common factors in corporate bond and bond fund returns factors in corporate bond and bond fund...
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Common factors in corporate bond and bond fund returns
Ronen Israel
AQR Capital Management LLC
Diogo Palhares
AQR Capital Management LLC
Scott Richardson
AQR Capital Management LLC
London Business School
July 22, 2016
Abstract
We identify four key characteristics (carry, defensive, momentum and value) that together
explain nearly 15% of the cross-sectional variation in corporate bond excess returns. The
positive risk-adjusted returns to these characteristics are diversifying with respect to both
market risk premia and equity characteristic returns. We use portfolios based on these
characteristics to explain both the returns and holdings of actively managed credit funds.
Credit hedge funds have very significant positive exposures to credit markets (beta) and
positive exposures to value. Credit mutual funds have the expected positive exposure to credit
markets and, unlike hedge funds, no exposure to value but positive exposures to momentum,
carry and defensive.
JEL classification: G12; G14; M41
Key words: corporate bonds, credit mutual funds, credit hedge funds
A previous version of this paper was titled βInvesting with style in corporate bonds.β We thank Demir Bektic,
Maria Correia, Wayne E. Ferson, Patrick Houweling, Antti Ilmanen, Sarah Jiang, Toby Moskowitz, Narayan
Naik, Lasse Pedersen, Kari Sigurdsson and participants at the 4th
Alliance Bernstein Quant Conference, 24th
European Pensions Symposium, 7th
Inquire UK Business School Meeting, Norwegian Ministry of Finance and
University of Cambridge, 2016 SFS Finance Cavalcade, London Quant Group and UBS Quantitative
Investment Conference 2016 for helpful discussion and comments. We acknowledge the outstanding research
assistance of Peter Diep, Johnny Kang and Mason Liang. The views and opinions expressed herein are those of
the authors and do not necessarily reflect the views of AQR Capital Management LLC (βAQRβ), its affiliates or
its employees. This information does not constitute an offer or solicitation of an offer, or any advice or
recommendation, by AQR, to purchase any securities or other financial instruments and may not be construed as
such.
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1. Introduction
Corporate bonds are an enormousβand growingβsource of financing for companies around the
world. As of the first quarter of 2016, there was $8.36 trillion of U.S. corporate debt outstanding, and there
had been a growing trend in corporate bond issuance from $343 billion in 1996 to $1.49 trillion in 2015
(Securities Industry and Financial Markets Association). Over this period, the investor base and trading
dynamics of corporate bonds changed dramatically. Melentyev and Sorid (2015) discuss the changing
market structure for the trading of corporate bonds. Dealer inventories have decreased as has average trade
size, and more retail investors have entered the market in recent years via open-ended mutual funds and
ETFs targeting corporate bonds. Indeed, Goldstein, Jiang and Ng (2015) note that the assets managed by
active mutual funds rose from $200 billion in 1996 to a little over $1.8 trillion in 2014. This translates to an
increase from 9 percent to nearly 25 percent of corporate bonds outstanding. Surprisingly little research,
however, has investigated the cross-sectional determinants of corporate bond returns as well as the
determinants of returns for actively managed credit hedge funds and mutual funds.
Prices of corporate bonds are not independent from equity prices, nor are they simply a mirror image.
First, while the fundamental value of bonds and equities both depend on the underlying value of the assets of
the firm (e.g., Merton, 1974), the way these two securities respond to changes in the properties of asset
values is not identical. Second, equity and bond values can change even when the underlying value of the
firm does not. Corporate events such as leveraged buyouts, for example, tend to benefit shareholders at the
expense of debtholders. Third, bonds and equities are traded in different markets and typically held by
different investors. This can make stock and bond prices diverge, as they are anchored to the risk aversion,
liquidity demands and sentiment of different investor clienteles. As a consequence, knowledge about the
cross-section of expected stock returns does not translate one-to-one to bonds (e.g., Chordia et al. 2014;
Choi and Kim 2015).
Our focus with this paper is threefold. First, we explore the role of characteristics in explaining the
cross-section of bond returns. In doing so, we examine excess returns rather than total returns. While it is
well known that changes in corporate bond prices have a component attributable to changes in interest rates
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(e.g., Gebhardt, Hvidkjaer and Swaminathan 2005a), this is not our focus. An extensive literature in
financial economics has documented robust evidence of positive associations between measures of carry,
defensive, momentum and value and future asset returns (e.g., Koijen, Moskowitz, Pedersen and Vrugt 2014
for carry; Frazzini and Pedersen 2013 for defensive; Asness, Moskowitz and Pedersen 2013 for momentum
and value; Asness, Ilmanen, Israel and Moskowitz 2015 for a combination of all four characteristics). We
construct measures of each of these characteristics in a manner that is appropriate for the credit risk
embedded in corporate bonds. Using a large sample of corporate bonds for North America, we can explain
nearly 15 percent of the cross-sectional variation in corporate bond excess returns. To put this number in
context, Lewellen (2015) shows that 15 well-known anomalies can explain 7.6% of the cross-sectional
variability of stocks returns.
Second, we demonstrate that the return predictability is economically meaningful. This is particularly
relevant in corporate bond markets since transaction costs are large, especially relative to equity markets. As
an example, Harris (2015) notes that trading costs are about 30 (50) basis points (bps) for investment grade
(high yield) bonds, and Frazzini, Israel and Moskowitz (2012) show that trading costs for stocks are about
15 bps for large cap stocks. When contrasted with the significantly lower volatility of corporate bonds
relative to stocks, it is clear that trading in corporate bonds is significantly more costly than trading in
common stocks. As such, past research, due to its failure to explicitly account for trading costs, cannot
address the economic importance of characteristics in explaining corporate bond excess returns. We show
that a long-only portfolio of corporate bonds with exposure to carry, defensive, momentum and value
themes generates high risk-adjusted returns, net of trading costs. Specifically, a long-only portfolio of North
American corporate bonds constructed with realistic position and trading-cost constraints yields a net (of
transaction cost) excess return of 5.26 percent annualized, which translates to a Sharpe ratio of 1.03.
Relative to a value-weighted benchmark of corporate bonds, the long-only portfolio yields a net (of
transaction cost) active return of 2.20 percent annualized, which translates to an information ratio of 0.86.
Third, we conduct a detailed analysis of the time-series and cross-sectional determinants of actively
managed credit hedge-fund and mutual-fund returns, as well credit mutual-fund holdings. While many
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studies have examined the performance of actively managed equity funds, few have investigated actively
managed credit funds. Surprisingly, we find that a significant portion of the variability of credit hedge fund
returns stems from passive exposures to term, credit and equity risk premia: 73% of the net returns to the
HFR index of fixed-income corporate relative-value hedge funds can be explained by these passive
exposures to market risk premium.
Going beyond fundsβ market exposures, we find that the four highlighted characteristics explain 7%
to 15% of the time-series variation in the active returns of a broad sample of 223 US-centric credit hedge
funds and 244 credit mutual funds. Specifically, hedge funds have positive exposure to value but not to the
other styles. Mutual fund exposures are a mirror image, with zero loadings on value but positive loadings on
the other styles, with carry being the strongest.
For 102 high-yield credit mutual funds with benchmarks tied to either the BAML or Barclays credit
indexes, we complement the active return investigation with an analysis of holdings. We focus on high-yield
mutual funds because most of their holdings are corporate bonds, whereas investment-grade funds
commonly have sizeable positions in U.S. Treasury and agency securities. We find that mutual funds tend to
overweight bonds with high carry, momentum and defensive characteristics but have mixed exposures to
value. These results are consistent with the exposures identified in the time series of returns. Importantly, we
see the same patterns when examining how changes in characteristics correlate with changes in mutual fund
holdings.
Our empirical analyses have several key implications. First, despite evidence of (i) a robust relation
between well-known characteristics (i.e., carry, defensive, momentum and value) and corporate bond excess
returns and (ii) feasible implementation of exposure to these characteristics in a long-only portfolio,
individual actively managed credit funds are underexposed to characteristics that generate meaningfully
positive risk-adjusted returns. Typically less than 15 percent of the variation in active returns can be
attributed to characteristics. Second, similar to the hidden beta exposure of equity hedge funds (e.g., Asness,
Krail and Liew 2001), actively managed credit hedge funds also contain significant exposure to interest rate
and credit beta. Investors in these funds would likely want to be aware of any beta they are exposed to and
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would likely prefer investment products designed to isolate exposure to well-compensated characteristics
that are orthogonal to market beta.
The remainder of the paper proceeds as follows. Section 2 discusses related papers exploring
determinants of cross-sectional variation in corporate bond excess returns. Section 3 explains our data
sources, sample selection criteria, characteristic measures and research design. Section 4 describes our
primary empirical analyses based on corporate bond excess returns and actively managed credit funds from
North America. Section 5 concludes.
2. Literature Review
Our paper relates to a growing literature on determinants of the cross-section of security returns.
While much of that literature has focussed on equity returns, a few related papers have examined cross-
sectional determinants of corporate bond excess returns. Correia, Richardson, and Tuna (2012) study value
investing in corporate bond markets by comparing market spreads to model-implied spreads estimated using
fundamental and market-based inputs. Kwan (1996) and Gebhardt, Hvidkjaer and Swaminathan (2005b)
document strong evidence for equity momentum in corporate bond markets by showing that past equity
returns strongly predict future corporate bond returns of the same issuer, even after controlling for corporate
bond momentum. Jostova et al. (2013) examine credit momentum and show that it is profitable when used to
trade high-yield US corporate bondsβeven when controlling for equity momentum. Koijen, Moskowitz,
Pedersen, and Vrugt (2014) evaluate carry factors across several markets: for credit markets, they test
corporate bond indices of varying durations and maturities. Carvalho, Dugnolle, Xiao, and Moulin (2014)
identify a low-risk anomaly across a broad universe of fixed income assets for various measures of risk.
Similarly, Frazzini and Pedersen (2014) document positive risk-adjusted returns for portfolios that take long
positions for short duration and higher-rated corporate bonds and take short positions for long duration and
lower-rated corporate bonds. In contrast, Ng and Phelps (2014) note that the low risk anomaly in corporate
bonds is sensitive to the selected measure of risk.
