, whereas the unexpanded models explain the

16 preponderance of the variability of bond ETFs that hold highly liquid Treasury securities.

In Chapter 2 “The Cross-Section of Expected Bond ETF Returns” I address the question of whether five Fama and French (1993) risk factors – including the market return, two bond-specific factors related to maturity and default risks, and firm-specific factors for size and book-to-market – explain variations in average excess bond ETF returns. More important, I test whether these factors are priced in the cross-section of bond ETF expected returns using robust cross-section asset pricing tests that account for errors in variables and model misspecification. The empirical results suggest that the

Fama-French small-minus-big (SMB) firm-specific factor is priced in the cross-section of expected excess bond ETF returns. Size has been interpreted in the financial literature as a state variable that proxies for default risk, financial distress, and the relative importance of growth options versus assets in place under shifts in aggregate monetary conditions i.e., interest rates (Chan, Chen, and Hsieh, 1985; Chan and Chen, 1991; and

Berk, Green, and Naik, 1999). Additionally, I show that market, default, and term factors help to explain the variation of bond ETF returns, including corporate and

Treasury bond ETF returns, which are consistent with the findings in Fama and French

(1993).

17 CHAPTER 2

Bond ETF Mean-Reversion Asymmetries

Abstract

This chapter analyzes the time series behavior of bond ETF premiums/discounts.

Overall, while intertemporal daily changes in net asset value (NAV) explain most of the changes in U.S. Treasury bond ETFs prices, they explain substantially less of corporate and municipal bond ETFs' variability. In the weekly time frame, NAV explanatory power substantially increases, which provides evidence of arbitrage activity at play.

Furthermore, this chapter finds evidence of asymmetric Price/NAV dynamics (i.e. premiums tend to be persistent and discounts tend to be intermittent). Finally, the inclusion of liquidity, behavioral, and market variables improves the explanatory power of the models.

18 2.1. Introduction

Exchange-traded funds (ETFs) that hold fixed-income assets (hereinafter,

'bonds') make it possible for retail traders, most of whom cannot trade actively in the bond market, to trade bond portfolios intra-day, to short-sell, and to buy on margin at a price that tends to be very close to the net asset value (NAV). The question arises whether this is because price tracks NAV as a more or less natural consequence or whether the Authorized Participant (AP) arbitrage mechanism actively brings price and

NAV back to parity, when price drifts from NAV.

In order for bond ETFs to serve as proxies for their underlying assets in active retail fixed-income trading strategies, they must be at least as convenient to trade as their underlying assets, and they must exhibit similar risk/reward characteristics when they respond to changes in the market that track the responses of their underlying assets.

This essay's major contribution is to examine whether bond ETF prices follow the law of one price in the short run as well as in the long run. I show that the AP arbitrage mechanism works relatively well, although imperfectly, and I present evidence of asymmetric mean reversion that results in a tendency for bond ETFs to trade at a small premium above NAV.

After I identify persistent premiums in the summary data (Table 1, Panels B and

C), the analysis begins with a standard error-correction model (ECM) (Engle & Granger,

1987) to test for the presence and speed of mean reversion, when price and NAV diverge.

The ECM works well for this, because it has within it a mechanism to describe this process in the form of the error-correction term (γ), discussed in detail below.

19 I find that price and NAV converge within one day for Treasury bond ETFs – the underlying assets of which are very liquid – and after as much as several days for ETFs that hold illiquid assets, perhaps due to differences in the difficulty of APs to assemble

Creation Units of Treasury bond versus, e.g., junk bonds or municipal bonds. This is rate of convergence is slower than the rates found by Engle and Sarkar (2006) and

Delcoure and Zhong (2007) for domestic equity ETFs, the prices and NAVs of which mean-revert within minutes, and for foreign equity ETFs that mean-revert within a few hours and occasionally a bit more than a day.

The analysis continues with a Rockets & Feathers (RF) model (Bachmeier &

Griffin, 2003; Geweke, 2004) that includes an additional quadratic lagged error term that detects the presence of asymmetric mean-reversion among the majority of the bond

ETFs in this sample. Most commonly, these asymmetries are upward – meaning that premiums are persistent, developing quickly and dissipating slowly, and discounts are fleeting, developing weakly and dissipating quickly – as evidenced by the mean and median positive premiums among all categories of bond ETFs in this sample.

Finally, the ECM and RF models are expanded to include liquidity, behavioral, and equity-market factors to explain bond ETF premiums that are analogous to those identified by Delcoure and Zhong (2007) in their analysis of factors other than changes in NAV that affect changes in ETF share price. I find that Treasury bond ETF returns are negatively correlated, low-grade corporate bond ETF returns are positively correlated, and broad-market and municipal bond ETF returns are uncorrelated with S&P 500 returns in the daily series and that all but five are uncorrelated with S&P 500 returns in

20 the weekly series, suggesting that arbitrage opportunities tend to be exploited within a week, but that it can take more than one day.

This result conforms to the findings of Geweke (2004) that finding the correct frequency is critical when analyzing asymmetric ECMs (i.e., RF models). For example, if asymmetric mean reversion holds over a daily or weekly interval, then intraday, monthly, or annual data frequencies will not catch the asymmetry. Based on the ECM results, both daily and weekly frequencies are examined here as a robustness check.

Engle and Sarkar (2006) address this issue, as well, when they go from daily to intraday data, because mean reversion with domestic equity ETFs take minutes.

With each expansion of the model from standard ECM to asymmetric RF to the final version that includes behavioral, liquidity, and market factors, the improvements of the R2s are more striking among bond ETFs that hold relatively illiquid municipal and corporate bonds, than among Treasury bond ETFs. The standard ECM explains virtually all of the variability of Treasury bond ETF premiums, and little is to be gained from making the model more complex, but expanded specifications substantially improve the model's explanatory power among bond ETFs for which the standard ECM explains as little as 10%-20% of a premiums daily variability and the expanded RF model explains almost twice as much of the variability.

Treasury bond ETFs tend to respond differently from other categories of bond

ETFs to changes in bid-ask spreads, intra-period high-low ranges, market capitalization, trading intensity (the ratio of volume and shares outstanding), the credit spread, the TED spread (the difference between the three-month LIBOR and three-month T-Bill rate), the

21 VIX Index (an index of the implied volatility of thirty-day options on the S&P 500, sometimes referred to at the 'fear index'), and the S&P 500. These differences suggest that trading strategies based on bond ETFs should control for liquidity, behavioral, and market factors for those that hold illiquid assets.

The remainder of this essay is organized as follows: Section 2 provides background on bond ETFs, in particular how they differ qualitatively from ETFs that hold assets that trade in transparent and highly liquid markets. Section 3 provides a description of the data and methodologies used in this essay. Section 4 discusses the results. Section 5 provides general concluding remarks.

2.2. Background

As discussed above, ETFs typically trade very close to their NAVs. When price and NAV diverge APs can deliver (receive) underlying assets when shares trade at a premium (discount). However, because ETF share creation and redemption is in increments on the order of 50,000 to 100,000 ETF shares (Creation Units) or the equivalent value of underlying assets, the price of a thinly traded ETF can diverge from its NAV by a substantial amount, before it becomes cost-effective for an AP to initiate a share creation or redemption.

Bond ETFs differ from equity ETFs because APs cannot assemble or liquidate

Creation Units on organized exchanges. Instead, they must trade in the OTC market, which is relatively easy with Treasury bonds but not with municipal and corporate bonds.

22 Each bond ETF holds bonds that fit the category described in its prospectus – e.g., MBS, TIPS, T-Bill, long-term Treasury bond, investment-grade corporate, junk, municipal, broad-market, etc. – enabling active retail traders to pursue strategies that either were prohibitively expensive or even impossible before bond ETFs began trading.

Different levels of liquidity in bond ETF shares confirm the finding of Chen,

Lesmond, and Wei (2007) that liquidity and yield spreads are negatively correlated, suggesting that, although bond ETFs might not 'perfect' proxies for their underlying assets, they might be 'good enough' for practical purposes in trading strategies that involve the taking of simultaneous long and short positions in different categories of fixed income assets.

2.2.1. Empirical Framework

In order to address the question of how well bond ETFs proxy for the bond indexes represented by their portfolios, I examine the effectiveness of the AP arbitrage mechanism to maintain the law of one price between bond ETF price and NAV. This analysis of the relationship between bond ETF price and NAV begins with a specification based on a two-step Engle-Granger (1987) error-correction model (ECM) that includes a Rockets-&-Feathers (RF) factor (Bachmeier & Griffin, 2003; Geweke,

2004) and behavioral and liquidity explanatory variables similar to those identified by

Delcoure and Zhong (2007).

I use an ECM, rather than other cointegration methodologies, because the ECM incorporates a factor that measures the rate of mean-reversion, and the existence of an

ECM implies cointegration (Campos & Ericsson, 1988; Hendry & Ericsson, 1991;

23 Kremers, 1989; Kremers, Ericsson & Dolado, 1992). An RF model is a generalized ECM that includes a lagged quadratic error term that captures mean-reversion asymmetries.

An RF model can be used to address questions related to the observation of persistent premiums, specifically if they are simply data anomalies or if they might reveal some relevant underlying factor, like the added value that bond ETFs bring to the fixed- income asset market by opening it to retail – especially 'noise' – traders, and by enabling short-selling, intraday trading, and buying on margin.

Black (1986) argues that 'noise' traders are a blessing as well as a curse, in that while they increase volatility, they do so by increasing liquidity in the form of transaction volume. As prices diverge from fundamental value, information traders have an incentive to enter the market, in order to exploit arbitrage opportunities created by noise traders. If this is correct, then by opening the market to active traders who cannot trade OEFs intraday or short, and who cannot exploit CEF premiums and discounts, bond ETF prices should exhibit greater volatility than NAV, which results in premiums and discounts.

If bond ETFs enabled traders to assemble portfolios of fixed-income assets more efficiently than by trading the underlying assets directly, demand for ETF shares should be driven higher relative to the demand for the underlying assets, leading to persistent premiums. However, because of the AP arbitrage mechanism, these premiums should be smaller than arbitrage costs. Therefore, one would expect to observe positive mean premiums over the entire sample of bond ETFs and larger premiums for bond ETFs that hold portfolios of less liquid assets; e.g., corporate bond vis-à-vis Treasury bond ETFs.

24 2.3. Data and Methodology

2.3.1. Data

This sample includes the 20 U.S. domestic bond ETFs with inception dates prior to 1 January 2008 and market capitalizations of at least $900 million on 31 December

2009. The focus is on domestic bond ETFs because of the relative dearth of international bond ETFs with inception dates early enough to allow meaningful analysis at the time of writing, and to avoid confounding issues related to tracking errors.

(Delcoure & Zhong, 2007; Engle & Sarkar, 2006; Johnson, 2009; Pennathur, et al.,

2002)

Daily data run from each bond ETF's inception date through 31 December 2009.

Daily price (open, high, low, close, closing ask, closing bid), volume, and shares outstanding data are from the Center for Research in Security Prices (CRSP) Daily Stock database. Daily NAV data are provided by the funds' issuers via their websites. Treasury

Bill and corporate bond (Aaa and Baa) rates are from the Federal Reserve Bank of St.

Louis's FRED database. 3-Month LIBOR rates are from Datastream. Missing observations are filled with the most recent prior data, and weekly data are drawn from every fifth daily observation corresponding to Friday of each week. When a holiday fell on a Friday, the most recent previous observation was used.

Table 1 provides descriptive statistics. Panel A presents ticker symbols, issuers' names, brief descriptions of underlying assets, inception dates, mean durations, mean maturities, dividend rates, expense ratios, and mean market capitalizations. Panel B presents mean and median daily high-low spreads, bid-ask spreads, premiums, and ratios

25 of premiums and bid-ask spreads for the period from 1 January 2008 through 31

December 2009. Panel C presents the same spreads and ratios as Panel B, calculated from each ETF's inception date through 31 December 2009.

Engle and Sarkar (2006) note that a closing transaction can be either a buy or a sell order, and that the reported closing price must be slightly above or below the closing price bid-ask midpoint (midquote), which introduces noise into reported closing prices.

They recommend using the closing midquote to reduce this noise. Therefore, market capitalization, premiums, and trading intensity are calculated using the closing midquote.

Market capitalization is calculated as the midquote times the number of shares outstanding. Daily high-low spread is calculated at ln(high/low); bid-ask spread as ln(ask/bid); premium as ln(midquote/NAV); and the premium/bid-ask spread ratio as ln(midquote/NAV)/ln(ask/bid). An absolute value of the premium/bid-ask spread ratio greater than 1.00 indicates that the magnitude of the premium (discount) exceeds the magnitude of the bid-ask spread. In all cases, the bond ETFs in this sample exhibit positive, though small, mean and median premiums.

Panel A shows that dividend rates reflect the liquidity of the underlying assets.

Short-term Treasury ETFs have dividend rates less than 1%; broad market, in the 2%-4% range; long-term Treasury, 3%-4%; and junk bond, on the order of 8%. Expense ratios reflect liquidity, as well, with Treasury bond ETFs at 0.14%-0.15%; broad market, between 0.12% and 0.20%; municipal, between 0.20% and 0.25%; and junk bond, between 0.40% and 0.50%.

26 Panels B and C show that mean premiums for the Treasury bond ETFs range between 2 and less than 6 basis points (bps, 0.01%); broad market, between 30 and 152 bps; and junk bond, between 150 and 185 bps. In all cases mean premiums are positive.

In comparison, Engle and Sarkar (2006) find average premiums for domestic equity ETFs of 0.25 bps with an average standard deviation of 11.8 bps, and 23.7 bps and 64.8 bps for international equity ETFs. They conclude that domestic equity ETFs are priced very close to their true NAVs with only sporadic significant premiums or discounts, and that international ETFs perform according to expectations, even though they are less actively traded and less accurately priced than domestic equity ETFs.

While some of the observed differences in premiums between bond and equity

ETFs might be caused by the turmoil in U.S. markets during the sample period used here versus Engle and Sarkar's sample period of the second and third quarters of 2000, the average bond ETF premiums above are between one and two orders of magnitude as large as the domestic equity ETFs, and domestic equity ETFs' underlying assets are highly liquid. It is reasonable to assume that these differences are representative of the essential reality.

Not surprisingly, the premiums of Treasury bond ETFs appear to behave differently from the premiums of broad market, municipal, investment-grade corporate, and junk bond ETFs, and the differences appear to reflect differences in the liquidity of the underlying assets of each category. Nonetheless, the existence of these persistent small premiums warrants investigation.

27 2.3.2. Methodology

2.3.2.1. Test of the Law of One Price

The presence of persistent small premiums in the bond ETFs in this sample leads to the question of whether they represent 'anomalies' that violate the law of one price, or if some more fundamental reasons are at work. Given that retail and institutional traders have access to bond ETFs, whereas the bond market's costs are prohibitive for active retail traders, and traders can trade bond ETFs intraday, short-sell, and buy on margin, it is reasonable to expect that they truly are more valuable, and that premiums are not cause for concern.

The two-step Engle-Granger (1987) cointegration methodology is an ideal starting point for this kind of analysis. The model below is based on the basic ECM, and does not test for causality, because the ETF market at the time of this writing represented a very small part of the overall bond market, and the ETFs in this sample were relatively new. It is unlikely that the bond ETF market significantly impacts the bond market, and it is sensible to assume that the arrow of causation points from changes in the bond market to changes in the bond ETF market, and not vice versa.

Here, log- midquote (hereinafter, 'price') is regressed on log-NAV for each bond

ETF in the sample, as shown in equation (1), and the lagged value of the error term is included in a second-pass ECM, as shown in equation (2).

pit = αi + βinit + εit (1)

for i = {1,...,n} and t = {1,...,T}, where n is the sample size; T is the length of the time series; pit and nit are the log of price and the log of NAV of ETF i at time t; αi is an

28 intercept term, expected to be equal to 0.00; βi is a slope coefficient, expected to be equal to 1.00; and εit is an error term that is assumed to follow an AR(1) process.

The second step is to construct an ECM by fitting the error term from the regression above to an AR(1) process, shown in equation (3), taking the first difference of equation (1), and substituting the error term with the right side of equation (3), yielding the model shown in equation (2):

∆pit = γ1iεi,t-1 + βi∆nit + νit (2)

where

εit = ai1εi,t-1 + νit (3)

and ∆pit = (pit-pi,t-1), ∆nit = (nit-ni,t-1), ai1 is a slope coefficient, νit is a white-noise error term, and γ1i = (ai1-1).

In practice, one includes an intercept term in equation (2), expecting that estimates will be insignificant:

∆pit = αi + γ1iεi,t-1 + βi∆nit + νit (4)

If ε can be fitted to an AR(1) process, then -1 < ai1 < 1, and γ1i = ai1-1 is negative, indicating that a deviation in one period should be followed by a reversion toward the mean in the next period. If γ1 is negative and significant, this supports the assumption of cointegration.

2.3.2.2. Test of Mean-Reversion Asymmetries

Given the existence of premiums in the summary data, a reasonable prediction is that if price and NAV are shown to be mean-reverting in the models specified above, the convergence might not be symmetrical, tending to favor premiums; due perhaps to

29 differences in how easy it is for APs to assemble Creation Units of ETF shares on the one hand and of bonds on the other. One expects that it is more difficult to assemble

Creation Units of bonds, particularly municipal and low-grade corporate bonds, than it is to purchase ETF shares, and that this asymmetric liquidity leads to asymmetric arbitrage and mean-reversion.

An extension of the ECM that has been used to analyze asymmetric price adjustments – particularly in the retail market for gasoline in response to changes in wholesale oil prices – is known as Rockets and Feathers (RF), in reference to anecdotal evidence that gasoline prices tend to rise quickly when wholesale oil prices rise and to fall slowly when wholesale oil prices fall (Bachmeier & Griffin, 2003; Geweke, 2004).

The RF model tests whether the magnitude of the previous period's divergence from price/NAV parity is generally associated with a subsequent increase or decrease of price relative to NAV. If large divergences are associated with subsequent increases in price relative to NAV, then discounts will tend to revert quickly, and premiums will tend to persist; if they are associated with subsequent decreases in price relative to NAV, then discounts will tend to persist, and premiums will tend to revert quickly.

Shleifer and Vishny (1997) point out that arbitrage is limited in even the best of circumstances and that arbitrage can become ineffective, when price diverges significantly from intrinsic value. Arbitrageurs might rationally avoid excessively volatile positions, like those involving junk bonds in the last quarter of 2008. Even if such positions seem to offer potentially attractive average returns, they also expose

30 arbitrageurs to the risk of having to liquidate their positions under unfavorable conditions.

If APs require some non-trivial amount of time and effort to assemble Creation

Units worth of bonds in response to very large premiums, those premiums could persist before being bid down when the AP sells the newly created ETF shares into the retail market. On the other hand, if an ETF drifts into a discount of similar magnitude, this eventually creates an incentive for APs to buy relatively 'underpriced' shares, bidding the price up, and exchange them for relatively 'overpriced' bonds.

One expects that this will be less of an issue with Treasury bond ETFs than with municipal and low-grade corporate bond ETFs. If this is the case, then persistent premiums might be symptoms of the relative difficulty of assembling Creation Units of bonds or of estimating bond ETF NAV – especially municipal and low-grade corporate bonds – vis-à-vis buying creations units of shares and estimating equity ETF NAV, than symptoms of behavioral 'anomalies'.

