Common factors in corporate bond and bond fund returns

Ronen Israel

AQR Capital Management LLC

ronen.israel@aqr.com

Diogo Palhares

AQR Capital Management LLC

diogo.palhares@aqr.com

Scott Richardson

AQR Capital Management LLC

London Business School

scott.richardson@aqr.com

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 “Investing with style in corporate bonds.” 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 (“AQR”), 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 enormous—and growing—source 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 funds’ 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 bonds—even 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.

Second—and more importantly—we 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 factors—duration and credit—on 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 funds’ 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 (“BAML”) investment-grade (“US Corporate Master”) and high-yield (“US High Yield Master”)

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 bond’s discounted

payments match its traded market price (accounting for embedded options). Duration, which measures a

bond’s 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 & Poor’s 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 “age percent,” 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 “graveyard” 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 “relative value” and the sub-strategy classification “fixed income – corporate” within

the HFR database. We then exclude funds that do not appear to have significant US corporate exposure by

excluding those whose names include “Emerging,” “European,” “Municipal,” “Tax,” “Europe,” “Brazil,”

“Latin,” “Structured,” “Loan,” “Interest Rate Arbitrage,” “Euro,” “Convertible,” “Russia,” “Latam,”

“Equities,” “Leveraged,” “Asian,” or “EM.” 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 “fixed income,” 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 asset’s carry as its “expected return

assuming its price does not change.” A simple and widely known measure of carry in fixed income

instruments is yield-to-maturity. While we could use each bond’s 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 curve—hence

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 − 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

markets—also our choice for the carry characteristic—and 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., “Q5 – Q1”). 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

“Q5 – Q1” portfolio weights by a scalar equal to 5% divided by the trailing 24-month realized volatility of

the “Q5 – Q1” 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:

𝑅𝑖,𝑡+1 = 𝛼 + 𝛽1𝐶𝐴𝑅𝑅𝑌𝑖,𝑡 + 𝛽2𝐷𝐸𝐹𝑖,𝑡 + 𝛽3𝑀𝑂𝑀𝑖,𝑡 + 𝛽4𝑉𝐴𝐿𝑈𝐸𝑖,𝑡 + 𝛾𝑍 + 𝜀𝑖,𝑡+1, (1)

where 𝑅𝑖,𝑡+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 markets—rating and duration—as 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 (‘CREDIT’),

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 (‘EQUITY’);

(iii) Treasury term premium (‘TSY’), 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-French’s SMB, HML and UMD and Asness et al.’s (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:

𝐶𝐻𝐴𝑅𝐴𝐶𝑇𝐸𝑅𝐼𝑆𝑇𝐼𝐶𝑡 = 𝛼 + 𝛽1𝑇𝑆𝑌𝑡 + 𝛽2𝐶𝑅𝐸𝐷𝐼𝑇𝑡 + 𝛽3𝑆𝑀𝐵𝑡 + 𝛽4𝐻𝑀𝐿𝑡 + 𝛽5𝑈𝑀𝐷𝑡 + 𝛽6𝑄𝑀𝐽𝑡 + 𝜀𝑖,𝑡. (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, −2.0 and −2.3 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 HML’s 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:

𝑀𝑎𝑥𝑖𝑚𝑖𝑧𝑒: ∑ 𝑤𝑖 . 𝐶𝑂𝑀𝐵𝑂𝑖

𝐼

𝑖=1

𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜:

𝑤𝑖 ≥ 0, ∀𝑖 (𝑛𝑜 𝑠ℎ𝑜𝑟𝑡𝑖𝑛𝑔 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡)

|𝑤𝑖 − 𝑏𝑖| ≤ 0.25%, ∀𝑖 (𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑓𝑟𝑜𝑚 𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡)

∑ 𝑤𝑖

𝐼

𝑖=1

= 1 (𝑓𝑢𝑙𝑙𝑦 𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑑 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡)

∑|𝑤𝑖,𝑡 − 𝑤𝑖,𝑡−1| ≤ 10% (𝑡𝑢𝑟𝑛𝑜𝑣𝑒𝑟 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡)