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Our work extends this literature. First, we study the standalone performance of characteristics and
investigate the relation between them and their combined efficacy. Second, we consider simple
unconstrained long-short portfolios and also more realistically investable long-only portfolios, which
account for transaction costs and shorting constraints typical for corporate bonds. The investable portfolios
show that our results are economically meaningful. Third, we link our characteristics to the returns and
holdings of actively managed credit hedge funds and mutual funds and document which exposures actively
managed credit funds provide to their investors.
A paper that relates closely to ours is that of Houweling and van Zundert (2014). These authors find
that size, low-risk, value and momentum are economically meaningful factors generating significant
abnormal returns in the corporate bond market. Like us, they consider the merits to combining factors within
a multi-factor portfolio and also consider the impact of transaction costs. However, there are two key
differences in our respective research designs. First, we construct optimized long-only portfolios that
resemble investable corporate bond portfolios by focusing on active risk and expected transaction costs.
Secondβand more importantlyβwe relate the characteristics we have identified to the holdings and returns
of actively managed credit hedge funds and mutual funds. On the one hand, we use our characteristics to
understand and explain the returns and holdings of actively managed credit hedge funds and mutual funds,
illuminating an increasingly important class of fixed income investors. On the other hand, we test the
hypothesis that useful predictors are likely to be at least partially reflected in the behavior of portfolio
managers. This additional test underscores the economic importance of the characteristics studied here
without having to rely solely on realized performance.
Our paper adds to the long line of research on mutual fund performance and risk taking. Most studies
have focused on equity-oriented funds, but our research is conducted entirely on credit-oriented funds. We
are aware of only one paper exploring the exposures of individual actively managed credit funds.
Specifically, Kahn and Lemmon (2015) study a two-year sample of 121 fixed income investment managers
and find that two beta factorsβduration and creditβon average explain about 67% of the time variation in
their returns. They do not examine the ability of characteristics to explain fund manager returns. The
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mandates of the funds included in their sample encompass both interest rate risk and credit risk. Our focus is
primarily on the latter, and thus our empirical analysis is new.
Fung and Hsieh (2002, 2006) also examine fixed-income hedge-fund index returns. For a sample of
20 high-yield hedge funds, reflecting $8.9 billion of assets under management as at December 2000, Fung
and Hsieh (2002) document that the first principal component across these 20 funds can explain nearly 70
percent of the time-series variation of their returns, consistent with a very strong market loading. Fung and
Hsieh (2006) extend this result into the mid-2000s by showing that changes in aggregate credit spreads are a
key determinant of credit hedge fund returns.
We greatly extend this past research in several dimensions. Most actively managed mutual funds and
even some hedge funds have mandates to provide both beta as well as active management. We carefully
disentangle the two by, first, showing the importance of market factors in explaining fund returns and,
second, studying the determinants of the active component using the same characteristics that we related to
bond excess returns. We also expand both the time series and cross section of actively managed credit funds
covered. Our analysis spans 1997 through to 2015 and covers 223 actively managed credit hedge funds and
244 actively managed credit mutual funds. In addition, while most studies focus on just returns, we also
study holdings, increasing the power of our analysis.
A key finding is that actively managed credit hedge funds load significantly on credit market beta,
while active mutual fund returns load on carry. This is an interesting and important result as (1) carry is the
least compensated characteristic we examine (although it is arguably the easiest to implement, which may
explain its widespread use) and (2) high exposures to carry add (potentially undesirable) implicit market risk
to investor portfolios. The finding that mutual fundsβ active returns load on carry is consistent with recent
empirical research showing that bond investors tend to reach for yield (Becker and Ivashina 2015).
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3. Data and Methodology
3.1 Corporate Bond Data
Our analysis is based on a comprehensive panel of U.S. corporate bonds between January 1997 and
April 2015 on a monthly frequency. This panel includes all constituents of the Bank of America Merrill
Lynch (βBAMLβ) investment-grade (βUS Corporate Masterβ) and high-yield (βUS High Yield Masterβ)
corporate bond indices.
Following the criteria of Haesen, Houweling and VanZundert (2013), we select a representative bond
for each issuer every month. The criteria used for identifying the representative bond are selected so as to
create a sample of liquid and cross-sectionally comparable bonds. Specifically, we select representative
bonds on the basis of (i) seniority, (ii) maturity, (iii) age and (iv) size.
First, we filter bonds on the basis of seniority, limiting ourselves to only senior debt. We then select
only bonds corresponding to the most prevalent rating of the issuer. To do this, we first compute the amount
of bonds outstanding for each rating category for a given issuer. We keep only those bonds that belong to the
rating category that contains the largest fraction of debt outstanding. This category of bonds tends to have
the same rating as the issuer. Second, we filter bonds on the basis of maturity. If the issuer has bonds with
time to maturity between five and 15 years, we remove all other bonds for that issuer from the sample. If
not, we keep all bonds in the sample. Third, we filter bonds on the basis of time since issuance. If the issuer
has any bonds that are at most two years old, we remove all other bonds for that issuer. If not, we keep all
bonds from that issuer in the sample. Finally, we filter on the basis of size. Of the remaining bonds, we pick
the one with the largest amount outstanding. A deliberate consequence of our bond selection criteria is that
we will not be exploring a liquidity premium (such as issue size) for our primary empirical analyses.
Our resulting sample includes 274,665 unique bond-month observations, corresponding to 11,804
bonds issued by 4,296 unique firms. Table 1 reports annual statistics describing the composition of our
sample over time. The average month in the sample consists of 1,247 bonds representing $573 billion of
total notional outstanding, of which 59% (37%) corresponds to investment grade (high yield) issues. To
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construct variables requiring financial statement information, we can link 48% of our universe to the
Compustat database (using CUSIP and Ticker identifiers contained in the BAML dataset).
Next we describe a few key variables contained in the BAML dataset. Option-adjusted-spread (OAS)
is the fixed spread that needs to be added to the Treasury curve such that the corporate bondβs discounted
payments match its traded market price (accounting for embedded options). Duration, which measures a
bondβs sensitivity to interest rates, is also adjusted for embedded optionality. BAML provides total returns
as well as excess returns, which are equal to total returns minus the return of a duration-matched Treasury.
Credit ratings are based on Standard & Poorβs ratings classification system. To construct numerical ratings
that can be used in our regressions, we map ratings of AAA, AA, A, BBB, BB, B, CCC, CC, C and D to
scores of 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10, respectively. A rating less (greater) than or equal to 4 (5) therefore
corresponds to investment grade (high yield). As newly issued bonds tend to be more liquid, we define a
measure of bond illiquidity labelled βage percent,β which is computed as time-since-issuance (in days)
divided by original maturity (in days).
Table 2 provides a description of several issue and issuer characteristics. All of our variable
definitions are contained in Table A.1. For each characteristic, we compute several statistics (e.g., mean,
standard deviation, and various percentiles) on a monthly basis and report the average of these monthly
statistics in the table. The average issue in our sample has an OAS of 386 basis points, duration of 5.1 years,
$437 million of notional outstanding, 7.8 years to maturity, and age percent of 28%. The average issuer in
our sample has a six-month bond excess return momentum of 5% and market leverage of 0.31.
For our empirical analysis of actively managed credit hedge funds, we source our data from HFRI
(HFR database). For our time-series analysis examining the beta and characteristic exposures of actively
managed credit hedge funds, we use the HFRI Relative Value: Fixed Income: Corporate Index. We have
monthly hedge fund index return data from January 1997 through to April 2015 inclusive. For our cross-
sectional analysis of the beta and characteristic exposures across actively managed credit hedge funds, we
use net-of-fees monthly return data for individual hedge funds whose return series are captured by HFR and
who have at least 24 months of return data. This includes all βgraveyardβ funds that fall out of the respective
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index return series as well. We have monthly return data for 223 individual credit hedge funds for the period
January 1997 through to April 2015, inclusive. The median fund is in the sample for 60 months, and at the
median month, there are 84 hedge funds present. Our starting fund sample includes all those with the main
strategy classification βrelative valueβ and the sub-strategy classification βfixed income β corporateβ within
the HFR database. We then exclude funds that do not appear to have significant US corporate exposure by
excluding those whose names include βEmerging,β βEuropean,β βMunicipal,β βTax,β βEurope,β βBrazil,β
βLatin,β βStructured,β βLoan,β βInterest Rate Arbitrage,β βEuro,β βConvertible,β βRussia,β βLatam,β
βEquities,β βLeveraged,β βAsian,β or βEM.β We scan the remaining dataset for multiple instances of the
same fund (e.g., same underlying portfolio but different share classes, legal structures, etc.) and remove
duplicates.
For our empirical analysis of actively managed credit mutual funds, we source our data from
Morningstar Direct. We limit ourselves only to the 1,386 open-end mutual funds that fall within the global
broad category βfixed income,β and then within that universe we further limit our focus to mutual funds that
have at least 80 percent of their exposures to the corporate sector and retain the oldest share class of each
fund. We also require each fund to have at least 24 monthly return observations. Our final sample of actively
managed credit mutual funds is 244 unique funds. To compute an index return for actively managed credit
mutual funds, we calculate an equal weighted average of the returns across these funds. Our return data
spans the period January 1997 through to April 2015, inclusive. For actively managed credit mutual funds,
we also can examine holdings based exposures to credit beta and characteristics. Our holdings data for high-
yield open-end funds is sourced from Lipper Emaxx. We identify active weights for 102 high-yield mutual
funds using the relevant high-yield benchmark for each fund. Our holdings-based analysis is limited to
September 1997 through to May 2014.
3.2 Characteristic Measures
In this section, we define the four key characteristics that we use to explain cross-sectional variation
in corporate bond excess returns. Our choices are driven by the desire to have intuitive and, to the extent
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possible, standard measures that span both public and private issuers of corporate bonds. When multiple
measures satisfy that criteria, we combine them using equal-risk weights to obtain a more robust portfolio
and make the results less susceptible to a specific variable selection.1 We deliberately do not select size as a
characteristic, as the corporate bond market is notoriously expensive to trade. Our interest is in the
identification of characteristics that explain excess returns of large and liquid corporate bonds.
