determinants of short-term corporate yield spreads

Determinants of Short-Term Corporate Yield Spreads:Evidence from the Commercial Paper Market∗

Jing-Zhi Huang†

Penn State UniversityBibo Liu‡

Tsinghua UniversityZhan Shi§

Tsinghua University

First draft: December 2018

This version: September 6, 2020

Abstract

What drives short-term credit spreads: credit risk, liquidity risk, or both? De-spite a large empirical literature on corporate yield spreads, very few studies haveexamined this important question. Using a novel data set of secondary markettransaction prices of Chinese commercial papers, we investigate the determinantsof short-term credit spreads within the structural framework of credit risk mod-eling. In particular, we propose and test a structural model with rollover risk,jump risk, and market illiquidity that allows us to decompose commercial paperyield spreads into a credit component and a liquidity component in a unified man-ner. We find that both credit and liquidity factors are important determinants ofshort-term spreads and that, on average, the proposed structural model can largelymatch levels of commercial paper spreads. Furthermore, our decomposition resultsindicate that jump risk and market liquidity make equally important contributionsto commercial paper spreads.

∗We thank Hui Chen, Zhi Da, Jens Dick-Nielsen, Rui Gong (discussant), Zhiguo He, Thien Nguyen(discussant), Jun Pan, Michael Schwert, Wei Xiong, Haoxiang Zhu, seminar participants at Shanghai JiaoTong University, Southwest University of Finance and Economics, Tsinghua University, and UNLV; andparticipants at the 2019 Five-Star Workshop at Hanqing Institute and 2020 Ohio State University AluminaConference for valuable comments and suggestions. We also thank Yanyi Ye for her excellent researchassistance.†Smeal College of Business, Penn State University, University Park, PA 16802, USA. [email protected].‡PBC School of Finance, Tsinghua University, Beijing, 100083, China. [email protected].§PBC School of Finance, Tsinghua University, Beijing, 100083, China. [email protected].

Electronic copy available at: https://ssrn.com/abstract=3530408

Determinants of Short-Term Corporate Yield Spreads: Evidencefrom the Commercial Paper Market

Abstract

What drives short-term credit spreads: credit risk, liquidity risk, or both? Despite a large

empirical literature on corporate yield spreads, there are very few studies examining this

important question. Using a novel data set of secondary market transaction prices of Chinese

commercial papers, we investigate the determinants of short-term credit spreads within the

structural framework of credit risk modeling. In particular, we propose and test a structural

model with rollover risk, jump risk, and market illiquidity that allows us to decompose

commercial paper yield spreads into a credit component and a liquidity component in a

unified manner. We find that both credit and liquidity factors are important determinants

of short-term spreads and that, on average, the proposed structural model can largely match

levels of commercial paper spreads. Furthermore, our decomposition results indicate that

jump risk and market liquidity make equally important contributions to commercial paper

spreads.

Keywords: Corporate yield spreads, commercial paper, structural credit risk models, jump

risk, bond market liquidity, rollover risk

JEL Classifications: G13, G12, G33, E43

1


1 Introduction

What drives short-term credit spreads is a very important question in credit markets, e-

specially given the role played by short-term corporate debt in the global financial crisis.

However, in spite of a large literature on the determinants of credit spreads in general, the

empirical literature on short-term spreads is thin, perhaps because of data limitations. One

exception is an interesting study by Covitz and Downing (2007), who examine a sample of

commercial paper (CP) issued by domestic US nonfinancial firms based on regression analysis

and conclude that credit risk is the more important determinant of CP spreads than liquid-

ity. As noted by the authors, this finding is somewhat surprising, given the view that CP

spreads are essentially driven by liquidity (Krishnamurthy 2002). Nonetheless, their study

is not focused on the no-arbitrage pricing of CP and, as a result, the relative importance of

credit risk or liquidity is based on regression R-squared, not on a direct decomposition of

CP spreads. Rollover risk in the CP market is not examined either.1 In addition, the data

set used in Covitz and Downing (2007) consists of mainly new issues in the primary market.

As such, how much of short-term yield spreads is due to credit risk or liquidity risk is still

an open question.

In this paper, we shed light on the determinants of short-term corporate credit spreads

from at least two new perspectives. First, we employ a novel data set of secondary market

transactions in Chinese commercial paper, the fastest-growing CP market in the world.

This market has three unique features that make it particularly suitable for addressing the

main question of this study: (1) Secondary market transactions account for 78% of total

daily transaction volumes in this market, compared with less than 10% in the US market.

This feature makes it possible to implement transaction-based liquidity measures for the

1This is not surprising, given that their empirical analysis is done using a (pre-crisis) sample periodJanuary 1998–October 2003.

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CP market. On the other hand, Covitz and Downing (2007) only see the offer side of

secondary market transactions, and the liquidity proxies they use are limited to trading

volume, dollar volume, and CP maturity. (2) The Chinese CP issuers are heterogeneous in

terms of creditworthiness, whereas almost all CP issuers in the US are large, well-capitalized

firms. (3) Longer-term corporate debts—for example, medium-term notes (MTNs) and

enterprise bonds (EBs)—are traded in the same (interbank) market in China. In summary,

CPs in China can be viewed as exactly equivalent to short-term corporate bonds and thus

provide an ideal setting to investigate how the relative importance of credit/liquidity changes

with the maturity.

Second, we quantify liquidity and default risk components in short-term spreads using

the well-known structural approach to credit risk modeling (Merton 1974). In particular,

we propose and implement a jump-diffusion structural model that incorporates the effect of

debt market illiquidity on yield spreads and therefore is particularly suitable for modeling CP

spreads. Among other things, this model allows us to decompose yield spreads into diffusive

and jump credit risk components as well as a liquidity component in a unified manner.

We begin our empirical analysis with a regression-based decomposition of CP yield

spreads—namely, we regress CP yield spreads on credit-risk-related variables suggested by

structural models, credit ratings, or seven liquidity measures as examined in Schestag, Schus-

ter, and Uhrig-Homburg (2016). We find that credit-risk-related determinants explain about

4%–6% of CP spread variations. On the other hand, we find that the liquidity measures have

an unconditional R2 of 26.1% and an incremental R2 of 22.7%. That is, our results indicate

that illiquidity is much more important than credit risk in explaining variations in the CP

spread in the Chinese market. This finding on the relative importance of credit and liquidity

proxies is different from the main finding of Covitz and Downing (2007). One possible reason

for this difference is that the samples of CP used are very different. Another possible reason

3


may have something to do with the liquidity proxies used in their study (e.g., maturity and

amount outstanding).

We then conduct a similar regression analysis using spreads on MTNs and EBs, which

have longer maturities than CP. We find that the credit-related variables indeed become more

important than liquidity in explaining variations in spreads on MTNs and EBs. Furthermore,

we observe the same pattern between shorter- (1–3 years) and longer-term (3–6 years) MTNs

and EBs.

Interestingly, our regression results also provide evidence on the potential role of struc-

tural credit risk models in the determination of short-term credit spreads. Specifically, we

find that the distance-to-default (Kealhofer 2003) subsumes equity volatility and has incre-

mental explanatory power for spreads over credit ratings. In addition, the regression results

indicate that jump risk matters.

As a result, we next examine the predictive power of structural models for short-term

credit spreads. We begin with the Black and Cox (1976) model, a simple pure-diffusion model

of risky zero-coupon bonds that allows for default prior to bond maturity. As such, it serves

as the benchmark model in our empirical analysis. The consensus is that pure diffusion-based

structural models are unable to generate sufficiently high short-term spreads consistent with

levels of observed spreads. Indeed, we find that the Black-Cox model-implied CP spreads

have a mean of 0.32% and median of 0.0%, way below their empirical counterparts of 1.53%

and 1.34%, respectively. Furthermore, the model has substantial pricing errors: the mean

pricing error is -1.09%, and the mean percentage pricing error is -66.87%. Nonetheless, the

model predicts lower-rating CP spreads better than higher-rating ones. For instance, the

mean percentage pricing error is -72.31% for AAA issues and -56.0% for AA issues.

We then consider the double-exponential jump-diffusion (DEJD) model of risky debt,

which is used in Huang and Huang (2002, 2012) among others. This model can be considered

4


to be an extension of the Black-Cox model to include jumps in its underlying asset return

process. As expected, the DEJD model significantly improves the pricing performance.

For instance, incorporating jumps raises the average and median model-implied spreads

from 0.32% and 0.0% for the Black-Cox model to 1.07% and 0.48% for the DEJD model,

respectively. In terms of pricing errors under the DEJD model, the mean pricing error is

-0.70%, and the mean percentage pricing error is -20.63% for the full sample.

Another way to improve the model performance is to incorporate market liquidity into

debt pricing. We achieve this by following He and Xiong (2012) and show that the average

spread under the resulting He-Xiong (pure-diffusion) model is basically the same as under

the DEJD model. Moreover, the He-Xiong model achieves a smaller mean pricing error

(-0.52%) but produces a worse percentage error (-26.08%). Nonetheless, both models show

limited ability to predict short-term spreads. In particular, they both generate a right-skewed

distribution of spreads and thus under-predict spreads of those CP issues on the left tail.

Finally, we incorporate market liquidity into the DEJD model to more accurately quantify

the incremental role of liquidity. The resulting proposed model can be considered as the

He-Xiong model augmented with jumps. Our empirical results show that on average, this

extended He-Xiong model largely explains CP spreads in our sample: the average of predicted

spreads is 1.62%, higher than the average observed spread of 1.53%. Moreover, although the

mean pricing error is still negative (-0.30%), the mean percentage pricing error is positive.

However, the model still underestimates the median CP spread. The model-implied CP

spreads are still right-skewed. Furthermore, the model overestimates spreads on the right

tail and underestimates spreads on the left tail, resulting in a positive mean percentage

pricing error of 10.31% for the full sample. That is, while incorporating endogenous liquidity

significantly improves the pricing performance, the resulting model suffers from the problem

of inaccuracy as described by Eom, Helwege, and Huang (2004).

5


To summarize, this paper contributes to the literature in three main aspects. First,

we provide a comprehensive study on the determinants of short-term credit spreads using

a novel data set of commercial paper secondary market transaction prices. Second, we

propose a structural model of credit risk with rollover risk, jump risk, and market illiquidity.

Importantly, this model allows us to decompose CP spreads into a credit component—

further divided into the diffusion and jump components—and a liquidity component in a

unified manner. Third, we conduct one of the first empirical studies of structural models

using CP data, finding that both credit and liquidity factors are important determinants

of short-term credit spreads and that on average, the proposed structural model can match

levels of CP spreads in our sample.

The remainder of the paper is organized as follows. Section 2 discusses the related

literature, followed by Section 3, which describes the data we use. Section 4 introduces the

structural models of credit risk to be examined in the study, including the proposed model

with rollover risk, jumps, and endogenous liquidity. Section 5 presents results from our

empirical analysis. Section 6 concludes.

2 Related Literature

This paper is most directly related to the literature on structural models of credit risk,

originated from Black and Scholes (1973) and Merton (1974). However, it departs from this

literature in two main aspects.

First, this paper contributes to the theoretical literature by proposing a new structural

model that incorporates rollover risk, endogenous liquidity, and jumps in the underlying asset

return process. There is a large theoretical literature on structural credit risk modeling (see,

e.g., Huang and Huang, 2012; Sundaresan, 2013; and references therein). For tractability and

comparison, we focus on three models with a flat default boundary—namely, the Black-Cox

6


model for zero-coupon risky debt, the DEJD model, and the proposed model that extends

the He-Xiong model to include jumps in the underlying asset return process.

The Black-Cox model is used in many studies, such as Bao (2009); Feldhutter and Schae-

fer (2018); Huang, Nozawa, and Shi (2018); Bai, Goldstein, and Yang (2020); and Huang,

Shi, and Zhou (2020). In addition to Huang and Huang (2002, 2012), other examples using

the DEJD-based structural model include Cremers et al. (2008); Bao (2009); Chen and Kou

(2009); Bai et al. (2020); and Huang et al. (2020).2 Studies using alternative structural

models with jumps include Mason and Bhattacharya (1981); Duffie and Lando (2001); and

Zhou (2001). We focus on the DEJD model in our study for analytical tractability reason-

s. He and Xiong (2012) and He and Milbradt (2014) consider both rollover risk and bond

illiquidity. Our proposed model builds on the former, a diffusion-based model.

Second, while the empirical literature on structural models has mainly investigated

medium- or long-term corporate bonds and single-name credit default swap (CDS) contracts,

this paper focuses on short-term debt claims, commercial papers. Importantly, we empiri-

cally examine the performance of the proposed structural model in predicting CP spreads.

The only other empirical study of individual CP issues that we are aware of is the one by

Covitz and Downing (2007). However, they do not include any structural models in their

analysis; they use equity volatility, credit ratings, and EDFs (expected default frequency)

from Moody’s KMV as credit proxies in their regressions.