A RF specification includes a squared-error term in equation (2):

2 ∆pit = αi + γ1iεi,t-1 + γ2iε i,t-1 + βi∆nit + ωit (5)

If γ1 is negative, if γ2 is positive, then this suggests that a deviation from parity will tend to favor a quick reversion from a discount and a slow reversion from a premium; if γ2 is negative, then the opposite is expected.

2.3.2.3. Liquidity and Behavioral Explanatory Variables

Houweling, Mentink, and Vorst (2005) test nine popular bond liquidity proxies and find that none is unequivocally superior to the others in all situations. Proxies

31 analyzed here include closing price bid-ask spread: ln(Ask/Bid); high-low range: ln(High/Low); market capitalization: the log of the product of the closing price bid-ask midpoint and the number of shares outstanding; and trading intensity: log of the ratio of the volume and number of shares outstanding.

Bid-Ask Spread: Delcoure and Zhong (2007) note that transaction costs impede

AP arbitrage strategies. Thus, the greater the bid-ask spread, the greater the premium is expected to become before APs initiate the creation or redemption of ETF shares.

High-Low Range: Given that APs might need several hours, or even days, to assemble Creation Units, the same rationale applies to the range between intra-period high and low prices as to the bid-ask spread. The greater the high-low range, the greater the premium is expected to become before APs initiate the creation or redemption of

ETF shares. Although one might expect the intra-period high-low range and the closing price bid-ask spread to be highly correlated, correlation matrices of each bond ETF in this sample (not reported here) reveal that the correlation ranges between 0.3 and 0.5 in most cases4. Although this is high enough to suggest some collinearity, results are very similar with models that omit one or the other and models that include both variables, and results for models that include both are reported below.

Market Capitalization: The rationale here and in the next paragraph follows

Black's (1986) observation that when noise traders increase the volume of transactions, they simultaneously increase the magnitudes of premiums and discounts. Since bond

ETFs open the market in fixed-income assets to large numbers of retail traders who

4 MUB, iShares S&P National Municipal Bond Index, is the lone exception with a correlation of 0.7.

32 previously were closed out of primary bond markets, it follows that the largest bond

ETFs with attract the greatest amount of interest among active traders. If increased liquidity is the prevalent force, market capitalization and premiums should be negatively correlated; if noise trading is the prevalent force, they should be positively correlated.

Trading Intensity: In order to avoid conflating trading volume effects with capitalization effects, relative volume (intensity) is analyzed here; specifically the log of the ratio of volume and the number of shares outstanding. Blume, Easley, and O'Hara

(1994) conclude that changes in volume reflect changes in information quality that cannot be inferred from changes in asset prices. They argue that differences in investors' beliefs about fundamental value result in changes in volume, information precision, and price movements. Thus, the greater the divergence of investors' beliefs are, the greater the divergence of asset price from fundamental value are expected to be. This implies a positive relationship between premiums and trading volume. If the increase in volume results from increased liquidity of the underlying assets, perhaps due to changing market conditions, one would expect the relationship between premiums and volume to be negative.

With regard to market conditions, Chandar and Patro (2000) observe that the volatility of international CEF premiums increases markedly during currency crises. In the context of U.S. domestic bond ETFs, indicators of relevant risk include:

Credit Spread: Huang and Huang (2002) find that credit risk accounts for more of the corporate-Treasury bond yield spread for junk bonds than for investment-grade corporate bonds, and Chen, et al. (2007) find that liquidity and yield spreads are

33 negatively correlated and that liquidity increases cause reductions in yield spreads. One expects that bond ETFs that hold relatively illiquid underlying assets would respond more negatively to an increase in the Credit Spread than Treasury bond ETFs.

TED Spread: Aggarwal, Chaudhry, Christie-David, and Koch (2001) find that the

TED Spread (3-Month Treasury Bill minus 3-Month LIBOR) responds to macroeconomic news and that the spread takes time to adjust to announcements.

Whereas the Credit Spread measures relative risk among categories within the U.S. market, the TED Spread provides a measure of systemic risk. One expects all categories of bond ETFs to respond negatively to increases in the TED Spread.

VIX: Palazzo and Nobili (2010) find some evidence for a positive relationship between bond risk premiums and the VIX Index (VIX), which is an index of the implied volatility of 30-day options on the S&P 500 that is used to measure expectations of future volatility of the S&P 500 (Hull & Basu, 2010, p.317) and serves as a proxy for the market price of risk (Palazzo and Nobili, 2010). If the VIX is a true proxy for 'fear', then one expects to find a negative relationship between the VIX and all categories of the

EFTs in this sample – Treasury, corporate, broad-market, and municipal – except perhaps the shortest-duration Treasury bond ETF.

S&P 500: As a control, the relationship between S&P 500 returns and bond returns should be negative for Treasury bond ETFs and positive for junk bond ETFs.

The expanded ECM that incorporates these explanatory variables takes the form:

∆ln(pt) = α + β∆ln(nt) + γ1εi,t-1 + φ∆ln(LIQt )+ ψ∆BEHt + δ∆ln(SP) + νt (6)

34 where,

LIQ is a Tx4 matrix that includes bid-ask spread, high-low range, market capitalization, and intensity.

BEH is a Tx3 matrix that includes credit spread, TED Spread, and VIX Index.

SP is the S&P 500.

The expanded RF model that incorporates these explanatory variables includes the squared-error term from equation (5) and takes the form:

2 ∆ln(pt) = α + β∆ln(nt) + γ1εi,t-1 + γ2iε i,t-1 +

φ∆ln(LIQt ) + ψ∆BEHt + δ∆ln(SP) + νt (7)

Daily and weekly results for standard and expanded versions of the ECM and the

RF model are presented below.

35 2.4. Empirical Results

The results presented below start with the basic ECM, followed by the basic RF model. The next two sections present the results of expanded ECM and RF models that include the explanatory variables discussed above. Where values are not included in the tables, the models were run with all variables and then again with the insignificant variables dropped.

2.4.1. Law of One Price

Table 2 presents OLS results of two-step error-correction (ECM) and Rockets &

Feathers (RF) models described above. The results in Panel A are for daily observations, and in Panel B for weekly observations. Geweke (2004) argues that it is critical to find the correct frequency when testing for asymmetric mean reversion, because, if asymmetric mean reversion occurs over, e.g., an interval measured in days or weeks, then tests using intraday, monthly, or annual frequencies will fail to find evidence of the asymmetry. For example, Engle and Sarkar (2006) encounter this issue, because domestic equity ETF mean reversion takes minutes, which is not apparent in daily open and closing price data. As a robustness check, based on the ECM results, daily and weekly frequencies are examined here.

These results indicate that daily is the appropriate level of time aggregation for the investigation of the law of one price in the bond ETF market, and that longer or shorter frequencies are not called for, unlike the analysis of equity ETFs, for which mean-reversion is measured in minutes.

36 In all cases, the ECM results are strong. The intercept terms (α) are insignificant, the error-correction terms (γ1) are negative and significant, and the slope coefficients (β) are insignificantly different from 1.00 at the 95% confidence level in 12 of the daily cases and in 14 of the weekly cases. In those cases where β is significantly different from 1.00, it is between 0.90 and 1.10 in all but 2 daily cases and 3 weekly cases.

R2 ranges from a high of 0.95 to a low of 0.09 in the daily cases and from 0.99 to

0.46 in the weekly cases. The top of the range over both frequencies is dominated by

Treasury bond, TIPS, and MBS ETFs, and the bottom by broad-market, municipal, and junk bond ETFs.

The magnitudes of the error-correction terms follow a similar pattern. Among the Treasury bond and MBS ETFs, γ1 ranges from -0.93 to -0.65 in both the daily and the weekly series, indicating that mean-reversion is swift. Two anomalies are the TIPS ETF

(TIP), with a γ1 of -0.19 in the daily series and -0.33 in the weekly series, and the iShares

0-1 year Treasury Bill ETF (SHV), with a γ1 of -0.46 in the daily series and -0.43 in the weekly series. Among the broad-market, municipal, and junk bond ETFs at the bottom of the list, γ1 ranges from approximately -0.40 to -0.10 in the daily series, and improves substantially to between -0.90 and -0.20 in the weekly series.

These results are intuitive, as one expects that APs would find it much easier to assemble Creation Units of Treasury bonds, and to settle in cash for non-transferrable assets like TIPS and MBS, than to assemble Creation Units of portfolios that contain municipal and junk bonds, including broad-market bond ETFs.

37 2.4.2. Mean-Reversion Asymmetries

The RF results tell a similar and more interesting story. As with the ECM results, the intercept terms are insignificant in all but one daily case (JNK), the error-correction terms (γ1) are negative and significant, and the slope coefficients (β) are insignificantly different from 1.00 in 12 of the daily cases and in 14 of the weekly cases. In those cases where β is significantly different from 1.00, it is between 0.90 and 1.10 in all but 3 daily cases and 3 weekly cases.

R2 ranges from a high of 0.95 to a low of 0.12 in the daily cases and from 0.99 to

0.46 in the weekly cases. As with the ECM, the top of the range over both frequencies is dominated by Treasury bond, TIPS, and MBS ETFs, and the bottom by broad-market, municipal, and junk bond ETFs. In virtually all cases, the RF R2 is slightly higher than the corresponding ECM.

The magnitudes of the error-correction terms follow a similar pattern. Among the Treasury bond and MBS ETFs, γ1 ranges from -0.96 to -0.66 in both the daily and the weekly series, indicating that mean-reversion is swift. As with the ECM, TIP, with a γ1 of -0.23 in the daily series and -0.37 in the weekly series, and SHV, with a γ1 of -0.46 in the daily series and -0.39 in the weekly series, are anomalous. Among the broad-market, municipal, and junk bond ETFs at the bottom of the list, γ1 ranges from approximately -

0.40 to -0.10 in the daily series, and improves substantially to between -0.90 and 0.20 in the weekly series.

Most intriguing are the results for the RF coefficient (γ2), which measures the effect of the magnitude of the deviation from price/NAV parity on mean-reversion. A

38 positive value for γ2 indicates that deviations, whether positive (premium) or negative

(discount) should be followed in the next period by an upward change in the deviation.

If the deviation is a discount, then γ2 enhances the reversion to parity. If the deviation is a premium, then γ2 dampens the error-correction mechanism and prolongs the premium.

Thus, premiums are more persistent and reversions to parity from discounts are swifter

(rockets) than reversions to parity from premiums and increases in the time span of discounts (feathers); if γ2 > 0, premiums rise like rockets and fall like feathers.

In the daily series, the values of γ2 are positive in 11 cases, insignificant in 7, and negative in 2: iShares 7-10 year (IEF) and 20+ year (TLT) Treasury bond ETFs. In the weekly series, the values of γ2 are positive in 11 cases, insignificant in 7, and negative in

2: the SPDR 1-3 month T-Bill (BIL) and Short-Term Tax-Exempt Municipal Bond

(SHM) ETFs.

In the preponderance of cases, the data exhibit evidence of the existence of asymmetric mean-reversion among the bond ETFs examined here.

2.4.3. Expanded ECM

Table 3 presents daily and weekly results of the expanded two-step ECM shown above in equation (7), which includes liquidity proxies (bid-ask spread, high-low range, market capitalization, and trading intensity), behavioral factors (credit spread, TED spread, and VIX Index), and S&P 500 data.

In all cases, at least 2 of the additional factors have significant coefficients, and in most case between 4 and 5.

39 With the additional factors, the intercept terms (α) become significant in 14 of the daily and in 8 of the weekly cases, the error-correction terms (γ1) all remain negative and significant, and the slope coefficients (β) are insignificantly different from 1.00 in 8 (as opposed to 12 in the basic ECM) of the daily cases and in 10 (as opposed to 14) of the weekly cases. As with the basic ECM, in those cases where β is significantly different from 1.00, it is between 0.90 and 1.10 in all but 2 daily cases and 3 weekly cases.

R2 ranges from a high of 0.96 (up from 0.95 in the basic ECM) to a low of 0.21

(up from 0.09) in the daily cases and from 0.99 (up slightly) to 0.54 (up from 0.46) in the weekly cases. The top of the range over both frequencies is dominated by Treasury bond, TIPS, and MBS ETFs, and the bottom by broad-market, municipal, and junk bond

ETFs.

The magnitudes of the error-correction terms (γ1) follow a similarly improved pattern. Among the Treasury bond and MBS ETFs, γ1 ranges from -0.95 to -0.68 (-0.93 to -0.65 in the basic ECM) in the daily and weekly series. Two anomalies are the TIPS

ETF (TIP), with a γ1 of -0.21 in the daily series and -0.37 in the weekly series (-0.19 and

-0.33 in the basic ECM), and the iShares 0-1 year T-Bill ETF (SHV), with a γ1 of -0.49 in the daily series and -0.52 in the weekly series (-0.46 and -0.43 in the basic ECM).

Among the broad-market, municipal, and junk bond ETFs, γ1 ranges from approximately

-0.50 to -0.15 (-0.40 to -0.10 in the basic ECM) in the daily series, and minimum of -

0.32 (-0.20 in the basic ECM) in the weekly series.

The results within the liquidity factors are mixed. Where the bid-ask coefficient is significant in the daily series, 7 are positive, and 7 are negative; in the weekly series,

40 10 positive and 2 negative. With market capitalization, it is 5 positive and 3 negative in the daily series, and 5 positive and 2 negative in the weekly series. With trading intensity, it is 3 positive and 5 negative in the daily series, and 3 positive and 3 negative in the weekly series. However, of the 10 significant high-low cases, all are positive; in the weekly series, the 3 significant are positive, as well.

The results within the behavioral factors are more intuitive. The coefficients associated with the credit spread and the TED spread are positive or insignificant for the

Treasuries and largely negative otherwise in both the daily and the weekly series. The

VIX coefficients are uniformly negative or insignificant at the 95% confidence level, indicating that bond ETF returns are negatively correlated with expected stock market volatility.

The S&P 500 coefficients are negative or insignificant in both the daily and the weekly series for all but the junk bond ETFs (HYG and JNK), for which they are positive. Significant coefficients indicate that a relationship exists between bond ETFs and the equity market, which was central the motivation for Fama and French (1993) to develop their five-factor model.

Particularly intriguing is how much stronger the daily S&P 500 results are than the weekly results, suggesting that the equity market has a more significant impact on bond ETF performance in the short run than it does in the long run. Given the reduction in significance with the lengthening of the frequency of the observations, when data become available for meaningful analysis, testing this model with monthly data might result in insignificant coefficients for behavioral, liquidity, and market factors.

41 2.4.4. Expanded Rockets & Feathers

Table 4 presents daily and weekly results of the expanded two-step RF model shown above in equation (7)

The patterns of results among the intercepts, slope coefficients, and error- correction terms are largely the same as with the expanded ECM. In the daily series, the value of the RF coefficient (γ2) is positive in 10 cases (down from 11 in the RF model), insignificant in 9 (up from 7), and negative in 1 (down from 2): iShares 7-10 year

Treasury bond (IEF). In the weekly series, the value of γ2 is positive in 12 cases (up from 11), insignificant in 4 (down from 7), and negative in 4 (up from 2): SPDR 1-3 month T-Bill (BIL), iShares 0-1 year Treasury (SHV), SPDR Short-Term Tax-Exempt

Municipal Bond (SHM), and Vanguard Broad Market 1-5 Year (BSV). This provides evidence in support of the hypothesis that bond ETF premiums tend to be positive and that mean-reversion tends to be upwardly asymmetric.

Within the liquidity factors, the expanded RF results show sharper distinctions among Treasury, corporate, and municipal bond ETFs than those in the expanded ECM results. Where bid-ask coefficients are significant, they are negative among corporate and municipal bond ETFs and positive otherwise in the daily series, and generally positive in the weekly series, suggesting that daily corporate and municipal bond ETF bid-ask spreads exhibit positive volatility/liquidity correlations suggested by Black

(1986), whereas daily Treasury bond and across-the-board weekly bond ETF bid-ask spreads are driven by transaction costs.

42 High-low range coefficients are insignificant or positive in all daily cases and insignificant or positive in all but one weekly case, indicating that premiums are positively correlated with high-low ranges.

Market capitalization coefficients are insignificant for all but two Treasury bond

ETFs, in which cases they are positive, and generally negative otherwise in the daily series, suggesting that daily Treasury bond ETF premiums either are unaffected by market capitalization, and that other categories of bond ETFs exhibit positive volatility/liquidity correlations suggested by Black (1986). In the weekly series, only the two junk bond ETFs have significant, negative market capitalization coefficients, suggesting that liquidity considerations are diminished at longer frequencies and only those categories with the most illiquid underlying assets will exhibit market capitalization effects.

In the very few cases in which the trading intensity coefficients are significant, they are negative for medium- and long-term Treasury bond ETFs in both daily and weekly series, positive for one municipal bond and for one junk bond ETF in the daily series, and positive otherwise in the weekly series, suggesting that liquidity in the form of trading volume tends to reduce Treasury bond ETF premiums – perhaps driven by the negative daily RF coefficients for medium- and long-term Treasury bond ETFs – and to be correlated with increased premiums in other categories, thereby providing support among bond ETFs that hold highly illiquid underlying assets for Blume, et al.'s (1994) conclusion that changes in volume reflect changes in information quality.

43 The credit spread, TED spread, VIX, and S&P 500 results are largely the same as with the expanded ECM, which support the hypothesis that risk, uncertainty, and 'fear' drive investors to relatively safe Treasury bonds and away from other categories of assets.

The overall pattern of RF results is more systematic than the ECM results, suggesting that mean-reversion asymmetries have a significant impact on the bond ETF premiums in this sample. In particular, the clustering of negative bid-ask coefficients among corporate and municipal bond ETFs in the daily RF models compares favorably to the inconclusive bid-ask results in the expanded ECM.

2.5. Conclusion

This essay begins by identifying persistent, though small, premiums in bond ETF price and NAV time series. It tests the law of one price with a standard error-correction model (ECM) that detects mean-reversion that can take from one to several days. Given the presence of persistent premiums and mean reversion, the paper tests for mean reversion asymmetries using a Rockets & Feathers (RF) model that is a generalization of a standard ECM that includes a quadratic error-correction term that indicates whether divergences from price/NAV parity tends precede price increases or decreases relative to

NAV.

The RF model detects the presence of asymmetric mean-reversion among the majority of the bond ETFs in this sample. Most commonly, these asymmetries are upward – meaning that premiums are persistent, developing quickly and dissipating slowly, and discounts are fleeting, developing weakly and dissipating quickly – as

44 evidenced by the mean and median positive premiums among all categories of bond

ETFs in this sample.

As the model controls for more factors, its explanatory power grows, particularly among those ETFs with weak results in the standard ECM. When liquidity, behavioral, and equity-market factors are included in the ECM and RF models, their explanatory power for the bond ETFs that are thinly traded or hold highly illiquid assets increases substantially.

The most relevant results of this analysis from the expanded models, vis-à-vis their relationship with the second chapter – which tests for the 'bondness' or 'stockness' of bond ETFs – are the coefficients of the S&P 500 factors, which indicate that a relationship exists between bond ETFs and the equity market that conforms with the motivation for the development of Fama and French's (1993) five-factor model.