Koijen, Moskowitz, Pedersen, and Vrugt (2014) define an assetβs carry as its βexpected return
assuming its price does not change.β A simple and widely known measure of carry in fixed income
instruments is yield-to-maturity. While we could use each bondβs yield-to-maturity, we prefer to use its OAS
for a couple reasons. First, OAS captures the credit spread in excess of the risk-free Treasury curveβhence
it is not affected by interest rate duration exposure, as our goal within this paper is to focus on credit excess
returns. Second, OAS resembles yield but adjusts for any embedded optionality and is thereby more
comparable across issues. Note that our measure of carry ignores spread roll-down and any expected default
losses. Given the challenges in reliably estimating issuer level credit curves, we ignore roll-down measures
of carry. We incorporate expectations of default losses in our measure of the value characteristic described
below.
Past research has identified a tendency for safer low-risk assets to deliver a higher risk-adjusted
return (e.g., Frazzini and Pedersen 2014; Carvalho, Dugnolle, Xiao and Moulin 2014). We apply this idea to
corporate bonds by building a defensive (or low-risk) measure issuers using multiple variables. By using
multiple measures, we will end up with a more robust measure of risk as well as being assured that our
results do not rely on any single specific variable choice.
Our first measure is market leverage, measured as the value of net debt (book debt + minority
interest + preferred stocks β cash) divided by the sum of the value of net debt and market value of equity.
Both intuitively and theoretically speaking, firms with higher levels of leverage (or greater use of debt) are
more likely to default and are hence fundamentally riskier (e.g., Altman 1968; Shumway 2001).
1 If one of the measures is missing, we assign a zero score such that the combination will have a nonmissing score for the union of
names which have at least one nonmissing score.
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Our second measure of safety is gross profitability as defined in Novy-Marx (2013). Unlike other
profitability measures, such as net income over equity value, gross profitability speaks to the quality of the
overall assets owned by the firm. As such, it reasonably proxies for the safety of the enterprise, covering
both equity and debt claims.
Our third measure of safety is simply low duration. Binsbergen and Koijen (2015) document that
short maturity securities across different asset classes tend to have higher risk-adjusted returns. Palhares
(2013) has shown that this also holds among single-name credit default swaps. Here we apply the same
concept to corporate cash bonds.
Note we have excluded beta and volatility as measures of the defensive theme. For financial
instruments that trade in cash markets (i.e., government bonds and equities), there is reliable evidence of a
negative relation between beta and future excess returns (e.g., Frazzini and Pedersen 2014). A reason for this
negative relation is the prevalence of leverage-averse investors in cash markets who seek higher returns by
buying higher beta assets as opposed to levering up the mean-variant efficient portfolio. Indeed, evidence
from holdings of equity mutual fund shows that the average stock held has a beta of about 1.08 (see Table
11 of Frazzini and Pedersen 2014).
For credit markets, both systematic and idiosyncratic volatility can be captured by the product of
duration and spread (Ben Dor et. al. 2007). The first component, duration, has been shown to be negatively
associated with risk-adjusted returns in equities, bonds and several other asset classes (e.g., Palhares 2013;
Binsbergen and Koijen 2015). The second component, credit spread, simply measures carry in credit
marketsβalso our choice for the carry characteristicβand is expected to have a positive relation with future
credit excess returns. Beta and idiosyncratic volatility, therefore, both combine two measures that have
confounding effects on expected returns, and hence their inadequacy as suitable characteristics to explain
corporate bond excess returns. Duration, however, is still viable as a defensive measure.
For our momentum characteristic, we use two widely studied momentum measures. The first is credit
momentum defined as the trailing six-month bond excess return. Jostova (2013) shows that, in a broad
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sample of corporate bonds, including both high-yield and investment-grade securities, past winners tend to
outperform past losers.
The second momentum measure is the six-month equity momentum of the bond issuer. Kwan (1996)
and Gebhardt et al. (2005b) show that stock returns tend to lead corporate bond returns. One drawback of
this measure is that it is only available for issuers with publicly traded equity, limiting the coverage in our
sample if this were a single momentum variable.
To construct a value signal, we need a market value measure (price, yield, spread, etc.), at least one
fundamental value measure and a way to compare the two. For example, Fama and French (2003) use the
price of a stock for the market measure, the book value for the fundamental measure and the ratio to make a
comparison.
We use credit spread as the market measure, two measures of fundamental value and a cross-
sectional regression of the logarithm of spread on the respective fundamental anchors. For the first, we
follow Correia et al. (2013) and use the issuer default probability. We measure the default probability as do
Bharath and Shumway (2008). One drawback of this approach is that it can only be computed for issuers
with publicly traded equity. To increase coverage, we use a second value anchor that combines three broadly
available fundamental measures: credit rating, bond duration and the volatility of bond excess return returns
in the last 12 months.
Before we can assess the relative importance of our four characteristic measures to explain cross-
sectional variation in corporate bond excess returns and the performance of actively managed credit funds,
we must adjust three of our characteristic measures. This is due to correlation between the four
characteristics. In particular, corporate bonds from issuers with less leverage, good recent performance or
both are safer and tend to command lower spreads than names that score poorly on those dimensions. Left
unadjusted, these characteristics will be strongly negatively correlated with carry, complicating the
interpretations of any analysis of those measures. We adjust our characteristic measures to un-do these
strong correlations with carry. To do this, we first rank the cross-section of corporate bonds into spread
groupings, and then within spread groupings, we rank on the relevant characteristic. This approach generates
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characteristic measures of defensive, momentum and value that have a greatly reduced correlation with
carry.
3.3 Portfolio Construction
We construct two types of characteristic portfolios. First, we follow the standard convention of
computing a zero-cost portfolio that is long corporate bonds in the highest quintile of a given characteristic
and short corporate bonds in the lowest quintile of a given characteristic. Within quintiles, we report excess
returns based on value-weighted returns. Our inferences are unaffected if we instead use equal weighting.
Second, given the well-known challenges in shorting corporate bonds (Asquith et al. 2013) and the
significant costs in trading corporate bonds relative to their underlying volatility (e.g., Bessembinder,
Maxwell and Venkataraman 2006; Edwards, Harris and Piwowar 2007), we also construct a long-only
portfolio that reflects what it would cost to trade corporate bonds. This portfolio corresponds to a realistic
investable portfolio.
To construct long-short quintile portfolios, we first rank the universe of bonds by each characteristic
and then assign each bond into one of five quintiles. We then weight each bond within each quintile
according to its outstanding market value. Given we have formed five long-only value-weighted portfolios
(i.e., Q1 to Q5), we construct a simple long-short portfolio by subtracting the bottom from the top quintile
portfolio (i.e., βQ5 β Q1β). A potentially undesirable feature of this quintile differenced portfolio is that the
risk of a given characteristic portfolio will vary both through time and across different characteristics. To
help ensure comparability of our results, we re-scale the returns to each long-short portfolio such that each
long-short portfolio targets a constant ex-ante annualized volatility of 5%. We do this by multiplying the
βQ5 β Q1β portfolio weights by a scalar equal to 5% divided by the trailing 24-month realized volatility of
the βQ5 β Q1β portfolio.2 We refer to this resulting portfolio as a constant-volatility single-characteristic
portfolio.
2 Between January 1997 and December 1998, we set the scalar equal to its value as of January 1999.
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We then combine our four individual characteristics into one composite multi-characteristic
portfolio. First, we combine the single-characteristic portfolios, weighting each equally. Second, we rank the
composite characteristic portfolio to form quintile portfolios and then, as before, construct a constant-
volatility multi-characteristic portfolio. We also utilize this multi-characteristic portfolio to construct a long-
only portfolio that takes into consideration realistic implementation by solving a linear optimization
problem.
4. Results
4.1 Regression Analysis
Before reporting the performance of our portfolios, we first report Fama-Macbeth regressions of
monthly corporate-bond excess returns regressed onto lagged characteristics along with several control
variables. Each month, we run cross-sectional regressions of the form:
π π,π‘+1 = πΌ + π½1πΆπ΄π π ππ,π‘ + π½2π·πΈπΉπ,π‘ + π½3ππππ,π‘ + π½4ππ΄πΏππΈπ,π‘ + πΎπ + ππ,π‘+1, (1)
where π π,π‘+1 denotes the duration-hedged excess return of bond i over month t+1. Each of the four
characteristics is converted to a normalized variable. Specifically, for each characteristic, for every month,
we rank issues by their characteristic values, subtract the mean rank and then divide by the standard
deviation of the ranks. We also fill missing values with zero, but the results are robust if we do not. As a
result, estimated coefficients may be interpreted as the future one-month excess return difference for a one
standard deviation difference in characteristic ranking. To rule out the hypothesis that the characteristics
predict returns because they proxy for traditional measures of risk, we include control variables in the
regression. The first variable is a market beta, where the market is defined as the credit return of the cap-
weighted portfolio of all bonds in our database. For robustness, we also include two other traditional
measures of risk in credit marketsβrating and durationβas well as a proxy for illiquidity, age percent.
Table 3 reports our Fama-Macbeth regression estimates for the monthly sample period from January
1997 to April 2015. Regression (1) includes just an intercept and beta, and regression (2) adds our control
variables. Regressions (3) through (6) evaluate the predictive ability of each of our characteristics on a
15
standalone basis. Both individually and combined, the value and momentum characteristics have
explanatory power for corporate bond excess returns. The carry characteristic does not exhibit a reliable
association with future bond excess returns as a standalone variable but is marginally significant when
controlling for the remaining characteristics. The opposite is true with defensive: it is highly significant as a
standalone variable but loses significance when controlling for value and momentum. This suggests that the
defensive theme in credit may be spanned by the value and momentum themes. This is not surprising as the
value factors we build for credit make explicit use of fundamental information. Our value measures identify
a bond as cheap when its spread is wide relative to default probabilities. Our measures of default
probabilities include distance to default and rating information. These fundamental anchors incorporate
measures of leverage and expected profitability. As a consequence it is not surprising that they help explain
the defensive premium.
The average R-squared of the Fama-Macbeth cross-sectional regressions is 15 percent, suggesting
that our characteristics collectively explain a nontrivial portion of the cross-sectional variation in bond
excess returns. The interpretation of the 15 percent average explanatory power is not that we can predict 15
percent of the variation in corporate bond excess returns but rather that knowledge of the four characteristics
combined with (unknown ex ante) time-varying exposures to our four characteristics can explain 15 percent
of the variation in corporate bond excess returns (e.g., Lewellen 2015). The value and momentum
characteristics have the strongest statistical relation with future excess returns, as indicated by the large
positive Fama-Macbeth test statistics in the final column.
