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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 of his 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 of Philosophy.
SUPERVISORY COMMTITEE:
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Dissertation Advisor
Emilio Zarruk, Ph.D.
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J. Dennis Coates, Ph.D.
Dean, College of Business
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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
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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 mortgagebacked 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
below.
For brevity, mortgage-backed and Treasury inflation-protected securities are referred to as 'bonds'
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 flowinduced 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 fixedincome 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):
∆pit = αi + γ1iεi,t-1 + γ2iε2i,t-1 + βi∆nit + ωit
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
(5)
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
34
(6)
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:
∆ln(pt) = α + β∆ln(nt) + γ1εi,t-1 + γ2iε2i,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 errorcorrection 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-tomarket. 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 crosssection 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 threefactor 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 BlackScholes (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 ndimensional 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 closedform 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 reinvestment 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 ,SMB SMBt   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
6
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
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-tomarket 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-invariables (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 timeseries, 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 FamaFrench 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 broadmarket, 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 smallsample 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.
ETF /
Type
Issuer
Description
Inception
Date
Duration
(years)
Maturity
(years)
Dividend
Rate (%)
Expense
Ratio
(%)
Broad Market
Mean Market
Capitalization
($Billion)
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
ln(High/Low)
(2008-2009)
ETF /
Type
Median
(%)
Mean
(%)
Closing Bid-Ask Spread
ln(Ask/Bid)
(2008-2009)
Std. Dev.
(%)
Median
(%)
Mean
(%)
Daily Premium
ln(Midquote/NAV)
(2008-2009)
Std. Dev.
(%)
Median
(%)
Mean
(%)
Premium / Bid-Ask
(2008-2009)
Std. Dev.
(%)
Median
Mean
Std. Dev.
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
ln(High/Low)
(inception-2009)
ETF /
Type
Median
(%)
Mean
(%)
Closing Bid-Ask Spread
ln(Ask/Bid)
(inception-2009)
Std. Dev.
(%)
Median
(%)
Mean
(%)
Daily Premium
ln(Midquote/NAV)
(inception-2009)
Std. Dev.
(%)
Median
(%)
Mean
(%)
Premium / Bid-Ask
(inception-2009)
Std. Dev.
(%)
Median
Mean
Std. Dev.
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
∆ln(pt) = α + β∆ln(nt) + γ1εt-1 + νt
ETF
α
β
γ
Rockets & Feathers
∆ln(pt) = α + β∆ln(nt) + γ1εt-1 + γ2ε2t-1 + νt
2
1
Adj. R
σ
α
β
γ
γ
2
1
2
Adj. R
σ
IEF
0.0000
(-0.003)
1.0110
(2.139**)
-0.9293
(-40.124***)
0.9522
0.0010
0.0000
(0.629)
1.0104
(2.019**)
-0.9579
(-38.344***)
-14.6569
(-3.018***)
0.9524
0.0010
TLT
0.0000
(0.023)
0.9856
(-2.844***)
-0.9341
(-39.928***)
0.9517
0.0017
0.0000
(0.547)
0.9854
(-2.894***)
-0.9410
(-39.872***)
-7.0398
(-2.108**)
0.9518
0.0017
IEI
0.0000
(-0.029)
1.0051
(0.499)
-0.8509
(-23.204***)
0.9251
0.0010
0.0000
(-0.019)
1.0051
(0.499)
-0.8521
(-20.351***)
-0.3690
(-0.058)
0.9250
0.0010
SHY
0.0000
(0.023)
0.9857
(-2.050**)
-0.6557
(-30.381***)
0.9122
0.0004
0.0000
(-0.675)
0.9867
(-1.908*)
-0.6586
(-30.491***)
40.5297
(2.222**)
0.9124
0.0004
TIP
0.0000
(0.021)
0.9560
(-4.502***)
-0.1908
(-12.809***)
0.8578
0.0017
0.0000
(-1.022)
0.9549
(-4.644***)
-0.2298
(-13.724***)
5.4857
(4.963***)
0.8599
0.0017
SHV
0.0000
(0.107)
0.9225
(-4.302***)
-0.4639
(-15.195***)
0.7788
0.0003
0.0000
(0.017)
0.9225
(-4.301***)
-0.4666
(-14.197***)
8.4761
(0.226)
0.7785
0.0003
MBB
0.0000
(0.045)
0.9768
(-1.047)
-0.7843
(-21.097***)
0.7405
0.0017
0.0000
(-0.317)
0.9779
(-0.996)
-0.7961
(-21.066***)
7.8669
(1.673*)
0.7412
0.0017
BIV
0.0000
(-0.006)
0.9960
(-0.153)
-0.2191
(-9.282***)
0.6720
0.0032
-0.0001
(-0.490)
0.9954
(-0.173)
-0.1984
(-8.048***)
2.2811
(2.783***)
0.6751
0.0032
0.5301
0.0004
0.0000
(0.401)
0.9751
(-0.642)
-0.3572
(-10.252***)
-24.1985
(-1.685*)
0.5314
0.0004
BIL
0.0000
(-0.029)
0.9807
(-0.498)
-0.3858
(-12.662***)
AGG
0.0000
(-0.029)
0.9696
(-1.266)
-0.1955
(-13.141***)
0.5125
0.0025
0.0000
(-0.708)
0.9679
(-1.347)
-0.1201
(-6.150***)
2.3497
(5.885***)
0.5224
0.0025
BND
0.0000
(-0.010)
0.9841
(-0.407)
-0.2633