The question remains whether bond ETF share returns behave like stocks, bonds, a combination, or neither, which is addressed in detail in the next chapter.

45 CHAPTER 3

The Cross-section of Bond ETFs Expected Returns

Abstract

This essay seeks to find the risk factors that are priced in a cross-section of expected bond ETF returns in the U.S. I use the multifactor asset pricing model of Fama and French (1993) that includes one market risk factor, two bond-specific factors related to maturity and default risks, and two firm-specific factors related to size and book-to- market. I run a battery of robust asset pricing tests that account for error in variables and model misspecification problems. Because ETF returns are defined as total returns – that is, they include the re-investment of dividends – returns in this sample show more variability than in the case of Fama and French's (1993) bond returns. I run a cross- section asset pricing test instead of a time-series test, as Fama and French (1993) did. I find robust evidence that the size factor is priced in the cross-section of expected bond

ETF returns, probably proxying for default risk, financial distress, and changing monetary conditions affecting firms' cash flows from growth options and assets in place

(Chan, Chen, and Hsieh, 1985; Chan and Chen, 1991; Berk, Green, and Naik, 1999) during the sample period. Additional time-series results suggest that market, default, and term risk premiums help to explain variation in average bond ETF returns, corporate bond ETF returns, and Treasury bond ETF returns, respectively.

46 3.1. Introduction

Bond exchange-traded funds (ETFs) are designed to track specific portfolios of fixed-income securities, the constituents of which are relatively illiquid (compared to stocks) given that they trade predominantly on OTC markets, and to trade like stocks on relatively liquid institutional exchanges.

The question that I seek to answer here is what risks are priced in a cross-section of bond ETF expected returns. In this essay, I investigate the degree to which bond ETF performance is similar to the performance of stocks or bonds.

Fama and French (1993, 1992) propose an augmented version of their three- factor model for stocks to explain the cross-section of average bond returns and stocks and bonds together. That is, besides systematic risk proxied by the market premium and the two firm-specific factors, size and book-to-market, they add two bond-specific factors that proxy for shifts in the term-structure of interest rates and default risk. They find that, when using the five-factor specification, only the two bond market specific factors help to explain the variability in bond returns and market risk explains most of the variability in low-grade corporate bonds. But these factors were not priced in the cross-section of average bond returns; i.e., their average premiums were not different from zero.

Fama and French (1993) used a time series asset pricing approach because of the low variability of bond returns and as a robustness check to their 1992 results that use a cross-section approach on stocks only. They ran pooled OLS regressions using as dependent variables the returns of seven bond portfolios: 1) two Treasury portfolios

47 including short-term and long-term securities; and 2) five corporate portfolios ranked by their credit ranking. The time-series asset pricing tests require as explanatory variables either excess returns or zero-investment portfolio returns and involves the Gibbons,

Ross, and Shanken (1989) test. Because their results suggest the presence of multicollinearity between the factors, they run OLS regressions between the market return and the rest of the risk factors to obtain orthogonalized returns. However,

Giliberto (1985) shows that orthogonalized residuals obtained from contemporaneous regressions of one factor on another can be misspecified.

I follow Petkova (2006) and include innovations, or unexpected changes in the factors or state variables, that drive systematic risk following the intertemporal CAPM

(ICAPM) theoretical framework of Merton (1973). This provides economic support for the inclusion of innovations in the bond-specific and firm-specific Fama-French (1993) factors; i.e., as state variables driving the time-varying opportunity set in a dynamic framework. The innovations where obtained using a first-order vector autoregression model that includes the five Fama-French factors with causality going from the innovations of the two bond-specific and the two firm-specific factors to the market return. This procedure tackles Giliberto's critique, as serial correlation is now explicitly modeled. Furthermore, because the risk factors, other than the market return, are not either market excess returns or zero-investment portfolio returns, I use generalized least squares (GLS) in the cross-section tests as suggested by Cochrane (2001, pp. 212-213).

Related to bond returns, Fama and French (1993) find that the two bond-specific factors help to explain variation in average bond returns, except for low grade corporate

48 bonds, where market is the driving factor. In any case, average premiums are not different from zero. These results are robust to the use of orthogonalized residuals. They make no adjustments in the t-statistics for error-in-variables (EIV) and model misspecification problems. Here, I find results similar to Fama and French (1993) with respect to the risk factors that help explain variation in average returns through time but unfortunately most of these results are not robust to EIV and model misspecification, as shown by the t-statistics. I also run a fixed effects panel data model, in order to check for any small-sample problem in the time-series results.

More important, I find that the size (SMB) factor is priced in the cross-section of expected ETF returns, and the result is robust to EIV and model misspecification. This result is not striking as the sample used in the analyses is limited to the "great recession" that started in 2007. Chan, Chen, and Hsieh (1985) argue that the negative relation between expected returns and size indicates that size is a proxy for default risk. They find that the default spread between high-yield and low-yield bonds is significantly correlated with the size factor. Chan and Chen (1991), interpret size as a "relative prospects" state variable that proxies for economic distress, because earning prospects of small firms are more sensitive to a shift to the trough of the real business cycle.

Berk, Green, and Naik (1999) developed an equilibrium model of firms' returns as a function of size and book to market. In their theoretical model, size is a state variable that proxies for the relative relevance of assets in place and growth options as a source of the firms' cash flows. In their analysis monetary conditions are a crucial factor in the interpretation of these two firm-specific factors as state variables. For example,

49 during a regime of high interest rates, large companies with relatively more growth options and a large base of assets in place will drop those projects with relatively riskier cash flows. Their exposure to systematic risk will be lower than those of relatively smaller firms that have fewer investment opportunities, which tend to be riskier, thereby making them more susceptible to systematic risk, especially when economic times are bad. That is the reason why size has been an elusive risk factor that seems to be priced when the sample includes relatively pronounced recessions.

The remainder of this essay is organized as follows. Section 2 provides a brief review of related literature. Section 3 provides a description of the data and methodologies used in this essay, specifically time series analyses following Fama and

French (1993); formal two-step cross-sectional asset pricing tests following Fama and

MacBeth (1973) and Kan, Robotti, and Shanken (2009); followed by panel data analyses as a robustness check. Section 4 discusses the results of the asset pricing tests, and compares them to the results of Fama and French (1993). Section 5 provides concluding remarks and suggestions for future research.

3.2. Literature Review

Fama and French (1993) seek to explain the cross-section of seven bond portfolio returns as test assets using two mimicking portfolio returns that proxy for unexpected changes in interest rates (TERM) and for shifts in economic conditions that affect the likelihood of default (DEF). TERM is intended to reflect changes in the slope of the yield curve, and DEF is intended to reflect relative changes in Treasury and corporate

50 debt of equivalent maturities on the assumption that, as corporate yields diverge from

Treasury yields, the likelihood of corporate bond default increases.

The study of the term structure of interest rates as a state variable that drives the time-varying opportunity set dates back to Merton's (1973) ICAPM, and was first fully explored by Vasicek (1977) who developed a one-factor model of interest rates. Cox,

Ingersoll, and Ross (1980, 1981) extended the Vasicek model in a general equilibrium setup to include a second factor. Nelson and Siegel (1987) developed a three-factor model – using maturity and yield to maturity to estimate level, slope, and curvature of the yield curve – that is well-behaved for long maturities and can be used to model essentially any yield curve.

Recent research that seeks to explain the term structure of interest rates includes

Ang, Bekaert, and Wei (2007), whose model identifies components of the nominal yield curve associated with changes in the real rate, inflation expectations, and inflation risk premium. They find that the real rate curve in the U.S. is fairly flat around 1.3%, and that changes in the slope of the yield curve are driven by changes in inflation expectations and risk premiums. The seminal article by Ang and Piazzesi (2003) develops a model that includes macroeconomic factors for inflation and employment, and latent factors for level, slope, and curvature driven by monetary policy to find that as much as 85% of the variance of the short end of the yield curve is explained by monetary policy, and that this proportion decreases as one moves toward the long end of the yield curve.

51 Christensen, Lopez, and Rudebusch (2008) develop a model of the term structure that finds long-term inflation expectations to be fairly stable, based on the difference between breakeven inflation rates and a decomposed volatile inflation risk premium estimator.

Evans and Marshall (2007) find that macroeconomic shocks account for most of the parallel shifts in the level of the yield curve, which would not be picked up by the

Fama-French TERM factor, and that technology shocks affect the slope of the yield curve through their effects on expected inflation and the term premium.

Two recent term structure studies that include both bond and stock markets are

Lettau and Wachter (2009) and Czaja, Scholz, and Wikens (2009). Lettau and Wachter

(2009) propose a dynamic risk-based model that jointly explains changes in the yield curve and aggregate market returns. They find that changes in the yield curve and relative changes in the returns of value and growth stocks (similar to the Fama-French book-to-market (HML) factor) convey information of investor expectations about future general business conditions. Czaja, et al. (2009) construct a model that includes the market risk premium and the three Nelson-Siegel (1987) factors for level, slope, and curvature, in place of the single Fama-French TERM factor that corresponds to slope.

They find that insurance firms and banks are exposed to level and curvature changes but only marginally to changes in slope.

Early research on default risk began with Merton (1974), who applies a Black-

Scholes (1973) type model that incorporates the risk-free rate, indenture provisions (e.g., maturity date, coupon rate, call terms, seniority, etc.), and default risk to the estimation

52 of bond prices. Around the same time, Geske (1977) derives a model that contains n- dimensional multivariate normal integrals to demonstrate that risky securities with sequential payouts can be valued as compound options.

Two decades later, Longstaff and Schwartz (1995) use a model that incorporates default and interest rate risk and finds that credit spreads (DEF) are negatively related to interest rate levels and that durations of risky bonds depend on the correlation with interest rates. Leland and Toft (1996) examine optimal capital structure with a closed- form model that predicts leverage, credit spreads, default rates, and write downs, and find that risky corporate debt behaves differently from risk-free government debt.

Collin-Dufresne and Goldstein (2001) present a structural model of corporate debt default with stochastic interest rates – rather than fixed interest rates, as Merton (1974) and others previously used – that allows the firm to alter its capital structure, and find that predicted credit spreads are larger for low-leverage firms and less sensitive to changes in firm value.

Eom, Helwege, and Huang (2004) test the five models described above, and find that predicted default spreads are relatively too low compared to realized spreads when using Merton's (1974) model and too high when using the other models. They conclude that no model accurately can predict credit spreads. This is particularly relevant with regard to the analysis of bond ETFs, as credit risk and the meaning, role, and influence of credit ratings have become an active area of research following the corporate credit crises in 2001-2002 (Cantor 2004).

53 More recent corporate credit default research includes Davies (2008) who analyzes the determinants of U.S. credit spreads using 85 years of AAA and BAA corporate bond yield data. He finds that credit spreads are inversely related to the level of the risk-free rate, and that when credit spreads for BAA bonds are low, they are more sensitive to changes in the risk free rate than AAA bonds. This contradicts Longstaff and

Schwartz (1995), who argue that higher grade debt should be more sensitive to changes in the level of the risk free rate. However, Bhanot (2005) analyzes the effects of the survival of constituent bonds in an index on reported credit spread behavior and finds that a large part of the negative correlation between spread changes and spread levels is a consequence of survival, as ratings changes lead to the removal and replacement of bonds in the index.

These results are relevant for the present analysis, because one of the components of the DEF term, as described below, is the Moody's AAA corporate bond index.

Tang and Yan (2010) find that credit spreads are negatively correlated with GDP growth rates and positively correlated with GDP growth volatility. They conclude that investor sentiment is the most important determinant of credit spreads at the market level, that cash flow volatility and beta are the most important at the individual firm level, and that firm-specific variables have a stronger influence on credit spreads than macroeconomic variables. This is particularly relevant for this analysis, because the sample period includes the stock market crash after Lehman Brothers default in

September 2008, the subsequent recession, and the current – albeit slow – recovery.

54 If bond ETFs behave like bonds, then DEF is expected to be negatively correlated with corporate bond ETF returns and positively with Treasury bond ETF returns. However, if they behave more like stocks than like bonds, then DEF is expected to have little correlation with bond ETF returns as it has been found in the asset pricing literature (see e.g., Petkova, 2006).

Fama and French (1992, 1993) find that risk factors related to market value

(SMB) and book-to-market ratio (HML) capture strong common variation in the returns of stocks and bonds, but only before introducing DEF and TERM in a five factor specification. Their results suggest that SMB and HML are picking up the effects of

DEF, TERM, or both. In this respect, Chan, Chen, and Hsieh (1985) argue that the relationship between expected returns and size is negative because size is a proxy for default risk. They find that the default spread between high-yield and low-yield bonds is significantly correlated with the size factor. Chan and Chen (1991) interpret size as a

"relative prospects" state variable that proxies for economic distress. Earning prospects of small firms are more sensitive to a shift to the trough of the real business cycle.

Berk, et al., (1999) develop an equilibrium model that gives economic support to the Fama and French (1992) firm-specific factors, and argue that firms that perform relatively well tend to be those that identify and exploit numerous growth opportunities given their large base of assets in place. In their analysis monetary conditions or interest rates are crucial in the interpretation of these two firm-specific factors as state variables.

When interest rates are high, a large firm with a large base of assets in place and relatively more projects will keep those that are in-the-money and drop those that are

55 out-of-the-money, reducing its exposure to adverse business conditions. On the same token, small firms with few out-of-the-money projects will be forced to "gamble" when business conditions are bad, making them more exposed to systematic risk.

Petkova (2006), and Hahn and Lee (2006) find that HML can be affected by surprises or news in the slope of the term structure, proxied by TERM, and that SMB seems to be correlated with news on DEF as shown by the previous literature. These suggest that four of the five factors have confounding effects in the setting of Fama and

French (1993).

3.3. Methodological Approach

3.3.1. Data

The sample of test assets used in the asset pricing tests includes 43 monthly total returns of 24 U.S. domestic bond ETFs with inception dates prior to July 2007 and market capitalizations of at least $100 million in March 2011. That is returns include re- investment of dividends.

Table 5 provides summary statistics in two panels. Panel A presents ticker symbol, issuer's name, brief description of underlying assets, inception date, mean duration, mean maturity, market capitalization, expense ratio, and breakdowns of holdings for each Treasury and Corporate bond ETF. Panel B presents the same information for Broad Market, TIPS, Mortgage-Backed Securities, and Government

Agency Credit ETFs.

56 Monthly total return time series are obtained from the Center for Research in

Security Prices (CRSP) Daily Stock database and run from May 2007 through

December 2010. This results in 24 series of 43 observations each.

Fama-French factors (MKTRF, SMB, HML) are from Kenneth French's website5 and are also available through WRDS. Treasury and Moody's Seasoned Aaa Corporate

Bond Yield data are from the Federal Reserve Bank of St. Louis's FRED database6. DEF and TERM are calculated by subtracting 20-year Treasury bond rates from Aaa rates

(DEF), and subtracting 1-month T-Bill rates from 20-year Treasury bond rates (TERM).

3.3.2. Asset Pricing Tests

Following Fama and French (1993), I test a five-factor asset pricing model that includes the excess market return (MKTRF), size (SMB), book-to-market (HML), the default spread (DEF), and term spread (TERM) as risk factors. Then, I run two-pass cross-sectional regression (CSR) asset pricing tests (Black, Jensen, and Scholes, 1972;

Fama and MacBeth, 1973) using GLS. The cross-sectional test follows Fama-MacBeth

(1973) by estimating full-sample rolling betas from first-pass time series regressions, and then returns are regressed on the betas in a second-pass cross-sectional regression.

The time-series regressions are specified as,

Ri,t  i  i,MKTRF MKTRFt  i,SMBSMBt  i,HML HMLt  i,DEF DEFt  i,TERM TERM t   t for all i = {1,...,n} and t = {1,...,T} (1), where n is the sample size; T is the length of the time series; Ri denotes total excess returns for ETF i at time t; MKTRFt is the excess market return as a proxy for systemic

5 http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html 6 http://research.stlouisfed.org/fred2/

57 risk, calculated by subtracting the risk free rate at time t-1 from the S&P 500 returns at time t; SMBt is the Fama-French small-minus-big size factor at time t calculated following Fama and French (1993); HMLt is the Fama-French high-minus-low book-to- market factor at time t calculated as in Fama and French (1993); DEFt is a proxy for default risk, calculated by subtracting the 20-Year Treasury Bond rate from the Moody's

Seasoned Aaa Corporate Bond Yield at time t; TERMt is a term-structure proxy, calculated by subtracting the 3-month Treasury Bill rate from the 20-year Treasury Bond rate at time t; αi is the intercept term, betas are factor loadings on risk factors; and εit is an error term that satisfies classical assumptions.

The cross-section regression is specified as,

E[Ri,t ]   i,MKTRF i,MKTRF   i,SMBi,SMB   i,HML i,HML   i,DEF i,DEF   i,TERM i,TERM  t , for all i = {1,...,n}, (2) where the gammas represent market prices of risk and the betas are factor loadings on the risk factors obtained from first-pass time-series regressions.

Because the betas are obtained from first-pass time-series regressions and used in second-pass cross-section regressions, they potentially are subject to an error-in- variables (EIV) problem. Consequently, I adjust t-statistics following Shanken (1992), yielding asymptotically correct standard errors. I make a second EIV correction following Jagannathan and Wang (1998) who extend Shanken‟s analysis by relaxing the assumption that returns are homoskedastic and normally distributed. In addition to EIV, the asset pricing model may be misspecified as there is no theory leading to the inclusion of the risk factors. Therefore, I correct t-statistics for this and test the null hypothesis of

58 zero misspricing using Kan, et al. (2009) robust standard errors and cross-sectional goodness-of-fit statistics (ρ2).

Fama and French (1993) spend some time explaining the difference between a state variable explaining variation in returns and what is meant by a risk factor priced in the cross-section of expected returns. Kan, et al., (2009) show that market prices of risk

(γ) and prices of covariance risk (λ) yield these two different messages. An explanatory variable can help to explain variation in returns but not be priced in the cross-section and vice-versa. Kan, et al., run the second-pass CSR regression using covariances instead of betas that minimize the pricing errors, arguing that a factor might not add to the model's cross-sectional explanatory power, even though t-statistics indicate strong significance, and it also can happen that the factor covariance does exhibit explanatory power in time- series, even though t-statistics indicate insignificance in the cross-section.

Focusing solely on γ, especially when the model includes more than one factor, can lead to erroneous conclusions and model misspecification, particularly if the factor's correlation with asset returns is low. I include results for both γ and λ.

Finally, I run the CSR asset pricing tests using an empirical specification consistent with the ICAPM of Petkova (2006); i.e., the five factor asset pricing model that includes as explanatory variables innovations or news in the factors. The innovations are obtained by estimating a first-order vector autoregression (VAR) with causality going from the two bond-specific and two firm-specific factors to the market return. A first-order specification is sufficient as it has been shown that any higher-order

59 VAR collapses to its companion first-order VAR. The CSR asset pricing tests are applied to this alternative specification as explained before.

Given that the sample used in the asset pricing tests is short and there might be a small-sample problem with the time-series first-pass estimates. I conclude by running a fixed effects static panel data model that has more power in samples with large N and short T. Note that this does not constitute an asset pricing test as the risk factors are not expressed as returns from mimicking portfolios. The results can be compared to the covariance analysis of Kan et al. (2009) in terms of explaining variation of returns.