4.2 Long-Short Quintile Portfolios
Table 4 reports performance statistics of our long-short quintile portfolios. Consistent with the Fama-
Macbeth results, we see the strongest positive association between characteristics and returns for defensive,
momentum and value. A portfolio that combines all of the factors at an equal weight (i.e., combined)
performs even better, with an annualized Sharpe Ratio of 2.19, a highly diversified set of exposures. While
the carry characteristic is relatively less attractive on a stand-alone basis, it has low correlation with the other
16
characteristics. (See the correlations reported in table 5.) This means that the combination of characteristics
provides additional diversification benefits than any one characteristic considered in isolation. Note also that
the realized volatilities of the constant-volatility portfolios are close to the targeted value of 5%, confirming
that our simple scalar methodology succeeds reasonably in estimating the volatility of the combined
portfolio.
Across all characteristics, we can see that the long-short returns are driven by positive performance
on the long-side and negative (or weaker) performance on the short-side. In fact, reading Sharpe ratios
across each of the rows clearly illustrates that performance is generally monotonically increasing across
quintiles for each of the characteristics.
Figure 1 plots cumulative excess characteristic returns over time. We can see that performance,
especially for the combination of characteristics, is not driven by any particular sub-period and has not
changed substantially over time. While different characteristics performed better and worse over different
sub-periods, it is clear that the combined portfolio has been relatively stable in its outperformance. This
pattern of robust performance of a combination of characteristics resembles that observed in equity markets
(Asness et al. 2015). Not surprisingly the most visible drawdown is carry during the Global Financial Crisis,
when investors sought safe assets and shunned riskier ones like high-yield bonds (e.g., Koijen et al. 2014).
To better understand the potential diversifying properties of the four characteristics, we report return
correlations for the various characteristics with well-known risk premia. We report the various pairwise
return correlations in Table 5 using the full time series of data for the period January 1997 through to April
2015, inclusive. We consider the following estimated risk premia: (i) credit risk premium (βCREDITβ),
measured as the value-weighted corporate-bond excess returns; (ii) equity risk premium, measured as the
difference between the total returns on the S&P500 index and one-month U.S. Treasury bills (βEQUITYβ);
(iii) Treasury term premium (βTSYβ), measured as the difference between total returns on 10-year U.S.
Treasury bonds and one-month U.S. Treasury bills; and (iv) returns for actively managed credit hedge funds
(Hedge Funds) in excess of the one-month U.S. Treasury Bills.
17
Several of the correlations in Table 5 are worth discussing. First, among the four characteristics, we
see negative correlations between carry and the other three measures. This is not surprising as issuers with
higher spreads will typically have considerable leverage and low profit margins (part of defensive), will
have experienced poor recent performance (poor momentum) or both. The correlations reported here are still
negative even after our attempt to mitigate the negative correlation with carry by first ranking bonds into
spread groups and then ranking on characteristic measures within spread groups. But they are considerably
less negative than without this adjustment. Conditional on each characteristic generating a positive risk-
adjusted return on a stand-alone basis as was evident in tables 3 and 4, the relatively low (and sometimes
negative) correlations across characteristics shows the potential benefit of diversifying across characteristics.
Second, the correlations between the various characteristic measures and well-known sources of risk premia
further emphasize the diversifying benefits of characteristics within corporate bonds. With the exception of
carry, the return correlations between the characteristic factors and risk premia are all less than 0.30 and are
often negative. Perhaps most interesting is the fact that actively managed credit hedge funds have very high
exposure to the carry characteristic (0.76) and credit risk premium (0.83) and negative exposures to
defensive and momentum, both of which offer positive risk-adjusted returns. We return to the exposures of
both actively managed credit mutual and hedge funds in Section 4.4.
To further examine the correlation structure of our corporate bond characteristics, we regress each
long/short characteristic return on credit risk premium (CREDIT), Treasury term premium (TSY) and factor
mimicking portfolio returns (Fama-Frenchβs SMB, HML and UMD and Asness et al.βs (2014) QMJ).
Specifically, using the full time series of data for the period January 1997 through to April 2015, inclusive,
we run the following regression:
πΆπ»π΄π π΄πΆππΈπ πΌπππΌπΆπ‘ = πΌ + π½1ππππ‘ + π½2πΆπ πΈπ·πΌππ‘ + π½3πππ΅π‘ + π½4π»ππΏπ‘ + π½5πππ·π‘ + π½6πππ½π‘ + ππ,π‘. (2)
Consistent with the simple correlations reported in Table 5, we see in Table 6 that the carry
characteristic has a significant positive exposure to credit risk premium. After controlling for other well-
known sources of return, the intercept is not significant for carry. The defensive characteristic is negatively
18
correlated with market risk premia (e.g. credit risk premium), consistent with it reflecting a flight to quality
or a risk-on/risk-off tendency of investors.
Momentum has a positive correlation with UMD and nothing else. Credit value exhibits a negative
loading on SMB and QMJ, β2.0 and β2.3 t-statistics respectively. Interestingly, the value characteristic in
credit markets is mildly negatively associated with the HML factor, a result consistent with the evidence that
characteristic portfolios in one asset class have limited correlations with those in other asset classes (Asness
et al. 2015). In the final column of Table 6, we regress the combined characteristic long-short portfolio
return onto the various market risk premia and equity factor returns. The combined portfolio does not have a
statistically significant loading on any of the equity factors and a mildly negative relation with term
premium. As a consequence, its intercept is a significant 123 basis points per month (test statistic of 9.6).
The combination is a well-compensated and diversifying source of returns.
The economic magnitude of the intercept requires further discussion. The literal interpretation would
suggest that 123 bps per month is available for investors. Such a statement needs to be interpreted very
cautiously. Corporate bond and equity markets differ substantially in terms of their trading costs. For
example, Chen et al. (2007) show that the average bid-mid spread for BBB-rated and B-rated medium
maturity bonds are 22 bps and 30 bps, respectively. Frazzini et al. (2012) report average value-weighted
trading costs for global equities of 20 bps. These numbers, however, severely understate the impact of
transaction costs, as stocks are much more volatile than bonds. Andersen et al. (2001) find that the median
stock volatility is 22%, whereas the median bond in our sample has an excess return volatility close to 7%.
More importantly, whereas our combined one-dollar-long-and-one-dollar-short portfolio from Table 4 has a
2.5% annualized volatility, Fama-French HMLβs factor has a 11.6% annual volatility over the same period.
Given the similarity in dollar transaction costs estimates across bonds and stocks, and similar turnover
across bond and stock portfolios, the bond portfolio must have a far greater gross Sharpe ratio to compensate
for the fact that it has nearly one fifth of the volatility of the stock portfolio.
To illustrate any time-varying performance across the various characteristics (in Figure 2), we use
the full-sample regression coefficients from Table 6 to compute 36-month rolling average alphas for each
19
respective long/short characteristic portfolio. While outperformance has been marginally attenuated in recent
years, it is clear that excess returns have been relatively stable and positive.
4.3 Long-Only Optimized Portfolio
While our long-short characteristic portfolios document relations between our selected characteristics
and future bond excess returns, they do not take into account actual portfolio implementation considerations.
To more realistically address the hypothetical performance of our characteristic portfolios, we build and test
optimized long-only portfolios with explicit portfolio implementation constraints. Hence our optimized
portfolios are designed to be comparable to traditional actively managed corporate bond portfolios, which
tend to be long-only (as individual bonds are difficult to short).
We build and rebalance long-only portfolios on a monthly frequency by solving a linear optimization
problem. While mean-variance optimization is a commonly utilized objective function in portfolio
construction, here we build our portfolios using a simpler objective function that does not require estimation
of an asset-by-asset covariance matrix (i.e., an asset-level risk model). Our optimization problem is specified
as follows:
πππ₯ππππ§π: β π€π . πΆπππ΅ππ
πΌ
π=1
π π’πππππ‘ π‘π:
π€π β₯ 0, βπ (ππ π βπππ‘πππ ππππ π‘πππππ‘)
|π€π β ππ| β€ 0.25%, βπ (πππ£πππ‘πππ ππππ ππππβππππ ππππ π‘πππππ‘)
β π€π
πΌ
π=1
= 1 (ππ’πππ¦ πππ£ππ π‘ππ ππππ π‘πππππ‘)
β|π€π,π‘ β π€π,π‘β1| β€ 10% (π‘π’ππππ£ππ ππππ π‘πππππ‘)
πΌ
π=1
β|(π€π,π‘ β π€π,π‘β1). ππ πΌπΆπΈπ,π‘| β₯ $100,000, βπ
πΌ
π=1
(ππππππ’π π‘ππππ π ππ§π ππππ π‘πππππ‘)
β|(π€π β ππ). ππ΄ππ| β€ 0.50% (πππ£πππ‘πππ ππππ ππππβππππ π πππππ ππππ π‘πππππ‘)
πΌ
π=1
20
β |(π€π β ππ). π·π’πππ‘ππππ| β€ 0.50 (πππ£πππ‘πππ ππππ ππππβππππ ππ’πππ‘πππ ππππ π‘πππππ‘)πΌπ=1 ,
where π€π is the portfolio weight for a given bond, and πΆπππ΅ππ is an equal-weighted combination of the
carry, defensive, momentum, and value long-short characteristic portfolios for a given bond. When
computing the realized returns from our optimal portfolio holdings, we subtract an estimate of transaction
costs based on each bondβs rating and maturity in line with Table 1 of Chen, Lesmond, and Wei (2007).
ππ πΌπΆπΈπ is the bond price for a given bond, ππ΄ππ is the option adjusted spread for a given bond,
π·π’πππ‘ππππ is the effective duration for a given bond, and ππ is the benchmark portfolio weight for a given
bond based on a value-weighted benchmark of all corporate bonds in our one-bond-per-issuer dataset.
The solution to this optimization problem is a long-only corporate bond portfolio that has maximal
exposure to the combined characteristic portfolio while taking into consideration the challenges of trading
corporate bonds as well as the risk contribution of individual positions to the final portfolio. Importantly, we
limit the portfolioβs differences from (or tracking error to) the benchmark by limiting the portfolioβs active
weights relative to the benchmark (i.e., at most 25 bps), limit the portfolioβs aggregate OAS exposure to be
within 50 bps of the benchmark, and limit the portfolioβs aggregate duration exposure to be within 0.50
years of the benchmark. As discussed earlier, Ben Dor et al. (2007) document that spread and duration are
the key determinants of volatility in credit markets. Hence constraining the aggregate active weights on
these two dimensions is a simple and transparent way to control the active risk of the long-only portfolio.