(-10.299***)
0.4953
0.0032
-0.0002
(-1.392)
1.0067
(0.180)
-0.1937
(-7.656***)
7.0401
(9.268***)
0.5493
0.0030
TFI
0.0000
(-0.018)
0.9416
(-1.229)
-0.6248
(-16.125***)
0.4775
0.0042
-0.0001
(-0.817)
0.9665
(-0.712)
-0.5344
(-12.368***)
6.7337
(4.460***)
0.4935
0.0041
MUB
0.0000
(-0.038)
0.9619
(-0.843)
-0.1951
(-7.957***)
0.4291
0.0037
-0.0001
(-0.382)
0.9651
(-0.772)
-0.1880
(-7.482***)
1.2796
(1.277)
0.4297
0.0037
LQD
0.0000
(0.002)
0.9461
(-2.083**)
-0.1835
(-13.831***)
0.4203
0.0043
-0.0002
(-1.803*)
0.9273
(-2.389***)
-0.0974
(-6.508***)
3.1012
(11.233***)
0.4556
0.0042
JNK
0.0000
(0.029)
1.0801
(1.287)
-0.2509
(-8.850***)
0.4022
0.0112
-0.0011
(-2.169**)
1.1651
(2.677***)
-0.3658
(-11.086***)
3.8972
(6.249***)
0.4416
0.0108
BSV
0.0000
(0.020)
0.9966
(-0.069)
-0.1359
(-7.212***)
0.3916
0.0026
-0.0001
(-1.015)
0.9831
(-0.341)
-0.1352
(-7.243***)
3.8519
(3.803***)
0.4030
0.0026
CIU
0.0000
(0.058)
0.8658
(-2.769***)
-0.1117
(-6.596***)
0.2964
0.0043
0.0000
(0.085)
0.8655
(-2.768***)
-0.1118
(-6.575***)
-0.0572
(-0.093)
0.2955
0.0043
SHM
0.0000
(0.013)
0.9228
(-0.632)
-0.3777
(-11.541***)
0.2336
0.0032
0.0000
(0.029)
0.9225
(-0.634)
-0.3798
(-8.586***)
-0.1311
(-0.073)
0.2323
0.0032
HYG
0.0000
(0.001)
0.9718
(-0.339)
-0.2059
(-7.955***)
0.1667
0.0109
-0.0008
(-1.910*)
0.9880
(-0.149)
-0.2365
(-9.226***)
2.4665
(6.401***)
0.2113
0.0106
CSJ
0.0000
(0.130)
0.7042
(-3.221***)
-0.0983
(-6.163***)
0.0948
0.0044
-0.0003
(-1.693*)
0.6787
(-3.541***)
-0.0930
(-5.899***)
3.0626
(4.744***)
0.1194
0.0043
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
∆ln(pt) = α + β∆ln(nt) + γ1εt-1 + νt
ETF
α
β
γ
Rockets & Feathers
∆ln(pt) = α + β∆ln(nt) + γ1εt-1 + γ2ε2t-1 + νt
2
1
Adj. R
σ
α
β
γ
γ
2
1
2
Adj. R
σ
TLT
0.0000
(0.071)
0.9801
(-4.069***)
-0.8841
(-17.713***)
0.9905
0.0017
-0.0001
(-0.895)
0.9811
(-3.888***)
-0.8738
(-17.584***)
29.1837
(2.622***)
0.9907
0.0017
IEF
0.0000
(0.085)
0.9898
(-2.072**)
-0.9410
(-18.364***)
0.9905
0.0009
-0.0001
(-1.053)
0.9918
(-1.681*)
-0.8814
(-16.826***)
61.4932
(4.025***)
0.9909
0.0009
IEI
0.0000
(0.117)
0.9816
(-1.542)
-0.9621
(-11.749***)
0.9778
0.0010
0.0000
(0.353)
0.9802
(-1.640)
-0.9809
(-11.500***)
-19.8602
(-0.800)
0.9778
0.0010
SHY
0.0000
(0.071)
0.9870
(-1.717*)
-0.7150
(-14.475***)
0.9777
0.0003
0.0000
(-1.624)
0.9849
(-2.037**)
-0.7466
(-15.372***)
242.9510
(4.686***)
0.9789
0.0003
TIP
0.0000
(0.015)
1.0231
(2.146**)
-0.3318
(-8.184***)
0.9665
0.0018
0.0000
(-0.386)
1.0253
(2.341**)
-0.3663
(-8.241***)
6.4558
(1.858*)
0.9667
0.0018
MBB
0.0000
(-0.001)
1.0156
(0.814)
-0.6638
(-8.295***)
0.9514
0.0014
-0.0002
(-1.258)
1.0213
(1.128)
-0.8012
(-8.473***)
77.4032
(2.602**)
0.9533
0.0013
SHV
0.0000
(0.016)
0.9767
(-1.232)
-0.4312
(-6.440***)
0.9455
0.0003
0.0000
(0.294)
0.9772
(-1.205)
-0.3918
(-4.943***)
-59.4942
(-0.929)
0.9454
0.0003
TFI
0.0000
(-0.104)
1.0492
(1.970*)
-0.7006
(-7.995***)
0.9383
0.0034
-0.0001
(-0.393)
1.0443
(1.693*)
-0.6852
(-7.508***)
8.6889
(0.622)
0.9380
0.0034
BIV
0.0000
(-0.083)
1.0525
(1.918*)
-0.4335
(-6.213***)
0.9157
0.0028
-0.0004
(-1.527)
1.0491
(1.865*)
-0.5338
(-7.349***)
31.3699
(3.572***)
0.9223
0.0027
BND
0.0000
(-0.123)
1.0380
(1.091)
-0.2975
(-4.965***)
0.8650
0.0026
0.0001
(0.317)
1.0349
(0.996)
-0.2360
(-2.621***)
-7.9655
(-0.917)
0.8648
0.0026
LQD
0.0000
(-0.014)
1.1620
(6.000***)
-0.3864
(-10.959***)
0.8278
0.0048
-0.0001
(-0.562)
1.1556
(5.771***)
-0.3385
(-8.420***)
2.7025
(2.432**)
0.8299
0.0048
0.7855
0.0128
-0.0016
(-1.145)
0.9714
(0.568)
-0.8196
(-6.589***)
8.0993
(2.177**)
0.7928
0.0125
JNK
-0.0001
(-0.107)
0.9552
(-0.884)
-0.6305
(-6.960***)
MUB
0.0000
(-0.057)
0.9872
(-0.267)
-0.8555
(-9.221***)
0.7810
0.0063
-0.0007
(-1.301)
0.9366
(1.350)
-0.7159
(-7.619***)
16.3286
(4.017***)
0.8061
0.0059
BIL
0.0000
(-0.069)
1.0708
(1.194)
-0.9054
(-10.405***)
0.7468
0.0006
0.0000
(0.532)
1.0550
(0.941)
-0.6806
(-5.525***)
-81.2665
(-2.528**)
0.7568
0.0006
CIU
0.0000
(-0.033)
1.3478
(4.818***)
-0.3801
(-6.977***)
0.7080
0.0065
0.0004
(0.653)
1.3059
(3.964***)
-0.3612
(-6.484***)
-4.2365
(-1.492)
0.7103
0.0065
HYG
0.0003
(0.212)
1.1835
(2.539***)
-0.7622
(-8.872***)
0.6554
0.0156
-0.0009
(-0.684)
1.1456
(2.037**)
-0.7422
(-8.850***)
3.8768
(2.971***)
0.6737
0.0152
AGG
0.0000
(-0.011)
1.0916
(1.726*)
-0.6421
(-12.333***)
0.6257
0.0053
-0.0001
(-0.406)
1.0936
(1.780*)
-0.4250
(-4.387***)
3.6125
(2.647***)
0.6325
0.0053
SHM
0.0000
(-0.029)
0.9551
(-0.605)
-0.3898
(-5.153***)
0.6016
0.0031
0.0003
(1.102)
0.9294
(-0.969)
-0.6923
(-5.174***)
-22.4491
(-2.706***)
0.6229
0.0030
BSV
0.0000
(-0.052)
1.0856
(0.970)
-0.3340
(-5.267***)
0.5582
0.0040
-0.0003
(-0.738)
1.0623
(0.711)
-0.3285
(-5.251***)
9.0123
(2.246**)
0.5707
0.0039
CSJ
0.0000
(0.030)
1.1540
(1.491)
-0.2015
(-4.559***)
0.4557
0.0051
-0.0004
(-0.804)
1.1446
(1.402)
-0.2221
(-4.789***)
4.7236
(1.421)
0.4594
0.0050
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 (***).
α
β
γ1
TLT
-0.0027
(-0.819)
0.9634
(-6.886***)
-0.9442
(-39.365***)
0.0901
(1.129)
0.0003
(0.667)
0.0000
(0.402)
IEF
-0.0038
(-1.529)
0.9875
(-2.259**)
-0.9334
(-39.709***)
-0.1633
(-2.729***)
0.0005