𝐼

𝑖=1

∑|(𝑤𝑖,𝑡 − 𝑤𝑖,𝑡−1). 𝑃𝑅𝐼𝐶𝐸𝑖,𝑡| ≥ $100,000, ∀𝑖

𝐼

𝑖=1

(𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑡𝑟𝑎𝑑𝑒 𝑠𝑖𝑧𝑒 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡)

∑|(𝑤𝑖 − 𝑏𝑖). 𝑂𝐴𝑆𝑖| ≤ 0.50% (𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑓𝑟𝑜𝑚 𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 𝑠𝑝𝑟𝑒𝑎𝑑 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡)

𝐼

𝑖=1

20

∑ |(𝑤𝑖 − 𝑏𝑖). 𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛𝑖| ≤ 0.50 (𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑓𝑟𝑜𝑚 𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡)𝐼𝑖=1 ,

where 𝑤𝑖 is the portfolio weight for a given bond, and 𝐶𝑂𝑀𝐵𝑂𝑖 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 bond’s rating and maturity in line with Table 1 of Chen, Lesmond, and Wei (2007).

𝑃𝑅𝐼𝐶𝐸𝑖 is the bond price for a given bond, 𝑂𝐴𝑆𝑖 is the option adjusted spread for a given bond,

𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛𝑖 is the effective duration for a given bond, and 𝑏𝑖 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 portfolio’s differences from (or tracking error to) the benchmark by limiting the portfolio’s active

weights relative to the benchmark (i.e., at most 25 bps), limit the portfolio’s aggregate OAS exposure to be

within 50 bps of the benchmark, and limit the portfolio’s 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:

𝑅2 = 1 −𝜎(𝐹𝑢𝑛𝑑−𝐵𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘)2

𝜎(𝐹𝑢𝑛𝑑)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 index—the

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%–15%.

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:

𝑎𝑐𝑡𝑖𝑣𝑒 𝑟𝑒𝑡𝑢𝑟𝑛𝑡+1 = 𝑏1 × 𝑣𝑎𝑙𝑢𝑒𝑡+1 + 𝑏2 × 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚𝑡+1 + 𝑏3 × 𝑐𝑎𝑟𝑟𝑦𝑡+1 + 𝑏4 × 𝑑𝑒𝑓𝑒𝑛𝑠𝑖𝑣𝑒𝑡+1 + 𝑏0 + 𝜀𝑡+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:

𝑎𝑐𝑡𝑖𝑣𝑒 𝑡𝑖𝑙𝑡 𝑐ℎ𝑎𝑟𝑓𝑢𝑛𝑑,𝑑𝑎𝑡𝑒 = ∑ (𝑤𝑏𝑜𝑛𝑑𝐹𝑢𝑛𝑑 − 𝑤𝑏𝑜𝑛𝑑

𝐵𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘) × 𝑐ℎ𝑎𝑟𝑏𝑜𝑛𝑑

𝑏𝑜𝑛𝑑∈𝐵𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘∪𝐹𝑢𝑛𝑑

.

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, 4 189–209

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, 6–

19.

Asness, C., A. Ilmanen, R. Israel and T. Moskowitz (2015). Investing with Style. Journal of Investment

Management, 13, 27–63.

Asness, C., T. Moskowitz and L. Pedersen (2013). Value and momentum everywhere. Journal of Finance,

68, 929–985.

Asquith, P., A. S. Au, T. Covert and P. A. Pathak (2013). The market for borrowing corporate bonds.

Journal of Financial Economics, 107, 155–182.

Becker, B., and V. Ivashina (2015). Reaching for yield in the bond market. Journal of Finance, 70, 1863–

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, 77–100.

Bessembinder, H., W. Maxwell and K. Venkataraman (2006). Market transparency, liquidity externalities,

and institutional trading costs in corporate bonds. Journal of Financial Economics, 82, 251–288.

Bharath, Sreedhar T., and Tyler Shumway (2008). Forecasting default with the Merton distance to default

model. Review of Financial Studies, 21.3, 1339–1369.