The empirical literature on structural models can be divided into two streams. One

stream, going back to Jones, Mason, and Rosenfeld (1984), focuses on implications of struc-

tural models under the risk-neutral measure using alternative empirical methodologies. See,

for example, Jones, Mason, and Rosenfeld (1984); Eom, Helwege, and Huang (2004); Erics-

son and Reneby (2005); Schaefer and Strebulaev (2008); Bao and Pan (2013); Bao and Hou

2Kou (2002) develops the first DEJD-based equity option pricing model. Ramezani and Zeng (2007) usethe DEJD to model individual stock returns.

7


(2017); Culp, Nozawa, and Veronesi (2018); and Huang, Shi, and Zhou (2020).

Another stream of research explores model implications under both the risk-neutral and

physical measures, such as studying the pricing performance of structural models by cali-

brating them to historical default losses. To resolve the credit spread puzzle documented

in Huang and Huang (2012), many studies propose various economic channels to account

for the credit component of yield spreads by incorporating additional sources of default pre-

mium. Examples include Bao (2009); Chen, Collin-Dufresne, and Goldstein (2009); Chen

(2010); Bhamra, Kuehn, and Strebulaev (2010); Christoffersen, Du, and Elkamhi (2017);

Du, Elkamhi, and Ericsson (2019); McQuade (2018); and Shi (2019).

One of our main findings is that liquidity plays an important role in CP spreads. Kr-

ishnamurthy (2002) argues that CP spreads are essentially entirely due to liquidity, whereas

Covitz and Downing (2007) find that credit risk is more important than liquidity in the

determination of CP spreads. There is a large empirical literature studying the effect of

bond market illiquidity on corporate yield spreads, however; see, for example, Bao, Pan,

and Wang (2011); Chen, Lesmond, and Wei (2007); Das and Hanouna (2009); Dick-Nielsen,

Feldhutter, and Lando (2012); Han and Zhou (2016); Helwege, Huang, and Wang (2014); He,

Khorrami, and Song (2019); Longstaff, Mithal, and Neis (2005); and Mahanti, Nashikkar,

Subrahmanyam, Chacko, and Mallik (2008), among others.

Our paper is also related to the new literature on the Chinese credit market. Amstad

and He (2019) and Mo and Subrahmanyam (2018) provide a comprehensive overview of this

market. Chen, Chen, He, Liu, and Xie (2019) study a unique feature of the Chinese corporate

bond markets—where bonds with identical fundamentals are simultaneously traded on two

segmented markets that feature different rules for repo transactions—and document causal

evidence for the value of asset pledgeability. Geng and Pan (2019) focus on the segmentation

of the Chinese corporate bond market. However, none of these studies focus on the Chinese

8


CP and MTN markets as we do. Ding, Xiong, and Zhang (2019) present robust evidence for

overpricing in the primary markets of commercial paper and MTNs in China and attribute

the overpricing to competition among underwriters. We focus on the secondary market of

CP in this paper. In addition, we study their secondary prices using structural models of

credit risk.

3 Data

3.1 Commercial Paper Data

In this study, we focus on the commercial paper data obtained from the China Foreign

Exchange Trade System (CFETS) over the period May 2014–December 2018.3 As a sub-

institution directly affiliated with the People’s Bank of China, CFETS plays a similar role

to Financial Industry Regulatory Authority (FINRA) in the US in terms of serving and

monitoring the over-the-counter bond market. Our data set consists of end-of-day transaction

summaries of all corporate debts traded in the interbank market. Compared to standard

data sets on exchange-traded markets (e.g. CRSP Daily Stock File), it contains additional

information on daily volume-weight average price, which is the key variable in our calculation

of yield spreads and liquidity measures.

Table 1 provides summary statistics on trading activities in the Chinese commercial paper

market. We partition the data into six maturity categories: 1 to 30 days, 31 to 60 days, 61

to 90 days, 91 to 180 days, 181 to 270 days, and greater than 270 days. Within each of these

3According to CFETS (also known as the National Interbank Funding Center), the transaction databefore 2014 are relatively sparse and unreliable. Mo and Subrahmanyam (2018) also find that in the earlyyears of the CFETS data set, which goes back to 2006, many data points have missing information ontransaction prices for all types of bonds. Our sample period starts after the first default of publicly issuedbonds, the default of Shanghai Chaori Solar on its one billion RMB bond on March 7, 2014. As such, weavoid the issue uncovered by Geng and Pan (2019) that, during the pre-default era, corporate debt pricing inChina is decoupled from the issuer’s fundamental default risk (with the widespread belief that bond investorswill always be paid in full).

9


maturity categories, we compute the average daily shares of the total par amount traded

accounted for by primary and secondary transactions.4 We find that, on average, secondary

market transactions account for more than 78% of total daily transaction volumes. This

finding stands in stark contrast to the US CP market, in which primary market transactions

completely dominate. Indeed, this ratio for the US market is about 8.34% according to

Covitz and Downing (2007). The intense transaction activity in the Chinese CP market

is largely attributable to the regulatory constraint imposed on money market funds (i.e.,

the overall duration of their portfolio cannot exceed 120 days). In response, fund managers

actively adjust their portfolios to make full use of the upper limit on the duration, given

that the overall term structure of CP yields is upward sloping. Consequently, while the

average initial maturity is 276 days, the trading volume of CPs with even less than 30 days

to maturity is substantial and makes up about 9% of all secondary transactions.

Another notable difference from the US CP market arises from the primary market.

Rather than concentrating on the shortest maturities—1 to 4 days as reported in Covitz and

Downing (2007)—primary issues in China have maturities evenly spread across ranges. If

the decision of the initial maturity is partially driven by the clientele effect, this evidence

suggests that institutional investors in China are not excessively concerned about the sec-

ondary market liquidity so that they do not aggressively demand extremely short maturities

to create de facto liquid.

The CP pricing data are then matched to the WIND IBQ database to obtain the char-

acteristics of each issue, including the name of the issuer, coupon rate, face value, issuance

date, maturity date, credit rating, redemption features, and so on. Panel A of Table 2 shows

that the total issuance amount of CPs reaches 15.9 trillion RMB (about 2.3 trillion USD)

from 2013 to 2018. For comparison, the total issuances of non-financial public debts amount

4Note that the shares do not sum to 100% in each panel because they are averages of daily shares.

10


to 43.6 trillion RMB during this sample period. In other words, CPs take a market share of

about 36.5% in terms of issuance size.

Since public information in financial statements is essential to any quantitative assessment

of credit risk, we limit our analysis to CPs that are issued by publicly listed firms. After

merging with (quarterly) financial statements and equity data from WIND, we obtain a

sample consisting of 1,901 CPs issued by 372 companies. Panel B of Table 2 summarizes

the issue-level information in our final sample. We find that a majority of CPs in the final

sample have an initial maturity of 9–12 months, and the average issuance size is 12.82 billion

RMB. Moreover, most CP issuers in China are covered in only three rating categories—AAA,

AA+, and AA—which reflect the extreme skewness of Chinese credit ratings. Only about

8% of CPs in our final sample fall into the rating category of AA- or below. As discussed

in Amstad and He (2019), the AA rating is generally seen as the lowest investment-grade

level in China. Attaching a numerical value to each credit rating as in AAA = 1, · · · , A+ =

5, we obtain an average rating of 2.05 for CP issues in the sample. It is worth noting that

the average ratings of MTNs and exchange-traded corporate bonds issued during the same

period are 1.82 and 2.21, respectively. Therefore, CP issuers as a group are not different

from firms issuing longer-term debts in terms of creditworthiness,5 which is in sharp contrast

with the US CP market. Finally, the average turnover of CPs in our sample is 436%, much

higher than the turnover for the entire CP universe (64.1%).

Panel C reports summary statistics for CP issuers in our final sample. Quasi-market

leverage is constructed as the book value of debt divided by the sum of the book value of

debt and the market value of equity. Both the leverage ratio and annualized equity volatility

average out at 44%, measures that comparable to those reported in previous studies on the

Chinese market (for example, Giannetti, Liao, and Yu 2015). On the other hand, CP issuers

5Base on private conversations with some licensed bond underwriters, it is even easier to issue CPscompared to longer-term public debts.

11


in our sample have larger than average equity market capitalization (30.42 bn vs. 26.98 bn).

They also tend to be profitable with a mean quarterly ROA of 2.06% as compared to an

average of 1.43% for the full A-share universe during the same sample period.

3.2 Corporate Yield Spreads

For corporate bond i at month t, we calculate its end-of-month yield using the volume-

weighted average price of all trades within 7 days of the month-end (Bao and Pan 2013).

As in the case of the US market, CPs in China do not carry a coupon, though the interest

is calculated on an actual/365 basis. Therefore, the credit spread can simply be measured

as the difference between the annualized CP yield and the default-free zero yield of the

same maturity. Following Covitz and Downing (2007), we use the yield curve derived from

repurchase agreements and relevant derivatives as the reference curve to calculate credit

spreads. Specifically, we collect from WIND the data of 7-day interbank fixed repo rate

(FR007) as well as swaps with a fixed rate versus it;6 the swap rates are means of the bid

and ask rates from major swap dealers’ quoted rates and cover maturities from one month

to ten years. The term structure of risk-free zero rates is then constructed via standard

bootstrapping techniques. Finally, we remove the upper 1% and lower 1% tails of the credit

spreads in order to avoid the influence of outliers (Campbell and Taksler 2003).

Figure 1 presents the face-value-weighted average CP yield spreads for different rat-

ing/maturity categories. Since five rating agencies dominate the Chinese interbank bond

market, we extract rating information from them in order of market share. That is, for

each CP issue we first search for its issuer’s rating in Chengxin International Rating. If it

6Interbank fixing repo rates (including FR001, FR007, and FR014) are based on the repo trading ratefor the interbank market between 9:00 a.m. and 11:30 a.m. and are released to the public at 11:30 a.m. oneach trading day. Among them, FR007 serves as the most important benchmark rate in the Chinese moneymarket. Accordingly, FR007-based swaps account for more than 70% of the trading volumes of all interestrate swaps, and swaps based on the 3-month SHIBOR constitute the second-largest market.

12


is missing, we use the rating from China Lianhe Rating, and if this information is missing

as well, we look up the rating from Dagong Global Credit Rating, and so on. This practice

is adopted by, for example, Dick-Nielsen et al. (2012), and switching to the lowest-rating

principal (Collin-Dufresne et al., 2001) makes little difference. The reason is that the rat-

ing industry in China is rather homogeneous and rating decisions across agencies offer little

variation (Amstad and He 2019).

As credit ratings in China are substantially inflated,7 it is not surprising to find that

for a given nominal rating, the average CP spread in China tends to be several times as

high as that in the US. For example, for AAA issuers it ranges from 82 basis points for

maturities of 1 to 60 days to 122 basis points for maturities of 301 to 365 days. Despite

the upward bias in rating assignment, the CP yield spread does monotonically decrease with

the credit rating in each maturity category. As shown in Geng and Pan (2019), China’s

domestic ratings contain information above and beyond the issuer’s financial state of health,

such as an implicit government guarantee. For this reason, we include credit ratings (along

with credit measures based on structural models) as a proxy for default risk in regression

analysis in Section 5. Another important takeaway from Figure 1 is that the term structure

of yield spreads is generally upward sloping for all rating classes. If money market funds

engage in reaching-for-yield behavior, they are supposed to exhaust the 120-day upper limit

on portfolio duration.

3.3 Liquidity Measures

There is no consensus on how to measure commercial paper liquidity. Because of the sparse-

ness of secondary market transactions, Covitz and Downing (2007) use issuance size and

time to maturity as liquidity proxies. On the other hand, studies on the corporate bond

7Amstad and He (2019) argue that AA is generally viewed by Chinese institutional investors “as thelowest investment-grade level while this is BBB in global ratings.”

13


market tend to employ liquidity measures based on intra-day and daily transaction data. In

this paper, we consider both types of liquidity variables to examine if market-based liquidity

measures contain additional information not captured by static or deterministic proxies.

Schestag et al. (2016) conduct a comprehensive analysis of dozens of liquidity measures

using data from the US corporate bond market. As our data set is not organized in a

transaction-by-transaction manner, we are able to implement only what they term “low-

frequency” measures based on daily data (Internet Appendix IA.A covers the definition and

implementation details of these measures). Panel A of Table 3 shows that, based on the

six transaction cost measures implemented in our analysis, average bid-ask spread estimates

range from 46 to 168 basis points in our CP sample. Compared to summary statistics for the

same measures as reported by Schestag et al. (2016), the overall trading cost in the Chinese

CP market is generally comparable to that in the US corporate bond market.