(1.493)
IEI
-0.0035
(-0.472)
0.9583
(-3.659***)
-0.8182
(-22.593***)
0.2365
(2.915***)
SHY
-0.0021
(-0.984)
0.9570
(-5.629***)
-0.6775
(-30.231***)
TIP
-0.0185
(-2.642***)
0.9551
(-4.423***)
SHV
-0.0714
(-3.251***)
ETF
φ bid_ask
φ hi_lo
φ mkt_cap
φ v_nosh
ψ
cred
ψ
ted
ψ vix
δ SP
Adj. R2
σ
0.9560
0.0017
0.0000
(-0.643)
0.0051
(3.076***)
0.0003
(0.450)
0.0000
(0.334)
-0.0340
(-6.561***)
0.0000
(0.146)
-0.0001
(-2.255**)
0.0018
(1.867*)
0.0006
(1.623)
0.0000
(1.100)
-0.0165
(-5.536***)
0.9557
0.0010
0.0004
(0.501)
-0.0001
(-0.683)
-0.0001
(-1.858*)
0.0014
(1.395)
-0.0000
(-0.072)
-0.0000
(-0.366)
-0.0202
(-5.757***)
0.9329
0.0009
-0.0441
(-1.153)
0.0002
(0.826)
0.0000
(2.936***)
0.0000
(-3.286***)
0.0007
(2.043**)
0.0002
(1.767*)
-0.0000
(-1.812*)
-0.0076
(-7.033***)
0.9193
0.0004
-0.2434
(-13.446***)
0.2653
(3.249***)
0.0016
(2.204**)
0.0002
(3.496***)
0.0003
(3.518***)
-0.0024
(-1.338)
-0.0023
(-3.674***)
-0.0001
(-1.283)
-0.0152
(-2.592***)
0.8625
0.0017
0.8839
(-6.072***)
-0.5153
(-15.971***)
0.0600
(1.117)
0.0077
(3.252***)
-0.0001
(-3.058***)
0.0000
(0.387)
0.0012
(4.183***)
0.0006
(5.269***)
0.0000
(0.844)
-0.0002
(-0.206)
0.7931
0.0003
MBB
-0.0558
(-2.654***)
0.9720
(-1.159)
-0.7644
(-18.734***)
0.3589
(9.461***)
0.0063
(2.653***)
-0.0003
(-2.388**)
0.0001
(0.875)
-0.0087
(-4.371***)
-0.0006
(-0.813)
-0.0001
(-2.657***)
-0.0148
(-2.256**)
0.7775
0.0017
BIV
-0.0328
(-1.574)
1.0259
(0.894)
-0.2811
(-10.689***)
0.1246
(2.668***)
0.0038
(1.513)
0.0000
(-0.057)
-0.0002
(-0.794)
-0.0090
(-2.533**)
-0.0026
(-2.068**)
-0.0004
(-4.290***)
-0.0331
(-2.709***)
0.6883
0.0031
-0.4200
(-3.301***)
-0.0015
(-0.794)
-0.0006
(-1.674*)
0.0013
(2.329**)
0.0207
(1.669*)
-0.0030
(-0.430)
-0.0004
(-1.344)
0.1185
(2.936***)
0.5718
0.0099
JNK
0.0159
(0.883)
1.0756
(1.179)
-0.3981
(-12.092***)
BIL
-0.0664
(-3.388***)
0.9187
(-1.954*)
-0.4347
(-13.061***)
-0.0396
(-0.669)
0.0088
(3.416***)
0.0000
(-2.603***)
0.0000
(0.259)
0.0002
(0.394)
0.0010
(5.833***)
-0.0000
(-2.517**)
-0.0065
(-4.037***)
0.5664
0.0004
AGG
-0.0478
(-2.836***)
0.9995
(-0.020)
-0.2483
(-14.760***)
-0.2155
(-3.611***)
0.0053
(2.941***)
0.0000
(-0.714)
-0.0002
(-1.801*)
-0.0150
(-5.411***)
-0.0022
(-2.352**)
-0.0002
(-2.831***)
-0.0078
(-0.886)
0.5368
0.0025
TFI
-0.0416
(-1.947*)
0.9228
(-1.615)
-0.6826
(-16.711***)
-0.1519
(-2.121**)
0.0066
(1.927*)
-0.0001
(-0.462)
0.0012
(4.078***)
-0.0045
(-0.925)
-0.0091
(-4.852***)
-0.0000
(-0.122)
0.0089
(0.558)
0.5362
0.0041
BND
-0.0176
(-0.511)
1.0696
(1.647*)
-0.3137
(-10.490***)
0.0685
(0.856)
0.0017
(0.414)
0.0002
(1.176)
-0.0001
(-0.267)
-0.0099
(-2.744***)
-0.0037
(-2.932***)
-0.0001
(-1.499)
0.0104
(0.844)
0.5254
0.0032
LQD
-0.0330
(-2.363**)
0.9588
(-1.592)
-0.2303
(-15.862***)
-0.3982
(-5.401***)
0.0026
(2.034**)
0.0006
(2.740***)
0.0002
(1.119)
-0.0207
(-4.904***)
-0.0058
(-3.736***)
-0.0005
(-5.225***)
0.0085
(0.663)
0.4799
0.0042
MUB
0.0098
(0.282)
0.9670
(-0.717)
-0.2137
(-7.969***)
-0.1756
(-3.514***)
-0.0015
(-0.412)
0.0003
(0.891)
0.0002
(0.673)
-0.0026
(-0.595)
-0.0038
(-2.272**)
-0.0003
(-2.419**)
-0.0042
(-0.295)
0.4674
0.0036
HYG
-0.0160
(-0.665)
0.7652
(-3.064***)
-0.1598
(-6.283***)
0.0226
(0.179)
0.0018
(0.853)
-0.0001
(-0.230)
0.0004
(0.751)
-0.0286
(-2.688***)
-0.0078
(-2.112**)
-0.0012
(-4.641***)
0.1540
(4.364***)
0.4352
0.0092
BSV
-0.2347
(-5.972***)
0.9252
(-1.331)
-0.2219
(-9.507***)
0.2406
(5.111***)
0.0291
(6.044***)
-0.0013
(-5.903***)
-0.0004
(-1.988**)
-0.0025
(-0.840)
-0.0011
(-1.014)
-0.0001
(-1.278)
-0.0223
(-2.192**)
0.4288
0.0026
CIU
-0.1249
(-5.212***)
0.9394
(-1.234)
-0.2155
(-10.130***)
0.2231
(6.385***)
0.0129
(5.017***)
0.0005
(3.715***)
0.0002
(1.087)
-0.0178
(-3.754***)
-0.0079
(-4.814***)
-0.0002
(-1.579)
-0.0115
(-0.727)
0.3897
0.0041
SHM
-0.1648
(-4.505***)
0.9749
(-0.207)
-0.4775
(-13.415***)
-0.1660
(-4.121***)
0.0280
(4.605***)
-0.0009
(-5.020***)
0.0000
(0.159)
-0.0010
(-0.273)
0.0002
(0.112)
0.0000
(0.297)
0.0212
(1.747*)
0.3229
0.0031
CSJ
-0.2197
(-4.841***)
0.8113
(-2.024**)
-0.2535
(-10.706***)
0.1506
(2.696***)
0.0226
(4.580***)
0.0008
(5.186***)
0.0003
(1.756*)
-0.0173
(-3.525***)
-0.0090
(-5.451***)
-0.0003
(-2.141**)
-0.0148
(-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 firstpass 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 (***).
ψ vix
δ SP
Adj. R2
σ
-0.0007
(-1.122)
-0.0001
(-2.333**)
-0.0224
(-3.807***)
0.9909
0.0016
0.0008
(1.040)
-0.0004
(-1.031)
-0.0000
(-0.886)
-0.0089
(-2.675***)
0.9909
0.0009
0.0000
(-0.942)
0.0007
(2.697***)
-0.0001
(-0.748)
-0.0000
(-1.528)
-0.0027
(-2.256**)
0.9792
0.0003
-0.0002
(-1.031)
-0.0002
(-1.390)
0.0022
(2.050**)
-0.0002
(-0.448)
0.0000
(0.291)
-0.0049
(-1.012)
0.9784
0.0010
0.0022
(1.287)
0.0003
(2.429**)
0.0003
(2.031**)
-0.0011
(-0.729)
-0.0017
(-2.458**)
-0.0001
(-3.688***)
-0.0131
(-2.255**)
0.9689
0.0018
0.1205
(1.108)
0.0069
(1.553)
-0.0004
(-1.715*)
0.0004
(1.978*)
0.0001
(0.112)
-0.0021
(-3.527***)
-0.0001
(-2.477**)
-0.0136
(-2.729***)
0.9588
0.0013
-0.5535
(-6.859***)
0.3197
(1.674*)
0.0119
(1.602)
-0.0001
(-1.433)
0.0000
(-0.028)
0.0001
(0.313)
0.0004
(3.559***)