3.4. Empirical Results

3.4.1. Stylized Time Series Properties of Bond ETF Excess Returns

Tables 6 through 8 provide results from 24 time series OLS regressions of individual bond ETF excess returns, first on the two Fama-French bond factors (Table

6), next on the market and the two stock factors (Table 7), and then on all five Fama-

French factors: MKTRF, SMB, HML, DEF, and TERM (Table 8).

The results in Tables 6 and 7 indicate that that bond ETFs tend to respond more strongly to market and stock factors than they do to bond factors. These results, together with the results in Table 8 are contrary to what Fama and French (1993) observe, with regard to bonds or stocks. They find that bonds respond strongly to bond factors in a two-factor model, and that the effect fades with the inclusion of the market and stock factors. They also find that stocks do not respond strongly to the bond factors in either the three-factor (MKTRF, SMB, HML) model or in the five-factor model.

60 Here, short-duration Treasury bond ETFs respond to bond, stock, and market factors in two- (bond), three- (market and stock), and five-factor models; most broad- market, long-duration Treasury, and government agency bond ETFs respond to none of the factors in any of the models; and corporate bond and TIPS ETFs respond strongly to the market factor (MKTRF).

In Table 8 time series estimates are presented in categories: Treasury, Corporate,

TIPS, Broad-Market, and Government Agency & MBS. In all categories, the intercept terms are insignificant.

In the Treasury group, estimates are significant among short-duration ETFs

(SHV, SHY, IEI) and insignificant for long-duration ETFs (IEF, TLH, and TLT) issued by iShares, and insignificant for the ETFs issued by SPDR Trust (BIL) and State Street

(ITE). This difference among issuers could be because of lower investor interest for the non-iShares ETFs, as evidenced by net assets, which are substantially smaller than those of the iShares ETFs, and because the iShares brand is virtually synonymous with ETFs

(Delcoure & Zhong, 2007; Pennathur, et al., 2002).

The DEF coefficient is insignificant for all but the iShares 0-1 Year T-Bill ETF

(SHV), suggesting that the preponderance of Treasury bond ETFs do not respond significantly to changes in default risk, whereas low-grade (HYG) and short-term (CSJ) corporate bond ETFs respond strongly to changes in default risk.

The TERM coefficients for T-Bill (BIL and SHV) and 1- to 3-year Treasury bond

(SHY) ETFs are negative and significant, whereas the coefficients of the ETFs that hold

Treasury debt with more than three years to maturity are insignificant. This conforms to

61 the expectation that changes in the yield curve tend to be more dramatic at the short end than at the long end.

Contrary to the bond portfolio time series results of Fama and French (1993), the five-factor model coefficients for MKTRF, SMB, and HML are significant and have the expected signs for short- and medium-term Treasury ETFs. The coefficient for MKTRF

(i.e., beta) is negative, indicating that, when the market risk premium increases, demand for short-term Treasury debt decreases, and vice versa, supporting the flight-to-safety hypothesis. Similarly, the SMB coefficient – which Petkova (2006) identifies as a proxy for a default risk surprise factor – for medium-term Treasury ETFs is significant and negative, meaning that an increase in the difference in returns between small and large firms coincides with a fall in medium-term Treasury ETF returns, thus an increase in their prices.

Estimates are significant for corporate bond, Treasury Inflation-Protected

Securities (TIPS), and Mortgage-Backed Securities (MBS) ETFs; and insignificant for broad-market and government agency bond ETFs.

That estimates for the broad-market bond ETFs are insignificant is not surprising, as they hold both corporate and Treasury bonds, and the signs of the coefficients for

MKTRF and HML for the Treasury bond and corporate bond ETFs are opposite.

However, SMB and TERM are negative throughout, and DEF is positive throughout; that none of these is significant among the broad-market bond ETFs could be the result of a small-numbers issue.

62 The MKTRF coefficients for corporate bond and TIPS ETFs are significant, with t-statistics close to 3.00, and almost 7.00 in the case of HYG, the iShares low-grade corporate bond ETF. Of all of the Non-Treasury ETFs, only HYG has a positive SMB coefficient, and HYG and CSJ – the iShares short-term corporate bond ETF – have significant DEF coefficients, suggesting unsurprisingly that their returns behave like those of a small firm.

In all cases, the pattern of results does not reflect the results of Fama and French.

Here, broad market, government agency, and MBS ETFs yield highly insignificant results, and the MKTRF coefficient predominates.

3.4.2. Fama-MacBeth CSR Asset Pricing Test Results

Tables 9 and 10 present the results from the CSR asset pricing tests (Black, et al.,

1972; Fama and MacBeth, 1973), reporting unadjusted Fama-MacBeth, and Shanken

(1992), Jagannathan and Wang (1998), and Kan, et al., (2009) adjusted t-statistics, respectively. Table 9 presents the results of the five-factor model with explanatory variables in levels, and Table 10 presents the CSR asset pricing test results with explanatory variables expressed as innovations.

The top panel of each table in Tables 9 and 10 corresponds to Kan, et al., (2009) tests of whether risk factors are priced (γ) in the cross-section, and the bottom panel presents the results for tests of whether each risk factor helps to explain variation in time series returns (λ).

63 The t-statistics provided are the unadjusted Fama-MacBeth (tfm), followed by

Shanken's EIV-corrected (ts), then Jagannathan-Wang EIV-corrected (tjw), and finally

Kan, et. al. (2009) corrected values for potential model misspecification (tkrs).

In both specifications using the whole-sample of ETFs, the γ estimates indicate that SMB is priced and significant even after correcting for EIV and model misspecification. In the Treasury sub-sample, γSMB and EIV-corrected λSMB are insignificant, suggesting that financial distress has little impact on Treasury bond ETFs.

In Panel A of Table 9a unadjusted t-statistics indicate that the cross-section intercept is significant, that is there is evidence of mispricing, but the significance disappears when EIV correction is applied. However in Panel B, the unadjusted value of the λ coefficient t-statistic for DEF implies that it has some explanatory power, but this significance also disappears with EIV correction.

Accompanying each table is the model‟s R2 statistic along with an estimate of the probability that R2 = 1.00. In all cases, one cannot reject the null hypothesis that

R2 = 1.00.

3.4.3. Fixed Effects Static Panel Data Results

The weak results in Tables 9 and 10 could be a result of time varying betas that are estimated with low precision and high error, due to the short length of the time period. The sample includes 43 monthly returns for 24 bond ETFs, yielding a total of

1,032 panel data observations in time-series and the cross-section.

As a robustness check, I ran and compared five-factor fixed effects and random effects models. A Hausman (1978) test did not reject the null hypothesis of consistency

64 between the models. I report results for fixed effects models for several reasons. One is that random effects models are more appropriate for random samples from a population, whereas fixed effects models are often used when a whole population is being studied, as is the case here. Another is that the random effects model requires that the composite error term be uncorrelated with all of the explanatory variables, whereas the fixed effects model does not require this assumption. Finally, this sample includes 1,032 observations across twenty-four bond ETFs, and the lost degrees of freedom associated with the fixed effects model is not problematic. (Kennedy, 2003)

Table 11 presents pooled OLS results from one-pass time-series regressions, for the whole sample and for the Treasury sub-sample that controls for fixed effects across the bond ETFs. The results are similar to the uncorrected (tfm) results in Panel B of

Tables 9 and 10. The coefficients for MKTRF, SMB, DEF, and TERM are significant in the whole sample and in the Treasury sub-sample. The coefficient for SMB is negative in both, and the coefficient for MKTRF is positive for the whole sample and negative for the Treasury sub-sample. It is important to note that this is not a formal asset pricing test; it is only evidence that the factors explain variability in the bond ETFs' total returns.

Taken together, these results – though not entirely inconclusive – are not compelling. However, they do suggest that further investigation of the dynamics of bond ETF returns is warranted, especially as more data for these relatively new instruments become available.

65 3.5. Concluding Remarks and Future Research

In this essay, I find that bond ETFs do not respond to bond-market factors in the same way that bonds respond. I find that their time series and cross-sectional behavior appears to be fall somewhere between bonds and stocks. I use the Fama-French (1993) five-factor asset pricing model and robust CSR asset pricing tests that take into account

EIV and model-misspecification problems. The cross-section of ETFs analyzed includes

Treasury, corporate, broad-market, government agency, TIPS, and MBS portfolios.

In spite of the limited sample used in the analyses and evidence of a small- sample problem, the empirical results are encouraging. Treasury bond ETFs, particularly those that hold Treasury Bills and short-term bonds, exhibit behavior that is generally harmonious with the results of Fama and French (1993) for portfolio bond returns. Meanwhile, corporate bond and TIPS ETFs behave more like stocks than like bonds in the time series regressions, similar to the result for high yield bonds in Fama and French (1993). Using panel data analyses, four of the five Fama-French factors yield significant coefficients with large t-statistics. These results suggest that variation of bond ETF returns follow somehow in between bonds and stocks.

The significant result is that I find that SMB – a proxy for financial distress or default risk – is priced in the cross-section of expected bond ETF returns, even after correcting for EIV and model misspecification.

An area of improvement for this essay will be the analysis of longer time series as data become available. Prior to 2007 only six bond ETFs had been issued in the U.S.

By the end of 2007 the number had risen to almost fifty, and today there are more than

66 100. As data become available, the time series can be lengthened and the cross-section can be broadened. This would enable the testing of the small-numbers problem conjectured above.

Another area of potential interest is indicated by the strong time series results in the medium-term coupled with the weak results in the short- and long-term Treasury bond ETFs, suggesting that not only changes in the slope of the yield curve – expressed in the TERM factor – but changes in the curvature of the yield curve might explain some of the behavior of bond ETF returns.

Similar to the model of Czaja, et al. (2009), the model here can be modified to include the three Nelson-Siegel (1987) factors for level, slope, and curvature, in place of the TERM factor, along with MKTRF, SMB, HML, and DEF. Czaja, et al., find that insurance firms and banks respond to changes in level and curvature changes but only marginally to changes in slope. It could be fruitful to see if a similar pattern emerges among bond ETFs.

Finally, the construction of matching portfolios of bonds as controls for the bond

ETFs that they mimic could help shed some light on the degree to which the returns behavior of bond ETFs diverges from bonds. The assumption throughout this essay has been that the results of Fama and French (1993) for the period from 1963 to 1990 should hold for the period from 2007 through 2010, during which bond ETFs have traded. It is possible that the standard of measure has changed.

67

Table 1 Descriptive Statistics Panel A

This table presents descriptive statistics for the ETFs in this sample. Panel A provides basic descriptions, time-invariant data, and mean market capitalization over the periods 2008-2009 and inception date through 31 December 2009, as indicated in the column headers. Panels B and C provide summary statistics related to daily price ranges, daily closing price bid-ask spreads, premiums, and premium/bid-ask ratios.

Expense Mean Market ETF / Inception Duration Maturity Dividend Ratio Capitalization Type Issuer Description Date (years) (years) Rate (%) (%) ($Billion)

Broad Market 2008-2009 incept-2009

AGG iShares Barclays Capital US Aggregate Index 09/22/03 4.18 5.97 3.04 0.20 9.50 4.99

BIV Vanguard Gov., Corp., Intl. 5-10 Year Maturity 04/03/07 6.40 7.30 3.80 0.12 0.62 0.48

BND Vanguard Barclays Capital Aggregate Bond Index 04/03/07 4.70 6.60 3.31 0.12 3.14 2.40

BSV Vanguard Gov., Corp., Intl. 1-5 Year Maturity 04/03/07 2.60 2.70 2.14 0.12 1.38 1.07

CIU iShares Barclays Capital Intermediate U.S. Credit Index 01/05/07 4.31 5.09 3.83 0.20 0.72 0.50

CSJ iShares Barclays Capital 1-3 Year U.S. Credit Index 01/05/07 1.93 2.02 2.08 0.20 1.46 1.01

Corporate

HYG iShares iBoxx $ Liquid High Yield Index 04/04/07 3.89 4.61 7.86 0.50 1.92 1.44

JNK SPDR US High Yield Corporate 11/28/07 4.72 7.70 8.33 0.40 1.06 1.02

LQD iShares Goldman Sachs $ InvesTop Index 07/22/02 7.17 12.09 4.60 0.15 7.47 3.80

Treasury

BIL SPDR 1-3 Month T-Bill 05/25/07 0.13 0.13 0.10 0.14 0.64 0.52

IEF iShares Barclays Capital 7-10 Year Treasury Index 07/22/02 7.30 8.68 2.83 0.15 0.52 1.05

IEI iShares 3-7 Year US Treasury 01/05/07 4.50 4.90 1.85 0.15 0.75 4.66

SHV iShares Barclays Capital Short US Treasury Index 01/05/07 0.40 0.40 0.10 0.15 1.42 0.54

SHY iShares Barclays Capital 1-3 Year Treasury Index 07/22/02 1.83 1.87 0.95 0.15 8.19 1.51

TLT iShares Barclays Capital 20+ Year Treasury Index 07/22/02 14.97 28.05 3.91 0.15 1.83 1.09

MBS & TIPS

MBB iShares Barclays Capital US MBS Fixed-Rate Index 03/13/07 2.02 2.68 2.33 0.25 1.00 0.74

TIP iShares Barclays Capital U.S. Treasury Inflation Notes Index 12/04/03 5.19 9.20 2.74 0.20 10.28 5.17

Municipal

MUB iShares S&P National Municipal Bond Index 09/07/07 7.50 7.38 3.43 0.25 0.40 0.82

SHM SPDR Short-Term Tax-Exempt Municipal 10/10/07 2.92 3.17 1.48 0.20 0.90 0.28

TFI SPDR US Municipal 09/11/07 9.66 14.22 3.55 0.20 0.31 0.35

68

Table 1 Descriptive Statistics Panel B : 2008-2009

This panel presents mean, median, and standard deviation data for each ETF in this sample over the period from 1 January 2008 through 31 December 2009, covering daily high-low range: ln(High/Low); closing price bid-ask spread: ln(Ask/Bid); premium: ln(Midquote/NAV); and premium/bid-ask ratio. High-low range, bid-ask spread, and premium are reported in percentages; i.e., a reported value for the median daily high-low range of 0.5044% indicates a value of 0.005044 or 50.44 basis points. The Premium/Bid-Ask ratio is the actual ratio.

Daily High-Low Range Closing Bid-Ask Spread Daily Premium ln(High/Low) ln(Ask/Bid) ln(Midquote/NAV) Premium / Bid-Ask (2008-2009) (2008-2009) (2008-2009) (2008-2009)

ETF / Median Mean Std. Dev. Median Mean Std. Dev. Median Mean Std. Dev. Median Mean Std. Dev. Type (%) (%) (%) (%) (%) (%) (%) (%) (%)

Broad Market

AGG 0.5044 0.6812 0.6203 0.1074 0.1521 0.1775 0.4291 0.3019 0.7724 3.81 4.96 15.79

BIV 0.6725 0.8357 0.5795 0.1767 0.2758 0.3254 0.5325 0.5998 0.5631 2.88 4.30 5.68

BND 0.5058 0.6567 0.5415 0.1154 0.1707 0.1947 0.4503 0.5312 0.5283 4.17 5.99 7.27

BSV 0.3734 0.6023 0.7888 0.1144 0.2062 0.2670 0.4208 0.5031 0.6133 3.73 5.20 6.91

CIU 0.5583 0.7777 0.7294 0.2791 0.3929 0.5444 1.2960 1.4767 1.0793 4.69 7.55 9.15

CSJ 0.4064 0.6251 0.6499 0.1734 0.2683 0.3865 1.0999 1.5217 1.0980 7.61 18.43 30.79

Corporate

HYG 1.0817 1.4962 1.4653 0.1799 0.2855 0.3536 1.5342 1.8420 2.1403 8.42 20.48 38.49

JNK 1.1341 1.6936 1.9076 0.2133 0.3278 0.3988 1.1010 1.5027 1.8263 5.64 12.41 24.96

LQD 0.7779 1.0770 1.2300 0.1073 0.1636 0.2218 1.0622 1.1162 1.3745 9.46 17.08 32.39

Treasury

BIL 0.0871 0.1254 0.3565 0.0436 0.0461 0.0298 0.0218 0.0248 0.0593 0.50 0.60 1.43

IEF 0.0545 0.0692 0.0703 0.0271 0.0284 0.0213 0.0407 0.0410 0.0350 1.50 2.02 2.41

IEI 0.1666 0.2011 0.1332 0.0239 0.0357 0.0351 0.0358 0.0356 0.0544 1.10 1.71 2.76

SHV 0.3691 0.4294 0.2782 0.0647 0.0775 0.0494 0.0361 0.0319 0.1061 0.50 0.36 6.13

SHY 0.5937 0.6744 0.3526 0.0567 0.0754 0.0601 0.0382 0.0291 0.1423 0.50 0.69 4.09

TLT 1.1345 1.2773 0.6347 0.0450 0.0771 0.0858 0.0543 0.0596 0.2702 0.88 0.88 10.23

MBS & TIPS

MBB 0.3817 0.5391 0.6803 0.1028 0.1572 0.2044 0.0975 0.1191 0.1925 0.90 1.46 3.58

TIP 0.6371 0.7900 0.7140 0.0743 0.0965 0.0847 0.2485 0.3728 0.4831 3.50 6.01 8.83

Municipal

MUB 0.5557 0.8377 1.0759 0.1901 0.2900 0.3701 0.4045 0.5798 0.7922 2.16 3.37 6.37

SHM 0.4367 0.8414 1.2396 0.2541 0.3442 0.3651 0.1883 0.1420 0.4315 0.75 1.11 1.81

TFI 0.7092 1.1120 1.3003 0.2646 0.3437 0.2965 0.1343 0.1119 0.4670 0.50 0.53 2.40

69

Table 1 Descriptive Statistics Panel C : Inception - 2009

This panel presents the same statistics as those presented in Panel B, over the period from each bond ETF's date of inception through 31 December 2009.