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, 171–181.

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, 51–70.

Chen, L., D. A. Lesmond and J. Wei (2007). Corporate yield spreads and bond liquidity. Journal of Finance,

62, 119–149.

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): 572–609.

Edwards, A. E., L.E. Harris and M.S. Piwowar (2007). Corporate bond market transaction costs and

transparency. Journal of Finance, 62, 1421–1451.

Fama, Eugene F., and Kenneth R. French. Common risk factors in the returns on stocks and bonds. Journal

of Financial Economics, 33.1 (1993): 3–56.

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, 1–25.

Fung, W., and D. A. Hsieh (2002). The risk in fixed-income hedge fund styles. Journal of Fixed Income, 12,

6–27.

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, 85–114.

Gebhardt, W. R., S. Hvidkjaer, and B. Swaminathan (2005b). Stock and bond market interaction: does

momentum spill over? Journal of Financial Economics, 75, 651–690.

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), 1649–1693.

Kahn, R., and M. Lemmon (2015). Smart Beta: The owner’s manual. Journal of Portfolio Management, 41,

76–83.

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, 63–80.

Lewellen, J. (2015). The cross-section of expected stock returns. Critical Finance Review, 4, 1–44.

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, 449–470.

Ng, K. Y., and B. Phelps (2014). Structure of US corporate excess returns: The hunt for a ‘low-risk’

anomaly. Working paper, Barclays.

Novy-Marx, R. (2013). The other side of value: The gross profitability premium. Journal of Financial

Economics, 108(1), 1–28.

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, 101–124.

30

Table 1: Universe Statistics (January 1997–April 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 1997–April 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 1997–April 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 1997–April 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). “ConstVol” 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 1997–April 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 1997–April 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 1997–April 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.

𝑀𝑎𝑥𝑖𝑚𝑖𝑧𝑒: ∑ 𝑤𝑖. 𝐶𝑂𝑀𝐵𝑂𝑖

𝐼

𝑖=1

𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜: 𝑤𝑖 ≥ 0, ∀𝑖 (𝑛𝑜 𝑠ℎ𝑜𝑟𝑡𝑖𝑛𝑔 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡)

|𝑤𝑖 − 𝑏𝑖| ≤ 0.25%, ∀𝑖 (𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑓𝑟𝑜𝑚 𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡)

∑ 𝑤𝑖

𝐼

𝑖=1

= 1 (𝑓𝑢𝑙𝑙𝑦 𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑑 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡)

∑|𝑤𝑖,𝑡 − 𝑤𝑖,𝑡−1| ≤ 10% (𝑡𝑢𝑟𝑛𝑜𝑣𝑒𝑟 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡)

𝐼

𝑖=1

∑|(𝑤𝑖,𝑡 − 𝑤𝑖,𝑡−1). 𝑃𝑅𝐼𝐶𝐸𝑖,𝑡| ≥ $100,000, ∀𝑖

𝐼

𝑖=1

(𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑡𝑟𝑎𝑑𝑒 𝑠𝑖𝑧𝑒 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡)

∑|(𝑤𝑖 − 𝑏𝑖). 𝑂𝐴𝑆𝑖| ≤ 0.50% (𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑓𝑟𝑜𝑚 𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 𝑠𝑝𝑟𝑒𝑎𝑑 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡)

𝐼

𝑖=1

∑|(𝑤𝑖 − 𝑏𝑖). 𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛𝑖|

𝐼

𝑖=1

≤ 0.50 (𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑓𝑟𝑜𝑚 𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡)

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 “HFRI RV:

Fixed Income—Corporate Index” 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 1997–April 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 “HFRI RV:

Fixed Income—Corporate Index.” 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 1997–April 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 1997–April 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 & Poor’s 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 – 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 seven–10 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 French’s website.

HML Monthly mimicking-factor portfolio return to the value factor, obtained

from Ken French’s website.

UMD Monthly mimicking-factor portfolio return to the momentum factor,

obtained from Ken French’s website.

QMJ Monthly mimicking-factor portfolio return to the quality factor, obtained

from AQR library website.