0.0000
(0.726)
0.0007
(0.562)
0.9504
0.0003
1.0137
(0.561)
-0.7796
(-8.641***)
-0.3258
(-2.752***)
-0.0054
(-0.846)
-0.0001
(-0.244)
0.0010
(2.440**)
-0.0068
(-2.159**)
0.0008
(0.529)
-0.0001
(-0.946)
-0.0152
(-1.144)
0.9483
0.0031
0.2069
(1.290)
0.0024
(0.426)
0.0002
(0.427)
-0.0002
(-0.338)
-0.0002
(-0.082)
-0.0027
(-2.489**)
-0.0001
(-2.277**)
-0.0112
(-1.331)
0.9230
0.0027
α
β
γ1
TLT
-0.0003
(-0.049)
0.9756
(-4.860***)
-0.9156
(-18.303***)
0.1571
(0.943)
-0.0000
(-0.002)
0.0001
(0.543)
-0.0001
(-1.538)
0.0009
(0.630)
IEF
0.0038
(0.666)
0.9870
(-2.519**)
-0.9639
(-18.724***)
0.4214
(2.197**)
-0.0004
(-0.559)
0.0000
(0.058)
-0.0001
(-1.334)
SHY
0.0033
(0.726)
0.9842
(-2.025**)
-0.7924
(-15.765***)
0.1737
(2.192**)
-0.0005
(-0.947)
0.0001
(3.318***)
IEI
-0.0162
(-0.862)
0.9704
(-2.281**)
-0.9758
(-11.679***)
-0.0806
(-0.288)
0.0021
(0.929)
TIP
-0.0247
(-1.562)
1.0176
(1.651*)
-0.3962
(-9.026***)
-0.2256
(-1.098)
MBB
-0.0606
(-1.553)
1.0096
(0.471)
-0.7680
(-8.712***)
SHV
-0.1107
(-1.603)
0.9515
(-2.398**)
TFI
0.0328
(0.830)
ETF
φ bid_ask
φ hi_lo
φ mkt_cap
φ v_nosh
ψ
cred
ψ
ted
BIV
-0.0222
(-0.494)
1.0310
(1.073)
-0.5289
(-6.335***)
BND
-0.0469
(-0.754)
1.0103
(0.302)
-0.6013
(-8.067***)
1.2568
(5.171***)
0.0049
(0.650)
0.0002
(0.664)
-0.0001
(-0.166)
-0.0014
(-0.661)
-0.0007
(-0.701)
-0.0002
(-3.246***)
0.0064
(0.885)
0.8929
0.0023
LQD
-0.0159
(-0.436)
1.1560
(6.062***)
-0.5054
(-12.989***)
0.3802
(1.390)
0.0005
(0.152)
0.0008
(1.437)
-0.0004
(-1.052)
-0.0202
(-4.914***)
-0.0045
(-2.631***)
-0.0002
(-1.929*)
0.0211
(1.289)
0.8494
0.0045
JNK
-0.0238
(-0.434)
1.0269
(0.376)
-0.7016
(-7.032***)
1.2172
(2.125**)
0.0036
(0.644)
-0.0011
(-1.113)
0.0019
(1.103)
-0.0146
(-1.342)
-0.0089
(-1.437)
0.0007
(2.571**)
0.1059
(2.285**)
0.8416
0.0112
MUB
-0.4653
(-3.272***)
0.9225
(-1.682*)
-0.9073
(-10.042***)
0.6359
(2.204**)
0.0449
(2.897***)
0.0024
(1.630)
0.0050
(3.456***)
-0.0071
(-1.270)
-0.0092
(-3.315***)
-0.0003
(-2.606**)
-0.0152
(-0.792)
0.8302
0.0055
CIU
-0.4109
(-5.569***)
1.2450
(4.103***)
-0.6182
(-10.704***)
1.2881
(7.480***)
0.0429
(5.428***)
0.0009
(2.480**)
0.0005
(0.970)
-0.0117
(-2.348**)
-0.0072
(-3.535***)
-0.0005
(-3.700***)
-0.0266
(-1.316)
0.8291
0.0050
BIL
-0.4668
(-3.779***)
1.0010
(0.019)
-1.1456
(-13.373***)
0.5750
(2.050**)
0.0610
(3.772***)
-0.0001
(-1.345)
0.0002
(2.742***)
-0.0002
(-0.304)
0.0000
(-0.206)
0.0000
(2.198**)
0.0017
(0.640)
0.8119
0.0006
AGG
-0.0143
(-0.224)
1.0778
(1.743*)
-0.8113
(-16.015***)
-2.5415
(-7.754***)
0.0022
(0.324)
-0.0002
(-0.782)
0.0000
(-0.019)
-0.0150
(-3.665***)
-0.0004
(-0.267)
-0.0005
(-5.608***)
-0.0145
(-1.034)
0.7626
0.0042
HYG
-0.0966
(-1.041)
1.2260
(2.806***)
-0.7409
(-8.840***)
2.0608
(2.743***)
0.0107
(1.349)
-0.0004
(-0.266)
0.0004
(0.196)
0.0252
(1.693*)
-0.0129
(-2.190**)
-0.0011
(-2.823***)
0.1187
(1.867*)
0.7372
0.0136
SHM
-0.2432
(-2.911***)
0.9140
(-1.250)
-0.5758
(-6.689***)
0.0363
(0.251)
0.0420
(3.014***)
-0.0016
(-3.799***)
-0.0006
(-1.115)
-0.0021
(-0.711)
-0.0019
(-1.414)
-0.0002
(-2.711***)
0.0108
(1.178)
0.6837
0.0028
BSV
-0.4537
(-3.497***)
0.9397
(-0.673)
-0.4080
(-5.649***)
0.2841
(1.340)
0.0568
(3.587***)
-0.0027
(-3.695***)
-0.0012
(-1.759*)
0.0024
(0.698)
-0.0020
(-1.339)
-0.0002
(-2.209**)
-0.0110
(-0.963)
0.6161
0.0037
CSJ
-0.2124
(-1.590)
1.1526
(1.532)
-0.5397
(-7.075***)
0.3624
(1.414)
0.0197
(1.359)
0.0020
(4.964***)
0.0011
(1.887*)
-0.0137
(-2.931***)
-0.0013
(-0.687)
-0.0003
(-2.311**)
-0.0410
(-2.224**)
0.5579
0.0046
74
Table 4
Expanded Rockets & Feathers
Panel A : Daily
∆ln(pt) = α + β∆ln(nt) + γ1εt-1 + γ2ε2t-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 (***).
ψ vix
δ SP
Adj. R2
σ
0.0002
(0.385)
0.0000
(0.347)
-0.0338
(-6.515)
***
0.9560
0.0017
0.0017
(1.845)
*
0.0005
(1.396)
0.0000
(1.122)
-0.0166
(-5.583)
***
0.9560
0.0010
-0.0001
(-1.767)
*
0.0014
(1.415)
-0.0000
(-0.101)
-0.0000
(-0.371)
-0.0202
(-5.756)
***
0.9329
0.0009
0.0000
(2.539)
**
0.0000
(-3.439)
***
0.0007
(1.965)
**
0.0003
(2.004)
**
-0.0000
(-1.895)
*
-0.0077
(-7.086)
***
0.9194
0.0004
0.0022
(2.958)
***
0.0002
(3.582)
***
0.0003
(3.633)
***
-0.0025
(-1.387)
-0.0022
(-3.461)
***
0.0000
(-0.878)
-0.0140
(-2.383)
**
0.8638
0.0017
0.0600
(1.064)
0.0077
(3.243)
***
-0.0001
(-3.017)
***
0.0000
(0.385)
0.0012
(4.180)
***
0.0006
(5.264)
***
0.0000
(0.843)
-0.0002
(-0.206)
0.7928
0.0003
-4.3930
(-0.800)
0.3710
(9.081)
***
0.0062
(2.605)
***
-0.0003
(-2.305)
**
0.0001
(0.874)
-0.0082
(-3.942)
***
-0.0007
(-0.888)
-0.0001
(-2.643)
***
-0.0150
(-2.284)
**
0.7774
0.0017
-0.2732
(-9.383)
***
0.5980
(0.634)
0.1224
(2.613)
***
0.0043
(1.630)
-0.0000
(-0.228)
-0.0002
(-0.886)
-0.0090
(-2.517)
**
-0.0026
(-2.040)
**
-0.0004
(-4.192)
***
-0.0329
(-2.689)
****
0.6881
0.0031
1.1092
(1.666)
*
-0.4296
(-12.066)
***
1.5592
(2.266)
**
-0.4361
(-3.437)
***
-0.0009
(-0.457)
-0.0006
(-1.700)
*
0.0013
(2.219)
**
0.0206
(1.670)
*
-0.0026
(-0.382)
-0.0004
(-1.193)
0.1131
(2.808)
***
0.5755
0.0099
-0.0810
(-2.415)
**
1.0597
(1.489)
-0.1769
(-5.443)
***
7.7716
(8.622)
***
-0.0528
(-0.684)
0.0097
(2.399)
**
-0.0002
(-1.007)
-0.0002
(-0.979)
-0.0098
(-2.867)