Daily High-Low Range Closing Bid-Ask Spread Daily Premium ln(High/Low) ln(Ask/Bid) ln(Midquote/NAV) Premium / Bid-Ask (inception-2009) (inception-2009) (inception-2009) (inception-2009)

ETF / Median Mean Std. Dev. Median Mean Std. Dev. Median Mean Std. Dev. Median Mean Std. Dev. Type (%) (%) (%) (%) (%) (%) (%) (%) (%)

Broad Market

AGG 0.3575 0.4488 0.4050 0.0897 0.1200 0.1199 0.3981 0.3004 0.6819 3.84 5.58 14.57

BIV 0.5611 0.7304 0.6342 0.1452 0.2282 0.2918 0.4303 0.5082 0.5089 3.01 4.23 5.21

BND 0.4409 0.5875 0.5997 0.0914 0.1454 0.1744 0.3608 0.4564 0.4728 4.00 5.84 6.81

BSV 0.3162 0.5078 0.7078 0.0899 0.1684 0.2378 0.3066 0.4034 0.5516 3.22 4.55 6.20

CIU 0.4230 0.5836 0.6655 0.1796 0.2879 0.4724 0.8374 1.1024 1.0421 4.67 7.16 8.41

CSJ 0.3195 0.4829 0.5768 0.1096 0.2067 0.3305 0.8777 1.1889 1.0932 5.26 14.73 27.19

Corporate

HYG 0.9750 1.3422 1.3427 0.1833 0.2722 0.3192 1.4282 1.7278 1.9256 8.02 17.83 34.08

JNK 1.0707 1.6420 1.8908 0.2084 0.3227 0.3930 1.1140 1.4921 1.7941 5.74 12.30 24.53

LQD 0.5616 0.6921 0.7341 0.0961 0.1342 0.1432 0.7362 0.9187 1.2194 7.90 14.87 29.30

Treasury

BIL 0.0872 0.1455 0.6450 0.0436 0.0491 0.0301 0.0218 0.0293 0.0555 0.50 0.72 1.42

IEF 0.0544 0.0737 0.2627 0.0272 0.0280 0.0189 0.0456 0.0459 0.0321 1.75 2.26 2.33

IEI 0.1233 0.1506 0.1036 0.0251 0.0336 0.0228 0.0418 0.0406 0.0555 1.50 2.07 3.08

SHV 0.3124 0.3735 0.2791 0.0704 0.0778 0.0446 0.0374 0.0337 0.1059 0.50 0.40 6.03

SHY 0.4100 0.4779 0.2809 0.0484 0.0582 0.0408 0.0443 0.0350 0.1333 0.90 1.00 3.91

TLT 0.7289 0.8496 0.5106 0.0429 0.0555 0.0547 0.0446 0.0460 0.1741 0.90 1.15 7.22

MBS & TIPS

MBB 0.3193 0.4495 0.5998 0.1038 0.1497 0.1783 0.0983 0.1172 0.1837 0.87 1.36 3.35

TIP 0.4250 0.5244 0.4758 0.0665 0.0752 0.0571 0.1445 0.2083 0.3091 2.36 3.87 6.04

Municipal

MUB 0.5368 0.8018 1.0196 0.1791 0.2709 0.3504 0.4018 0.5666 0.7589 2.23 3.35 6.44

SHM 0.4193 0.8050 1.2338 0.2526 0.3393 0.3698 0.1737 0.1356 0.4141 0.72 1.05 1.75

TFI 0.6758 1.0812 1.3279 0.2284 0.3263 0.2855 0.1533 0.1373 0.4486 0.66 0.78 2.56

70

Table 2 ECM / Rockets & Feathers Panel A : Daily

This table presents OLS results of two-step error-correction (ECM) and Rockets & Feathers (RF) models shown below, where ε is the vector of error terms from the first-pass regression of the log of price (midquote) on the log of NAV. The columns marked σ report the residual standard error. The results in Panel A are for daily observations.

Values in parentheses are t-statistics for the hypotheses: α=0, β=1, γ=0. Values in boldface are significant at the 0.05 level or higher. Significance levels are indicated with asterisks: 0.10 (*), 0.05 (**), and 0.01 (***).

ECM Rockets & Feathers 2 ∆ln(pt) = α + β∆ln(nt) + γ1εt-1 + νt ∆ln(pt) = α + β∆ln(nt) + γ1εt-1 + γ2ε t-1 + νt γ 2 γ γ 2 ETF α β σ α β σ 1 Adj. R 1 2 Adj. R

0.0000 1.0110 -0.9293 0.0000 1.0104 -0.9579 -14.6569 IEF 0.9522 0.0010 0.9524 0.0010 (-0.003) (2.139**) (-40.124***) (0.629) (2.019**) (-38.344***) (-3.018***)

0.0000 0.9856 -0.9341 0.0000 0.9854 -0.9410 -7.0398 TLT 0.9517 0.0017 0.9518 0.0017 (0.023) (-2.844***) (-39.928***) (0.547) (-2.894***) (-39.872***) (-2.108**)

0.0000 1.0051 -0.8509 0.0000 1.0051 -0.8521 -0.3690 IEI 0.9251 0.0010 0.9250 0.0010 (-0.029) (0.499) (-23.204***) (-0.019) (0.499) (-20.351***) (-0.058)

0.0000 0.9857 -0.6557 0.0000 0.9867 -0.6586 40.5297 SHY 0.9122 0.0004 0.9124 0.0004 (0.023) (-2.050**) (-30.381***) (-0.675) (-1.908*) (-30.491***) (2.222**)

0.0000 0.9560 -0.1908 0.0000 0.9549 -0.2298 5.4857 TIP 0.8578 0.0017 0.8599 0.0017 (0.021) (-4.502***) (-12.809***) (-1.022) (-4.644***) (-13.724***) (4.963***)

0.0000 0.9225 -0.4639 0.0000 0.9225 -0.4666 8.4761 SHV 0.7788 0.0003 0.7785 0.0003 (0.107) (-4.302***) (-15.195***) (0.017) (-4.301***) (-14.197***) (0.226)

0.0000 0.9768 -0.7843 0.0000 0.9779 -0.7961 7.8669 MBB 0.7405 0.0017 0.7412 0.0017 (0.045) (-1.047) (-21.097***) (-0.317) (-0.996) (-21.066***) (1.673*)

0.0000 0.9960 -0.2191 -0.0001 0.9954 -0.1984 2.2811 BIV 0.6720 0.0032 0.6751 0.0032 (-0.006) (-0.153) (-9.282***) (-0.490) (-0.173) (-8.048***) (2.783***)

0.0000 0.9807 -0.3858 0.0000 0.9751 -0.3572 -24.1985 BIL 0.5301 0.0004 0.5314 0.0004 (-0.029) (-0.498) (-12.662***) (0.401) (-0.642) (-10.252***) (-1.685*)

0.0000 0.9696 -0.1955 0.0000 0.9679 -0.1201 2.3497 AGG 0.5125 0.0025 0.5224 0.0025 (-0.029) (-1.266) (-13.141***) (-0.708) (-1.347) (-6.150***) (5.885***)

0.0000 0.9841 -0.2633 -0.0002 1.0067 -0.1937 7.0401 BND 0.4953 0.0032 0.5493 0.0030 (-0.010) (-0.407) (-10.299***) (-1.392) (0.180) (-7.656***) (9.268***)

0.0000 0.9416 -0.6248 -0.0001 0.9665 -0.5344 6.7337 TFI 0.4775 0.0042 0.4935 0.0041 (-0.018) (-1.229) (-16.125***) (-0.817) (-0.712) (-12.368***) (4.460***)

0.0000 0.9619 -0.1951 -0.0001 0.9651 -0.1880 1.2796 MUB 0.4291 0.0037 0.4297 0.0037 (-0.038) (-0.843) (-7.957***) (-0.382) (-0.772) (-7.482***) (1.277)

0.0000 0.9461 -0.1835 -0.0002 0.9273 -0.0974 3.1012 LQD 0.4203 0.0043 0.4556 0.0042 (0.002) (-2.083**) (-13.831***) (-1.803*) (-2.389***) (-6.508***) (11.233***)

0.0000 1.0801 -0.2509 -0.0011 1.1651 -0.3658 3.8972 JNK 0.4022 0.0112 0.4416 0.0108 (0.029) (1.287) (-8.850***) (-2.169**) (2.677***) (-11.086***) (6.249***)

0.0000 0.9966 -0.1359 -0.0001 0.9831 -0.1352 3.8519 BSV 0.3916 0.0026 0.4030 0.0026 (0.020) (-0.069) (-7.212***) (-1.015) (-0.341) (-7.243***) (3.803***)

0.0000 0.8658 -0.1117 0.0000 0.8655 -0.1118 -0.0572 CIU 0.2964 0.0043 0.2955 0.0043 (0.058) (-2.769***) (-6.596***) (0.085) (-2.768***) (-6.575***) (-0.093)

0.0000 0.9228 -0.3777 0.0000 0.9225 -0.3798 -0.1311 SHM 0.2336 0.0032 0.2323 0.0032 (0.013) (-0.632) (-11.541***) (0.029) (-0.634) (-8.586***) (-0.073)

0.0000 0.9718 -0.2059 -0.0008 0.9880 -0.2365 2.4665 HYG 0.1667 0.0109 0.2113 0.0106 (0.001) (-0.339) (-7.955***) (-1.910*) (-0.149) (-9.226***) (6.401***)

0.0000 0.7042 -0.0983 -0.0003 0.6787 -0.0930 3.0626 CSJ 0.0948 0.0044 0.1194 0.0043 (0.130) (-3.221***) (-6.163***) (-1.693*) (-3.541***) (-5.899***) (4.744***)

71 Table 2 ECM / Rockets & Feathers Panel B : Weekly

This table presents OLS results of the two-step error-correction (ECM) and Rockets & Feathers (RF) models shown below, where ε is the vector of error terms from the first-pass regression of the log of price (midquote) on the log of NAV. The columns marked σ report the residual standard error. The results in Panel B are for weekly (Friday) observations. If a holiday fell on a Friday, the most recent previous value was used.

Values in parentheses are t-statistics for the hypotheses: α=0, β=1, γ=0. Values in boldface are significant at the 0.05 level or higher. Significance levels are indicated with asterisks: 0.10 (*), 0.05 (**), and 0.01 (***).

ECM Rockets & Feathers 2 ∆ln(pt) = α + β∆ln(nt) + γ1εt-1 + νt ∆ln(pt) = α + β∆ln(nt) + γ1εt-1 + γ2ε t-1 + νt γ 2 γ γ 2 ETF α β σ α β σ 1 Adj. R 1 2 Adj. R

0.0000 0.9801 -0.8841 -0.0001 0.9811 -0.8738 29.1837 TLT 0.9905 0.0017 0.9907 0.0017 (0.071) (-4.069***) (-17.713***) (-0.895) (-3.888***) (-17.584***) (2.622***)

0.0000 0.9898 -0.9410 -0.0001 0.9918 -0.8814 61.4932 IEF 0.9905 0.0009 0.9909 0.0009 (0.085) (-2.072**) (-18.364***) (-1.053) (-1.681*) (-16.826***) (4.025***)

0.0000 0.9816 -0.9621 0.0000 0.9802 -0.9809 -19.8602 IEI 0.9778 0.0010 0.9778 0.0010 (0.117) (-1.542) (-11.749***) (0.353) (-1.640) (-11.500***) (-0.800)

0.0000 0.9870 -0.7150 0.0000 0.9849 -0.7466 242.9510 SHY 0.9777 0.0003 0.9789 0.0003 (0.071) (-1.717*) (-14.475***) (-1.624) (-2.037**) (-15.372***) (4.686***)

0.0000 1.0231 -0.3318 0.0000 1.0253 -0.3663 6.4558 TIP 0.9665 0.0018 0.9667 0.0018 (0.015) (2.146**) (-8.184***) (-0.386) (2.341**) (-8.241***) (1.858*)

0.0000 1.0156 -0.6638 -0.0002 1.0213 -0.8012 77.4032 MBB 0.9514 0.0014 0.9533 0.0013 (-0.001) (0.814) (-8.295***) (-1.258) (1.128) (-8.473***) (2.602**)

0.0000 0.9767 -0.4312 0.0000 0.9772 -0.3918 -59.4942 SHV 0.9455 0.0003 0.9454 0.0003 (0.016) (-1.232) (-6.440***) (0.294) (-1.205) (-4.943***) (-0.929)

0.0000 1.0492 -0.7006 -0.0001 1.0443 -0.6852 8.6889 TFI 0.9383 0.0034 0.9380 0.0034 (-0.104) (1.970*) (-7.995***) (-0.393) (1.693*) (-7.508***) (0.622)

0.0000 1.0525 -0.4335 -0.0004 1.0491 -0.5338 31.3699 BIV 0.9157 0.0028 0.9223 0.0027 (-0.083) (1.918*) (-6.213***) (-1.527) (1.865*) (-7.349***) (3.572***)

0.0000 1.0380 -0.2975 0.0001 1.0349 -0.2360 -7.9655 BND 0.8650 0.0026 0.8648 0.0026 (-0.123) (1.091) (-4.965***) (0.317) (0.996) (-2.621***) (-0.917)

0.0000 1.1620 -0.3864 -0.0001 1.1556 -0.3385 2.7025 LQD 0.8278 0.0048 0.8299 0.0048 (-0.014) (6.000***) (-10.959***) (-0.562) (5.771***) (-8.420***) (2.432**)

-0.0001 0.9552 -0.6305 -0.0016 0.9714 -0.8196 8.0993 JNK 0.7855 0.0128 0.7928 0.0125 (-0.107) (-0.884) (-6.960***) (-1.145) (0.568) (-6.589***) (2.177**)

0.0000 0.9872 -0.8555 -0.0007 0.9366 -0.7159 16.3286 MUB 0.7810 0.0063 0.8061 0.0059 (-0.057) (-0.267) (-9.221***) (-1.301) (1.350) (-7.619***) (4.017***)

0.0000 1.0708 -0.9054 0.0000 1.0550 -0.6806 -81.2665 BIL 0.7468 0.0006 0.7568 0.0006 (-0.069) (1.194) (-10.405***) (0.532) (0.941) (-5.525***) (-2.528**)

0.0000 1.3478 -0.3801 0.0004 1.3059 -0.3612 -4.2365 CIU 0.7080 0.0065 0.7103 0.0065 (-0.033) (4.818***) (-6.977***) (0.653) (3.964***) (-6.484***) (-1.492)

0.0003 1.1835 -0.7622 -0.0009 1.1456 -0.7422 3.8768 HYG 0.6554 0.0156 0.6737 0.0152 (0.212) (2.539***) (-8.872***) (-0.684) (2.037**) (-8.850***) (2.971***)

0.0000 1.0916 -0.6421 -0.0001 1.0936 -0.4250 3.6125 AGG 0.6257 0.0053 0.6325 0.0053 (-0.011) (1.726*) (-12.333***) (-0.406) (1.780*) (-4.387***) (2.647***)

0.0000 0.9551 -0.3898 0.0003 0.9294 -0.6923 -22.4491 SHM 0.6016 0.0031 0.6229 0.0030 (-0.029) (-0.605) (-5.153***) (1.102) (-0.969) (-5.174***) (-2.706***)

0.0000 1.0856 -0.3340 -0.0003 1.0623 -0.3285 9.0123 BSV 0.5582 0.0040 0.5707 0.0039 (-0.052) (0.970) (-5.267***) (-0.738) (0.711) (-5.251***) (2.246**)

0.0000 1.1540 -0.2015 -0.0004 1.1446 -0.2221 4.7236 CSJ 0.4557 0.0051 0.4594 0.0050 (0.030) (1.491) (-4.559***) (-0.804) (1.402) (-4.789***) (1.421)

72 Table 3 Expanded ECM Panel A : Daily

∆ln(pt) = α + β∆ln(nt) + γ1εt-1 + φ∆ln(LIQ)t + ψ∆BEHt + δ∆ln(SP) + νt

This table presents results of the expanded two-step ECM shown above, where ε is the vector of error terms from the first-pass regression of the log of price (midquote) on the log of NAV, LIQ is a Tx4 matrix of bid-ask spread, high-low range, market capitalization, and trading intensity data; BEH is a Tx3 matrix of credit spread, TED Spread, and VIX data; and SP is a Tx1 vector of S&P 500 data. The results in Panel A are for daily observations. The columns marked σ report the residual standard error.

Values in parentheses are t-statistics for the hypotheses: α=0, β=1, γ=0, φ=0, ψ=0, δ=0. Values in boldface are significant at the 0.05 level or higher. Significance levels are indicated with asterisks: 0.10 (*), 0.05 (**), and 0.01 (***).

2 ETF α β γ1 φ bid_ask φ hi_lo φ mkt_cap φ v_nosh ψ cred ψ ted ψ vix δ SP Adj. R σ

-0.0027 0.9634 -0.9442 0.0901 0.0003 0.0000 0.0000 0.0051 0.0003 0.0000 -0.0340 TLT (-0.819) (-6.886***) (-39.365***) (1.129) (0.667) (0.402) (-0.643) (3.076***) (0.450) (0.334) (-6.561***) 0.9560 0.0017

-0.0038 0.9875 -0.9334 -0.1633 0.0005 0.0000 -0.0001 0.0018 0.0006 0.0000 -0.0165 IEF (-1.529) (-2.259**) (-39.709***) (-2.729***) (1.493) (0.146) (-2.255**) (1.867*) (1.623) (1.100) (-5.536***) 0.9557 0.0010

-0.0035 0.9583 -0.8182 0.2365 0.0004 -0.0001 -0.0001 0.0014 -0.0000 -0.0000 -0.0202 IEI (-0.472) (-3.659***) (-22.593***) (2.915***) (0.501) (-0.683) (-1.858*) (1.395) (-0.072) (-0.366) (-5.757***) 0.9329 0.0009

-0.0021 0.9570 -0.6775 -0.0441 0.0002 0.0000 0.0000 0.0007 0.0002 -0.0000 -0.0076 SHY (-0.984) (-5.629***) (-30.231***) (-1.153) (0.826) (2.936***) (-3.286***) (2.043**) (1.767*) (-1.812*) (-7.033***) 0.9193 0.0004

-0.0185 0.9551 -0.2434 0.2653 0.0016 0.0002 0.0003 -0.0024 -0.0023 -0.0001 -0.0152 TIP (-2.642***) (-4.423***) (-13.446***) (3.249***) (2.204**) (3.496***) (3.518***) (-1.338) (-3.674***) (-1.283) (-2.592***) 0.8625 0.0017

-0.0714 0.8839 -0.5153 0.0600 0.0077 -0.0001 0.0000 0.0012 0.0006 0.0000 -0.0002 SHV (-3.251***) (-6.072***) (-15.971***) (1.117) (3.252***) (-3.058***) (0.387) (4.183***) (5.269***) (0.844) (-0.206) 0.7931 0.0003

-0.0558 0.9720 -0.7644 0.3589 0.0063 -0.0003 0.0001 -0.0087 -0.0006 -0.0001 -0.0148 MBB (-2.654***) (-1.159) (-18.734***) (9.461***) (2.653***) (-2.388**) (0.875) (-4.371***) (-0.813) (-2.657***) (-2.256**) 0.7775 0.0017

-0.0328 1.0259 -0.2811 0.1246 0.0038 0.0000 -0.0002 -0.0090 -0.0026 -0.0004 -0.0331 BIV (-1.574) (0.894) (-10.689***) (2.668***) (1.513) (-0.057) (-0.794) (-2.533**) (-2.068**) (-4.290***) (-2.709***) 0.6883 0.0031

0.0159 1.0756 -0.3981 -0.4200 -0.0015 -0.0006 0.0013 0.0207 -0.0030 -0.0004 0.1185 JNK (0.883) (1.179) (-12.092***) (-3.301***) (-0.794) (-1.674*) (2.329**) (1.669*) (-0.430) (-1.344) (2.936***) 0.5718 0.0099

-0.0664 0.9187 -0.4347 -0.0396 0.0088 0.0000 0.0000 0.0002 0.0010 -0.0000 -0.0065 BIL (-3.388***) (-1.954*) (-13.061***) (-0.669) (3.416***) (-2.603***) (0.259) (0.394) (5.833***) (-2.517**) (-4.037***) 0.5664 0.0004

-0.0478 0.9995 -0.2483 -0.2155 0.0053 0.0000 -0.0002 -0.0150 -0.0022 -0.0002 -0.0078 AGG (-2.836***) (-0.020) (-14.760***) (-3.611***) (2.941***) (-0.714) (-1.801*) (-5.411***) (-2.352**) (-2.831***) (-0.886) 0.5368 0.0025