The six transaction cost measures are closely correlated, with the pairwise correlation

coefficient ranging from 13% to 80%. To summarize most of their relevant information using

a low-dimensional vector, we perform a principal component (PC) analysis in Panel B. The

first PC loads somewhat evenly on the six measures and explains 44% of their variations. We

therefore define a trading cost factor, TC, as the average of these six measures. This factor

not only serves as our primary liquidity variable in regression analysis but also provides a

comprehensive and robust estimate of effective bid-ask spreads, which is a key model input

when we quantify the liquidity component in CP yield spreads in Section 5.3.

Regarding another important dimension of market liquidity, we consider two price impact

measures that are proposed by Amihud (2002) and Pastor and Stambaugh (2003). Compared

to transaction cost measures, these two measures incorporate the volume information in a

more direct way and thus may offer additional explanatory power for CP yield spreads (Dick-

Nielsen et al., 2012; Rossi, 2014; He et al., 2019).

14


4 Structural Models of Credit Risk

In this section, we introduce the credit risk models to be used in our empirical analysis. We

first review the general framework that underlies these models. We then begin with the Black

and Cox (1976) model, the benchmark model in our empirical analysis (Section 4.1.1). We

next consider the double-exponential jump-diffusion model, an extension of the Black-Cox

model to include jumps in the asset return process (Section 4.1.2). We then add liquidity

and obtain a jump-diffusion model with endogenous liquidity, which can be considered as

the He and Xiong (2012) model augmented with jumps (Section 4.1.3). Lastly, we discuss

the implementation of these models (Section 4.2).

4.1 Modeling Framework

To place default risk and debt market illiquidity into a unified framework, we consider a firm

maintaining a stationary debt structure. Specifically, the firm continuously issues a constant

amount of new zero-coupon debt with an initial maturity of T years; new bond principal is

issued at a rate f = F/T per year, where F is the total principal value of all outstanding

bonds. As long as the firm remains solvent, at any time t, the total outstanding debt principal

will be F and has a uniform distribution over maturities in the interval (t, t+ T ). It follows

that the average maturity of the firm’s outstanding bonds is T/2. Overall, this structure of

zero-coupon debt rollover is particularly relevant to the CP pricing.

Following the standard assumption for zero-coupon debts (see, e.g., Bao 2009), we define

the recovery rate R as an exogenously specified fraction of the price of an otherwise identical

Treasury (non-defaultable) bond. The time-t price of a debt with τ years to maturity is thus

given by

dt(τ) = e−rτf [1− π(τ)(1−R)] , (1)

15


where π denotes the risk-neutral default probability as derived from the model. We follow

Leland and Toft (1996) by postulating that the firm’s liability cannot be financed through

the sale of assets. In other words, if the firm’s cash flow is insufficient to cover the rollover

cost, f − dt(τ), new equity will be issued.

4.1.1 The Black-Cox Model

The Black-Cox (1976) model provides a framework to price a corporate bond that can default

before maturity because of covenant violation. The idea is, if the firm value falls enough

relative to the face value of debt, the firm may default even before the maturity of its debt.

The firm value threshold K at which firms choose to or are forced to default is called default

boundary.

The dynamics of the firm’s asset value At under the risk-neutral measure is specified as

dAtAt

= (r − δ)dt+ σdWt, (2)

where r denotes the risk-free rate, δ the payout rate, and σ the asset volatility. It follows

that the resultant risk-neutral default probability has the following expression (Bao, 2009):

πBC(τ) = N(h1(ν)) + (K/At)2ν/σ2

N(h2(ν)), (3)

where

h1,2(ν) =log(K/At)∓ ντ

σ√τ

,

ν = r − δ − σ2/2,

and N(·) is the cumulative standard normal density function. Based on Eq. (1), we have the

Black-Cox credit spread

csBC(τ) = − log (1− πBC(τ)(1−R))

τ. (4)

16


4.1.2 The Double-Exponential Jump-Diffusion Model

It is well known that pure-diffusion models are unable to generate sizable credit spreads on

short-maturity bonds (see, for example, Duffie and Lando 2001). In this paper, we focus on

the double-exponential jump-diffusion (DEJD) model which allows for analytically tractable

solutions,

dAtAt

= (r − δ)dt+ σdWt + d

[Nt∑i=1

(Zi − 1)

]− λξdt,

where N is a Poisson process with a constant intensity λ, and Y ≡ ln(Z1) has a double-

exponential distribution

f(y|pu, pd, ηu, ηd) = puηue−ηuy1{y≥0} + pdηde

ηdy1{y<0}.

It follows that the mean percentage jump size ζ is given by

ζ = E[eY − 1

]=

puηuηu − 1

+pdηdηd + 1

− 1.

The default-triggering mechanism and default recovery rule are assumed to be the same

as those in the Black-Cox model. Therefore, the impact of discontinuous movements in the

asset return is mainly reflected in the modified function of the default probability, which is

denoted by πJD. We can calculate πJD numerically through an inverse Laplace transform

(see, e.g., Huang and Huang 2012). Replacing πBC with πJD in Eq. (4) results in the DEJD

model credit spread csJD.

4.1.3 The He-Xiong Model with Jumps

To quantify the liquidity component in CP yield spreads, we model endogenous liquidity

through a market structure similar to Amihud and Mendelson (1986) and He and Xiong

(2012). That is, we assume that each bond investor is hit by a liquidity shock with probability

ξ. Liquidity shocks bring about liquidity needs, which have to be covered by selling the bonds

in the illiquid secondary market. As such, the (fractional) transaction cost k enters bond

17


pricing through its product with the liquidity shock intensity

dt(τ) = e−(r+ξk)τf (1− π(τ)) + e−rτfRG(ξk, τ), (5)

where G(z, ·) denotes the Arrow-Debreu default claim with the discount rate equal to z. If

the asset value process follows Eq. (2), we have π = πBC and G = GBC , where

GBC(ξk, τ) = (K/At)(ν−g(ξk))/σ2

N (h1(g(ξk))) + (K/At)(ν+g(ξk))/σ2

N (h2(g(ξk))) ,

g(ξk) =√ν2 + 2ξkσ2.

As illustrated in He and Xiong (2012), ξk represents the adjustment made to the discount

rate and thus determines the liquidity premium in corporate yield spreads. If bond investors

are not exposed to liquidity shocks (ξ = 0), G(ξk, τ) degenerates to πBC(τ) and Eq. (5)

coincides with dBC(τ).

Given the crucial importance of jump risk to short-term credit spreads, we consider

π = πJD as well in our model-based spread decomposition to fully account for the credit

component. Accordingly, G() needs to be computed numerically, as shown in Huang et al.

(2020), and the corresponding model spread is denoted by csHXJ . It follows that the incre-

mental contribution of liquidity risk to yield spreads is given by csHXJ − csJD.

4.2 Implementation

We start with the calculation of Black-Cox credit spreads, which requires estimates of (1)

the market value of the firm’s asset and (2) asset volatility. Following Bao (2009), we extend

the estimation method of Jones, Mason, and Rosenfeld (1984) to the Black-Cox model to

identify the values of At and σ.8 Specifically, by matching the model-implied values of market

8Applications of the Jones et al. (1984) estimator to the original Merton (1974) model include Campbellet al. (2008), Hillegeist et al. (2004), and Bai and Wu (2016).

18


leverage and equity volatility to their observed values, we obtain the following equation set:

Lt =F

Et(At, σ) + F, (6)

σE =∂E

∂A

AtEtσ, (7)

where L is termed quasi-market leverage by Schaefer and Strebulaev (2008), and σE denotes

the equity volatility. The modeled equity value E(At, σ) is derived as

Et(At, σ) = At −[KGBC −

FR

rT(GBC(r, T )− e−rTπBC(T ))

]−Dt(At, σ), (8)

where the three terms on the right-hand side capture the unlevered value of the firm, the

deadweight loss of default, and the total market value of outstanding debt, respectively. The

solution for Dt follows Leland and Toft (1996),

Dt =

∫ T

0

dt(τ)dτ,

=F

rT

[1−GBC(r, T )(1−R)− e−rT (1− πBC(T )(1−R))

].

Following the standard established by Moody’s KMV (Crosbie and Bohn, 2003), the

default boundary K is measured as the firm’s book measure of short-term debt, plus one

half of its long-term debt, based on its quarterly accounting balance sheet. This specification

of the default boundary is especially suitable for the pricing of default risk at a short horizon,

which explains why it was initially employed in KMV’s Expected Default Frequency (EDF)

measure.9 Studies that have used the same specification include Eom, Helwege, and Huang

(2004); Vassalou and Xing (2004); Duffie, Saita, and Wang (2007).

Estimation of jump parameters {λ, pu, ηu, ηd} involves estimating their counterparts un-

der the physical measure {λP, pPu, ηPu, ηPd} and converting them to the risk-neutral measure.

We adopt the specification of Huang and Huang (2012) that the transformation from P-

9The EDF measure initially focused on one-year default probabilities.

19


measure jump parameters to Q-measure ones is controlled by a single parameter,

γ =λζ

λPζP.

Since a joint estimation of all these parameters is fairly complicated and might not be

numerically robust, we identify them separately by carrying out the following scheme.

First, we use index option prices to identify the jump risk premium parameter γ. Until

December 23, 2019, options on the Shanghai Stock Exchange (SSE) 50 Index ETF were the

only option product traded in mainland China. To make the estimation of γ independent of

other jump parameters, we assume that the SSE 50 Index returns follow a DEJD process

dStSt

= rdt+ σsdWt + d

[Ns,t∑i=1

(Zs,i − 1)

]− λsζsdt (9)

= µsdt+ σsdWPt + d

NPs,t∑

i=1

(ZPs,i − 1)

− λPsζPs dt. (10)

In the spirit of Eraker (2004), we employ a Markov chain Monte Carlo (MCMC) estimator

for joint options and index returns data. To reduce the computational burden, we follow

Pan (2002) and select near-the-money short-dated option contracts for our estimation. As

such, we obtain an estimate of γ at 2.30, along with the estimates of other parameters in

Eqs. (9) and (10).

Next, we use high-frequency equity returns to pin down the values of λ and pu for each

debt issuer. To be specific, we apply the jump detection method of Tauchen and Zhou (2011)

to five-minute returns on individual stocks. The intra-day equity data are retrieved from the

CSMAR China Security Market Trade & Quote Research Database, and we eliminate days

with fewer than 60 trades. Once the individual jump size is filtered out, we can estimate the

jump intensity and the probability of upward jumps. We find that, on average, CP issuers

have 3.95 jumps per year, and upward jumps are slightly more likely than downward jumps,

with the mean of pu equal to 0.53.

20


Finally, we adopt the assumption of Huang and Huang (2012), ηu = ηd = η, when

estimating parameters on the jump size. In our estimation of η, we follow Bao (2009)’s

procedures in the sense that (1) we use the moment condition that equalizes the empirical

and model-implied fourth moments of equity returns; and (2) we do not adjust the estimate

of diffusion volatility σ for the inclusion of jumps, such that the differential csJD − csBC

purely reflects the incremental contribution of the additive jump component.10

The implementation of the He and Xiong (2012) model with double-exponential jumps

(HX-DEJ model hereinafter) requires estimates of the fractional trading cost k and liquidity

shock intensity ξ. The former can be calibrated to our transaction cost measure TC, which

varies across issues and over time. The latter is identified by targeting the average turnover

rate in the Chinese CP market, as in the calibration analysis of He and Xiong (2012). The

average turnover over our sample period is 64.1%, close to the 70% estimated by He and

Milbradt (2014) with the TRACE database for the US corporate bond market.

5 Empirical Results

In this section, we present our empirical results. We consider regressions of CP spreads first,

which are followed by regression analysis of the determinants of MTNs and EBs. We then

investigate the pricing performance of structural models.

5.1 Determinants of CP Spreads: Evidence from Regressions

Table 4 reports results from panel regressions of CP yield spreads on credit-risk-related vari-

ables. Model M1 considers three key variables as suggested by the original Merton model: the

risk-free rate, leverage, and equity volatility (e.g., Ericsson et al. 2009). Model M2 is closer

10According to Cremers et al. (2008), the inclusion of double-exponential jumps has a minimal impact onthe estimation of diffusion volatility, merely decreasing its estimate from 19.95% to 19.88%.

21


to the Merton model in that it examines the distance-to-default (DD), a nonlinear function

of the aforementioned three variables that in theory directly determines the risk-neutral de-

fault probability. The results from these two regression models show that individual equity

volatility is significantly positive and DD is significantly negative. Model M3, a combination

of M2 and M1, indicates that DD subsumes equity volatility, which lends support to the

functional form of the model spread.