***
-0.0037
(-3.059)
***
-0.0001
(-1.367)
0.0052
(0.446)
0.5731
0.0030
BIL
-0.0665
(-3.382)
***
0.9186
(-1.951)
*
-0.4339
(-11.335)
***
-0.6506
(-0.044)
-0.0391
(-0.651)
0.0088
(3.411)
***
0.0000
(-2.547)
**
0.0000
(0.260)
0.0002
(0.392)
0.0010
(5.818)
***
-0.0000
(-2.515)
**
-0.0065
(-4.020)
***
0.5657
0.0004
TFI
-0.0443
(-2.094)
**
0.9433
(-1.190)
-0.6011
(-12.932)
***
5.4142
(3.554)
***
-0.1601
(-2.258)
**
0.0070
(2.089)
**
-0.0001
(-0.456)
0.0011
(3.526)
***
-0.0048
(-0.989)
-0.0085
(-4.576)
***
0.0000
(-0.192)
0.0091
(0.576)
0.5459
0.0040
AGG
-0.0601
(-3.552)
***
0.9904
(-0.380)
-0.1769
(-8.020)
***
2.1289
(4.959)
***
-0.2174
(-3.671)
***
0.0067
(3.687)
***
-0.0001
(-1.159)
-0.0003
(-2.145)
**
-0.0138
(-4.992)
***
-0.0021
(-2.172)
**
-0.0002
(-2.722)
***
-0.0106
(-1.206)
0.5440
0.0025
LQD
-0.0415
(-3.080)
***
0.9270
(-2.909)
***
-0.1210
(-7.233)
***
3.5617
(11.901)
***
-0.5915
(-8.122)
***
0.0041
(3.310)
***
0.0003
(1.291)
0.0000
(-0.038)
-0.0171
(-4.191)
***
-0.0048
(-3.212)
***
-0.0005
(-4.842)
***
0.0048
(0.391)
0.5178
0.0040
MUB
-0.0101
(-0.279)
0.9685
(-0.685)
-0.2016
(-7.337)
****
2.2920
(1.944)
*
-0.1951
(-3.837)
****
0.0008
(0.199)
0.0002
(0.601)
0.0001
(0.411)
-0.0027
(-0.623)
-0.0040
(-2.367)
**
-0.0002
(-2.346)
**
-0.0044
(-0.313)
0.4700
0.0036
HYG
-0.0298
(-1.255)
0.7449
(-3.386)
****
-0.1743
(-6.935)
****
1.9592
(5.059)
****
-0.1263
(-0.990)
0.0034
(1.620)
-0.0001
(-0.149)
0.0001
(0.094)
-0.0305
(-2.920)
***
-0.0084
(-2.329)
**
-0.0012
(-4.598)
***
0.1397
(4.021)
***
0.4557
0.0090
BSV
-0.2618
(-6.623)
***
0.9027
(-1.740)
*
-0.2029
(-8.589)
***
4.9394
(3.848)
***
0.1643
(3.246)
***
0.0324
(6.702)
***
-0.0015
(-6.553)
***
-0.0004
(-2.274)
**
-0.0028
(-0.965)
-0.0006
(-0.588)
-0.0001
(-0.951)
-0.0197
(-1.957)
*
0.4406
0.0026
CIU
-0.1177
(-4.699)
***
0.9386
(-1.250)
-0.2173
(-10.177)
***
-0.6374
(-0.991)
0.2254
(6.436)
***
0.0121
(4.494)
***
0.0005
(3.783)
***
0.0002
(1.113)
-0.0179
(-3.771)
***
-0.0079
(-4.825)
***
-0.0002
(-1.599)
-0.0110
(-0.697)
0.3897
0.0041
SHM
-0.1708
(-4.641)
***
0.9837
(-0.134)
-0.4366
(-9.460)
***
2.5036
(1.388)
-0.1688
(-4.190)
***
0.0290
(4.739)
***
-0.0010
(-5.078)
***
0.0000
(0.035)
-0.0012
(-0.320)
0.0001
(0.076)
0.0000
(0.318)
0.0221
(1.815)
*
0.3241
0.0031
CSJ
-0.2434
(-5.308)
***
0.7729
(-2.425)
**
-0.2406
(-10.044)
***
2.0299
(2.935)
***
0.1301
(2.323)
**
0.0253
(5.068)
***
0.0006
(4.351)
***
0.0003
(1.406)
-0.0165
(-3.371)
***
-0.0085
(-5.156)
***
-0.0002
(-2.039)
**
-0.0166
(-1.038)
0.2228
0.0042
α
β
γ1
φ v_nosh
ψ
TLT
-0.0031
(-0.963)
0.9633
(-6.890)
***
-0.9490
(-39.239)
***
0.0000
(0.601)
-0.0000
(-0.511)
0.0049
(2.998)
***
-5.2252
(-1.513)
0.1107
(1.367)
0.0003
(0.746)
IEF
-0.0041
(-1.637)
0.9869
(-2.375)
**
-0.9716
(-37.994)
***
-18.1541
(-3.720)
***
-0.1323
(-2.199)
**
0.0005
(1.494)
0.0000
(0.616)
-0.0001
(-2.032)
**
IEI
-0.0031
(-0.413)
0.9585
(-3.641)
***
-0.8358
(-20.109)
***
-5.4401
(-0.864)
0.2493
(3.022)
***
0.0004
(0.436)
-0.0000
(-0.589)
SHY
-0.0017
(-0.752)
0.9573
(-5.844)
***
-0.6770
(-30.226)
***
34.0977
(1.788)
*
-0.0544
(-1.409)
0.0002
(0.624)
TIP
-0.0241
(-3.383)
***
0.9528
(-4.661)
***
-0.2680
(-14.008)
***
4.9115
(3.823)
***
0.1904
(2.278)
**
SHV
-0.0714
(-3.243)
***
0.8839
(-6.066)
***
-0.5152
(-15.262)
***
-0.1123
(-0.003)
MBB
-0.0550
(-2.609)
***
0.9708
(-1.202)
-0.7585
(-18.285)
***
BIV
-0.0365
(-1.686)
*
1.0241
(0.831)
0.0113
(0.627)
BND
ETF
JNK
γ2
φ bid_ask
φ hi_lo
φ mkt_cap
75
cred
ψ
ted
Table 4
Expanded Rockets & Feathers
Panel B : Weekly
∆ln(pt) = α + β∆ln(nt) + γ1εt-1 + γ2ε2t-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 (***).
ψ vix
δ SP
Adj. R2
σ
-0.0004
(-1.129)
-0.0000
(-0.652)
-0.0087
(-2.659)
***
0.9912
0.0009
0.0008
(0.578)
-0.0007
(-1.155)
-0.0001
(-2.309)
**
-0.0221
(-3.774)
***
0.9910
0.0016
-0.0000
(-1.183)
0.0006
(2.170)
**
-0.0001
(-0.762)
-0.0000
(-1.327)
-0.0025
(-2.133)
**
0.9800
0.0003
-0.0001
(-0.809)
-0.0002
(-1.237)
0.0035
(2.949)
***
-0.0003
(-0.592)
0.0000
(0.420)
-0.0041
(-0.846)
0.9790
0.0010
0.0032
(1.838)
*
0.0003
(2.443)
**
0.0004
(2.135)
**
-0.0023
(-1.452)
-0.0014
(-1.974)
**
-0.0001
(-3.803)
***
-0.0137
(-2.382)
**
0.9694
0.0018
0.0612
(0.520)
0.0068
(1.537)
-0.0004
(-1.818)
*
0.0004
(1.982)
**
0.0003
(0.261)
-0.0019
(-3.102)
***
-0.0001
(-2.118)
**
-0.0131
(-2.629)
***
0.9591
0.0013
-120.1896
(-1.747)
*
0.4460
(2.197)
**
0.0094
(1.257)
-0.0001
(-0.976)
0.0000
(0.044)
0.0001
(0.385)
0.0004
(3.560)
***
0.0000
(0.658)
0.0005
(0.399)
0.9511
0.0003
-0.7349
(-7.736)
***
23.3568
(1.439)
-0.3174
(-2.691)
***
-0.0005
(-0.074)
-0.0001
(-0.219)
0.0010
(2.340)
**
-0.0075
(-2.383)
**
0.0002
(0.153)
-0.0001
(-1.161)
-0.0168
(-1.266)
0.9488
0.0031
1.0300
(1.058)
-0.6097
(-6.948)
***
26.6500
(2.544)
**
0.1356
(0.850)
0.0021
(0.388)
0.0002
(0.597)
-0.0002
(-0.457)
-0.0025
(-0.930)
-0.0017
(-1.456)
-0.0001
(-2.001)
**
-0.0076
(-0.911)
0.9261
0.0027
-0.0585
(-0.905)
1.0065
(0.187)
-0.5486
(-5.057)
***
-5.9711
(-0.669)
1.2803
(5.202)
***
0.0064
(0.815)
0.0001
(0.313)
-0.0001
(-0.240)
-0.0014
(-0.619)
-0.0006
(-0.659)
-0.0002
(-3.261)
***
0.0068
(0.943)
0.8925
0.0023
JNK
-0.0355