-0.0416 0.9228 -0.6826 -0.1519 0.0066 -0.0001 0.0012 -0.0045 -0.0091 -0.0000 0.0089 TFI (-1.947*) (-1.615) (-16.711***) (-2.121**) (1.927*) (-0.462) (4.078***) (-0.925) (-4.852***) (-0.122) (0.558) 0.5362 0.0041

-0.0176 1.0696 -0.3137 0.0685 0.0017 0.0002 -0.0001 -0.0099 -0.0037 -0.0001 0.0104 BND (-0.511) (1.647*) (-10.490***) (0.856) (0.414) (1.176) (-0.267) (-2.744***) (-2.932***) (-1.499) (0.844) 0.5254 0.0032

-0.0330 0.9588 -0.2303 -0.3982 0.0026 0.0006 0.0002 -0.0207 -0.0058 -0.0005 0.0085 LQD (-2.363**) (-1.592) (-15.862***) (-5.401***) (2.034**) (2.740***) (1.119) (-4.904***) (-3.736***) (-5.225***) (0.663) 0.4799 0.0042

0.0098 0.9670 -0.2137 -0.1756 -0.0015 0.0003 0.0002 -0.0026 -0.0038 -0.0003 -0.0042 MUB (0.282) (-0.717) (-7.969***) (-3.514***) (-0.412) (0.891) (0.673) (-0.595) (-2.272**) (-2.419**) (-0.295) 0.4674 0.0036

-0.0160 0.7652 -0.1598 0.0226 0.0018 -0.0001 0.0004 -0.0286 -0.0078 -0.0012 0.1540 HYG (-0.665) (-3.064***) (-6.283***) (0.179) (0.853) (-0.230) (0.751) (-2.688***) (-2.112**) (-4.641***) (4.364***) 0.4352 0.0092

-0.2347 0.9252 -0.2219 0.2406 0.0291 -0.0013 -0.0004 -0.0025 -0.0011 -0.0001 -0.0223 BSV (-5.972***) (-1.331) (-9.507***) (5.111***) (6.044***) (-5.903***) (-1.988**) (-0.840) (-1.014) (-1.278) (-2.192**) 0.4288 0.0026

-0.1249 0.9394 -0.2155 0.2231 0.0129 0.0005 0.0002 -0.0178 -0.0079 -0.0002 -0.0115 CIU (-5.212***) (-1.234) (-10.130***) (6.385***) (5.017***) (3.715***) (1.087) (-3.754***) (-4.814***) (-1.579) (-0.727) 0.3897 0.0041

-0.1648 0.9749 -0.4775 -0.1660 0.0280 -0.0009 0.0000 -0.0010 0.0002 0.0000 0.0212 SHM (-4.505***) (-0.207) (-13.415***) (-4.121***) (4.605***) (-5.020***) (0.159) (-0.273) (0.112) (0.297) (1.747*) 0.3229 0.0031

-0.2197 0.8113 -0.2535 0.1506 0.0226 0.0008 0.0003 -0.0173 -0.0090 -0.0003 -0.0148 CSJ (-4.841***) (-2.024**) (-10.706***) (2.696***) (4.580***) (5.186***) (1.756*) (-3.525***) (-5.451***) (-2.141**) (-0.922) 0.2145 0.0042

73 Table 3 Expanded ECM Panel B : Weekly

∆ln(pt) = α + β∆ln(nt) + γ1εt-1 + φ∆ln(LIQ)t + ψ∆BEHt + δ∆ln(SP) + νt

This panel presents results for weekly (Friday) observations of the expanded two-step ECM shown above, where ε is the vector of error terms from the first- pass regression of the log of price (midquote) on the log of NAV, LIQ is a Tx4 matrix of bid-ask spread, high-low range, market capitalization, and trading intensity data; BEH is a Tx3 matrix of credit spread, TED Spread, and VIX data; and SP is a Tx1 vector of S&P 500 data. If a holiday fell on a Friday, the most recent previous value was used. The columns marked σ report the residual standard error.

Values in parentheses are t-statistics for the hypotheses: α=0, β=1, γ=0, φ=0, ψ=0, δ=0. Values in boldface are significant at the 0.05 level or higher. Significance levels are indicated with asterisks: 0.10 (*), 0.05 (**), and 0.01 (***).

2 ETF α β γ1 φ bid_ask φ hi_lo φ mkt_cap φ v_nosh ψ cred ψ ted ψ vix δ SP Adj. R σ

-0.0003 0.9756 -0.9156 0.1571 -0.0000 0.0001 -0.0001 0.0009 -0.0007 -0.0001 -0.0224 TLT (-0.049) (-4.860***) (-18.303***) (0.943) (-0.002) (0.543) (-1.538) (0.630) (-1.122) (-2.333**) (-3.807***) 0.9909 0.0016

0.0038 0.9870 -0.9639 0.4214 -0.0004 0.0000 -0.0001 0.0008 -0.0004 -0.0000 -0.0089 IEF (0.666) (-2.519**) (-18.724***) (2.197**) (-0.559) (0.058) (-1.334) (1.040) (-1.031) (-0.886) (-2.675***) 0.9909 0.0009

0.0033 0.9842 -0.7924 0.1737 -0.0005 0.0001 0.0000 0.0007 -0.0001 -0.0000 -0.0027 SHY (0.726) (-2.025**) (-15.765***) (2.192**) (-0.947) (3.318***) (-0.942) (2.697***) (-0.748) (-1.528) (-2.256**) 0.9792 0.0003

-0.0162 0.9704 -0.9758 -0.0806 0.0021 -0.0002 -0.0002 0.0022 -0.0002 0.0000 -0.0049 IEI (-0.862) (-2.281**) (-11.679***) (-0.288) (0.929) (-1.031) (-1.390) (2.050**) (-0.448) (0.291) (-1.012) 0.9784 0.0010

-0.0247 1.0176 -0.3962 -0.2256 0.0022 0.0003 0.0003 -0.0011 -0.0017 -0.0001 -0.0131 TIP (-1.562) (1.651*) (-9.026***) (-1.098) (1.287) (2.429**) (2.031**) (-0.729) (-2.458**) (-3.688***) (-2.255**) 0.9689 0.0018

-0.0606 1.0096 -0.7680 0.1205 0.0069 -0.0004 0.0004 0.0001 -0.0021 -0.0001 -0.0136 MBB (-1.553) (0.471) (-8.712***) (1.108) (1.553) (-1.715*) (1.978*) (0.112) (-3.527***) (-2.477**) (-2.729***) 0.9588 0.0013

-0.1107 0.9515 -0.5535 0.3197 0.0119 -0.0001 0.0000 0.0001 0.0004 0.0000 0.0007 SHV (-1.603) (-2.398**) (-6.859***) (1.674*) (1.602) (-1.433) (-0.028) (0.313) (3.559***) (0.726) (0.562) 0.9504 0.0003

0.0328 1.0137 -0.7796 -0.3258 -0.0054 -0.0001 0.0010 -0.0068 0.0008 -0.0001 -0.0152 TFI (0.830) (0.561) (-8.641***) (-2.752***) (-0.846) (-0.244) (2.440**) (-2.159**) (0.529) (-0.946) (-1.144) 0.9483 0.0031

-0.0222 1.0310 -0.5289 0.2069 0.0024 0.0002 -0.0002 -0.0002 -0.0027 -0.0001 -0.0112 BIV (-0.494) (1.073) (-6.335***) (1.290) (0.426) (0.427) (-0.338) (-0.082) (-2.489**) (-2.277**) (-1.331) 0.9230 0.0027

-0.0469 1.0103 -0.6013 1.2568 0.0049 0.0002 -0.0001 -0.0014 -0.0007 -0.0002 0.0064 BND (-0.754) (0.302) (-8.067***) (5.171***) (0.650) (0.664) (-0.166) (-0.661) (-0.701) (-3.246***) (0.885) 0.8929 0.0023

-0.0159 1.1560 -0.5054 0.3802 0.0005 0.0008 -0.0004 -0.0202 -0.0045 -0.0002 0.0211 LQD (-0.436) (6.062***) (-12.989***) (1.390) (0.152) (1.437) (-1.052) (-4.914***) (-2.631***) (-1.929*) (1.289) 0.8494 0.0045

-0.0238 1.0269 -0.7016 1.2172 0.0036 -0.0011 0.0019 -0.0146 -0.0089 0.0007 0.1059 JNK (-0.434) (0.376) (-7.032***) (2.125**) (0.644) (-1.113) (1.103) (-1.342) (-1.437) (2.571**) (2.285**) 0.8416 0.0112

-0.4653 0.9225 -0.9073 0.6359 0.0449 0.0024 0.0050 -0.0071 -0.0092 -0.0003 -0.0152 MUB (-3.272***) (-1.682*) (-10.042***) (2.204**) (2.897***) (1.630) (3.456***) (-1.270) (-3.315***) (-2.606**) (-0.792) 0.8302 0.0055

-0.4109 1.2450 -0.6182 1.2881 0.0429 0.0009 0.0005 -0.0117 -0.0072 -0.0005 -0.0266 CIU (-5.569***) (4.103***) (-10.704***) (7.480***) (5.428***) (2.480**) (0.970) (-2.348**) (-3.535***) (-3.700***) (-1.316) 0.8291 0.0050

-0.4668 1.0010 -1.1456 0.5750 0.0610 -0.0001 0.0002 -0.0002 0.0000 0.0000 0.0017 BIL (-3.779***) (0.019) (-13.373***) (2.050**) (3.772***) (-1.345) (2.742***) (-0.304) (-0.206) (2.198**) (0.640) 0.8119 0.0006

-0.0143 1.0778 -0.8113 -2.5415 0.0022 -0.0002 0.0000 -0.0150 -0.0004 -0.0005 -0.0145 AGG (-0.224) (1.743*) (-16.015***) (-7.754***) (0.324) (-0.782) (-0.019) (-3.665***) (-0.267) (-5.608***) (-1.034) 0.7626 0.0042

-0.0966 1.2260 -0.7409 2.0608 0.0107 -0.0004 0.0004 0.0252 -0.0129 -0.0011 0.1187 HYG (-1.041) (2.806***) (-8.840***) (2.743***) (1.349) (-0.266) (0.196) (1.693*) (-2.190**) (-2.823***) (1.867*) 0.7372 0.0136

-0.2432 0.9140 -0.5758 0.0363 0.0420 -0.0016 -0.0006 -0.0021 -0.0019 -0.0002 0.0108 SHM (-2.911***) (-1.250) (-6.689***) (0.251) (3.014***) (-3.799***) (-1.115) (-0.711) (-1.414) (-2.711***) (1.178) 0.6837 0.0028

-0.4537 0.9397 -0.4080 0.2841 0.0568 -0.0027 -0.0012 0.0024 -0.0020 -0.0002 -0.0110 BSV (-3.497***) (-0.673) (-5.649***) (1.340) (3.587***) (-3.695***) (-1.759*) (0.698) (-1.339) (-2.209**) (-0.963) 0.6161 0.0037

-0.2124 1.1526 -0.5397 0.3624 0.0197 0.0020 0.0011 -0.0137 -0.0013 -0.0003 -0.0410 CSJ (-1.590) (1.532) (-7.075***) (1.414) (1.359) (4.964***) (1.887*) (-2.931***) (-0.687) (-2.311**) (-2.224**) 0.5579 0.0046

74 Table 4 Expanded Rockets & Feathers Panel A : Daily

2 ∆ln(pt) = α + β∆ln(nt) + γ1εt-1 + γ2ε t-1 + φ∆ln(LIQ)t + ψ∆BEHt + δ∆ln(SP) + νt

This table presents results of the expanded two-step Rockets & Feathers model shown above, where ε is the vector of error terms from the first-pass regression of the log of price (midquote) on the log of NAV, LIQ is a Tx4 matrix of bid-ask spread, high-low range, market capitalization, and trading intensity data; BEH is a Tx3 matrix of credit spread, TED Spread, and VIX data; and SP is a Tx1 vector of S&P 500 data. The columns marked σ report the residual standard error. The results in Panel A are for daily observations.

Values in parentheses are t-statistics for the hypotheses: α=0, β=1, γ=0, φ=0, ψ=0, δ=0. Values in boldface are significant at the 0.05 level or higher. Significance levels are indicated with asterisks: 0.10 (*), 0.05 (**), and 0.01 (***).

2 ETF α β γ1 γ2 φ bid_ask φ hi_lo φ mkt_cap φ v_nosh ψ cred ψ ted ψ vix δ SP Adj. R σ

-0.0031 0.9633 -0.9490 -5.2252 0.1107 0.0003 0.0000 -0.0000 0.0049 0.0002 0.0000 -0.0338 TLT (-0.963) (-6.890) (-39.239) (-1.513) (1.367) (0.746) (0.601) (-0.511) (2.998) (0.385) (0.347) (-6.515) 0.9560 0.0017 *** *** *** ***

-0.0041 0.9869 -0.9716 -18.1541 -0.1323 0.0005 0.0000 -0.0001 0.0017 0.0005 0.0000 -0.0166 IEF (-1.637) (-2.375) (-37.994) (-3.720) (-2.199) (1.494) (0.616) (-2.032) (1.845) (1.396) (1.122) (-5.583) 0.9560 0.0010 ** *** *** ** ** * ***

-0.0031 0.9585 -0.8358 -5.4401 0.2493 0.0004 -0.0000 -0.0001 0.0014 -0.0000 -0.0000 -0.0202 IEI (-0.413) (-3.641) (-20.109) (-0.864) (3.022) (0.436) (-0.589) (-1.767) (1.415) (-0.101) (-0.371) (-5.756) 0.9329 0.0009 *** *** *** * ***

-0.0017 0.9573 -0.6770 34.0977 -0.0544 0.0002 0.0000 0.0000 0.0007 0.0003 -0.0000 -0.0077 SHY (-0.752) (-5.844) (-30.226) (1.788) (-1.409) (0.624) (2.539) (-3.439) (1.965) (2.004) (-1.895) (-7.086) 0.9194 0.0004 *** *** * ** *** ** ** * ***

-0.0241 0.9528 -0.2680 4.9115 0.1904 0.0022 0.0002 0.0003 -0.0025 -0.0022 0.0000 -0.0140 TIP (-3.383) (-4.661) (-14.008) (3.823) (2.278) (2.958) (3.582) (3.633) (-1.387) (-3.461) (-0.878) (-2.383) 0.8638 0.0017 *** *** *** *** ** *** *** *** *** **

-0.0714 0.8839 -0.5152 -0.1123 0.0600 0.0077 -0.0001 0.0000 0.0012 0.0006 0.0000 -0.0002 SHV (-3.243) (-6.066) (-15.262) (-0.003) (1.064) (3.243) (-3.017) (0.385) (4.180) (5.264) (0.843) (-0.206) 0.7928 0.0003 *** *** *** *** *** *** ***

-0.0550 0.9708 -0.7585 -4.3930 0.3710 0.0062 -0.0003 0.0001 -0.0082 -0.0007 -0.0001 -0.0150 MBB (-2.609) (-1.202) (-18.285) (-0.800) (9.081) (2.605) (-2.305) (0.874) (-3.942) (-0.888) (-2.643) (-2.284) 0.7774 0.0017 *** *** *** *** ** *** *** **

-0.0365 1.0241 -0.2732 0.5980 0.1224 0.0043 -0.0000 -0.0002 -0.0090 -0.0026 -0.0004 -0.0329 BIV (-1.686) (0.831) (-9.383) (0.634) (2.613) (1.630) (-0.228) (-0.886) (-2.517) (-2.040) (-4.192) (-2.689) 0.6881 0.0031 * *** *** ** ** *** ****

0.0113 1.1092 -0.4296 1.5592 -0.4361 -0.0009 -0.0006 0.0013 0.0206 -0.0026 -0.0004 0.1131 JNK (0.627) (1.666) (-12.066) (2.266) (-3.437) (-0.457) (-1.700) (2.219) (1.670) (-0.382) (-1.193) (2.808) 0.5755 0.0099 * *** ** *** * ** * ***

-0.0810 1.0597 -0.1769 7.7716 -0.0528 0.0097 -0.0002 -0.0002 -0.0098 -0.0037 -0.0001 0.0052 BND (-2.415) (1.489) (-5.443) (8.622) (-0.684) (2.399) (-1.007) (-0.979) (-2.867) (-3.059) (-1.367) (0.446) 0.5731 0.0030 ** *** *** ** *** ***

-0.0665 0.9186 -0.4339 -0.6506 -0.0391 0.0088 0.0000 0.0000 0.0002 0.0010 -0.0000 -0.0065 BIL (-3.382) (-1.951) (-11.335) (-0.044) (-0.651) (3.411) (-2.547) (0.260) (0.392) (5.818) (-2.515) (-4.020) 0.5657 0.0004 *** * *** *** ** *** ** ***

-0.0443 0.9433 -0.6011 5.4142 -0.1601 0.0070 -0.0001 0.0011 -0.0048 -0.0085 0.0000 0.0091 TFI (-2.094) (-1.190) (-12.932) (3.554) (-2.258) (2.089) (-0.456) (3.526) (-0.989) (-4.576) (-0.192) (0.576) 0.5459 0.0040 ** *** *** ** ** *** ***

-0.0601 0.9904 -0.1769 2.1289 -0.2174 0.0067 -0.0001 -0.0003 -0.0138 -0.0021 -0.0002 -0.0106 AGG (-3.552) (-0.380) (-8.020) (4.959) (-3.671) (3.687) (-1.159) (-2.145) (-4.992) (-2.172) (-2.722) (-1.206) 0.5440 0.0025 *** *** *** *** *** ** *** ** ***

-0.0415 0.9270 -0.1210 3.5617 -0.5915 0.0041 0.0003 0.0000 -0.0171 -0.0048 -0.0005 0.0048 LQD (-3.080) (-2.909) (-7.233) (11.901) (-8.122) (3.310) (1.291) (-0.038) (-4.191) (-3.212) (-4.842) (0.391) 0.5178 0.0040 *** *** *** *** *** *** *** *** ***

-0.0101 0.9685 -0.2016 2.2920 -0.1951 0.0008 0.0002 0.0001 -0.0027 -0.0040 -0.0002 -0.0044 MUB (-0.279) (-0.685) (-7.337) (1.944) (-3.837) (0.199) (0.601) (0.411) (-0.623) (-2.367) (-2.346) (-0.313) 0.4700 0.0036 **** * **** ** **

-0.0298 0.7449 -0.1743 1.9592 -0.1263 0.0034 -0.0001 0.0001 -0.0305 -0.0084 -0.0012 0.1397 HYG (-1.255) (-3.386) (-6.935) (5.059) (-0.990) (1.620) (-0.149) (0.094) (-2.920) (-2.329) (-4.598) (4.021) 0.4557 0.0090 **** **** **** *** ** *** ***

-0.2618 0.9027 -0.2029 4.9394 0.1643 0.0324 -0.0015 -0.0004 -0.0028 -0.0006 -0.0001 -0.0197 BSV (-6.623) (-1.740) (-8.589) (3.848) (3.246) (6.702) (-6.553) (-2.274) (-0.965) (-0.588) (-0.951) (-1.957) 0.4406 0.0026 *** * *** *** *** *** *** ** *

-0.1177 0.9386 -0.2173 -0.6374 0.2254 0.0121 0.0005 0.0002 -0.0179 -0.0079 -0.0002 -0.0110 CIU (-4.699) (-1.250) (-10.177) (-0.991) (6.436) (4.494) (3.783) (1.113) (-3.771) (-4.825) (-1.599) (-0.697) 0.3897 0.0041 *** *** *** *** *** *** ***

-0.1708 0.9837 -0.4366 2.5036 -0.1688 0.0290 -0.0010 0.0000 -0.0012 0.0001 0.0000 0.0221 SHM (-4.641) (-0.134) (-9.460) (1.388) (-4.190) (4.739) (-5.078) (0.035) (-0.320) (0.076) (0.318) (1.815) 0.3241 0.0031 *** *** *** *** *** *

-0.2434 0.7729 -0.2406 2.0299 0.1301 0.0253 0.0006 0.0003 -0.0165 -0.0085 -0.0002 -0.0166 CSJ (-5.308) (-2.425) (-10.044) (2.935) (2.323) (5.068) (4.351) (1.406) (-3.371) (-5.156) (-2.039) (-1.038) 0.2228 0.0042 *** ** *** *** ** *** *** *** *** **

75 Table 4 Expanded Rockets & Feathers Panel B : Weekly

2 ∆ln(pt) = α + β∆ln(nt) + γ1εt-1 + γ2ε t-1 + φ∆ln(LIQ)t + ψ∆BEHt + δ∆ln(SP) + νt

This panel presents results for weekly (Friday) observations of the expanded two-step Rockets & Feathers model shown above, where ε is the vector of error terms from the first-pass regression of the log of price (midquote) on the log of NAV, LIQ is a Tx4 matrix of bid-ask spread, high-low range, market capitalization, and trading intensity data; BEH is a Tx3 matrix of credit spread, TED Spread, and VIX data; and SP is a Tx1 vector of S&P 500 data. If a holiday fell on a Friday, the most recent previous value was used.