Interestingly, augmenting M3 with credit ratings (Ratingi,t) slightly strengthens the im-

pact of DD (model M4). This result implies that DD contains incremental information

about spreads over credit ratings, consistent with Campbell and Taksler (2003) to some ex-

tent. M5 and M6 consider other explanatory variables included in the benchmark regression

model of Collin-Dufresne et al. (2001). Including the slope of yield curves and the equity

market return (CSI300t) does not drive out DD and Ratingi,t (model M5). Finally, the

option-implied volatility (CIV IXt) and the slope of its “smirk” (Jumpt) are used as proxies

for variations in volatility and jump magnitude/probability. Augmenting M5 with these two

variables raises the adjusted R2 substantially from 4.8% to 6.4%. In particular, Jumpt is

highly significant with the expected sign, consistent with the notion that jumps are essential

for structural models to generate plausible spreads for short-maturity debts (Zhou 2001).

Next, we explore the importance of market illiquidity in determining CP spreads. Uni-

variate regression results reported in Table 5 indicate that all six transaction cost measures

are significantly positive. In particular, they coincide with the finding of Schestag et al.

(2016) that Roll (1984)’s measure and Hasbrouck (2009)’s Gibbs measure deliver the best

performance among low-frequency ones, as each of them captures more than 15% of varia-

tions in CP spreads. On the other hand, the Pastor and Stambaugh (2003) liquidity measure

for price impact is associated with an insignificant coefficient with a counterintuitive sign.

To assess the relative importance of liquidity- and credit-related variables in explaining

22


the CP spreads, we estimate nine regression models and report the results in Table 6. M1

starts with four traditional liquidity proxies considered in Covitz and Downing (2007). We

find that, while OfferAmt i and InitMati are significant with expected signs, the four proxies

explain little variation in the spread with an R2 of merely 0.7%. In contrast, our proposed

measure for trading cost, TCi, is significantly positive with an R2 of 21.4% (M2), which is

greater than any individual measure. Augmenting M2 with Amihudi,t raises the R2 to 26.1%

(M3). Augmenting M3 with the four traditional liquidity proxies has only a marginal impact

on R2 and renders OfferAmt i and InitMati insignificant. This evidence suggests that the

conclusion of Covitz and Downing (2007) on the role of liquidity is likely driven by their

focus on static/deterministic measures.

Given the results in Table 4, we use DDi,t and Ratingi,t as our baseline credit variables

and consider the incremental contribution of Jumpt as well. M5 shows that both DDi and

Ratingi are significant with expected signs albeit with a low R2 of 3.4%. Augmenting M5

with TCi and Amihudi weakens the impact of DDi,t and Ratingi,t, although the two credit-

related variables are still significant (M6). Interestingly, M6 has an R2 of 26.1%, much higher

than that of M5 and the same as that of M3. In other words, the results from M2 through M6

indicate that the liquidity proxies are much more important than the credit-related variables

in explaining the variation in the CP spread. The results from M7 and M8—M5 and M6

augmented with Jumpt, respectively—confirm this conclusion. Still, including Jumpt raises

the R2 significantly percentage-wise, increasing R2 = 3.4% for M5 to 4.1% for M7 (a 20%

increase in the relative term). Lastly, we augment M8 with more market-wide variables,

including Slopet, CSI300t, CIV IXt, and TEDt, along with control dummies Y earEnd and

SOE (M9). Among these variables, only CIV IXt is significant at the 5% level, but with

a counterintuitive sign. In particular, while SOE has an expected, negative effect on yield

spreads, the dummy is insignificant in the presence of other credit variables. This result is

23


consistent with findings by Geng and Pan (2019), which suggest that rating agencies have

taken debt issuers’ nature into account. Moreover, M9 has an R2 of 27.8%, almost the same

as that of M8 (27.2%).

The dominance of liquidity variables as shown in Table 6 is reconcilable with the findings

of Covitz and Downing (2007) through three alternative explanations. First, as we aim to

argue, the sparsity of secondary market transactions in the US CP market confines their

analysis to static/deterministic liquidity measures, which underestimate the explanatory

power for CP spreads. Second, the relative importance of liquidity and credit risk in the

primary market somehow dramatically differs from that in the secondary market. Third, the

moderate R2 values generated by credit variables are unique to the Chinese CP market.

We explore the last two explanations in Appendices B and C. We first examine if credit

variables capture a substantially larger portion of variations in new issue yield spreads of

Chinese CP compared to results in Table 4. It turns out that, while some explanatory

variables (e.g., credit rating) show greater significance in the primary market, the overall

explanatory power of credit risk variables seems to be of the same magnitude as documented

in the secondary market. Next, we present corresponding results based on US data over

the same period. Specifically, we retrieve CP pricing information from US money market

funds’ month-end portfolio holdings and then estimate regression models similar to those in

Table 4. Again, we do not find that credit risk plays a significantly larger role in determining

CP spreads in the US market. For instance, the R2 as achieved by specification M6 is 6.4%,

8.1%, and 7.5% for the Chinese secondary market, Chinese primary market, and US market

(dominated by primary market transactions), respectively. Therefore, while the different

market structure prevents us from implementing dynamic liquidity measures for the US

market, at least issuers’ fundamental default risk appears to play a similar (and rather

limited) role in shaping CP yield spreads for both countries.

24


5.2 Determinants of Spreads on MTNs and EBs

Intuitively, credit-related variables become more important in determining the spreads of

longer-maturity corporate debts. In this subsection, we repeat the analysis of Section 5.1

using MTNs and EBs to examine if the relative importance of firm’s fundamentals increases

with the debt maturity.

Consider short-term MTNs and EBs with maturities of 1–3 years first. We make several

observations from the results reported in Table 7. First, while both TCi and Amihudi

are highly significant, the former alone has an R2 of 24.0% (M1), and the latter has an

incremental R2 of 0.8% only (M2). Namely, Amihudi becomes less important than it is

for the CP spreads (see M2 and M3 in Table 6). Second, the credit variables, DDi and

Ratingi, are both significant with expected signs and together have an R2 of 9.3% (M3),

much higher than their counterpart for CP spreads (3.4% of M5 in Table 6). Furthermore,

DDi and Ratingi together have a marginal R2 of 0.03 (a more than 10% increase) over

TCi and Amihudi (M4 and M2). Third, Jumpt is highly significant with the correct sign,

but its incremental explanatory power over DDi and Ratingi becomes weaker than it does

for CP spreads. For instance, including Jumpt raises the R2 of 9.3% for M3 to 9.8% for

M5, a 5% increase in the relative term (as opposed to a 20% increase in the case of CP

spreads). Fourth, the results from M6 and M7 show that Slopet, CSI300t, CIV IXt, TEDt,

and Y earEnd together add little incremental explanatory power over TCi, DDi, Ratingi,

and Jumpt.

To summarize, the main takeaway from Table 7 is that when we move from CP to longer

maturity, short-term MTNs and EBs, the credit variables become relatively more important

than the liquidity proxies, but the jump risk becomes less important relative to the other

credit variables.

Next we repeat the above analysis using intermediate MTNs and EBs with maturities of

25


3–6 years and report the results in Table 8.11 We make the following observations. First, a

comparison of M1 and M2 with their counterparts for short-term MTNs and EBs (Table 7)

indicates that while TCi is equally important for intermediate-term MTNs and EBs as it is

for the short-term ones, Amihudi is no longer significant conditional on TCi (M2). Second,

DDi and Ratingi are both highly significant with expected signs and together have an

R2 of 39.0%, higher than that of TCi (M1) and, in particular, much higher than their

counterpart for either CP spreads (3.4% of M5 in Table 6) or short-term MTNs and EBs

(9.3% of M3 in Table 7). Third, Jumpt is only marginally significant now and has very little

incremental explanatory power over either DDi and Ratingi (M5) or these variables along

with TCi (M6). Fourth, all credit and liquidity variables jointly capture almost half of the

variations in yield spreads (M6), and CIVIX is the only significant market-wide variables

(M7). When comparing the results on CIVIX in Tables 6 and 7, we find from its positive

sign and significance in Table 8 that stochastic volatility matters in corporate debts as the

time to maturity increases. In summary, Table 8 provides more evidence supporting the

main takeaway from Table 7.

To further illustrate the relative importance of credit- or liquidity-related proxies in

explaining yield spreads, Figure 2 plots their R2’s for CPs, short-maturity MTNs and EBs,

and intermediate-maturity MTNs and EBs, respectively. Credit-related variables considered

include DDi and Ratingi with (in blue) and without Jumpt (in navy blue). Liquidity proxies

considered include TC with (in yellow) and without Amihudi (in green). The main takeaway

from the figure is that while the liquidity proxies together have a relatively stable R2 of

around 25%, the credit-risk proxies have an increasing R2 as maturities of issues become

longer.

11In China, the typical MTN maturity at issuance is between 3 to 5 years. While the initial maturity forEBs ranges from 7 to 20 years, they are mainly issued by SOEs not publicly listed in stock exchanges. Forthis reason, there are only 43 monthly observations in our sample with greater than 6 years to maturity. Weexclude them from our regression analysis to obtain a more homogeneous maturity group.

26


5.3 Pricing Performance of Structural Models

The regression-based evidence in Sections 5.1 and 5.2 sheds light on the role of credit and

liquidity in capturing spread variations. However, since there is a nontrivial overlap in the

information covered by those credit and liquidity variables, we are unable to perform a yield

spread accounting without a structural framework. In this subsection, we aim to quantify

the contributions of default and liquidity risks to the level of CP yield spreads. To this end,

we examine the pricing performance of the four structural models reviewed in Section 4.

5.3.1 Empirical Distributions of Observed and Predicted CP Spreads

We implement each of these four models as described in Section 4.2 and calculate the model-

predicted spread of every CP issue in our final sample. Before analyzing the pricing perfor-

mance of these models, we examine the empirical distributions of observed CP spreads as

well as the model-predicted spreads, which are illustrated for both the full sample and the

subsamples by credit ratings in Table 9.

Consider the full sample first. The consensus is that pure diffusion-based structural

models are unable to generate sufficiently high short-term spreads consistent with the levels

of observed spreads. Clearly, the Black-Cox (pure-diffusion) model substantially underesti-

mates CP spreads, though this problem has been alleviated by a small number of soaring

model predictions in the right tail. For instance, the model-implied CP spreads have a mean

of 0.32% and median of 0.00% (6 × 10−4 bps), way below their empirical counterparts of

1.53% and 1.34%, respectively. It follows that the distribution of modeled spreads is severe-

ly right-skewed compared to the empirical distribution. This finding indicates that judging

the models’ performance by the mean spread alone may point to a misleading conclusion.

As expected, the DEJD model significantly improves the pricing performance, especially

at the right tail. For instance, the Black-Cox, DEJD, and observed spreads at the 90th

27


percentile are 0.96%, 2.62%, and 2.88%, respectively. Also, incorporating jumps raises the

average and median model-predicted spreads from 0.32% and 0.00% for the Black-Cox mod-

el to 1.07% and 0.48% for the DEJD model, respectively. However, the left tail DEJD

spreads are still substantially below their empirical counterparts. For example, the DEJD

and observed spreads at the 10th percentile are 0.06% and 0.45%, respectively. Nonetheless,

although the DEJD model still generates credit spreads that are more right-skewed than

those in the data, it brings out nontrivial improvements on the spread distribution over the

Black-Cox model.

Another way to improve the pricing performance on the baseline Black-Cox model is by

introducing a liquidity premium, as in He and Xiong (2012). We find that this extension

increases the average model spread to the same level as the DEJD specification. On the other

hand, the He-Xiong model leads to a heavier right tail in the spread distribution compared

to the DEJD model; its median spread is lower by about 14 bps. This pattern is attributable

to the fact that transaction costs tend to rise dramatically for corporate debts with lower

rating classes (Edwards et al., 2007; Friewald et al., 2012). Consequently, the calibrated

model implies that corporate debts with a higher level of default risk are likely to have a

greater incremental liquidity component in their yield spreads.

It is worth noting that the He-Xiong spreads reported in Table 9 essentially reflect the

lower bound of the model’s predictions. First, the parameter k in their model should be

broadly interpreted as encompassing both transaction costs and the price impact of trades.

In our model calibration, we only take into account the information on effective bid-ask

spreads, owing to the difficulty in quantifying the effect of another liquidity dimension.

Therefore, once the adjustment of the effective discount rate to the price impact is built in,

the model-predicted spreads are likely to have a nontrivial increase. Second, the original

He-Xiong model features a liquidity-driven credit component in corporate yield spreads. In

28


our model specification analysis, to calibrate all models to the same benchmark, we do not

consider the endogenous default boundary. Consequently, the reported model spreads are

possibly lower than they are when market liquidity is allowed to influence corporate default

risk, depending on the tax benefit and bankruptcy cost in China.