(-0.675)
1.0589
(0.852)
-0.9616
(-7.637)
***
11.0159
(3.158)
***
1.3440
(2.450)
**
0.0059
(1.100)
-0.0015
(-1.520)
0.0012
(0.747)
-0.0184
(-1.758)
*
-0.0062
(-1.036)
0.0008
(2.807)
***
0.1036
(2.340)
**
0.8555
0.0107
LQD
-0.0310
(-0.851)
1.1438
(5.591)
***
-0.4373
(-9.913)
***
3.7998
(3.156)
***
0.1955
(0.707)
0.0025
(0.765)
0.0006
(1.040)
-0.0005
(-1.358)
-0.0197
(-4.862)
***
-0.0040
(-2.355)
**
-0.0002
(-2.057)
**
0.0241
(1.491)
0.8529
0.0045
MUB
-0.5322
(-3.989)
***
0.8686
(-2.934)
***
-0.7931
(-8.970)
***
18.5678
(4.205)
***
0.6289
(2.340)
**
0.0546
(3.738)
***
0.0010
(0.725)
0.0035
(2.501)
**
-0.0125
(-2.333)
**
-0.0045
(-1.588)
-0.0003
(-2.784)
***
-0.0075
(-0.417)
0.8528
0.0052
CIU
-0.3358
(-4.411)
***
1.1963
(3.250)
***
-0.5473
(-8.963)
***
-7.8373
(-2.979)
***
1.3868
(8.114)
***
0.0350
(4.301)
***
0.0007
(2.022)
**
0.0006
(1.018)
-0.0083
(-1.670)
*
-0.0081
(-4.000)
***
-0.0004
(-3.679)
***
-0.0263
(-1.340)
0.8379
0.0049
BIL
-0.5342
(-4.443)
***
0.9748
(-0.478)
-0.8602
(-7.321)
***
-97.7361
(-3.402)
***
0.5800
(2.154)
**
0.0697
(4.433)
***
0.0000
(-0.585)
0.0002
(2.615)
***
-0.0004
(-0.765)
0.0000
(0.068)
0.0000
(1.928)
*
0.0006
(0.213)
0.8267
0.0005
AGG
-0.0595
(-0.933)
1.0770
(1.762)
*
-0.5578
(-6.731)
***
4.4780
(3.818)
***
-2.3444
(-7.214)
***
0.0075
(1.085)
-0.0004
(-1.356)
-0.0003
(-0.534)
-0.0164
(-4.060)
***
0.0014
(0.837)
-0.0005
(-6.050)
***
-0.0134
(-0.974)
0.7725
0.0042
HYG
-0.0892
(-0.978)
1.1527
(1.794)
*
-0.7125
(-8.555)
***
3.0347
(2.351)
**
1.4413
(1.838)
*
0.0102
(1.309)
-0.0006
(-0.384)
0.0004
(0.189)
0.0184
(1.230)
-0.0115
(-1.972)
*
-0.0010
(-2.779)
***
0.1142
(1.826)
*
0.7460
0.0134
SHM
-0.2390
(-2.819)
***
0.9110
(-1.279)
-0.6126
(-4.521)
***
-3.5945
(-0.352)
0.0525
(0.345)
0.0412
(2.917)
***
-0.0016
(-3.700)
***
-0.0006
(-1.047)
-0.0018
(-0.604)
-0.0019
(-1.427)
-0.0002
(-2.646)
***
0.0098
(1.011)
0.6810
0.0028
BSV
-0.4549
(-3.531)
***
0.9365
(-0.714)
-0.3854
(-5.284)
***
7.8073
(1.688)
*
0.1420
(0.627)
0.0569
(3.620)
***
-0.0027
(-3.721)
***
-0.0012
(-1.682)
*
0.0019
(0.551)
-0.0013
(-0.828)
-0.0002
(-2.106)
**
-0.0070
(-0.600)
0.6215
0.0037
CSJ
-0.2767
(-2.058)
**
1.1296
(1.315)
-0.5850
(-7.540)
***
7.2678
(2.337)
**
0.3698
(1.465)
0.0266
(1.823)
*
0.0020
(5.125)
***
0.0010
(1.795)
*
-0.0131
(-2.842)
***
-0.0012
(-0.642)
-0.0003
(-2.423)
**
-0.0385
(-2.122)
**
0.5712
0.0045
ETF
α
β
γ1
γ2
φ bid_ask
φ hi_lo
φ mkt_cap
φ v_nosh
ψ
IEF
0.0062
(1.102)
0.9895
(-2.041)
**
-0.9006
(-16.783)
***
56.5122
(3.592)
***
0.3908
(2.067)
**
-0.0006
(-0.875)
-0.0000
(-0.319)
-0.0001
(-1.480)
0.0003
(0.360)
TLT
0.0024
(0.349)
0.9768
(-4.621)
***
-0.9034
(-18.065)
***
26.4764
(2.320)
**
0.1322
(0.797)
-0.0002
(-0.280)
0.0000
(0.192)
-0.0002
(-1.644)
0.0076
(1.668)
*
0.9837
(-2.134)
**
-0.8069
(-16.321)
***
212.4487
(3.966)
***
0.1597
(2.051)
**
-0.0010
(-1.851)
*
0.0001
(2.878)
***
-0.0145
(-0.782)
0.9614
(-2.889)
***
-1.0550
(-11.832)
***
-67.0017
(-2.312)
**
-0.0270
(-0.098)
0.0018
(0.831)
-0.0341
(-2.104)
**
1.0185
(1.747)
*
-0.4537
(-9.082)
***
8.8129
(2.351)
**
-0.2018
(-0.988)
MBB
-0.0595
(-1.528)
1.0123
(0.606)
-0.8431
(-8.001)
***
44.4166
(1.293)
SHV
-0.0880
(-1.261)
0.9559
(-2.182)
**
-0.4998
(-5.824)
***
TFI
0.0027
(0.061)
0.9952
(-0.176)
BIV
-0.0206
(-0.468)
BND
SHY
IEI
TIP
76
cred
ψ
ted
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 $100 million in March 2011. Panel A presents ticker symbols, issuer names, descriptions of underlying assets, inception dates, average duration (Dur.)
and maturity (Mat.), net assets as of March 2011, expense ratio (Exp. Ratio), and breakdown of holdings showing number of issues held as of March 2011,
percent held in US Treasury assets (Fed. Gov.), non-governmental investment-grade assets (Non-Gov. A), and low-grade assets (B-, C-, and Un-Rated) for
Treasury and corporate bond ETFs.
Holdings Mar. 2011
ETF /
Type
Issuer
Description
Incept.
Date
Dur.
Mat.
Net
Assets
($Bill.)
Mar. 2011
Exp.
Ratio
(%)
#
Fed.
Gov.
(%)
NonGov. A
(%)
B-, C- &
UnRated
(%)
Treasury
BIL
SPDR
1-3 Month T-Bill
05/25/07
0.12
0.12
0.9
0.14
9
100
-
-
SHV
iShares
Barclays Capital Short
US Treasury Index
01/05/07
0.39
0.39
4.1
0.15
13
100
-
-
SHY
iShares
Barclays Capital 1-3
Year Treasury Index
07/22/02
1.82
1.86
7.9
0.15
37
100
-
-
IEI
iShares
01/05/07
4.44
4.82
1.3
0.15
37
100
-
-
IEF
iShares
Barclays Capital 7-10
Year Treasury Index
07/22/02
7.17
8.53
2.8
0.15
15
100
-
-
TLH
iShares
Barclays Capital 10-20
Year Treasury Index
01/05/07
9.31
14.08
0.2
0.15
23
100
-
-
TLT
iShares
Barclays Capital 20+
Year Treasury Index
07/22/02
14.69
27.61
2.9
0.15
15
100
-
-
ITE
State Street
1-10 year sector of the
United States Treasury
05/23/07
3.95
4.26
0.19
0.14
161
100
-
-
3-7 Year US Treasury
Corporate
CSJ
iShares
Barclays Capital 1-3 Year
US Credit Index
01/05/07
1.81
1.9
7.5
0.2
702
-
75
25
CIU
iShares
Barclays Capital Intermediate-term
US Credit Index
01/05/07
4.2
5
3.1
0.2
1,318
-
65
35
CFT
iShares
Barclays Capital US Credit
Bond Index
01/05/07
5.98
9.84
0.7
0.2
1,231
-
60
40
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
ETF /
Type
Issuer
Description
Incept.