We also constrain turnover to at most 10% per month and force trades to be at least $100,000. Despite our
best efforts to incorporate constraints and transaction costs, the trading of corporate bonds is challenging.
Thus we add the caveat to our empirical results that dynamic trading strategies in corporate bonds are not as
implementable as those in more liquid assets.
Table 7 reports performance statistics for the optimized long-only portfolio as well as the
benchmark. The portfolio earned an annual average excess return of 5.72% per year (and 5.26% after taking
into account estimated transaction). Given its realized annualized volatility of 5.1%, the net Sharpe ratio
over this period was 1.03. By comparison, the gross (net) benchmark earned a 4.14% (3.84%) annualized
excess return with a Sharpe ratio of 0.69. The active portfolio (i.e., portfolio minus beta times the
21
benchmark) realized an annualized net information ratio of 0.86 with a tracking error of 2.56%. Figure 3
shows the cumulative performance of the portfolio and the benchmark.
4.4 Credit Fund Characteristic Exposures
Next we investigate how actively managed credit hedge funds and mutual funds load on each of our
characteristic portfolios. For actively managed credit hedge funds, we are limited to an analysis of aggregate
and individual hedge fund returns. For actively managed credit mutual funds, we can examine both
aggregate and individual fund returns as well as individual fund holdings.
The first step in our analysis is to disentangle the active and passive exposures embedded in fund
returns. For mutual funds, we extract the active returns by subtracting a benchmark return from their returns.
For each fund, we find its benchmark by searching for the index that maximally explains a fund return
across seven possible indexes: a broad high-yield index from BAML (H0A0), a constrained version that
caps weights at 2% (HUC4), a version that excludes distressed names (H4ND), a version that excludes
financials (H0NF), a version that restricts the lowest rating to B3 (H0A4), an investment-grade index
(C0A0), and an overall credit return that contains all the bonds in both the main high-yield and investment-
grade indexes. In unreported analysis, we use H0A0 across all funds and find similar results.
Table 8 reports the fraction of the variance of the fund return explained by its selected benchmark:
π 2 = 1 βπ(πΉπ’ππβπ΅πππβππππ)2
π(πΉπ’ππ)2 .
On average 70% of the variance of the return of mutual funds comes from the benchmark. The
distribution is skewed to the left, with a few funds running at lower correlations, whereas the median fund
has an 89% R-squared.
Credit hedge funds usually do not have an explicit benchmark, but given the evidence that several
hedge fund indices exhibit beta (Asness et al. 2001), it is likely that credit hedge funds also do. We remove
these passive exposures from their returns using a more flexible framework. We run regressions of credit
hedge fund returns onto measures of the passive return from credit, equity and government bond markets.
We then use these estimated regression coefficients to create a custom benchmark for each credit hedge
22
fund. For our sample of 223 US-oriented credit hedge funds, 41% of the variation in its returns can be
attributed to passive exposures. Similar to credit mutual funds, this distribution also has a wide distribution,
and notably more than 25 percent of credit hedge funds have half of their active returns explained by passive
exposure to credit, equity and bond markets.
In panel B of Table 8, we apply the same methodology to an externally built hedge fund indexβthe
HFRI Relative Value: Fixed Income Corporate Index. A benefit of this index is that it is constructed by HFR
using point-in-time data, but it contains credit hedge funds whose primary exposures are beyond corporate
credit. In any case, the returns to this index can be largely explained by passive exposure to credit, equity
and bond markets. In the final column of panel B, the explanatory power is 73 percent. Overall both at the
aggregate and single-fund level, credit mutual funds and credit hedge funds exhibit considerable passive
exposure to market risk premia.
Table 9 reports time-series regressions of credit hedge fund and mutual fund active return indices
onto our characteristic long-short portfolios. Active returns are computed as the difference between total
returns for each fund and the estimated benchmark identified from Table 8. Panel A reports results for the
active returns on the HFRI Relative Value Fixed Income: Corporate Index. Panel B and C report results for
an equal- and a value-weighted average of our 223 US-oriented credit hedge funds, respectively. Panel D
reports results for an equal-weighted average of our 244 actively managed credit mutual funds.
In Table 9 Panel A, we see that the HFRI Fixed Income Relative Value: Corporate index is
significantly exposed to value, carry and defensive but not momentum. All these factors combined explain
11.3 % of the time-series variation of the hedge fund index active returns. Panels B and C display the results
for our custom benchmarks. Those funds have a stronger and statistically significant exposure to value, but
all remaining loadings are insignificant. Value returns alone explain 10 percent of the time-series variation
of our equal-weighted hedge fund index and 5.6 percent of the value-weighted index.
For credit mutual funds index in Panel D, we find positive and significant exposures to carry and
momentum as well as weaker positive exposure to defensive. Overall, the ability of our four characteristics
23
to explain time-series variation in the active returns of credit hedge funds and credit mutual funds is limited
to between 7%β15%.
The results above are based only on time-series regression of fund aggregates on different portfolio
returns. Next we consider an approach that instead relies on the cross-sectional variation in factor exposures
across different funds. For each credit hedge fund and mutual fund in our sample, we estimate the following
regression:
πππ‘ππ£π πππ‘π’πππ‘+1 = π1 Γ π£πππ’ππ‘+1 + π2 Γ ππππππ‘π’ππ‘+1 + π3 Γ πππππ¦π‘+1 + π4 Γ ππππππ ππ£ππ‘+1 + π0 + ππ‘+1.
Given the short sample period for many funds (the median sample size is 60 months), we estimate
this regression in two steps. We first orthogonalize each characteristic portfolio return with respect to the
remaining characteristics and then run four univariate regressions of fund active returns on those
orthogonalized characteristic portfolio returns. Figure 4 shows the cross-sectional distribution of t-statistics
on each of the characteristic portfolios through density plots. The average t-statistic on carry is 0.11 for
hedge funds and 1.22 for mutual funds. We then test whether these average t-statistics differ from zero and
find that the hedge fund result is marginally significant whereas the mutual fund result is strong (t-statistic of
6.03). The average t-statistics on defensive and momentum are also much smaller for hedge funds compared
with mutual funds, 0.19 versus 0.44 (defensive) and 0.03 and 0.36 (momentum), respectively. For the value
characteristic, we see the reverse pattern. Hedge funds have an average t-statistic of 0.72 (p-value <0.01),
while mutual funds have a very slight loading average of 0.06, statistically indistinguishable from zero.
Our final empirical analysis utilizes actual holdings for a sample of 3,890 reports of unique 102 high
yield mutual funds for the period September 1997 through May 2014. We source mutual fund holdings from
Lipper Emaxx. Many fixed income funds invest in a broad variety of fixed income instruments including
government bonds, agency bonds and corporate bonds. Given our focus is on security selection within
corporate bonds, we limit our attention to only high yield mutual funds as they primarily invest only in
corporate bonds, leaving us with 102 distinct funds.
In our first exercise, we examine the holdings exposure of high yield mutual funds to our four
characteristics. For each fund, we take every holding report contained within Lipper Emaxx. The typical
24
fund will report holdings at a quarterly frequency. For all corporate bonds in both the mutual fund and its
benchmark portfolio, we measure our standardized characteristics, subject to data availability. We then
compute the fund-report active tilt as:
πππ‘ππ£π π‘πππ‘ πβππππ’ππ,πππ‘π = β (π€πππππΉπ’ππ β π€ππππ
π΅πππβππππ) Γ πβππππππ
ππππβπ΅πππβππππβͺπΉπ’ππ
.
For each characteristic, we report the average across both funds and reports in Panel A of Table 10.
Consistent with what we found in Panel D of Table 9, the value active tilt is indistinguishable from zero (1.8
t-statistic) but positive for the other characteristics, being largest for carry at 0.10.
In panel B of Table 10, we extend the test of differences across individual characteristics to a
multiple regression that includes all four characteristics simultaneously. This analysis is estimated by fund
report, and we average results across all fund reports. Actively managed credit mutual funds tend to hold
bonds that score positively on the carry, defensive and momentum characteristics and tend to avoid bonds
that score positively on the value characteristic. The economic interpretation of the regression coefficients is
as follows. The median portfolio weight of a given bond in the BAML high yield index is 4 bps. A one
standard deviation increase in the carry characteristic is associated with a 2 bps greater bond weight, a 50
percent increase in the unconditional weight of a bond.
Overall, the results are consistent with the return-based ones displayed in panel D of table 9 and in
Figure 4. In both set of analyses, we see positive loadings on carry, momentum and defensive. The value
exposure was positive but statistically insignificant in the return-based analysis but negative and significant
when we examined holdings. The holdings based analysis is, however, arguably the more powerful research
design to capture the true exposures of actively managed credit mutual funds. The negative exposure to the
value characteristic suggests that the average credit mutual fund is pursuing an investment strategy based on
bond characteristics that are distinct from underlying default risk. In part, this avoidance can be viewed as a
basis for the strength of the value characteristic itself.
The correlation between characteristics and holdings is informative but it is far from causal. For
example, mutual funds may not dislike good value bonds per se. But those bonds may tend to have other
features (e.g., maybe they were issued by a sector for which sentiment is low), and it is those correlated
25
omitted characteristics that explain portfolio manager interest in holding or avoiding those bonds. To help
address the issue of correlated omitted variables, we next examine correlations between changes in holdings
of credit mutual funds with changes in the underlying characteristics. The key identifying assumption is that
omitted variables that affect holdings that are also correlated with our characteristics are stable over time.
The changes analysis is estimated for each fund report, and, as before, results reported are averages
across all fund reports. Mutual funds typically report holdings quarterly. We can thus measure changes in
bond holdings quarterly and can measure changes in characteristics monthly. To allow for sluggish response
in portfolio manager trading decisions to changing characteristics, we regress bond-holding changes onto the
changes in bond characteristics over the most recent five months. The idea is to include enough lags to
capture the characteristic changes since the last rebalance date that is unobservable to us but plausibly
contained in the previous two months before the last holding report. The results are reported in Table 11.