Consider next the extended He-Xiong model with jumps, proposed in this paper. Recall

that this model can also be interpreted as an extension of the DEJD model that incor-

porates the effect of market liquidity. The top panel of Table 9 shows that the average

model-predicted spread is 1.62%, slightly higher than the average observed spread of 1.53%.

The model-implied spreads at the right tail exceed their empirical counterparts even more:

the model-implied and observed spreads at the 90th percentile are 3.29% and 2.88%, respec-

tively. However, the model-implied median spread, and especially those spreads at the left

tail, are substantially below their empirical counterparts. Moreover, the extended He-Xiong

model-implied spreads are still right skewed. That is, while incorporating external market

liquidity significantly improves overall pricing performance, the resulting model may still

under-estimate those “safer” CP spreads but overestimate the spreads of those “riskier” CP

issues. To some extent, this problem is analogous to what is noted in Eom, Helwege, and

Huang (2004) about some other structural models that they use to predict corporate bond

yield spreads. One caveat to keep in mind, however: the modeled and observed spreads at

a given percentile may come from different CP issues.

The results for four different subsamples by credit ratings, as reported in Table 9, provide

patterns similar to those for the full sample. While the pricing performance of the DEJD

model is fairly stable across rating categories, the fitting of the He-Xiong model to the data

improves, in terms of both the spread level and distributional shape, as the credit rating falls.

This pattern is also illustrated by Figure 3, which visualizes the contributions of different

components to CP yield spreads. Judging from the median spread, the He-Xiong model

29


accounts for about one-quarter of the observed spreads for AAA-rated issues, increasing to

more than one-third for AA issues. This result contrasts with the conclusion drawn from

the mean spread that modeled spreads capture around two-thirds of the observed spreads in

all rating classes.

Moreover, focusing on the median spread gives rise to more conclusive evidence on the

contribution of market illiquidity to yield spreads, which turns out to be consistently around

one-third across rating groups regardless of whether the jump risk is controlled for. Instead,

judging from the mean spread renders the conclusion rather sensitive to the model specifi-

cation. Specifically, the liquidity component accounts for one half of the observed spreads if

we focus on csHX − csBC and accounts for only one-third if we focus on csHXJ − csJD.

5.3.2 Pricing Errors

We now examine the pricing errors of the four structural models, which are reported for

both the full sample and the subsamples by credit ratings in Table 10. We make several

observations from the mean pricing errors reported in Panel A. First, all four models have

negative pricing errors, regardless of the credit ratings considered. The mean pricing error

ranges from -2.11% for the “Other” group from the Black-Cox model to -0.17% for the AAA

group from the extended He-Xiong model (the HX-DEJ model). Second, incorporating

jumps or market illiquidity into the benchmark Black-Cox model each separately reduces

the magnitudes of the mean pricing errors, and the reduction achieved by the He-Xiong

model is slightly more remarkable. Third, under a given model, the higher the credit rating,

the lower the magnitude of the mean pricing error. Fourth, the average pricing error of the

HX-DEJ model is statistically insignificantly different from zero for the full sample as well

as for the AAA and AA+ subsamples; namely, on average the model can match the levels

of CP spreads for the full sample, the AAA group, or the AA+ subsample.

The mean percentage pricing errors, reported in Panel B of Table 10, show different

30


patterns from the mean pricing errors in Panel A. First, the mean percentage pricing error

is negative except for the full sample and for the AAA and AA+ subsamples, all under the

HX-DEJ model. The mean percentage pricing error ranges from -72.31% for the AAA group

under the Black-Cox model to 19.88% for the AAA group under the HX-DEJ model. Second,

while adding jumps or market illiquidity to the benchmark Black-Cox model once again leads

to smaller pricing errors, the DEJD model tends to slightly outperform the He-Xiong model

when we judge from the mean percentage error. Third, under a given model, there is no

monotonic relation between the magnitude of the mean percentage pricing error and the

credit rating. Fourth, the t-test results indicate that the mean percentage pricing error of

either the DEJD model or the HX-DEJ model is not statistically significantly different from

zero for the entire sample, though the nonparametric signed-rank test rejects all models at

the 5% significance level.

Overall, there are four main takeaways from Table 10. First, the Black-Cox model sub-

stantially underestimates the CP spreads, regardless of the credit ratings considered. Second,

augmenting the model with double-exponential jumps significantly improves the model per-

formance, especially for AA–AAA groups on a relative basis. The resulting DEJD model,

however, still underestimates the CP spreads across all rating groups. Third, augmenting the

DEJD model with endogenous liquidity substantially improves the pricing performance. In

fact, on average, the resulting HX-DEJ model can match the CP spread for the full sample

as well as for the AAA and AA+ subsamples. Fourth, both the DEJD and HX-DEJ mod-

els suffer from an accuracy problem: they both have high mean percentage pricing errors,

although they are statistically insignificant except for the “AA- or below” rating group.

31


6 Conclusions

Although short-term corporate debt played an important role in the recent financial crisis,

very few studies have been done on the determinants of short-term credit spreads. In this

paper, we examine the determinants of commercial papers within the structural framework

of default risk, using a novel data set of secondary market transactions in the Chinese

commercial paper market. In particular, we propose and empirically test a structural model

with rollover risk, jump risk, and endogenous liquidity, a model particularly suitable for

predicting commercial paper spreads. Among other things, the model allows us to decompose

CP spreads into a credit component and a liquidity component in a unified manner.

We find that credit and liquidity risks are both important in the determination of short-

term yield spreads and that the former is more important for longer-maturity debt. For

instance, in the absence of jump risk and endogenous liquidity, the proposed model reduces

to the Black and Cox (1976) pure-diffusion model: we find that the model substantially

under-estimates CP spreads, regardless of the credit ratings considered. Not surprisingly,

augmenting the Black-Cox model with a double-exponential jump (DEJ) component in the

underlying asset return process significantly improves the model performance, especially for

AA–AAA groups on a relative basis. However, the resulting model—the double-exponential

jump-diffusion (DEJD) model of corporate debt pricing—still underestimates CP spreads

across all rating groups. In other words, we need more than jump risk to explain short-term

spreads.

Incorporating endogenous liquidity into the DEJD model results in our proposed model;

alternatively, it can be regarded as an extension of the He and Xiong (2012) model to include

a DEJ component in the asset return process. We find that this extended He-Xiong model

substantially improves the model performance except for the AAA group. Furthermore, on

average the model can match the level of CP spreads for either the full sample or the AAA

32


and AA+ subsamples. These findings provide evidence that liquidity risk is an important

component of short-term spreads.

Nonetheless, our empirical results indicate that the proposed model has limitations in

terms of its accuracy: although the average percentage pricing errors of the model are

insignificantly different from zero, they are high regardless of the rating groups considered.

Moreover, the average percentage pricing errors are positive for the full, AAA, or AA+

samples but negative for the AA and lower rating groups—namely, on average the proposed

model overestimates relative spreads for the AAA and AA+ groups but underestimates

relative spreads for AA and AA- or lower groups. These findings indicate that the liquidity

component in the model has an asymmetric impact between safer and more risky CP issues.

Overall, this paper provides a comprehensive study on the determinants of short-term

credit spreads using secondary transaction data and a structural model with both rollover

risk and endogenous liquidity. Our results indicate that to better capture the behavior of

short-term credit spreads, we need to incorporate a liquidity component that can help raise

spreads on the riskiest issues without raising them too much for the safer issues.

33


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A The Chinese Commercial Paper Market

In the Chinese bond market, commercial papers are widely used by non-financial firms for

short-term financing.12 The standard commercial papers were first introduced to the market

in May 2005, followed by the introduction of the super commercial papers in 2010. The

major differences between these two types of commercial papers are the maturity at issuance

and borrowing capacity. The value of the outstanding standard commercial paper, with a

maturity of less than one year, cannot exceed 40% of the issuing firm’s net asset. There is

no such limit for super commercial papers, for which the maturity is restricted to less than

270 days. Since the borrowing cost of commercial papers is typically lower than that of bank

loans with similar maturities, and there is no explicit restriction on the usage of funds raised,

the market for commercial papers has grown fast since its inception. In 2005, 61 firms raised

142.4 billion RMB with commercial papers. By the end of 2018, the outstanding bond value

had reached 1.9 trillion RMB, which accounted for 2.3% of the overall bond market.

A.1 Registration and issuance

Commercial papers are issued and traded in the interbank bond market.13 This is an OTC

market, only allowing the participation of institutional investors such as commercial banks,

rural credit cooperatives, security firms, insurance companies, mutual funds, and foreign

institutions. The market was established in 1997 and regulated by China’s central bank,

the People’s Bank of China. The market significantly dominates bond issuance and trading

in China, as the balance of outstanding bonds amounted to 76 trillion (89% of the bond

market) at the end of 2018.14

12Security firms are also allowed to issue commercial papers. However, they are subject to differentregulations, and the market size is relatively small. We exclude them from our analysis.

13See Amstad and He (2019) for an in-depth overview of the interbank bond market in China.14Another important bond market in China is the exchange market (i.e., the Shanghai Stock Exchange

and the Shenzhen Stock Exchange). The exchange market is regulated by the China Security Regulatory

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Bond issuance in the interbank bond market is based on a registration system. The

National Association of Financial Market Investors (NAFMII), a self-regulation industry

organization under the central bank’s guidance, makes the registration rules and oversees the

registration process. With a book-building process, the offering interest rate is determined by

underwriters based on bids collected from market investors. Since the maturity is quite short,

typically firms issue commercial papers to repay bank loans or other bonds and fund their

working capital. In 2018, 827 firms, including both SOEs and privately owned enterprises,

issued 2,918 commercial papers, raising 3.1 trillion RMB. This accounted for 7.2% of the

total bond issuance in the Chinese market. The maturity of an average bond was 0.66 years,

and it was offered at 4.94% per year.

A.2 Trading and investors

The interbank bond market is an OTC market by nature. However, the China Foreign

Exchange Trade System offers a centralized trading system for bonds including commercial

papers. Similarly, the Shanghai Clearing House provides unified depository and clearing

services to commercial paper investors. All the participants in the interbank bond market

are allowed to invest in commercial papers. As of the end of 2018, the largest investor was a

non-legal-person investor (mutual funds, wealth management products, trusts, etc.), which

held 69.9% of the outstanding commercial papers. The second and third largest investors

were commercial banks and security firms, holding 23.1% and 4.3%, respectively. Commercial

papers are among the most liquid products in the bond market. In 2018, the spot transaction

volume amounted to 7.0 trillion RMB, which could be translated to an annual turnover rate

of 4.1.

Commission, the counterpart of the SEC in China. A variety of bond products, including corporate bonds,government bonds, and financial bonds, is available on this market. By the end of 2018, the value ofoutstanding bonds in the exchange market was 9.2 trillion RMB.

40


A.3 Credit rating and defaults

NAFMII requires that standard commercial paper issuers be rated AA- or above. For super

commercial papers, two ratings from different rating agencies are mandatory with one at AA

or above. These rating requirements seem to be not strictly binding in many cases, however,

given that the distribution of the Chinese rating scale is upwardly skewed. Among the 2,918

bonds issued in 2018, 51.6% were rated AAA, 34.5% were rated AA+, and 13.5% were rated

AA. Only 5 bonds (0.2%) were rated AA-. Credit enhancements were also seldom used as

only 36 (1.2%) bonds were provided enhancements such as guarantees or collateral.

Although Chinese regulators have been striving to eliminate implicit government guaran-

tees in the bond market, the overall bond default rate remains relatively low in China. It is

the same case for commercial papers. The first real default in the commercial paper market

occurred in November 2015, as Sunnsy Group failed to repay its 2 billion RMB bond. From

2014 to 2018, only 62 commercial papers of the 42.2 billion outstanding amount defaulted,

representing a default rate of 0.53% in terms of bond number and 0.29% in terms of val-

ue. Moreover, 10 of these defaulted bonds of the 4.6 billion outstanding amount were fully

recovered by November 2019.

B Regression Evidence from the Primary CP Market

In Section 5.1, we include a short discussion of the evidence from our regression analysis of

the primary CP market. In this appendix, we present the details of this analysis. Recall

that the objective of this analysis is to examine whether credit variables can capture a

substantially larger portion of variations in yield spreads of newly issued CP, compared to

the results based on secondary issues (Table 4).

To this end, we collect the issuance yields of all CPs that have been outstanding over our

sample period May 2014–December 2018 and are issued by public firms. Since we do not

41


require that CPs be traded in the secondary market during this period, the total number

of issues considered in this appendix (2,023) is slightly larger than the 1,901 as reported

in Table 2. We then regress the issuance yields of CPs in this sample on credit variables,

liquidity measures, or both. Note that we focus on the offering date of each CP in this

analysis, and thus we ensure that the information on each explanatory variable is available

at the offering date.15

We report the regression results for seven different model specifications in Table A1.