Date
Dur.
Mat.
Net
Assets
($Bill.)
Mar. 2011
Exp.
Ratio
(%)
#
Fed.
Govt.
(%)
NonGov. A
(%)
B-, C- &
UnRated
(%)
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
BLV
Vanguard
Barclays Capital US Long Govt/Cred.
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
IPE
TIP
MBB
State Street
Barclays U.S. Govt. Inflationlinked Bond Index
05/25/07
8.26
9.24
0.38
0.19
32
100
-
-
iShares
Barclays Capital US Treasury
Inflation Notes Index
12/04/03
5.22
8.7
19.2
0.2
32
100
-
-
iShares
Barclays Capital US MBS
Fixed-Rate Index
03/13/07
4.66
3.77
2.3
0.25
127
-
97
3
iShares
Barclays Capital US Govt/
Credit Bond Index
01/05/07
5.15
7.58
0.11
0.2
314
64
23
13
iShares
Barclays Capital US Intermed.
Govt/Credit Bond Index
01/05/07
3.75
4.28
0.53
0.2
407
68
21
11
Government Agency
GBF
GVI
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
BIL
0.0003
(0.389)
0.0097
(1.386)
-0.0034
(-1.788*)
0.0436
SHV
0.0006
(0.808)
0.0157
(2.114**)
-0.0053
(-2.638**)
0.1377
SHY
0.0036
(1.212)
0.0435
(1.452)
-0.0183
(-2.236**)
0.0785
IEI
0.0058
(0.717)
0.1032
(1.254)
-0.0372
(-1.652)
0.0299
IEF
0.0041
(0.291)
0.1669
(1.171)
-0.0488
(-1.251)
0.0050
TLH
0.0012
(0.063)
0.1832
(0.904)
-0.0429
(-0.774)
-0.0226
TLT
-0.0020
(-0.069)
0.2629
(0.901)
-0.0584
(-0.732)
-0.0238
ITE
0.0036
(0.527)
0.1004
(1.466)
-0.0311
(-1.661)
0.0391
CFT
-0.0027
(-0.185)
0.0504
(0.344)
0.0105
(0.262)
-0.0428
CIU
-0.0016
(-0.139)
0.0548
(0.469)
0.0047
(0.147)
-0.0416
CSJ
-0.0027
(-0.390)
0.0857
(1.234)
-0.0066
(-0.350)
-0.0114
HYG
-0.0084
(-0.266)
-0.0114
(-0.036)
0.0515
(0.586)
-0.0404
LQD
-0.0144
(-0.730)
0.1877
(0.938)
0.0089
(0.163)
-0.0212
Treasury
Corporate
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
AGG
-0.0010
(-0.111)
0.1027
(1.127)
-0.0144
(-0.578)
-0.0165
BIV
-0.0005
(-0.041)
0.1133
(0.873)
-0.0150
(-0.422)
-0.0299
BLV
-0.0026
(-0.121)
0.1044
(0.487)
-0.0037
(-0.064)
-0.0436
BND
0.0003
(0.039)
0.0800
(0.975)
-0.0111
(-0.494)
-0.0248
BSV
0.0007
(0.116)
0.0872
(1.363)
-0.0183
(-1.044)
0.0061
LAG
-0.0021
(-0.320)
0.1029
(1.516)
-0.0094
(-0.505)
0.0070
IPE
0.0193
(1.372)
-0.0238
(-0.166)
-0.0459
(-1.174)
-0.0067
TIP
0.0178
(1.230)
-0.0026
(-0.018)
-0.0472
(-1.174)
-0.0106
GBF
-0.0022
(-0.223)
0.1206
(1.207)
-0.0158
(-0.576)
-0.0122
GVI
-0.0002
(-0.029)
0.1034
(1.211)
-0.0178
(-0.763)
-0.0092
MBB
-0.0024
(-0.401)
0.0873
(1.443)
-0.0040
(-0.241)
0.0034
Broad-Market
TIPS
Govt. Agency & MBS
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
BIL
0.0002
(1.023)
-0.0750
(-1.833*)
0.0973
(1.006)
0.0810
(1.061)
0.0251
SHV
0.0006
(3.400***)
-0.1147
(-2.759***)
-0.1313
(-1.335)
0.1875
(2.416**)
0.1901
SHY
0.0030
(4.444***)
-0.4695
(-3.118***)
-0.8625
(-2.421*)
0.7597
(2.702*)
0.3064
IEI
0.0061
(3.099***)
-0.9070
(-2.075**)
-2.1974
(-2.125**)
1.1778
(1.443)
0.1834
IEF
0.0072
(1.976*)
-0.9094
(-1.124)
-2.8558
(-1.492)
1.1351
(0.752)
0.0453
TLH
0.0080
(1.538)
-0.7194
(-0.623)
-4.0591
(-1.486)
1.6738
(0.776)
0.0091
TLT
0.0081
(1.083)
-2.3041
(-1.398)
-3.9120
(-1.003)
3.7265
(1.211)
0.0252
ITE
0.0049
(2.851***)
-0.7134
(-1.877*)
-1.4621
(-1.627)
0.8754
(1.234)
0.1189
CFT
0.0049
(1.402)
2.3647
(3.071***)
-0.9987
(-0.548)
-1.2628
(-0.879)
0.1383
CIU
0.0045
(1.634)
1.9389
(3.175***)
-0.7784
(-0.539)
-2.0216
(-1.773*)
0.1515
CSJ
0.0033
(1.925*)
0.9952
(2.600**)
-0.5319
(-0.587)
-0.5638
(-0.789)
0.0840
HYG
0.0019
(0.369)
7.5747
(6.677***)
5.3752
(2.003.)
-3.1401
(-1.483)
0.6130
LQD
0.0046
(0.934)
2.7962
(2.555**)
-0.2532
(-0.098)
-1.7182
(-0.841)
0.0891
Treasury
Corporate
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
AGG
0.0049
(2.069**)
0.6761
(1.284)
-1.3253
(-1.064)
0.3025
(0.308)
-0.0109
BIV
0.0062
(1.838*)
0.8831
(1.175)
-1.7202
(-0.968)
-0.1762
(-0.126)
-0.0286
BLV
0.0068
(1.213)
1.1405
(0.918)
-2.2722
(-0.774)
0.4440
(0.192)
-0.0426
BND
0.0051
(2.372**)
0.5619
(1.187)
-1.2748
(-1.139)
0.2717
(0.308)
-0.0151
BSV
0.0042
(2.456**)
0.2403
(0.639)
-1.2012
(-1.350)
0.3649
(0.520)
-0.0239
LAG
0.0052
(2.941***)
0.3261
(0.827)
-1.6035
(-1.720*)
0.2729
(0.371)
0.0024
IPE
0.0056
(1.565)
1.9669
(2.484**)
-2.4140
(-1.289)
-1.4556
(-0.985)
0.0806
TIP
0.0056
(1.530)
2.1115
(2.610**)
-2.1828
(-1.141)
-1.1778
(-0.780)
0.0870
Broad-Market
TIPS
Govt. Agency & MBS
GBF
0.0050
(1.912*)
0.7700
(1.332)
-1.7238
(-1.261)
-0.3089
(-0.286)
-0.0081
GVI
0.0046
(2.054**)
0.5565
(1.115)
-1.2081
(-1.023)
-0.3359
(-0.361)
-0.0278
MBB
0.0050
(3.153***)
0.1061
(0.304)
-1.5022
(-1.818*)
0.1949
(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
BIL
0.0004
(0.550)
-0.0658
(-1.652)
0.1168
(1.237)
0.1133
(1.509)
0.0106
(1.484)
-0.0042
(-2.144**)
0.0977
SHV
0.0006
(0.959)
-0.1005
(-2.632**)
-0.1105
(-1.221)
0.2334
(3.241***)
0.0165
(2.404**)
-0.0054
(-2.870***)
0.3321
SHY
0.0036
(1.465)
-0.4340
(-2.974***)
-0.7908
(-2.285**)
0.8829
(3.208***)
0.0409
(1.564)
-0.0158
(-2.202**)
0.3632
IEI
0.0057
(0.768)
-0.8335
(-1.884*)
-2.0983
(-2.000*)
1.4121
(1.692*)
0.0854
(1.077)
-0.0269
(-1.237)
0.1827
IEF
0.0037
(0.263)
-0.7824
(-0.948)
-2.7735
(-1.417)
1.5026
(0.965)
0.1490
(1.007)
-0.0360
(-0.889)
0.0283
TLH
-0.0001
(-0.006)
-0.5659
(-0.477)
-4.0775
(-1.448)
2.0686
(0.924)
0.1820
(0.855)
-0.0297
(-0.510)
-0.0230
TLT
-0.0018
(-0.063)
-2.0923
(-1.235)
-3.8961
(-0.969)
4.2887
(1.342)
0.2505
(0.825)
-0.0459
(-0.552)
-0.0071
ITE
0.0036
(0.554)
-0.6368
(-1.668)
-1.3872
(-1.531)
1.1075
(1.538)
0.0894
(1.306)
-0.0247
(-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