Values in parentheses are t-statistics for the hypotheses: α=0, β=1, γ=0, φ=0, ψ=0, δ=0. Values in boldface are significant at the 0.05 level or higher. Significance levels are indicated with asterisks: 0.10 (*), 0.05 (**), and 0.01 (***).

2 ETF α β γ1 γ2 φ bid_ask φ hi_lo φ mkt_cap φ v_nosh ψ cred ψ ted ψ vix δ SP Adj. R σ

0.0062 0.9895 -0.9006 56.5122 0.3908 -0.0006 -0.0000 -0.0001 0.0003 -0.0004 -0.0000 -0.0087 IEF (1.102) (-2.041) (-16.783) (3.592) (2.067) (-0.875) (-0.319) (-1.480) (0.360) (-1.129) (-0.652) (-2.659) 0.9912 0.0009 ** *** *** ** ***

0.0024 0.9768 -0.9034 26.4764 0.1322 -0.0002 0.0000 -0.0002 0.0008 -0.0007 -0.0001 -0.0221 TLT (0.349) (-4.621) (-18.065) (2.320) (0.797) (-0.280) (0.192) (-1.644) (0.578) (-1.155) (-2.309) (-3.774) 0.9910 0.0016 *** *** ** ** ***

0.0076 0.9837 -0.8069 212.4487 0.1597 -0.0010 0.0001 -0.0000 0.0006 -0.0001 -0.0000 -0.0025 SHY (1.668) (-2.134) (-16.321) (3.966) (2.051) (-1.851) (2.878) (-1.183) (2.170) (-0.762) (-1.327) (-2.133) 0.9800 0.0003 * ** *** *** ** * *** ** **

-0.0145 0.9614 -1.0550 -67.0017 -0.0270 0.0018 -0.0001 -0.0002 0.0035 -0.0003 0.0000 -0.0041 IEI (-0.782) (-2.889) (-11.832) (-2.312) (-0.098) (0.831) (-0.809) (-1.237) (2.949) (-0.592) (0.420) (-0.846) 0.9790 0.0010 *** *** ** ***

-0.0341 1.0185 -0.4537 8.8129 -0.2018 0.0032 0.0003 0.0004 -0.0023 -0.0014 -0.0001 -0.0137 TIP (-2.104) (1.747) (-9.082) (2.351) (-0.988) (1.838) (2.443) (2.135) (-1.452) (-1.974) (-3.803) (-2.382) 0.9694 0.0018 ** * *** ** * ** ** ** *** **

-0.0595 1.0123 -0.8431 44.4166 0.0612 0.0068 -0.0004 0.0004 0.0003 -0.0019 -0.0001 -0.0131 MBB (-1.528) (0.606) (-8.001) (1.293) (0.520) (1.537) (-1.818) (1.982) (0.261) (-3.102) (-2.118) (-2.629) 0.9591 0.0013 *** * ** *** ** ***

-0.0880 0.9559 -0.4998 -120.1896 0.4460 0.0094 -0.0001 0.0000 0.0001 0.0004 0.0000 0.0005 SHV (-1.261) (-2.182) (-5.824) (-1.747) (2.197) (1.257) (-0.976) (0.044) (0.385) (3.560) (0.658) (0.399) 0.9511 0.0003 ** *** * ** ***

0.0027 0.9952 -0.7349 23.3568 -0.3174 -0.0005 -0.0001 0.0010 -0.0075 0.0002 -0.0001 -0.0168 TFI (0.061) (-0.176) (-7.736) (1.439) (-2.691) (-0.074) (-0.219) (2.340) (-2.383) (0.153) (-1.161) (-1.266) 0.9488 0.0031 *** *** ** **

-0.0206 1.0300 -0.6097 26.6500 0.1356 0.0021 0.0002 -0.0002 -0.0025 -0.0017 -0.0001 -0.0076 BIV (-0.468) (1.058) (-6.948) (2.544) (0.850) (0.388) (0.597) (-0.457) (-0.930) (-1.456) (-2.001) (-0.911) 0.9261 0.0027 *** ** **

-0.0585 1.0065 -0.5486 -5.9711 1.2803 0.0064 0.0001 -0.0001 -0.0014 -0.0006 -0.0002 0.0068 BND (-0.905) (0.187) (-5.057) (-0.669) (5.202) (0.815) (0.313) (-0.240) (-0.619) (-0.659) (-3.261) (0.943) 0.8925 0.0023 *** *** ***

-0.0355 1.0589 -0.9616 11.0159 1.3440 0.0059 -0.0015 0.0012 -0.0184 -0.0062 0.0008 0.1036 JNK (-0.675) (0.852) (-7.637) (3.158) (2.450) (1.100) (-1.520) (0.747) (-1.758) (-1.036) (2.807) (2.340) 0.8555 0.0107 *** *** ** * *** **

-0.0310 1.1438 -0.4373 3.7998 0.1955 0.0025 0.0006 -0.0005 -0.0197 -0.0040 -0.0002 0.0241 LQD (-0.851) (5.591) (-9.913) (3.156) (0.707) (0.765) (1.040) (-1.358) (-4.862) (-2.355) (-2.057) (1.491) 0.8529 0.0045 *** *** *** *** ** **

-0.5322 0.8686 -0.7931 18.5678 0.6289 0.0546 0.0010 0.0035 -0.0125 -0.0045 -0.0003 -0.0075 MUB (-3.989) (-2.934) (-8.970) (4.205) (2.340) (3.738) (0.725) (2.501) (-2.333) (-1.588) (-2.784) (-0.417) 0.8528 0.0052 *** *** *** *** ** *** ** ** ***

-0.3358 1.1963 -0.5473 -7.8373 1.3868 0.0350 0.0007 0.0006 -0.0083 -0.0081 -0.0004 -0.0263 CIU (-4.411) (3.250) (-8.963) (-2.979) (8.114) (4.301) (2.022) (1.018) (-1.670) (-4.000) (-3.679) (-1.340) 0.8379 0.0049 *** *** *** *** *** *** ** * *** ***

-0.5342 0.9748 -0.8602 -97.7361 0.5800 0.0697 0.0000 0.0002 -0.0004 0.0000 0.0000 0.0006 BIL (-4.443) (-0.478) (-7.321) (-3.402) (2.154) (4.433) (-0.585) (2.615) (-0.765) (0.068) (1.928) (0.213) 0.8267 0.0005 *** *** *** ** *** *** *

-0.0595 1.0770 -0.5578 4.4780 -2.3444 0.0075 -0.0004 -0.0003 -0.0164 0.0014 -0.0005 -0.0134 AGG (-0.933) (1.762) (-6.731) (3.818) (-7.214) (1.085) (-1.356) (-0.534) (-4.060) (0.837) (-6.050) (-0.974) 0.7725 0.0042 * *** *** *** *** ***

-0.0892 1.1527 -0.7125 3.0347 1.4413 0.0102 -0.0006 0.0004 0.0184 -0.0115 -0.0010 0.1142 HYG (-0.978) (1.794) (-8.555) (2.351) (1.838) (1.309) (-0.384) (0.189) (1.230) (-1.972) (-2.779) (1.826) 0.7460 0.0134 * *** ** * * *** *

-0.2390 0.9110 -0.6126 -3.5945 0.0525 0.0412 -0.0016 -0.0006 -0.0018 -0.0019 -0.0002 0.0098 SHM (-2.819) (-1.279) (-4.521) (-0.352) (0.345) (2.917) (-3.700) (-1.047) (-0.604) (-1.427) (-2.646) (1.011) 0.6810 0.0028 *** *** *** *** ***

-0.4549 0.9365 -0.3854 7.8073 0.1420 0.0569 -0.0027 -0.0012 0.0019 -0.0013 -0.0002 -0.0070 BSV (-3.531) (-0.714) (-5.284) (1.688) (0.627) (3.620) (-3.721) (-1.682) (0.551) (-0.828) (-2.106) (-0.600) 0.6215 0.0037 *** *** * *** *** * **

-0.2767 1.1296 -0.5850 7.2678 0.3698 0.0266 0.0020 0.0010 -0.0131 -0.0012 -0.0003 -0.0385 CSJ (-2.058) (1.315) (-7.540) (2.337) (1.465) (1.823) (5.125) (1.795) (-2.842) (-0.642) (-2.423) (-2.122) 0.5712 0.0045 ** *** ** * *** * *** ** **

76 Table 5

Descriptive Statistics Panel A

This table presents descriptive statistics for the sample 24 US domestic bond ETFs with inception dates prior to July 2007 and market capitalizations of at least $100 million in March 2011. Panel A presents ticker symbols, issuer names, descriptions of underlying assets, inception dates, average duration (Dur.) and maturity (Mat.), net assets as of March 2011, expense ratio (Exp. Ratio), and breakdown of holdings showing number of issues held as of March 2011, percent held in US Treasury assets (Fed. Gov.), non-governmental investment-grade assets (Non-Gov. A), and low-grade assets (B-, C-, and Un-Rated) for Treasury and corporate bond ETFs.

Holdings Mar. 2011

Net B-, C- & Assets Exp. Fed. Non- Un- ETF / Incept. ($Bill.) Ratio Gov. Gov. A Rated Type Issuer Description Date Dur. Mat. Mar. 2011 (%) # (%) (%) (%)

Treasury

BIL SPDR 1-3 Month T-Bill 05/25/07 0.12 0.12 0.9 0.14 9 100 - -

Barclays Capital Short SHV iShares 01/05/07 0.39 0.39 4.1 0.15 13 100 - - US Treasury Index

Barclays Capital 1-3 SHY iShares 07/22/02 1.82 1.86 7.9 0.15 37 100 - - Year Treasury Index

3-7 Year US Treasury IEI iShares 01/05/07 4.44 4.82 1.3 0.15 37 100 - -

Barclays Capital 7-10 IEF iShares 07/22/02 7.17 8.53 2.8 0.15 15 100 - - Year Treasury Index

Barclays Capital 10-20 TLH iShares 01/05/07 9.31 14.08 0.2 0.15 23 100 - - Year Treasury Index

Barclays Capital 20+ TLT iShares 07/22/02 14.69 27.61 2.9 0.15 15 100 - - Year Treasury Index

1-10 year sector of the ITE State Street 05/23/07 3.95 4.26 0.19 0.14 161 100 - - United States Treasury

Corporate

Barclays Capital 1-3 Year CSJ iShares 01/05/07 1.81 1.9 7.5 0.2 702 - 75 25 US Credit Index

Barclays Capital Intermediate-term CIU iShares 01/05/07 4.2 5 3.1 0.2 1,318 - 65 35 US Credit Index

Barclays Capital US Credit CFT iShares 01/05/07 5.98 9.84 0.7 0.2 1,231 - 60 40 Bond Index

HYG iShares iBoxx $ Liquid High Yield Index 04/04/07 4.02 4.57 8.2 0.5 423 - - 100

LQD iShares Goldman Sachs $ InvesTop Index 07/22/02 6.98 11.73 12.9 0.15 598 - 67 33

77

Table 5

Descriptive Statistics Panel B

Panel B presents ticker symbols, issuer names, descriptions of underlying assets, inception dates, average duration (Dur.) and maturity (Mat.), net assets as of March 2011, expense ratio (Exp. Ratio), and breakdown of holdings showing number of issues held as of March 2011, percent held in US Treasury assets (Fed. Gov.), non-governmental investment-grade assets (Non-Gov. A), and low-grade assets (B-, C-, and Un-Rated), for broad-market, TIPS, MBS, and government agency assets.

Holdings Mar. 2011

Net B-, C- & Assets Exp. Fed. Non- Un- ETF / Incept. ($Bill.) Ratio Govt. Gov. A Rated Type Issuer Description Date Dur. Mat. Mar. 2011 (%) # (%) (%) (%)

Broad Market

AGG iShares Barclays Capital US Aggregate Index 09/22/03 4.61 6.5 11 0.24 723 40 48 12

BND Vanguard Barclays Capital Aggregate Bond Index 04/03/07 5.1 7.1 86.4 0.12 4,778 43 48 9

BSV Vanguard Gov., Corp., Intl. 1-5 Year Maturity 04/03/07 2.6 2.7 20.9 0.12 1,301 72 21 7

BIV Vanguard Gov., Corp., Intl. 5-10 Year Maturity 04/03/07 6.3 7.3 11.6 0.12 1,100 57 25 18

Barclays Capital US Long Govt/Cred. BLV Vanguard Float Adj. Index 04/03/07 12.8 23.2 3.8 0.12 1,120 44 33 23

LAG State Street USD investment grade bond 05/23/07 4.84 6.97 0.22 0.13 406 42 50 8

TIPS & Mortgage-Backed

Barclays U.S. Govt. Inflation- IPE State Street linked Bond Index 05/25/07 8.26 9.24 0.38 0.19 32 100 - -

Barclays Capital US Treasury TIP iShares Inflation Notes Index 12/04/03 5.22 8.7 19.2 0.2 32 100 - -

Barclays Capital US MBS MBB iShares Fixed-Rate Index 03/13/07 4.66 3.77 2.3 0.25 127 - 97 3

Government Agency

Barclays Capital US Govt/ GBF iShares Credit Bond Index 01/05/07 5.15 7.58 0.11 0.2 314 64 23 13

Barclays Capital US Intermed. GVI iShares Govt/Credit Bond Index 01/05/07 3.75 4.28 0.53 0.2 407 68 21 11

78

Table 6a Time Series: Bond Factors Treasury & Corporate

This table presents results for time series OLS regressions of individual corporrate bond ETF excess returns on the two Fama-French bond factors: DEF, and TERM. Significance at the 0.10 level is indicated by boldface, and significance levels are indicated by asterisks: 0.10 (*), 0.05 (**), and 0.01 (***).

intercept DEF TERM Adj. R2

Treasury

0.0003 0.0097 -0.0034 BIL (0.389) (1.386) (-1.788*) 0.0436

0.0006 0.0157 -0.0053 SHV (0.808) (2.114**) (-2.638**) 0.1377

0.0036 0.0435 -0.0183 SHY (1.212) (1.452) (-2.236**) 0.0785

0.0058 0.1032 -0.0372 IEI (0.717) (1.254) (-1.652) 0.0299

0.0041 0.1669 -0.0488 IEF (0.291) (1.171) (-1.251) 0.0050

0.0012 0.1832 -0.0429 TLH (0.063) (0.904) (-0.774) -0.0226

-0.0020 0.2629 -0.0584 TLT (-0.069) (0.901) (-0.732) -0.0238

0.0036 0.1004 -0.0311 ITE (0.527) (1.466) (-1.661) 0.0391

Corporate

-0.0027 0.0504 0.0105 CFT (-0.185) (0.344) (0.262) -0.0428

-0.0016 0.0548 0.0047 CIU (-0.139) (0.469) (0.147) -0.0416

-0.0027 0.0857 -0.0066 CSJ (-0.390) (1.234) (-0.350) -0.0114

-0.0084 -0.0114 0.0515 HYG (-0.266) (-0.036) (0.586) -0.0404

-0.0144 0.1877 0.0089 LQD (-0.730) (0.938) (0.163) -0.0212

79

Table 6b Time Series: Bond Factors Broad-Market, TIPS, MBS, and Agency

This table presents results for time series OLS regressions of individual corporrate bond ETF excess returns on the two Fama-French bond factors: DEF, and TERM. Significance at the 0.10 level is indicated by boldface, and significance levels are indicated by asterisks: 0.10 (*), 0.05 (**), and 0.01 (***).

intercept DEF TERM Adj. R2

Broad-Market

-0.0010 0.1027 -0.0144 AGG (-0.111) (1.127) (-0.578) -0.0165

-0.0005 0.1133 -0.0150 BIV (-0.041) (0.873) (-0.422) -0.0299

-0.0026 0.1044 -0.0037 BLV (-0.121) (0.487) (-0.064) -0.0436

0.0003 0.0800 -0.0111 BND (0.039) (0.975) (-0.494) -0.0248

0.0007 0.0872 -0.0183 BSV (0.116) (1.363) (-1.044) 0.0061

-0.0021 0.1029 -0.0094 LAG (-0.320) (1.516) (-0.505) 0.0070

TIPS

0.0193 -0.0238 -0.0459 IPE (1.372) (-0.166) (-1.174) -0.0067

0.0178 -0.0026 -0.0472 TIP (1.230) (-0.018) (-1.174) -0.0106

Govt. Agency & MBS

-0.0022 0.1206 -0.0158 GBF (-0.223) (1.207) (-0.576) -0.0122

-0.0002 0.1034 -0.0178 GVI (-0.029) (1.211) (-0.763) -0.0092

-0.0024 0.0873 -0.0040 MBB (-0.401) (1.443) (-0.241) 0.0034

80

Table 7a Time Series: Stock and Market Factors Treasury & Corporate

This table presents results for time series OLS regressions of individual corporrate bond ETF excess returns on the two Fama-French stock factors, SMB, HML, and the market factor, MKTRF. Significance at the 0.10 level is indicated by boldface, and significance levels are indicated by asterisks: 0.10 (*), 0.05 (**), and 0.01 (***).