For comparison, these specifications are the same as those considered in Table 4. Consider

regression M1, which includes the risk-free rate, leverage, and equity volatility (three key

structural-model variables). As noted earlier, the estimation of these variables uses no future

information. Specifically, the risk-free rate is the bootstrapped repo rate on the date prior

to the offering date, leverage is calculated using the most recent (quarterly) balance sheet

information by the offering date, and equity volatility is estimated with the 22 consecutive

daily stock returns prior to the offering date. These three variables jointly explain about

2.1% of the variations in issuance yield spreads of CPs.

Consistent with our findings in Section 5.1, results for M2 and M3 show that distance-to-

default largely captures the explanatory power of individual elements in the Merton (1974)

model. But the uniqueness of the primary CP market shows up in regression M4, as credit

ratings appear to carry significant incremental information on yield spreads. Besides its

massive statistical significance, the rating variable alone increases the R2 value from 3.5%

to 7.0%. This result suggests that the issuer’s credit rating might have a benchmark effect

on CP issuance yields. Columns M5 and M6 present the impact of other aggregate variables

that proxy for the jump risk, stochastic volatility, and the macroeconomic condition; they

jointly boost the R2 to 8.1%. Finally, we include two static liquidity proxies applicable to the

15In the Chinese bond markets, the offering date is usually a few days earlier than the so-called listingdate, the first date on which bonds can be traded in the secondary market.

42


primary market in regression M7. In line with results in Table 6, both the offering amount

and initial maturity are significant with expected signs, but their explanatory power even

for newly issued CPs is rather weak. Also, their economic importance is fairly limited as

well, as a 6-month increase in the initial maturity raises the yield spread by merely 2.4 bps.

Another notable finding in Table A1 concerns the effect of the risk-free rate, which is

persistently and significantly positive. It implies that, at least in the Chinese CP market,

repo rates are more relevant as a proxy for (investors’ perception of) monetary policy shock-

s.16 A contractionary monetary policy increases the lending rates in the repo market and

simultaneously tightens the supply of credit, which leads to higher CP spreads. As a result,

CP yield spreads positively comove with repo rates.

Overall, the results in Table A1 indicate that, while some explanatory variables (e.g.,

credit rating) show greater significance in the primary market, the overall explanatory power

of credit risk variables seems to be of the same magnitude as documented in the secondary

market. In other words, they are unlikely to overturn the dominance of dynamic liquidity

measures as documented in Table 6. On the other hand, static liquidity measures are not of

the first order importance in the primary market either.

C Regression Evidence from the US Commercial Pa-

per Market

To investigate whether the limited explanatory power of credit-related variables is limited

to the Chinese CP market, we examine the US commercial paper market in this section.

We first compile a data set of CP yield spreads based on data on holdings of money

market funds (MMF) in the US. The holdings information at the security level is collected

16The seven-day repo rate for depository institutions (labeled as “DR007”) is the primary policy rate inChina.

43


by the SEC at a monthly frequency and available to the public through the EDGAR system.

We retrieve data from Form N-MFP—which discloses portfolio holdings of each MMF at

the CUSIP level since 2011—and aggregate them to the security level by computing volume-

weighted prices for $1 face value. For comparison, we confine our analysis to securities in

the “Non-Financial Company Commercial Paper” category that are traded by prime funds

over the period 2014.05–2018.12. For each CP issue, we manually link it to a public firm in

CRSP and Capital IQ through CUSIP and issuer names,17 if possible, and then extract the

information on firm fundamentals. After matching the equity and accounting information to

the CP observations, we obtain a panel of 7,419 issue-month spread observations with 4,475

CPs issued by 113 firms.

We then reimplement the six regression models in Table 4 with the US data and present

the results in Table A2. The M1 column shows that three basic elements in structural

models—the risk-free rate, firm leverage, and volatility—all have significant coefficients with

expected signs. The resulting regression R2 of 1.1%, albeit still moderate, is higher than

that of 0.5% as reported from the Chinese market. Results in the next few columns confirm

our finding in Section 5.1 that distance-to-default and credit rating seem to summarize

information on the firm fundamental default risk.

The messages delivered by columns M5 and M6 are also similar to our baseline results: the

proxy for jump risk offers nontrivial additive explanatory power for CP yield spreads, whereas

the yield curve slope and market index returns do not. A notable difference in Table A2

is that VIX becomes highly significant, possibly because VIX captures information on the

US financial markets above and beyond variations in risk-neutral variance, e.g., funding

liquidity (Nagel, 2012) and investor sentiment (Baker and Wurgler, 2007). The overall R2

as achieved by all these explanatory variables is 7.5%, slightly higher than its counterpart

17Commercial papers do not necessarily share the first six digits of CUSIP with their issuers.

44


in the Chinese CP market.

Finally, since it is infeasible to implement dynamic liquidity measures for the US market,

we can still assess the importance of those static ones in determining CP yield spreads. We

consider the dollar trading volume and time to maturity as examined by Covitz and Downing

(2007).18 Consistent with their finding, the M7 column shows that a rise in trading volume

significantly decreases CP spreads, and the Maturity variable seems to lose its significance

when controlling for V olume and other variables.

18Since we do not have access to the issuance information of each CP issue, we are unable to determinethe total amount outstanding nor identify whether a particular transaction is in the primary or secondarymarket.

45


Table 1: Trading Activity in the Chinese Commercial Paper Market

This table reports average trading volumes for different segments in the Chinese commercialpaper market, as well as their average shares of total daily trading volumes. The “PrimaryMarket” includes new issues, and the “Secondary Market” is for paper traded after itsissuance date in the primary market. The volumes are reported in billion RMB and shares areexpressed in percentages. The figures below each average volume/share are the correspondingstandard deviations.

Days to Maturity

1-30 31-60 61-90 91-180 181-270 271-360 Sum

Primary Market Volume (bn)

Mean 2.27 2.34 2.27 3.06 6.25 3.31 19.50

SD 2.62 2.23 2.58 3.26 4.59 2.94

% of Total

Mean 4.08 4.49 4.35 5.96 11.93 6.95 37.76

SD 4.8 4.01 4.31 6.46 8.77 6.99

No. Issues 1.17 1.12 1.31 1.76 4.73 3.69 13.78

Secondary Market Volume (bn)

Mean 3.39 3.61 3.59 10.64 13.39 5.97 40.60

SD 2.09 2.22 2.37 6.13 7.63 3.78

% of Total

Mean 6.72 7.18 7.03 20.34 25.37 11.95 78.58

SD 3.98 4.02 3.99 7.2 8.51 7.25

No. Issues 23.85 23.1 20.22 60.83 61.46 34.37 223.82

46


Table 2: Descriptive Statistics for CP Issuance and Issuers

Panel A reports the number of commercial papers (CP) issued, the number of issuing companies, and thetotal issuance amount for each year over the period 2013–2018. Panel B provides issue-level informationfor all commercial papers used in model specification and regression analyses. Panel C summarizes the(quarterly) financial metrics of commercial paper issuers that have observations included in the final datasample. Maturity is the issue’s initial time to maturity in years. Issuance Amount is the issue’s amountoutstanding in billions of RMB. Issuance Yield is the promised (annualized) interest rate at issuance. Ratingis a numerical translation of credit rating: 1=AAA and 5=A+. Turnover is the issue’s annualized tradingvolume scaled by the amount outstanding. Leverage denotes the ratio of the book value of debt to the sumof the book value of debt plus the market value of equity. Equity Volatility is the annualized volatility ofdaily log equity returns for a quarter. Payout Ratio is the ratio of payment to outside stakeholders over thepast one year divided by the asset value. Equity market capitalization is defined as the product of shareprice and shares outstanding in billions of RMB. Return on Assets is a firm’s income before extraordinaryitems divided by the mean of total assets at the start and end of the quarter. Interest Coverage is EBITdivided by the interest expense.

Panel A: CP Issuance and Issuers by Year

Year 2013 2014 2015 2016 2017 2018

No. of Issues 1080 1521 2540 2639 2136 2919

No. of Issuers 710 849 1002 950 709 810

Issuance Amount (bn) 1614.98 2184.95 3276.93 3370.78 2376.19 3125.43

Panel B: Characteristics of CP Issues

Obs Mean Std Dev 25th 50th 75th

Maturity (yr) 1901 0.76 0.24 0.74 0.75 1

Issuance Amount (bn) 1901 12.82 14.60 5 8 16

Issuance Yield 1901 4.49 1.27 3.40 4.50 5.35

Rating 1901 2.05 1.02 1 2 3

Turnover 1800 4.36 5.26 2.14 3.18 4.67

Panel C: Characteristics of CP Issuers

Obs Mean Std Dev 25th 50th 75th

Leverage 3104 0.44 0.21 0.27 0.42 0.62

Equity Volatility 3282 0.44 0.26 0.26 0.38 0.56

Payout Ratio 3345 0.02 0.01 0.01 0.02 0.03

Market Cap (bn) 3124 30.42 79.98 8.01 15.87 29.71

Return on Assets (%) 3349 2.06 2.77 0.49 1.45 3.00

Interest Coverage 3213 7.46 48.24 1.82 3.22 6.34

47


Table 3: Transaction Cost Measures and Effective Bid-Ask Spread

Panel A shows descriptive summary statistics (in basis points) for ourlow-frequency transaction cost measures: Roll (1984)’s measure, Hasbrouck(2009)’s measure, effective tick (Goyenko, Holden, and Trzcinka 2009; Holden2009), Fong, Holden, and Trzcinka (2017)’s measure (FHT ), high-low spreadestimator (HLsprd) (Corwin and Schultz 2012), and close-high-low estimator(CHL) (Abdi and Ranaldo 2017). The comprehensive measure for effectivebid-ask spread, TC, is defined as an equally weighted linear combination ofthese six measures. Panel B shows the principal component analysis loadingson each of the six measures, along with the cumulative explanatory power ofthe components. Monthly liquidity measures are computed based on dailytransaction prices and volumes provided by CFETS.

Panel A: Descriptive statistics (bps)

Mean 10% 25% 50% 75% 90%

Roll 75 0 3 44 103 182

Hasbrouck 80 7 16 34 76 160

EffectiveTick 46 2 8 22 50 110

FHT 85 12 23 46 94 163

HLsprd 48 0 1 4 29 118

CHL 168 8 25 60 151 384

TC 75 10 21 45 89 158

Panel B: Principal component loadings

PC1 PC2 PC3 PC4

Roll 0.45 −0.41 0.01 0.12

Hasbrouck 0.42 −0.04 0.03 −0.36

EffectiveTick 0.35 0.26 0.07 −0.46

FHT 0.44 0.03 0.02 −0.31

HLsprd 0.31 0.40 −0.22 0.51

CHL 0.32 0.45 −0.19 0.33

Cumulative 0.44 0.63 0.77 0.87

48


Table 4: Regression of CP Spreads on Credit Risk Determinants

This table reports results from six specifications of regressions of commercial pa-per (CP) spreads on credit-risk-related variables. Explanatory variables usedinclude the risk-free rate (rft), firm-i’s leverage ratio (Levi,t), equity volatility(σEi,t), distance-to-default (DDi,t), credit ratings (Ratingi,t), the slope of yieldcurves (Slopet), the equity market index (CSI300t), the option-implied volatil-ity (CIV IXt), and the slope of its “smirk” (Jumpt).

Dependent variable: CP spreads

M1 M2 M3 M4 M5 M6

Intercept 0.009 0.023∗∗∗ 0.012 0.012 0.012 0.012

(0.68) (5.22) (0.87) (0.65) (0.68) (0.63)

rft 0.244 0.531∗∗ 0.303 0.451∗ 0.565

(0.97) (2.11) (1.34) (1.74) (1.35)

Levi,t −0.004 −0.009 −0.007 −0.008 −0.010

(−0.59) (−1.04) (−0.67) (−0.71) (−0.76)

σEi,t 0.021∗∗∗ 0.009 −0.009 −0.016 −0.021

(2.75) (0.97) (−0.84) (−1.24) (−1.64)

DDi,t −0.002∗∗∗ −0.003∗∗∗ −0.003∗∗∗ −0.004∗∗∗ −0.004∗∗∗

(−2.66) (−2.60) (−2.93) (−3.01) (−3.06)

Ratingi,t 0.010∗∗∗ 0.011∗∗∗ 0.011∗∗∗

(9.19) (10.17) (9.07)

Slopet −0.501 −0.590

(−0.88) (−0.72)

CSI300t −0.061∗ −0.081∗∗

(−1.70) (−1.99)

CIV IXt −0.046

(−1.52)

Jumpt 0.125∗∗∗

(3.56)

R2 0.005 0.037 0.044 0.043 0.048 0.064

Obs 5755 5755 5755 5755 5755 4920

49


Table 5: Explanatory Power of Liquidity Measures for CP Spreads

This table reports results from regressions of commercial paper (CP) spreads on a variety of illiq-uidity measures. They include six transaction cost proxies: measures of Roll (1984) and Hasbrouck(2009), the effective tick of Goyenko, Holden, and Trzcinka (2009); Holden (2009), the Fong, Holden,and Trzcinka (2017) measure (FHTi,t), the Corwin and Schultz (2012) high-low spread estimator(HighLowi,t), and the Abdi and Ranaldo (2017) close-high-low estimator (CHLi,t); and two priceimpact proxies: Amihudi,t and PSi,t, representing those of Amihud (2002) and Pastor and Stam-baugh (2003), respectively.