(-0.460)
2.4764
(3.139***)
-1.1682
(-0.624)
-1.0406
(-0.699)
0.1351
(0.955)
-0.0034
(-0.088)
0.1155
CIU
-0.0041
(-0.390)
2.0165
(3.216***)
-0.9268
(-0.623)
-1.8800
(-1.590)
0.0943
(0.839)
0.0012
(0.039)
0.1257
CSJ
-0.0043
(-0.666)
1.1014
(2.898***)
-0.6054
(-0.672)
-0.3159
(-0.441)
0.1269
(1.864*)
-0.0135
(-0.723)
0.1174
HYG
-0.0163
(-0.851)
7.8732
(6.961***)
5.2680
(1.964*)
-2.4020
(-1.126)
0.3551
(1.752*)
-0.0495
(-0.892)
0.6239
LQD
-0.0183
(-0.986)
3.0459
(2.768***)
-0.5814
(-0.223)
-1.2006
(-0.578)
0.3010
(1.526)
-0.0135
(-0.250)
0.0994
CFT
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
AGG
-0.0028
(-0.308)
0.8018
(1.516)
-1.3714
(-1.093)
0.6130
(0.615)
0.1496
(1.578)
-0.0207
(-0.799)
0.0030
BIV
-0.0026
(-0.200)
1.0115
(1.318)
-1.7979
(-0.988)
0.1282
(0.089)
0.1533
(1.115)
-0.0176
(-0.467)
-0.0489
BLV
-0.0054
(-0.250)
1.2825
(1.002)
-2.4329
(-0.801)
0.7493
(0.310)
0.1707
(0.745)
-0.0107
(-0.171)
-0.0823
BND
-0.0012
(-0.149)
0.6604
(1.378)
-1.3190
(-1.160)
0.5115
(0.566)
0.1173
(1.366)
-0.0153
(-0.650)
-0.0180
BSV
-0.0003
(-0.054)
0.3351
(0.893)
-1.1968
(-1.344)
0.6154
(0.869)
0.1121
(1.667)
-0.0202
(-1.097)
0.0027
LAG
-0.0035
(-0.528)
0.4302
(1.096)
-1.7146
(-1.842*)
0.4996
(0.675)
0.1252
(1.779*)
-0.0086
(-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
IPE
0.0162
(1.191)
1.9923
(2.474**)
-2.0500
(-1.073)
-1.2367
(-0.814)
0.0241
(0.167)
-0.0479
(-1.211)
0.0701
TIP
0.0144
(1.042)
2.1730
(2.652**)
-1.8189
(-0.936)
-0.8644
(-0.559)
0.0668
(0.455)
-0.0553
(-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 mortgagebacked 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
GBF
-0.0041
(-0.413)
0.8960
(1.534)
-1.8122
(-1.308)
-0.0152
(-0.014)
0.1507
(1.440)
-0.0159
(-0.553)
-0.0063
GVI
-0.0016
(-0.185)
0.6611
(1.309)
-1.2408
(-1.036)
-0.0750
(-0.079)
0.1245
(1.375)
-0.0179
(-0.723)
-0.0293
0.1828
(0.521)
-1.6421
(-1.975*)
0.3376
(0.511)
0.0931
(1.482)
0.0004
(0.024)
0.0253
MBB
-0.0033
(-0.565)
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) tstatistics. 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
γ
0.0002
MKT
0.0007
SMB
Panel A
-0.0012
HML
-0.0002
DEF
0.0076
TERM
-0.0140
tfm
1.7684
0.0686
-2.8238
-0.3458
1.2565
-0.6016
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
Panel B
-0.3515
1.0188
-0.3639
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
R2
0.3433
2
p(R =1)
0.3095
R2
0.8887
Table 9b
GLS Treasury
intercept
γ
-0.0002
MKT
0.0045
SMB
Panel A
-0.0011
HML
0.0002
DEF
0.0019
TERM
-0.1058
tfm
-0.7064
0.1843
-1.5730
0.1573
0.0698
-1.3891
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
Panel B
0.0918
0.0362
-0.6430
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
2
p(R =1)
0.6557
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 (t fm), Shanken
EIV-corrected (ts), Jagannathan and Wang EIV-corrected (tjw), and Kan, et al., misspecificationcorrected (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
Panel A
HML
DEF
TERM
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
Panel B
-0.5179
0.8731
0.3672
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
intercept
MKT
SMB
Panel A
HML
DEF
TERM
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
Panel B
0.4660
0.5638
-0.4152
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
R2
0.2933
p(R2=1)
0.2364
R2
0.7217
2
p(R =1)
0.7699
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 nonTreasury 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
Whole Sample
0.0744
(5.394***)
-0.1091
(-3.336***)
0.0210
(0.806)
0.1302
(4.388***)
-0.0207
(-2.549**)
0.0449
Treasury
-0.0574
(-2.458**)
-0.1564
(-2.824***)
0.1209
(2.745***)
0.1030
(2.051**)
-0.0236
(-1.713*)
0.0753
87
Fig. 1 : iSheres iBoxx $ Liquid High Yield Index (HYG)
Monthly Number of Shares Outstanding
9OOOO~--
80000
70000
60000
88
50000
• HYG Shares
40000
I
'~ L-,.,o,.,o,o,o,I,I,I,I",l,IlU,Il ,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,
30000
20000
041301070&31107 12/3110704130108 06129108 12/31108 04I301W 0&31/W 12131/W 04130110 0&31110
DATE Ct6I29/07 1013110702129108 06130108 10131108 02/27109 06I301W 101301W 02126110 06130110 10129110
Fig. 2 : iSheres iBoxx $ Liquid High Yield Index (HYG)
Monthly Percentage Growth in Shares Outstanding
08
06
89
• HYO Share Growth
04
02
-02 DATE
1
~4~'--
31107
02129108
06129108
02l27/W
06I31/W
02126110
06131110 ~
J
~
I
(')
>I
x
"
"0
C
"0
a;
>=
.c
Cl
I
C
80"
is
:Q
:>
E
.2
CE
::J
~
'"~
Q.
'"'"
0
0
~
.~
"
.c
~
OJ
Ul
'"
,
Cl
u:
I ~
~
~0
j
~
8
0
0
~
0
§-
0"
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
-~-~-~-~-~
2007
2002
2003
2004
2005
2006
2006
2009
2010
2006
2009
2010
Bond ElF Assets
$Billion
140
120
100
80
60
40
20
0
-~-~_~.~.~I~
2002
2003
2004
2005
2006
Data: Morningstar and National Stock Exchange
91
2007
Fig. 5 ETF, CEF, OEF, OTC Comparison
ETF
CEF
OEF
OTC
Small
Premium
Large
Discount
At NAV
Spot
('NAV')
Intraday Trading
Yes
Yes
No
No
Short-Sell
Yes
Yes
No
No
Buy on Margin
Yes
Yes
No
No
Variable
Fixed
Variable
Spot
(n/a)
No
No
Yes
Yes
Premium/Discount
Fund Size
Rebalancing Taxable
Market
Typical Increment
Retail: Secondary
AP: Primary
Secondary
Primary
Secondary
Broker/Dealer
$100
$100
$2,500 (to open)
$10,000
92
Fig. 6 Trading Strategies
Yield Curve
TLT/SHY
Treasury/Corporate
IEF/LQD
Investment-Grade/Low-Grade
LQD/HYG
Corporate Debt/Equity
LQD/SPY
93
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