The first five columns report regression coefficients for the most recent five month change in characteristics
individually. The final column reports the sum of regression coefficients across those five months. The
results here resemble the inferences from Table 10. Actively managed credit mutual funds tend to increase
holdings of bonds that have had an increase in their carry, momentum and defensive characteristics and
decrease holdings of bonds that have had an increase in the value characteristic.
5. Conclusion
We undertake a comprehensive analysis of the cross-sectional determinants of corporate bond excess
returns. We find strong evidence of positive risk-adjusted returns to measures of carry, defensive,
momentum and value. These returns are diversifying with respect to both known sources of market risk
(e.g., equity risk premium, credit risk premium and term premium) and characteristic returns that have been
documented in equity markets (e.g., size, value and momentum).
Realistic long-only portfolios can be constructed to achieve maximal exposure to the four
characteristics we investigate. For a broad sample of corporate bonds in the U.S. for the period January 1997
through to April 2015, inclusive, we find that an active long-only portfolio earns 2.2% in excess of the
26
benchmark annually with an information ratio of 0.86. This long-only portfolio reflects transaction costs,
trading limits and position constraints, suggesting that it is possible to build meaningful portfolios with
exposures to well-compensated characteristics within the corporate bond universe.
Our final analyses examine the exposures of actively managed credit hedge funds and actively
managed credit mutual funds. We find that both sets of actively managed credit funds have significant
exposure to beta through exposure to credit risk premium. Hedge funds tend to have positive exposures to
value but muted exposure to the other characteristics. Mutual fund exposures are approximately a mirror
image of that of hedge funds, with zero or negative exposures to value but positive exposures to carry,
momentum and defensive.
Overall, despite evidence of (i) a robust relation between well-known characteristics (i.e., carry,
defensive, momentum and value) and corporate bond excess returns and (ii) feasible implementation of
exposure to these characteristics in a long-only portfolio, individual credit funds are underexposed to
characteristics that generate meaningfully positive risk-adjusted returns. Investors in actively managed credit
funds should be aware of the hidden beta they are exposed to and should prefer an investment product
designed to isolate exposure to well-compensated characteristics that diversify market risk premium.
27
References
Altman, Edward I. (1968). Financial Ratios, Discriminant Analysis and the Prediction of Corporate
Bankruptcy. Journal of Finance, 23, 4 189β209
Andersen, Torben G., et al. (2001). The distribution of realized stock return volatility. Journal of Financial
Economics, 61.1: 43-76.
Asness, Clifford S., Andrea Frazzini and Lasse Heje Pedersen (2014). Quality minus junk. Working paper.
Asness, C., R. Krail and J. Liew (2001). Do hedge funds hedge? Journal of Portfolio Management, 28, 6β
19.
Asness, C., A. Ilmanen, R. Israel and T. Moskowitz (2015). Investing with Style. Journal of Investment
Management, 13, 27β63.
Asness, C., T. Moskowitz and L. Pedersen (2013). Value and momentum everywhere. Journal of Finance,
68, 929β985.
Asquith, P., A. S. Au, T. Covert and P. A. Pathak (2013). The market for borrowing corporate bonds.
Journal of Financial Economics, 107, 155β182.
Becker, B., and V. Ivashina (2015). Reaching for yield in the bond market. Journal of Finance, 70, 1863β
1902.
Ben Dor, A., L. Dynkin, J. Hyman, P. Houweling, E, Van Leeuwen and O. Penniga (2007). DTS (duration
times spread). The Journal of Portfolio Management, 33, 77β100.
Bessembinder, H., W. Maxwell and K. Venkataraman (2006). Market transparency, liquidity externalities,
and institutional trading costs in corporate bonds. Journal of Financial Economics, 82, 251β288.
Bharath, Sreedhar T., and Tyler Shumway (2008). Forecasting default with the Merton distance to default
model. Review of Financial Studies, 21.3, 1339β1369.
Binsbergen, J. H., and R. S. J. Koijen (2015). The Term Structure of Returns: Facts and Theory. Working
paper.
Black, F. (1976). Studies of stock price volatility changes. In: Proceedings of the 1976 Meetings of the
American Statistical Association, 171β181.
Carvalho, R., P. Dugnolle, L. Xiao and P. Moulin (2014). Low-risk anomalies in global fixed income:
Evidence from major broad markets. The Journal of Fixed Income, 23, 51β70.
Chen, L., D. A. Lesmond and J. Wei (2007). Corporate yield spreads and bond liquidity. Journal of Finance,
62, 119β149.
Choi, J., and Y. Kim (2015) Anomalies and market (dis)integration. Working paper, University of Illinois at
Urbana-Champaign.
Chordia, T., A. Goyal, Y. Nozawa, A. Subrahmanyam and Q. Tong (2015). Are Capital Market Anomalies
Common to Equity and Corporate Bond Markets? Working paper, Emory University.
28
Correia, M., S. Richardson and I. Tuna (2012). Value investing in credit markets. Review of Accounting
Studies, 17 (3): 572β609.
Edwards, A. E., L.E. Harris and M.S. Piwowar (2007). Corporate bond market transaction costs and
transparency. Journal of Finance, 62, 1421β1451.
Fama, Eugene F., and Kenneth R. French. Common risk factors in the returns on stocks and bonds. Journal
of Financial Economics, 33.1 (1993): 3β56.
Frazzini, A., R. Israel and T. J. Moskowitz (2012). Trading costs of asset pricing anomalies. Working paper,
AQR Capital Management.
Frazzini, A., and L. H. Pedersen (2014). Betting against beta. Journal of Financial Economics, 111, 1β25.
Fung, W., and D. A. Hsieh (2002). The risk in fixed-income hedge fund styles. Journal of Fixed Income, 12,
6β27.
Fung, W., and D. A. Hsieh (2006). Hedge funds: An industry in its adolescence. Federal Reserve Bank of
Atlanta Economic Review.
Gebhardt, W. R., S. Hvidkjaer and B. Swaminathan (2005a). The cross-section of expected corporate bond
returns: betas or characteristics? Journal of Financial Economics, 75, 85β114.
Gebhardt, W. R., S. Hvidkjaer, and B. Swaminathan (2005b). Stock and bond market interaction: does
momentum spill over? Journal of Financial Economics, 75, 651β690.
Goldstein, I., H. Jiang, and D. T. Ng (2015). Investor flows and fragility in corporate bond funds. Working
paper, Wharton School, University of Pennsylvania.
Haesen, D., P. Houweling and J. van Zundert (2013). Residual equity momentum for corporate bonds.
Working paper, Robeco Quantitative Strategies.
Harris, L. (2015). Transaction costs, trade throughs, and riskless principal trading in corporate bond markets.
Working paper, USC.
Houweling, P., and J. van Zundert (2014). Factor investing in the corporate bond market. Working paper,
Robeco Quantitative Strategies.
Jostova, G., S. Nikolova, A. Philipov and C.W. Stahel (2013). Momentum in corporate bond returns. Review
of Financial Studies, 26(7), 1649β1693.
Kahn, R., and M. Lemmon (2015). Smart Beta: The ownerβs manual. Journal of Portfolio Management, 41,
76β83.
Koijen, R., T. Moskowitz, L. Pedersen and E. Vrugt (2014). Carry. Working paper, University of Chicago
Booth School of Business, New York University, University of Amsterdam.
Kwan, S. H. (1996). Firm-specific information and the correlation between individual stocks and bonds.
Journal of Financial Economics, 40, 63β80.
Lewellen, J. (2015). The cross-section of expected stock returns. Critical Finance Review, 4, 1β44.
29
Melentyev, O., and D. Sorid (2015). Signs of Liquidity Vacuum in Unexpected Places. Deutsche Bank
Markets Research.
Merton, R. (1974). On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance,
29, 449β470.
Ng, K. Y., and B. Phelps (2014). Structure of US corporate excess returns: The hunt for a βlow-riskβ
anomaly. Working paper, Barclays.
Novy-Marx, R. (2013). The other side of value: The gross profitability premium. Journal of Financial
Economics, 108(1), 1β28.
Palhares, D. (2013). Cash-flow maturity and risk premia in CDS markets. Working paper, AQR Capital
Management.
Shumway, Tyler (2001). Forecasting bankruptcy more accurately: A simple hazard model. Journal of
Business, 740, 101β124.
30
Table 1: Universe Statistics (January 1997βApril 2015)
The table below reports annual summary statistics of the Bank of America Merrill Lynch
(BAML) bond sample. Each column statistic is computed monthly and averaged within the
specified year. Investment grade (IG) and high yield (HY) classifications are based on S&P
ratings. Bond issues are linked to Compustat based on CUSIPs and Tickers as described in the
text. Total notional is reported in billions of dollars.
Year Count Total Notional %IG %HY
% Linked to
Compustat
1997 1,096 239 60% 40% 54%
1998 1,188 278 61% 39% 53%
1999 1,104 306 63% 37% 52%
2000 1,026 335 65% 35% 50%
2001 1,026 375 70% 30% 49%
2002 1,099 443 70% 30% 49%
2003 1,263 511 63% 37% 49%
2004 1,398 562 60% 40% 47%
2005 1,291 569 59% 41% 45%
2006 1,268 560 58% 42% 43%
2007 1,256 578 56% 44% 43%
2008 1,046 553 64% 36% 47%
2009 967 540 66% 34% 49%
2010 1,269 689 56% 44% 46%
2011 1,380 768 53% 47% 46%
2012 1,406 812 53% 47% 46%
2013 1,521 893 51% 49% 45%
2014 1,564 936 50% 50% 45%
2015 1,533 948 51% 49% 46%
Average 1,247 573 59% 41% 48%
31
Table 2: Issue and Issuer Characteristics (January 1997βApril 2015)
The table below reports summary statistics of bond issue and issuer characteristics (as defined
in Table A.1). For each characteristic, the column statistic is computed on a monthly basis and
then averaged over the full sample period.