(1) (2) (3) (4) (5) (6) (7) (8)

Intercept 0.017∗∗∗ 0.008∗∗ 0.012∗∗∗ 0.011∗∗∗ 0.016∗∗∗ 0.011∗∗∗ 0.017∗∗∗ 0.018∗∗∗

(11.92) (2.33) (5.05) (3.41) (12.54) (3.06) (11.99) (9.96)

Rolli,t 3.309∗∗∗

(2.90)

Hasbroucki,t 3.672∗∗

(2.48)

EffT icki,t 8.225∗∗

(2.30)

FHTi,t 5.871∗∗

(2.38)

HighLowi,t 2.934∗∗∗

(6.67)

CHLi,t 4.279∗∗

(2.07)

Amihudi,t 0.017

(1.44)

PSi,t −0.736

(−0.36)

R2 0.154 0.164 0.040 0.165 0.005 0.062 0.018 0.002

Obs 4582 4543 4582 4581 4582 4582 4582 4582

50


Table 6: Regressions of CP Spreads on Liquidity- and Credit-Related Vari-ables

This table reports results from nine specifications of regressions of commercial paper (CP)spreads on liquidity- and credit-related variables. Liquidity variables used include the CPoffer amount (OfferAmt i), trading volume (V olumei,t), time to maturity (Mati,t), the initialmaturity (InitMati), the average trading cost (TCi,t), and price impact proxy Amihudi,t.Credit-related variables used include distance-to-default (DDi,t), credit ratings (Ratingi,t),the slope of yield curves (Slopet), the equity market index (CSI300t), the option-impliedvolatility (CIV IXt), and the slope of its “smirk” (Jumpt). Additional variables used includethe year-end dummy (Y earEndt), the SOE dummy equal to one if the issuer is state-owned(SOEi), and the difference between the interest rates on interbank loans and short-termgovernment debt (TEDt).


M1 M2 M3 M4 M5 M6 M7 M8 M9

Intercept 0.005∗ 0.002 −0.003 0.008∗∗ 0.013∗∗∗ −0.000 0.016∗∗∗ 0.001 0.004

(1.66) (0.37) (−0.49) (2.50) (2.77) (−0.11) (2.60) (0.30) (0.45)

OfferAmti −0.156∗∗∗ −0.030

(−6.01) (−0.77)

V olumei,t −0.004 0.018∗∗

(−0.95) (2.56)

Mati,t −0.010 −0.024∗∗∗

(−1.43) (−2.58)

InitMati 0.024∗∗∗ −0.002

(3.11) (−0.38)

TCi,t 2.273∗∗∗ 3.172∗∗∗ 3.284∗∗∗ 3.198∗∗∗ 3.347∗∗∗ 3.359∗∗∗

(2.81) (2.98) (3.03) (2.90) (3.01) (3.06)

Amihudi,t 0.005∗∗∗ 0.006∗∗∗ 0.005∗∗∗ 0.005∗∗∗ 0.005∗∗∗

(3.06) (2.71) (3.25) (2.92) (2.79)

DDi,t −0.002∗∗∗ −0.001∗∗∗ −0.002∗∗∗ −0.001∗∗ −0.002∗∗∗

(−2.98) (−2.62) (−2.83) (−2.41) (−2.58)

Ratingi,t 0.007∗∗∗ 0.003∗∗ 0.007∗∗∗ 0.003∗ 0.004∗∗

(6.35) (1.99) (5.25) (1.65) (2.39)

Jumpt 0.068∗∗∗ 0.039∗∗∗ 0.049∗∗∗

(3.08) (4.06) (2.79)

Slopet 0.028

(0.10)

CSI300t −0.035∗

(−1.78)

Y earEndt 0.008

(0.76)

SOEi −0.007

(−1.14)

CIV IXt −0.031∗∗

(−2.05)

TEDt 0.127

(0.40)

R2 0.007 0.214 0.261 0.270 0.034 0.261 0.041 0.272 0.278

Obs 5755 4543 4543 4543 4543 4543 3853 3853 3853

51


Table 7: Explanatory Power of Credit- and Liquidity-Related Variables forSpreads on 1–3 Year MTNs and EBs

This table reports results from nine specifications of regressions of 1–3 year MTNs and enterprisebonds (EBs) spreads on liquidity- and credit-related variables. Liquidity variables used includethe average trading cost (TCi,t), and price impact proxy Amihudi,t. Credit-related variables usedinclude distance-to-default (DDi,t), credit ratings (Ratingi,t), the slope of yield curves (Slopet),the equity market index (CSI300t), the option-implied volatility (CIV IXt), and the slope of its“smirk” (Jumpt). Additional variables used include the year-end dummy (Y earEndt), the SOEdummy equal to one if the issuer is state-owned (SOEi), and the difference between the interestrates on interbank loans and short-term government debt (TEDt).

Dependent variable: Spreads on short-term MTNs and EBs

M1 M2 M3 M4 M5 M6 M7

Intercept 0.015∗∗∗ 0.017∗∗∗ 0.015∗∗∗ 0.013∗∗∗ 0.017∗∗∗ 0.015∗∗∗ 0.016∗∗∗

(7.14) (11.98) (6.84) (7.09) (6.75) (7.81) (3.07)

TCi,t 2.207∗∗∗ 2.323∗∗∗ 1.830∗∗∗ 1.703∗∗∗ 1.704∗∗∗

(3.67) (3.64) (3.49) (3.05) (3.03)

Amihudi,t 0.017∗∗∗ 0.007 0.007 0.008

(2.72) (1.21) (1.26) (1.36)

DDi,t −0.003∗∗∗ −0.002∗∗∗ −0.003∗∗∗ −0.003∗∗∗ −0.003∗∗∗

(−5.47) (−6.21) (−5.82) (−6.75) (−6.12)

Ratingi,t 0.008∗∗∗ 0.006∗∗∗ 0.008∗∗∗ 0.006∗∗∗ 0.005∗∗∗

(8.07) (7.03) (7.47) (6.51) (4.46)

Jumpt 0.024∗∗∗ 0.022∗∗∗ 0.020∗∗∗

(3.94) (4.02) (3.65)

Slopet 0.224∗

(1.90)

CSI300t −0.006

(−0.81)

Y earEndt −0.002

(−1.35)

SOEi −0.001

(−0.36)

CIV IXt 0.005

(0.98)

TEDt −0.280

(−1.04)

R2 0.240 0.248 0.093 0.278 0.098 0.304 0.309

Obs 2123 2123 2123 2123 1883 1883 1883

52


Table 8: Explanatory Power of Credit- and Liquidity-Related Variables forSpreads on 3–6 Year MTNs and EBs

This table reports results from nine specifications of regressions of 3–6 years MTNs and enterprisebonds (EBs) spreads on liquidity- and credit-related variables. Liquidity variables used includethe average trading cost (TCi,t), and price impact proxy Amihudi,t Credit-related variables usedinclude distance-to-default (DDi,t), credit ratings (Ratingi,t), the slope of yield curves (Slopet),the equity market index (CSI300t), the option-implied volatility (CIV IXt), and the slope of its“smirk” (Jumpt). Additional variables used include the year-end dummy (Y earEndt), the SOEdummy equal to one if the issuer is state-owned (SOEi), and the difference between the interestrates on interbank loans and short-term government debt (TEDt).

Dependent variable: Spreads on 3–6 year MTNs and EBs

M1 M2 M3 M4 M5 M6 M7

Intercept 0.018∗∗∗ 0.019∗∗∗ 0.016∗∗∗ 0.014∗∗∗ 0.017∗∗∗ 0.016∗∗∗ 0.018∗∗∗

(5.47) (5.46) (15.39) (4.39) (13.79) (4.54) (3.87)

TCi,t 1.848∗∗∗ 1.893∗∗∗ 1.152∗∗ 1.255∗∗ 1.232∗∗

(2.85) (2.94) (2.15) (2.13) (1.98)

Amihudi,t −0.000 −0.004 −0.004 −0.004

(−0.10) (−1.44) (−1.39) (−1.57)

DDi,t −0.001∗∗∗ −0.001∗∗∗ −0.001∗∗∗ −0.001∗∗∗ −0.000∗

(−5.61) (−4.62) (−4.66) (−3.74) (−1.88)

Ratingi,t 0.006∗∗∗ 0.005∗∗∗ 0.006∗∗∗ 0.005∗∗∗ 0.005∗∗∗

(7.97) (7.01) (7.38) (6.72) (5.37)

Jumpt 0.012∗ 0.014∗ 0.007

(1.71) (1.91) (1.22)

Slopet 0.051

(0.47)

CSI300t 0.004

(0.55)

Y earEndt −0.002

(−1.18)

SOEi −0.004

(−1.60)

CIV IXt 0.022∗∗∗

(3.84)

TEDt −0.133

(−1.06)

R2 0.239 0.239 0.390 0.472 0.441 0.493 0.531

Obs 1147 1147 1147 1147 975 975 975

53


Table 9: Distributions of Observed and Predicted Credit Spreads

This table reports summary statistics of observed and predicted yield spreads for a sample ofcommercial papers during May 2014–December 2018. The predicted spreads are generatedfrom the Black-Cox (1976) model, the double-exponential jump-diffusion (DEJD) model,the He-Xiong (2012) model (HX), and the He-Xiong model with double-exponential jumps(HX-DEJ). N denotes the number of observations in each rating category. All entries areexpressed in percentage points.

Mean 10% 25% 50% 75% 90% N

all Observed Spread 1.53 0.45 0.80 1.34 1.96 2.88 5755

Black-Cox Spread 0.32 0.00 0.00 0.00 0.03 0.96

DEJD Spread 1.07 0.06 0.20 0.48 1.08 2.62

HX Spread 1.07 0.07 0.15 0.34 0.88 2.79

HX-DEJ Spread 1.58 0.27 0.46 0.84 1.61 3.29

AAA Observed Spread 0.99 0.32 0.53 0.92 1.34 1.71 2554

Black-Cox Spread 0.22 0.00 0.00 0.00 0.02 0.70

DEJD Spread 0.71 0.05 0.19 0.39 0.71 1.55

HX Spread 0.72 0.06 0.11 0.22 0.55 1.87

HX-DEJ Spread 1.00 0.21 0.36 0.62 1.10 2.05

AA+ Observed Spread 1.55 0.62 1.04 1.45 1.90 2.51 1403

Black-Cox Spread 0.31 0.00 0.00 0.00 0.02 0.90

DEJD Spread 1.06 0.06 0.20 0.52 1.12 2.71

HX Spread 1.11 0.11 0.19 0.38 0.96 3.04

HX-DEJ Spread 1.56 0.31 0.51 0.93 1.66 3.90

AA Observed Spread 2.11 0.94 1.35 1.94 2.69 3.50 1443

Black-Cox Spread 0.48 0.00 0.00 0.00 0.13 1.68

DEJD Spread 1.44 0.05 0.23 0.72 1.65 3.71

HX Spread 1.59 0.17 0.33 0.65 1.49 4.70

HX-DEJ Spread 2.62 0.40 0.76 1.39 2.52 4.97

AA- or below Observed Spread 2.76 1.34 1.92 2.68 3.63 4.18 355

Black-Cox Spread 0.39 0.00 0.00 0.00 0.03 0.97

DEJD Spread 1.98 0.09 0.25 0.71 1.84 4.57

HX Spread 1.90 0.22 0.36 0.71 1.22 3.39

HX-DEJ Spread 2.65 0.47 0.76 1.29 2.36 5.03

54


Table 10: Pricing Errors of Structural Models

This table reports means of pricing errors and percentage errors of structural modelsfor a sample of commercial papers during May 2014–December 2018. Pricing errors arereported as the difference (in percentages) between predicted and observed yield spreads,and percentage pricing errors the difference between predicted and observed yield spreadsdivided by the observed spread. The predicted spreads are generated from the Black-Cox (1976) model, the double-exponential jump-diffusion (DEJD) model, the He-Xiong(2012) model (HX), and the He-Xiong model with double-exponential jumps (HX-DEJ).p-values are computed from the t-test (in parentheses) and Wilcoxon signed-rank test(in braces), respectively.

all AAA AA+ AA AA- or below

Panel A: Mean pricing error (%)