intercept MKTRF SMB HML Adj. R2

Treasury

0.0002 -0.0750 0.0973 0.0810 BIL (1.023) (-1.833*) (1.006) (1.061) 0.0251

0.0006 -0.1147 -0.1313 0.1875 SHV (3.400***) (-2.759***) (-1.335) (2.416**) 0.1901

0.0030 -0.4695 -0.8625 0.7597 SHY (4.444***) (-3.118***) (-2.421*) (2.702*) 0.3064

0.0061 -0.9070 -2.1974 1.1778 IEI (3.099***) (-2.075**) (-2.125**) (1.443) 0.1834

0.0072 -0.9094 -2.8558 1.1351 IEF (1.976*) (-1.124) (-1.492) (0.752) 0.0453

0.0080 -0.7194 -4.0591 1.6738 TLH (1.538) (-0.623) (-1.486) (0.776) 0.0091

0.0081 -2.3041 -3.9120 3.7265 TLT (1.083) (-1.398) (-1.003) (1.211) 0.0252

0.0049 -0.7134 -1.4621 0.8754 ITE (2.851***) (-1.877*) (-1.627) (1.234) 0.1189

Corporate

0.0049 2.3647 -0.9987 -1.2628 CFT (1.402) (3.071***) (-0.548) (-0.879) 0.1383

0.0045 1.9389 -0.7784 -2.0216 CIU (1.634) (3.175***) (-0.539) (-1.773*) 0.1515

0.0033 0.9952 -0.5319 -0.5638 CSJ (1.925*) (2.600**) (-0.587) (-0.789) 0.0840

0.0019 7.5747 5.3752 -3.1401 HYG (0.369) (6.677***) (2.003.) (-1.483) 0.6130

0.0046 2.7962 -0.2532 -1.7182 LQD (0.934) (2.555**) (-0.098) (-0.841) 0.0891

81

Table 7b Time Series: Stock and Market Factors Broad-Market, TIPS, MBS, and Agency

This table presents results for time series OLS regressions of individual corporrate bond ETF excess returns on the two Fama-French stock factors, SMB, HML, and the market factor, MKTRF. Significance at the 0.10 level is indicated by boldface, and significance levels are indicated by asterisks: 0.10 (*), 0.05 (**), and 0.01 (***).

intercept MKTRF SMB HML Adj. R2

Broad-Market

0.0049 0.6761 -1.3253 0.3025 AGG (2.069**) (1.284) (-1.064) (0.308) -0.0109

0.0062 0.8831 -1.7202 -0.1762 BIV (1.838*) (1.175) (-0.968) (-0.126) -0.0286

0.0068 1.1405 -2.2722 0.4440 BLV (1.213) (0.918) (-0.774) (0.192) -0.0426

0.0051 0.5619 -1.2748 0.2717 BND (2.372**) (1.187) (-1.139) (0.308) -0.0151

0.0042 0.2403 -1.2012 0.3649 BSV (2.456**) (0.639) (-1.350) (0.520) -0.0239

0.0052 0.3261 -1.6035 0.2729 LAG (2.941***) (0.827) (-1.720*) (0.371) 0.0024

TIPS

0.0056 1.9669 -2.4140 -1.4556 IPE (1.565) (2.484**) (-1.289) (-0.985) 0.0806

0.0056 2.1115 -2.1828 -1.1778 TIP (1.530) (2.610**) (-1.141) (-0.780) 0.0870

Govt. Agency & MBS

0.0050 0.7700 -1.7238 -0.3089 GBF (1.912*) (1.332) (-1.261) (-0.286) -0.0081

0.0046 0.5565 -1.2081 -0.3359 GVI (2.054**) (1.115) (-1.023) (-0.361) -0.0278

0.0050 0.1061 -1.5022 0.1949 MBB (3.153***) (0.304) (-1.818*) (0.299) 0.0106

82

Table 8a Time Series: Five-Factor Model Treasury

This table presents results for time series OLS regressions of individual Treasury bond ETF excess returns on the five Fama-French factors: MKTRF, SMB, HML, DEF, and TERM. Significance at the 0.10 level is indicated by boldface, and significance levels are indicated by asterisks: 0.10 (*), 0.05 (**), and 0.01 (***).

intercept MKTRF SMB HML DEF TERM Adj. R2

0.0004 -0.0658 0.1168 0.1133 0.0106 -0.0042 BIL (0.550) (-1.652) (1.237) (1.509) (1.484) (-2.144**) 0.0977

0.0006 -0.1005 -0.1105 0.2334 0.0165 -0.0054 SHV (0.959) (-2.632**) (-1.221) (3.241***) (2.404**) (-2.870***) 0.3321

0.0036 -0.4340 -0.7908 0.8829 0.0409 -0.0158 SHY (1.465) (-2.974***) (-2.285**) (3.208***) (1.564) (-2.202**) 0.3632

0.0057 -0.8335 -2.0983 1.4121 0.0854 -0.0269 IEI (0.768) (-1.884*) (-2.000*) (1.692*) (1.077) (-1.237) 0.1827

0.0037 -0.7824 -2.7735 1.5026 0.1490 -0.0360 IEF (0.263) (-0.948) (-1.417) (0.965) (1.007) (-0.889) 0.0283

-0.0001 -0.5659 -4.0775 2.0686 0.1820 -0.0297 TLH (-0.006) (-0.477) (-1.448) (0.924) (0.855) (-0.510) -0.0230

-0.0018 -2.0923 -3.8961 4.2887 0.2505 -0.0459 TLT (-0.063) (-1.235) (-0.969) (1.342) (0.825) (-0.552) -0.0071

0.0036 -0.6368 -1.3872 1.1075 0.0894 -0.0247 ITE (0.554) (-1.668) (-1.531) (1.538) (1.306) (-1.317) 0.1300

Table 8b Time Series: Five-Factor Model Corporate

This table presents results for time series OLS regressions of individual corporrate bond ETF excess returns on the five Fama-French factors: MKTRF, SMB, HML, DEF, and TERM. Significance at the 0.10 level is indicated by boldface, and significance levels are indicated by asterisks: 0.10 (*), 0.05 (**), and 0.01 (***).

intercept MKTRF SMB HML DEF TERM Adj. R2

-0.0061 2.4764 -1.1682 -1.0406 0.1351 -0.0034 CFT (-0.460) (3.139***) (-0.624) (-0.699) (0.955) (-0.088) 0.1155

-0.0041 2.0165 -0.9268 -1.8800 0.0943 0.0012 CIU (-0.390) (3.216***) (-0.623) (-1.590) (0.839) (0.039) 0.1257

-0.0043 1.1014 -0.6054 -0.3159 0.1269 -0.0135 CSJ (-0.666) (2.898***) (-0.672) (-0.441) (1.864*) (-0.723) 0.1174

-0.0163 7.8732 5.2680 -2.4020 0.3551 -0.0495 HYG (-0.851) (6.961***) (1.964*) (-1.126) (1.752*) (-0.892) 0.6239

-0.0183 3.0459 -0.5814 -1.2006 0.3010 -0.0135 LQD (-0.986) (2.768***) (-0.223) (-0.578) (1.526) (-0.250) 0.0994

83

Table 8c Time Series: Five-Factor Model Broad-Market

This table presents results for time series OLS regressions of individual broad-market bond ETF excess returns on the five Fama-French factors: MKTRF, SMB, HML, DEF, and TERM. Significance at the 0.10 level is indicated by boldface, and significance levels are indicated by asterisks: 0.10 (*), 0.05 (**), and 0.01 (***).

intercept MKTRF SMB HML DEF TERM Adj. R2

-0.0028 0.8018 -1.3714 0.6130 0.1496 -0.0207 AGG (-0.308) (1.516) (-1.093) (0.615) (1.578) (-0.799) 0.0030

-0.0026 1.0115 -1.7979 0.1282 0.1533 -0.0176 BIV (-0.200) (1.318) (-0.988) (0.089) (1.115) (-0.467) -0.0489

-0.0054 1.2825 -2.4329 0.7493 0.1707 -0.0107 BLV (-0.250) (1.002) (-0.801) (0.310) (0.745) (-0.171) -0.0823

-0.0012 0.6604 -1.3190 0.5115 0.1173 -0.0153 BND (-0.149) (1.378) (-1.160) (0.566) (1.366) (-0.650) -0.0180

-0.0003 0.3351 -1.1968 0.6154 0.1121 -0.0202 BSV (-0.054) (0.893) (-1.344) (0.869) (1.667) (-1.097) 0.0027

-0.0035 0.4302 -1.7146 0.4996 0.1252 -0.0086 LAG (-0.528) (1.096) (-1.842*) (0.675) (1.779*) (-0.449) 0.0327

Table 8d Time Series: Five-Factor Model TIPS

This table presents results for time series OLS regressions of individual Treasury Inflation Protected Securties ETF excess returns on the five Fama-French factors: MKTRF, SMB, HML, DEF, and TERM. Significance at the 0.10 level is indicated by boldface, and significance levels are indicated by asterisks: 0.10 (*), 0.05 (**), and 0.01 (***).

intercept MKTRF SMB HML DEF TERM Adj. R2

0.0162 1.9923 -2.0500 -1.2367 0.0241 -0.0479 IPE (1.191) (2.474**) (-1.073) (-0.814) (0.167) (-1.211) 0.0701

0.0144 2.1730 -1.8189 -0.8644 0.0668 -0.0553 TIP (1.042) (2.652**) (-0.936) (-0.559) (0.455) (-1.376) 0.0846

Table 8e Time Series: Five-Factor Model Government Agency & MBS

This table presents results for time series OLS regressions of individual US federal agency credit and mortgage- backed securities ETF excess returns on the five Fama-French factors: MKTRF, SMB, HML, DEF, and TERM. Significance at the 0.10 level is indicated by boldface, and significance levels are indicated by asterisks: 0.10 (*), 0.05 (**), and 0.01 (***).

intercept MKTRF SMB HML DEF TERM Adj. R2

-0.0041 0.8960 -1.8122 -0.0152 0.1507 -0.0159 GBF (-0.413) (1.534) (-1.308) (-0.014) (1.440) (-0.553) -0.0063

-0.0016 0.6611 -1.2408 -0.0750 0.1245 -0.0179 GVI (-0.185) (1.309) (-1.036) (-0.079) (1.375) (-0.723) -0.0293

-0.0033 0.1828 -1.6421 0.3376 0.0931 0.0004 MBB (-0.565) (0.521) (-1.975*) (0.511) (1.482) (0.024) 0.0253

84

Table 9a GLS Whole Sample

This table presents results of two-step cross-sectional asset pricing tests following Kan, Robotti, and Shanken (2009) that begin by estimating betas from first-pass time series regressions, and then regressing returns on the first-pass betas in a second-pass cross-sectional regression, as per Fama and MacBeth (1973). The first row in each panel reports the estimates of each factor's price of covariance risk (γ) or risk premium (λ), followed by uncorrected (tfm), Shanken EIV-corrected (ts), Jagannathan and Wang EIV-corrected (tjw), and Kan, et al., misspecification-corrected (tkrs) t- statistics. In other words, γ tests for whether the factor is priced (Panel A), and λ tests for whether the factor helps to explain variation in returns (Panel B). These results are calculated using GLS, and significance is indicated with boldface. R2 and the probability value of the null hypothesis that R2=1 are provided to the right of each table. Table 2.3a covers the whole sample, and Table 2.3b covers the Treasury sub-sample.

intercept MKT SMB HML DEF TERM Panel A

γ 0.0002 0.0007 -0.0012 -0.0002 0.0076 -0.0140 R2 0.3433

2 tfm 1.7684 0.0686 -2.8238 -0.3458 1.2565 -0.6016 p(R =1) 0.3095

ts 1.4254 0.0661 -2.5590 -0.3519 1.1046 -0.5241

tjw 1.2722 0.0630 -2.4419 -0.3346 1.1326 -0.4857

tkrs 1.1964 0.0633 -2.3661 -0.3515 1.0188 -0.3639 Panel B λ 0.0002 5.4578 -338.2269 57.8686 16.0944 -2.0229

tfm 1.7684 1.5990 -3.3594 0.6871 1.6745 -0.7509

ts 1.4254 1.2647 -2.5029 0.5519 1.3221 -0.6027

tjw 1.2722 1.8852 -3.0096 0.7172 1.4030 -0.5842

tkrs 1.1964 1.6359 -2.8022 0.6797 1.2192 -0.4653

Table 9b GLS Treasury

intercept MKT SMB HML DEF TERM Panel A

γ -0.0002 0.0045 -0.0011 0.0002 0.0019 -0.1058 R2 0.8887

2 tfm -0.7064 0.1843 -1.5730 0.1573 0.0698 -1.3891 p(R =1) 0.6557

ts -0.4208 0.1225 -0.9721 0.0973 0.0418 -0.8375

tjw -0.4160 0.1249 -1.3041 0.1057 0.0592 -0.9462

tkrs -0.4162 0.1162 -1.1583 0.0918 0.0362 -0.6430 Panel B λ -0.0002 6.0596 -278.6630 177.1338 24.2372 -13.2334

tfm -0.7069 1.0099 -1.7639 1.0789 0.6637 -1.9494

ts -0.4208 0.5987 -1.0368 0.6392 0.3944 -1.1427

tjw -0.4160 0.6840 -1.4904 0.7393 0.5600 -1.1517

tkrs -0.4162 0.6843 -1.4771 0.6259 0.3725 -0.9555

85

Table 10a ICAPM Whole Sample

This table presents results for the five-factor intertemporal CAPM proposed by Petkova (2006), following Kan, Robotti, and Shanken (2009). The first row in each panel reports the estimates of each factor's price of covariance risk (γ) or risk premium (λ), followed by uncorrected (tfm), Shanken EIV-corrected (ts), Jagannathan and Wang EIV-corrected (tjw), and Kan, et al., misspecification- corrected (tkrs) t-statistics. In other words, γ tests for whether the factor is priced (Panel A), and λ tests for whether the factor helps to explain variation in returns (Panel B). These results are calculated using GLS, and significance is indicated with boldface. R2 and the probability value of the null hypothesis that R2=1 are provided to the right of each table. Table 2.3a covers the whole sample, and Table 2.3b covers the Treasury sub-sample. R2 0.2933

intercept MKT SMB HML DEF TERM p(R2=1) 0.2364 Panel A

γ 0.0003 0.0126 -0.0011 -0.0004 0.0017 0.0025

tfm 3.0705 1.3216 -2.8289 -0.7008 1.0261 0.5087

ts 2.4160 1.2472 -2.5221 -0.6258 0.9380 0.4675

tjw 2.5415 1.2630 -2.3875 -0.5755 0.9822 0.4267

tkrs 2.2461 1.1894 -2.3388 -0.5179 0.8731 0.3672 Panel B λ 0.0003 10.9751 -341.5841 -84.9609 32.9684 2.9990

tfm 3.0705 2.6352 -3.2030 -0.8348 1.4647 0.4357

ts 2.4160 1.9749 -2.3489 -0.6535 1.1347 0.3423

tjw 2.5415 2.3654 -2.7854 -0.6512 1.4026 0.2867

tkrs 2.2461 2.1226 -2.5793 -0.5546 1.1357 0.2617

Table 10b ICAPM Treasury R2 0.7217

intercept MKT SMB HML DEF TERM p(R2=1) 0.7699 Panel A

γ -0.0000 0.1051 0.0008 0.0049 0.0135 -0.0091

tfm -0.0017 2.1163 0.7661 2.0938 2.2814 -1.2355

ts -0.0006 0.7104 0.2638 0.7021 0.7748 -0.4828

tjw -0.0005 0.8530 0.2906 0.7499 0.9698 -0.4703

tkrs -0.0004 0.5132 0.2106 0.4660 0.5638 -0.4152 Panel B λ -0.0000 32.1156 -304.8039 458.5230 193.3640 -13.8055

tfm -0.0017 2.0686 -1.7513 1.9553 2.2533 -1.3653

ts -0.0006 0.6814 -0.5778 0.6445 0.7415 -0.4511

tjw -0.0005 0.8263 -0.5075 0.5137 0.9225 -0.4720

tkrs -0.0004 0.5488 -0.5095 0.3778 0.5586 -0.4177

86

Table 11 Fixed Effects

This table presents results from fixed-effects regressions. The sample includes 43 monthly returns for 24 bond ETFs, yielding a total of 1,032 observations in the full sample; for 8 Treasury ETFs, yielding a total of 344 observations; and for 16 non- Treasury ETFs, yielding a total of 688 observations. A Hausman (1978) test fails to reject the null hypothesis that random effects is incompatible with fixed effects. Significance at the 0.10 level is indicated by boldface, and significance levels are indicated by asterisks: 0.10 (*), 0.05 (**), and 0.01 (***).

MKTRF SMB HML DEF TERM Adj. R2

0.0744 -0.1091 0.0210 0.1302 -0.0207 Whole Sample (5.394***) (-3.336***) (0.806) (4.388***) (-2.549**) 0.0449

-0.0574 -0.1564 0.1209 0.1030 -0.0236 Treasury (-2.458**) (-2.824***) (2.745***) (2.051**) (-1.713*) 0.0753

87

Shares HYG • 10129110 0&31110 (HYG) 04130110 Index 02126110 06130110 12131/W Yield 101301W Outstanding 0&31/W High 06I301W Shares 04I301W of Liquid 02/27109 $ ,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-, I 12/31108 Number 10131108 iBoxx 06129108 06130108 Monthly iSheres 1 : 12/3110704130108 Fig. 1013110702129108 Ct6I29/07 041301070&31107 L-,.,o,.,o,o,o,I,I,I,I",l,IlU,Il DATE '~ 20000 30000 70000 50000 9OOOO~-- 40000 60000 80000

88 Growth Share HYO • ~ J (HYG) Index Outstanding Yield 02126110 06131110 Shares High in 06I31/W Liquid Growth $ 02l27/W iBoxx Percentage 06129108 iSheres Monthly 2 : 02129108 Fig. 31107 1 DATE 08 06 04 02 ~4~'-- -02

89 ~ I

(') >- I -x "0 "C "0a; >= C .c Cl 8" 0 I is :Q E :> - .2 C- E ::J ~ Q. '" ~ ~ .~ 0 '" 0 '"~ "OJ .c Ul

'"Cl , u: I ~ ~

~- j 0 0 0 0" 0 ~ ~ ~ 8 0 §- 0 8 0 0 0 0 9 9

90 Fig. 4 Bond ETF Market Growth

Number of Bond ElFs

140 I

120

100

80

60

40

20

0 -~-~-~-~-~ 2002 2003 2004 2005 2006 2007 2006 2009 2010 Bond ElF Assets $Billion 140

120

100

80

60

40 20 -~-~_~.~.~I~ 0 2002 2003 2004 2005 2006 2007 2006 2009 2010

Data: Morningstar and National Stock Exchange

91 Fig. 5 ETF, CEF, OEF, OTC Comparison

ETF CEF OEF OTC Small Large Spot Premium/Discount At NAV Premium Discount ('NAV') Intraday Trading Yes Yes No No Short-Sell Yes Yes No No Buy on Margin Yes Yes No No Spot Fund Size Variable Fixed Variable (n/a) Rebalancing Taxable No No Yes Yes Retail: Secondary Secondary Market Secondary Primary AP: Primary Broker/Dealer Typical Increment $100 $100 $2,500 (to open) $10,000

92 Fig. 6 Trading Strategies

Yield Curve Treasury/Corporate TLT/SHY IEF/LQD

Investment-Grade/Low-Grade Corporate Debt/Equity LQD/HYG LQD/SPY

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