Mean Std 5% 10% 25% 50% 75% 90% 95%
OAS 386 308 85 107 161 302 512 783 1,002
Duration 5.1 2.2 1.6 2.4 3.8 5.0 6.3 7.3 8.2
Total Ret. 0.6% 3.1% -2.9% -1.6% -0.4% 0.6% 1.7% 3.0% 4.2%
Excess Ret. 0.2% 3.0% -3.2% -1.9% -0.7% 0.2% 1.2% 2.4% 3.6%
Amt. Out. 437 442 134 159 208 309 495 811 1,123
Time to Mat. 7.8 5.1 2.7 3.9 5.5 7.1 8.7 10.4 15.5
Age Percent 28% 19% 5% 7% 12% 24% 39% 54% 67%
Rating 4.7 1.4 2.5 3.0 3.8 4.7 6.0 6.6 6.9
Dist. to Def. 6.0 3.5 1.4 2.0 3.4 5.5 8.0 10.6 12.2
Momentum 5% 16% -16% -10% -3% 2% 11% 24% 36%
Leverage 0.31 0.41 -0.02 0.03 0.13 0.28 0.47 0.66 0.77
32
Table 3: Fama-Macbeth Regressions (January 1997βApril 2015)
The table below reports Fama-Macbeth regressions of monthly bond excess returns regressed onto
normalized carry, defensive, momentum, and value style measures along with controls for market beta,
rating, duration, and age percent variables (as defined in Table A.1).
(1) (2) (3) (4) (5) (6) (7)
Intercept 0.10 -0.02 0.04 -0.01 0.05 -0.10 -0.02
[1.5] -[0.2] [0.5] -[0.1] [0.5] -[1.2] -[0.2]
Carry 0.00 0.14
[1.0] [2.3]
Defensive 0.15 0.03
[5.0] [0.9]
Momentum 0.15 0.22
[3.3] [7.1]
Value 0.26 0.30
[5.8] [10.7]
Mkt Beta 0.05 0.04 0.10 0.04 0.06 0.08 0.14
[0.7] [0.6] [1.6] [0.7] [0.9] [1.2] [2.3]
Rating 0.02 -0.03 0.02 0.00 0.03 0.00
[0.8] -[1.0] [0.6] [0.1] [1.0] -[0.1]
Duration -0.01 -0.01 0.01 0.00 0.01 0.01
-[0.5] -[0.5] [0.8] -[0.4] [1.1] [1.1]
Age Percent 0.25 0.23 0.22 0.23 0.14 0.09
[2.2] [2.0] [1.9] [2.0] [1.2] [0.9]
Avg. R-squared 0.07 0.10 0.14 0.10 0.11 0.11 0.15
Avg. Num. Obs. 723 671 671 671 671 671 671
33
Table 4: Quintile Portfolio Tests (January 1997βApril 2015)
The table below reports performance annualized performance statistics for value-weighted
quintile portfolios formed on carry, defensive, momentum, value, and combined style factors
(as described in the text). βConstVolβ correponds to quintile long-short portfolios targeting a
constant volatility of 5% per annum (as described in the text).
Q1 Q2 Q3 Q4 Q5 Q5 - Q1 ConstVol
Carry Ret. -0.4% 1.1% 1.5% 3.7% 3.7% 4.1% 1.1%
Vol. 2.9% 4.4% 6.6% 8.7% 13.9% 11.7% 5.8%
S.R. -0.12 0.26 0.22 0.43 0.27 0.35 0.19
Defensive Ret. 0.0% 1.4% 2.0% 1.9% 2.7% 2.7% 8.3%
Vol. 6.0% 5.8% 6.4% 6.2% 5.6% 2.4% 6.9%
S.R. 0.00 0.24 0.31 0.32 0.49 1.11 1.21
Momentum Ret. -0.2% 1.3% 1.5% 1.4% 2.7% 2.9% 7.5%
Vol. 7.2% 6.1% 5.2% 5.3% 6.5% 3.4% 6.7%
S.R. -0.03 0.21 0.28 0.27 0.41 0.85 1.12
Value Ret. -0.4% 0.7% 1.6% 2.4% 3.5% 3.9% 10.7%
Vol. 5.5% 5.8% 6.3% 6.8% 5.6% 2.2% 6.0%
S.R. -0.07 0.13 0.25 0.35 0.62 1.75 1.80
Combined Ret. -0.5% 1.0% 1.5% 2.3% 4.9% 5.4% 14.0%
Vol. 5.6% 5.6% 6.3% 6.8% 6.0% 2.5% 6.0%
S.R. -0.09 0.18 0.24 0.34 0.81 2.19 2.32
34
Table 5: Return Correlation Matrix (January 1997βApril 2015)
The table below reports monthly excess return correlations for each of the carry, defensive,
momentum, value, and combined style factors along with market indices corresponding to
credit, equity, Treasury, and credit-oriented hedge funds.
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Carry 1.00
Defensive -0.18 1.00
Momentum -0.30 0.40 1.00
Value -0.09 0.28 -0.16 1.00
Combined 0.15 0.79 0.43 0.38 1.00
CREDIT 0.80 -0.24 -0.17 -0.10 0.01 1.00
EQUITY 0.55 -0.27 -0.05 -0.17 -0.05 0.59 1.00
TSY -0.49 0.02 0.03 0.10 -0.16 -0.50 -0.25 1.00
Hedge Funds 0.76 -0.13 -0.10 0.00 0.15 0.83 0.58 -0.28 1.00
35
Table 6: Style Factor Return Regressions ( January 1997βApril 2015)
The table below reports monthly excess return regressions of the carry, defensive, momentum,
value, and combined style factors (as defined in the text) onto Treasury and credit excess returns
as well as the Fama-French equity-style factors.
Carry Defensive Momentum Value Combined
Intercept 0.05% 0.75% 0.55% 1.02% 1.23%
[0.7] [5.3] [3.9] [8.1] [9.6]
TSY -0.12 -0.12 -0.10 0.05 -0.18
-[2.9] -[1.4] -[1.2] [0.7] -[2.4]
CREDIT 0.58 -0.22 -0.19 -0.02 -0.07
[10.5] -[2.1] -[1.8] -[0.2] -[0.7]
EQUITY 0.04 -0.07 0.09 -0.11 -0.02
[0.0] [0.0] [0.0] [0.0] [0.0]
SMB 0.01 0.06 0.01 -0.08 0.02
[0.4] [1.3] [0.2] -[2.0] [0.5]
HML -0.02 0.05 0.06 -0.02 0.06
-[0.7] [1.2] [1.4] -[0.6] [1.4]
UMD 0.00 -0.01 0.06 -0.01 0.04
[0.1] -[0.2] [2.3] -[0.4] [1.6]
QMJ -0.04 0.03 0.11 -0.14 -0.06
-[1.2] [0.4] [1.6] -[2.3] -[0.9]
R-squared 0.67 0.10 0.09 0.07 0.05
36
Table 7: Long-Only Backtest Portfolio Performance (January 1997βApril 2015)
The table below reports performance statistics for the long-only optimized backtest
portfolio based on the optimization problem outlined below. The optimized portfolio
refers to the stream of returns generated by the optimized long-only portfolio that
maximizes the score of the bonds held as explained in the text. Benchmark is a cap-
weighted portfolio of all the corporate bonds in our database; i.e., it includes both
investment-grade and high-yield bonds. The active returns reported below are the
returns from the optimized portfolio less the benchmark using a 24-month rolling beta.
Gross returns are returns in excess of the risk free-rate only. Net returns subtract
estimated transaction costs from gross returns.
πππ₯ππππ§π: β π€π. πΆπππ΅ππ
πΌ
π=1
π π’πππππ‘ π‘π: π€π β₯ 0, βπ (ππ π βπππ‘πππ ππππ π‘πππππ‘)
|π€π β ππ| β€ 0.25%, βπ (πππ£πππ‘πππ ππππ ππππβππππ ππππ π‘πππππ‘)
β π€π
πΌ
π=1
= 1 (ππ’πππ¦ πππ£ππ π‘ππ ππππ π‘πππππ‘)
β|π€π,π‘ β π€π,π‘β1| β€ 10% (π‘π’ππππ£ππ ππππ π‘πππππ‘)
πΌ
π=1
β|(π€π,π‘ β π€π,π‘β1). ππ πΌπΆπΈπ,π‘| β₯ $100,000, βπ
πΌ
π=1
(ππππππ’π π‘ππππ π ππ§π ππππ π‘πππππ‘)
β|(π€π β ππ). ππ΄ππ| β€ 0.50% (πππ£πππ‘πππ ππππ ππππβππππ π πππππ ππππ π‘πππππ‘)
πΌ
π=1
β|(π€π β ππ). π·π’πππ‘ππππ|
πΌ
π=1
β€ 0.50 (πππ£πππ‘πππ ππππ ππππβππππ ππ’πππ‘πππ ππππ π‘πππππ‘)
Optimized
Portfolio Benchmark
Active:
Portfolio - Beta * Benchmark
Excess Return (gross) 5.72 4.14 2.45
Excess Return (net) 5.26 3.84 2.20
Volatility (net) 5.10 5.59 2.56
Sharpe Ratio (net) 1.03 0.69 0.86
37
Table 8 : Market Risk Premia in Credit Fund Returns
Panel A below displays summary statistics for the distribution of the fraction of returns of a
given fund that can be explained by their respective benchmark. For hedge funds, the benchmark
is specific to each of our 223 hedge funds, estimated as a linear combination of equity, credit and
Treasury market returns with weights determined by a full sample regression of fund returns
onto those three variables. For mutual funds, the benchmark is specific to each of 244 mutual
funds and is based on the index that maximally explains fund returns out of a set of eight
selected bond indexes. Panel B reports regressions of monthly excess returns of the βHFRI RV:
Fixed IncomeβCorporate Indexβ on equity, credit and Treasury market returns. Treasuries and
equites correspond to returns on 10-year U.S. Treasuries and the S&P 500 index over one-month
Treasuries. Credit is the return of a market-cap weighted corporate bond portfolio in excess to a
treasury portfolio with similar cash flows.
Panel A: Explanatory Power of Benchmarks for Hedge Fund and Mutual
Funds
Hedge Funds Mutual Funds
Average 41%
70%
Median 42%
89%
75th Percentile 60%
93%
Maximum 92%
97%
Panel B: Explanatory Power of Benchmarks for the HFRI Fixed Income: Corporate Index
Credit Equity Treasury All
Credit 0.78
0.78
[22.2]
[17.2]
Equity 0.22
0.05
[10.5] [2.9]
Treasury
-0.24 0.15
-[3.9] [4.1]
Intercept (Annual) 1.44 1.38 3.39 0.62
[1.9] [1.2] [2.5] [0.8]
R-squared 69% 34% 7% 73%
Num. Obs 220 220 220 220
38
Table 9: Credit Fund Indices Exposures to Characteristics (January 1997βApril 2015)
The table below reports regressions of monthly active returns of credit hedge fund and credit
mutual fund indices onto characteristic portfolio return. The index used in Panel A is βHFRI RV:
Fixed IncomeβCorporate Index.β The index used in Panel B is an equal-weighted average of our
223 US-centric credit hedge funds from the HFR index. The index used in Panel C is an equal-
weighted average of our 244 corporate bond mutual funds in our Morningstar sample. The index
used in Panel D is an asset-weighted average of our 223 US-centric credit hedge funds from the
HFR index. Active returns are the difference between the returns of each credit fund or fund index
and that of its respective benchmark. For hedge funds, the benchmark is a linear combination of
equity, credit and Treasury market returns where the weight is determined by a full sample
regression of fund returns onto those three market returns. For mutual funds, the benchmark is the
BAML bond market that maximally explains the time-series variation in each mutual funds total
return. See Table 8 for additional details.
Panel A: Credit Hedge Fund HFRI Index Active Return
Value Momentum Carry Defensive All
Value 0.09
0.08
[2.5]
[2.2]
Momentum 0.02
0.04
[0.8]
[1.1]
Carry
0.10
0.13
[2.7]
[3.7]
Defensive
0.09 0.08
[3.1] [2.3]
Intercept (Annual) -0.32 0.45 0.52 -0.15 -1.32
-[0.4] [0.6] [0.7] -[0.2] -[1.6]
R-squared 2.86% 0.26% 3.33% 4.29% 11.32%
Num. Obs 220 220 220 220 220
Panel B: Credit Hedge Fund US-Centric Corporate Index Active Return
Value Momentum Carry Defensive All
Value 0.12
0.12
[4.9]
[4.3]
Momentum -0.01
0.01
-[0.3]
[0.4]
Carry
0.02
0.04
[0.6]
[1.4]
Defensive
0.05 0.03
[2.4] [1.1]
Intercept (Annual) 1.29 2.64 2.57 2.14 1.00
[2.3] [4.7] [4.8] [3.8] [1.6]
R-squared 10.02% 0.04% 0.19% 2.62% 11.39%
Num. Obs 220 220 220 220 220
39
Panel C: Credit Hedge Fund US-Centric Corporate Index Active Return - Value Weighted
Value Momentum Carry Defensive All
Value 0.11
0.13
[3.6]
[4.0]
Momentum 0.00
0.05
[0.2]
[1.5]
Carry
0.02
0.05
[0.8]
[1.5]
Defensive
0.01 -0.03
[0.5] -[1.0]
Intercept (Annual) 0.39 1.49 1.49 1.42 -0.01
[0.6] [2.3] [2.4] [2.1] [0.0]
R-squared 5.60% 0.01% 0.29% 0.10% 7.26%
Num. Obs 220 220 220 220 220
Panel D: Credit Mutual Fund Index Active Return
Value Momentum Carry Defensive All
Value 0.00
0.00
-[0.2]
[0.1]
Momentum 0.03
0.03
[2.1]
[2.5]
Carry
0.06
0.08
[4.3]
[5.5]
Defensive
0.03 0.03
[2.4] [2.0]
Intercept (Annual) -0.89 -1.11 -0.99 -1.16 -1.50
-[2.8] -[3.8] -[3.6] -[3.9] -[4.7]
R-squared 0.02% 1.96% 7.85% 2.66% 15.35%
Num. Obs 220 220 220 220 220
40
Table 10 : Analysis of High-Yield Mutual Fund Holdings
The table below reports summary statistics for the distribution of quantities of interest across
3,890 mutual fund reports by 102 unique high-yield credit mutual funds between September
1997 and May 2014. We identify the 102 funds by limiting to only mutual funds in the
Morningstar database with an explicit high-yield benchmark belonging to the two most popular
benchmark providers: Bank of America Merrill Lynch and Barclays Capital. We then source
bond-holding information from Lipper Emaxx for these 102 funds. Panel A displays averages
across funds for the characteristics of bonds held in a fund versus those that are not held. Panel
B displays the average coefficients from regressions of active weights onto bond
characteristics. Active weights are weights in excess of the benchmark where the benchmark is
specific to each fund. T-statistics of the averages are clustered at the fund and date level.
Panel A: Active Tilt of Mutual Funds on Factors
Active Tilt
Value 0.02
[1.8]
Momentum 0.05
[7.2]
Carry 0.10
[5.5]
Defensive 0.09
[6.4]
Panel B: Average Loadings from Regressions of Mutual Fund Holdings on Characteristics
Dependent Variable:
Active Weights in Bps
Value -0.81
-[4.2]
Momentum 0.48
[3.9]
Carry 1.93
[3.8]
Defensive 1.09
[6.1]
41
Table 11 : Analyses of High-Yield Mutual Fund Holdings
The table below reports average coefficients from Tobit regressions of quarterly changes in fund holdings on monthly change in
characteristics for each of the last six months until the change. The averages are taken across 3.890 mutual fund reports by 102
different high-yield funds between September 1997 and May 2014. We arrive at those 102 funds by identifying all funds in the
Morningstar database with an explicit high-yield benchmark belonging to the two most popular benchmark providers: Bank of
America Merrill Lynch and Barclays Capital. T-statistics are computed as the t-statistic of the sample mean of the list of
coefficients, one for each report.
0 1 2 3 4 0-4
Value -0.003% 0.000% 0.000% 0.001% 0.000% -0.002%
-[5.9] -[0.8] [0.4] [1.4] [1.0]
Momentum 0.001% 0.003% 0.001% 0.001% 0.001% 0.007%
[3.3] [8.3] [2.8] [3.2] [1.8]
Carry 0.010% 0.007% 0.008% 0.003% 0.003% 0.031%
[12.7] [9.4] [11.1] [4.4] [4.2]
Defensive 0.002% 0.004% 0.006% 0.005% 0.001% 0.017%
[3.2] [4.9] [8.3] [7.5] [2.3]
42
Figure 1: Cumulative Style Factor Returns (January 1997βApril 2015)
The figure below shows cumulative arithmetic returns for each of the carry, defensive,
momentum, value and combined style factors (as defined in the text).
-40%
0%
40%
80%
120%
160%
200%
240%
280%
1997 1999 2001 2003 2005 2007 2009 2011 2013 2015
Carry Defensive Momentum Value Combined
43
Figure 2: Rolling Regression Alphas
The figure below shows three-year rolling average regression alphas for each of the value, momentum,
carry, defensive and combined style factors (as defined in the text). Regression alphas are computed
monthly using the full-sample beta estimates (as reported in Table 6) and averaged over a trailing 36-
month period.
-1.0%
-0.5%
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
2000 2002 2004 2006 2008 2010 2012 2014
Carry Defensive Momentum Value Combined
44
Figure 3: Cumulative Long-Only Portfolio Returns (January 1997βApril 2015)
The figure below shows cumulative returns for the optimized multi-style long-only portfolio (as
described in the text) as well as a corporate bond market index constructed based on the value-
weighted average of all corporate bonds in the BAML bond sample.
-20%
0%
20%
40%
60%
80%
100%
120%
1997 1999 2001 2003 2005 2007 2009 2011 2013 2015
Portfolio Benchmark
45
Figure 4: Distribution of Credit Hedge Fund and Mutual Fund Exposures
Credit Mutual FundsCredit Hedge Funds
The figures below plot empirical densities of the cross-sectional distribution of t-statistics from regressions of funds active returns
on the bond characteristics (Value, Momentum, Carry and Defensive) for our sample of 223 US credit-oriented hedge funds and
244 mutual funds between January 1997 and April 2015.
46
Table A.1: Variable Definitions
Variable Definition
Duration Option-adjusted duration as reported by BAML.
Total Return Monthly total return on the corporate bond, inclusive of coupons and
accrued interest.
Excess Return
Monthly excess return on the corporate bond, computed as the
difference between the monthly total return on the corporate bond and
the monthly return of a duration-matched US Treasury bond.
Amt. Out. The face value of the corporate bond measured in USD millions.
Time to Maturity Number of years before bond matures.
Age Percent Fraction of bond life that has expired (time since issuance divided by
original maturity).
Rating Standard & Poorβs issuer-level rating, coded from 1 (AAA) to 10 (D).
Car
ry
OAS Option-adjusted spread as reported in the Bank of America Merrill
Lynch (BAML) bond database.
Val
ue
Empirical The residual from a cross-sectional regression of the log of OAS onto
the log of duration, rating and bond excess return volatility (12 month).
Structural
The residual from a cross-sectional regression of the log of OAS onto
the log of the default probability implied by a structural model
parametrized (Shumway 2001).
Mom
entu
m
Credit The most recent six-month cumulative corporate-bond excess return.
Equity Equity momentum, defined as the most recent six-month cumulative
issuer equity return.
Def
ensi
ve
Leverage
Market leverage, measured as the ratio of net debt (book debt + minority
interest + preferred stocks β cash) to the sum of net debt and market
capitalization. Measured using data available at the start of each month
(assuming a six-month lag for the release of financial statement
information).
Duration Effective duration as reported in the Bank of America Merrill Lynch
(BAML) bond database.
Profitability Gross profits over assets.
TSY
Excess returns to long-term government bonds, measured as the
difference between monthly total returns on the Bank of America
Merrill Lynch US Treasuries sevenβ10 year index and one-month U.S.
Treasury bills.
47
Variable
Definition
CREDIT
Excess returns to corporate bonds, measured as the difference between
the value-weighted monthly total returns of corporate bonds included in
the BAML dataset and a portfolio of duration-matched US Treasury
bond.
EQUITY
Excess returns to the S&P 500 Index, measured as the difference
between monthly total returns to the S&P 500 and one-month US
Treasury bills.
SMB Monthly mimicking-factor portfolio return to the size factor, obtained
from Ken Frenchβs website.
HML Monthly mimicking-factor portfolio return to the value factor, obtained
from Ken Frenchβs website.
UMD Monthly mimicking-factor portfolio return to the momentum factor,
obtained from Ken Frenchβs website.
QMJ Monthly mimicking-factor portfolio return to the quality factor, obtained
from AQR library website.