Black-Cox −1.09 −0.72 −1.17 −1.30 −2.11

[0.000] [0.000] [0.000] [0.000] [0.000]

{0.000} {0.000} {0.000} {0.000} {0.000}DEJD −0.70 −0.41 −0.75 −0.92 −1.42

[0.000] [0.084] [0.139] [0.000] [0.000]

{0.000} {0.000} {0.000} {0.000} {0.000}HX −0.52 −0.41 −0.52 −0.58 −1.24

[0.000] [0.000] [0.000] [0.000] [0.000]

{0.000} {0.000} {0.000} {0.000} {0.000}HX-DEJ −0.30 −0.17 −0.38 −0.35 −0.84

[0.161] [0.531] [0.594] [0.000] [0.000]

{0.000} {0.000} {0.000} {0.000} {0.000}

Panel B: Mean percentage error (%)

Black-Cox −66.87 −72.31 −75.04 −56.00 −48.46

[0.000] [0.000] [0.000] [0.000] [0.001]

{0.000} {0.000} {0.000} {0.000} {0.000}DEJD −20.63 −17.46 −31.12 −8.55 −46.15

[0.158] [0.466] [0.317] [0.756] [0.000]

{0.000} {0.000} {0.000} {0.000} {0.000}HX −26.08 −36.54 −21.78 −11.78 −19.74

[0.000] [0.000] [0.000] [0.026] [0.214]

{0.000} {0.000} {0.000} {0.000} {0.000}HX-DEJ 10.31 19.88 10.84 −2.60 −18.85

[0.556] [0.507] [0.801] [0.454] [0.004]

{0.023} {0.000} {0.015} {0.000} {0.000}

55


Figure 1: Term Structure of Average Commercial Paper Yield Spreads

1-60 61-120 121-180 181-240 241-300 301-365

Maturity(days)

0.5

1

1.5

2

2.5

3

3.5

Yie

ld S

pre

ad (

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AAAAA+AAAA- or below

This figure plots the par-value-weighted average yield spread of commercial papers againstmaturity over the period from May 2014 to December 2018. Yield spreads are calculatedas the annualized continuously compounded money market yield less the zero yield ofcomparable maturity as implied from general collateral repurchase agreements and interestrate swaps.

56


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57


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58


Table A1: Regression of CP Yield Spreads in the Primary Market

This table reports results from seven specifications of regressions aiming to explaincommercial paper (CP) spreads at issuance. Explanatory variables used include therisk-free rate (rft), firm i’s leverage ratio (Levi,t), equity volatility (σEi,t), distance-to-default (DDi,t), credit ratings (Ratingi,t), the slope of yield curves (Slopet), theequity market index (CSI300t), the option-implied volatility (CIV IXt), the slope ofits “smirk” (Jumpt), the CP offering amount (OfferAmt i), and the initial maturity(InitMati).


M1 M2 M3 M4 M5 M6 M7

Intercept −0.007∗∗ 0.006∗∗ 0.004∗∗ −0.003 −0.003 −0.005∗∗ −0.006∗∗

(−2.19) (2.06) (2.33) (−0.92) (−1.55) (−2.18) (−2.37)

rft 0.232∗∗∗ 0.229∗∗∗ 0.163∗∗ 0.112∗∗ 0.144∗∗∗ 0.136∗∗

(2.92) (3.18) (2.13) (1.98) (2.69) (2.38)

Levi,t 0.006 −0.001 0.001 0.002 0.002 0.002

(0.40) (−0.74) (0.52) (1.31) (1.25) (1.44)

σEi,t 0.010∗∗ 0.003 0.001 0.001 −0.002 −0.001

(2.13) (1.55) (0.54) (−0.62) (−0.49) (−0.37)

DDi,t −0.001∗∗∗ −0.001∗∗∗ −0.001∗∗∗ −0.001∗∗∗ −0.002∗∗∗ −0.001∗∗∗

(−5.51) (−5.65) (−6.26) (−5.16) (−5.29) (−4.87)

Ratingi,t 0.005∗∗∗ 0.002∗∗∗ 0.002∗∗∗ 0.002∗∗∗

(9.31) (9.16) (8.55) (7.29)

Slopet 0.117∗ 0.167∗∗∗ 0.189∗∗∗

(1.67) (2.60) (2.84)

CSI300t 0.002 −0.008∗∗∗ −0.005∗∗

(0.43) (−2.75) (−2.19)

CIV IXt 0.009∗∗∗ 0.009∗∗∗

(2.86) (2.65)

Jumpt −0.008∗ −0.009∗∗

(−1.85) (−2.00)

OfferAmti −0.042∗∗∗

(−3.27)

InitMati 0.005∗∗∗

(4.78)

R2 0.021 0.034 0.035 0.070 0.074 0.081 0.085

Obs 2023 2023 2023 2023 2023 1635 1635

59


Table A2: Regression of CP Yield Spreads in the US Market

This table reports results from seven specifications of regressions of commercial pa-per (CP) spreads on explanatory variables in the US market. Explanatory variablesused include the risk-free rate (rft), firm i’s leverage ratio (Levi,t), equity volatil-ity (σEi,t), distance-to-default (DDi,t), credit ratings (Ratingi,t), the slope of yieldcurves (Slopet), the return on S&P 500 index (S&Pt), the option-implied volatility(V IXt), the slope of its “smirk” (Jumpt), the logarithm of total transaction volumes(V olumei,t), and the time to maturity of the paper (Maturityi,t).


M1 M2 M3 M4 M5 M6 M7

Intercept −0.010 −0.012∗∗ −0.007∗ −0.012∗ −0.013 −0.007 0.006

(−1.37) (−2.39) (−1.72) (−1.76) (−1.55) (−1.38) (1.25)

rft −0.727∗∗ −0.965∗ −1.012∗ −0.184 0.749 0.699

(−2.31) (−1.77) (−1.74) (−0.44) (1.40) (0.95)

Levi,t 0.055∗∗ 0.054∗ 0.046 0.049 0.049 0.049

(2.51) (1.78) (1.57) (1.56) (1.57) (1.59)

σEi,t 0.050∗∗ 0.067 0.076 0.062 0.064 0.056

(2.01) (1.63) (1.55) (1.39) (1.43) (1.44)

DDi,t −0.013∗∗∗ −0.012∗∗∗ −0.014∗∗∗ −0.014∗∗ −0.014∗∗ −0.012∗∗

(−2.97) (−2.69) (−2.61) (−2.51) (−2.50) (−2.46)

Ratingi,t 0.016∗∗∗ 0.011∗∗∗ 0.015∗∗∗ 0.010∗∗

(2.70) (2.60) (2.59) (2.44)

Slopet 0.758 0.857 0.590

(1.48) (1.58) (1.46)

S&Pt −0.020 0.043 0.040

(−0.93) (1.19) (1.17)

V IXt 0.223∗∗ 0.203∗∗

(2.49) (2.56)

Jumpt 0.096∗∗ 0.073∗∗

(2.46) (2.53)

V olumei,t −0.036∗∗∗

(−2.70)

Maturityi,t −0.017

(−1.45)

R2 0.011 0.036 0.042 0.058 0.059 0.075 0.139

Obs 7419 7419 7419 7419 7419 7419 7419

60


Internet Appendix to

“Determinants of Short-Term Corporate Yield Spreads:

Evidence from the Commercial Paper Market”


IA.A Measuring Liquidity in the Secondary CP Mar-

ket

To examine the impact of market illiquidity on CP yield spreads, we consider in Section 3.3

eight liquidity measures—six related to effective bid-ask spreads and two on price impact—

and analyze their empirical properties. Since we are not granted transaction-level data,

we focus on the so-called low-frequency proxies (Schestag, Schuster, and Uhrig-Homburg

2016), whose implementation requires daily information. In this section we review these

eight liquidity measures and their implementation details.

IA.A.1 Bid-Ask Spread Measures

• Roll measure

Roll (1984) shows that the strength of serial covariation of price movements can be

employed as a proxy for effective bid-ask spreads. Following Bao et al. (2011), who

propose a related measure on the corporate bond market, we focus on the price return

instead of the total return. That is, we compute the monthly Roll measure as

Roll =√

max (−4Cov(rt+1, rt), 0),

where rt = Pt/Pt−1 − 1 denotes the total return on day t.

• Hasbrouck measure

Hasbrouck (2009) develops a Gibbs sampler estimation of the extended Roll model,

rt = c ·∆Dt + βrMt + εt, (IA.A1)

where Dt is a sell side indicator, c is half of the effective bid-ask spread, and rMt denotes

the market return on day t. By making inference of the latent Dt with Gibbs sampling,

this estimator overcomes the negative spread estimates. We estimate Eq. (IA.A1) on

1


a monthly basis and define Hasbrouck = 2c.

• Effective tick

Holden (2009), jointly with Goyenko et al. (2009), develops a proxy for the effective

bid-ask spread based on observable price clustering. Larger spreads are associated with

larger effective tick sizes. Suppose that we consider K possible (mutually exclusive)

effective spreads. Effective tick is then defined as a probability-weighted average of all

possible spreads sk,

EffectiveT ick =

∑Kk=1 γksk

P,

where γk denotes the imputed probability of effective spread sk, and P is the average

trading price in the month. Based on the price clustering patterns in the Chinese CP

market, we refine the price grid and consider nine possible spreads: 1, 0.5, 0.25, 0.1,

0.05, 0.01, 0.005, 0.001, and 0.0001.

• FHT measure

Lesmond, Ogden, and Trzcinka (1999) develop an effective spread estimator (LOT)

based on the idea that an observed return is different from zero only if the true return

exceeds the trading costs. Fong, Holden, and Trzcinka (2017; FHT hereafter) propose

a related measure that is easier to implement and shown to deliver better performance

than the original LOT measure as well as a modified version considered in Goyenko,

Holden, and Trzcinka (2009). Therefore, we focus on FHT estimator of the effective

bid-ask spread,

FHT = 2σΦ−1(

1 + ZTD

2

),

where ZTD denotes the proportion of days when the bond does not trade in the month,

and σ2 is the variance of the “true daily return” on the bond. We estimate σ using the

ChinaBond valuation prices for each security.

2


• High-low spread estimator

Corwin and Schultz (2012) develop a spread estimator based on the assumption that

high (low) prices are almost always buyer (seller) initiated. Therefore, the daily price

range reflects both the efficient price volatility and its bid-ask spread. It follows that

two-day price ranges should twice reflect the variance of one-day price ranges, but they

should have the same bid-ask spread. This reasoning gives an estimate of the bid-ask

spread as a function of two parameters that can be determined by solving a system of

two nonlinear equations.

• Spread estimator based on daily close, high, and low prices

Building on the Roll (1984) model, Abdi and Ranaldo (2017) derive a new way to

estimate bid-ask spreads using daily close, high, and low prices. They focus on the

mid-range—the mean of the daily high and low log-prices—and use it to proxy for

the efficient price. As such, the effective bid-ask spread can be estimated with the

covariance of close-to-mid-range returns around the same close price,

CHL =

√√√√max

(4

N

N∑t=1

(pt − ηt)(pt − ηt+1), 0

),

where pt represents the close log-price on day t, and ηt is the average of daily high and

low log-prices.

IA.A.2 Price Impact Measures

• Amihud measure

The price impact proxy developed by Amihud (2002) is defined as

Amihud =1

N

N∑t=1

|rt|Qt

,

3


where rt and Qt are the return and traded dollar volume on day t, and N denotes the

number of positive volume days in the month.

• Pastor-Stambaugh price impact measure

The Pastor and Stambaugh (2003) measure is obtained by running the following re-

gression:

ret+1 = θ + φrt + γ sign(ret )Qt + εt, (IA.A2)

where ret is the CP’s excess return above the ChinaBond commercial paper total return

index on day t and Qt is the corresponding dollar volume. We estimate Eq. (IA.A2)

on a monthly basis and define the price impact measure as PS = −γ.

4


References

Abdi, F., and A. Ranaldo. 2017. A simple estimation of bid-ask spreads from daily close,high, and low prices. Review of Financial Studies 30(12):4437–4480.

Amihud, Y. 2002. Illiquidity and stock returns: cross-section and time-series effects. Journalof Financial Markets 5(1):31–56.

Bao, J., J. Pan, and J. Wang. 2011. The illiquidity of corporate bonds. Journal of Fi-nance 66(3):911–946.

Corwin, S. A., and P. Schultz. 2012. A simple way to estimate bid-ask spreads from dailyhigh and low prices. Journal of Finance 67(2):719–760.

Fong, K. Y., C. W. Holden, and C. A. Trzcinka. 2017. What are the best liquidity proxiesfor global research? Review of Finance 21(4):1355–1401.

Goyenko, R. Y., C. W. Holden, and C. A. Trzcinka. 2009. Do liquidity measures measureliquidity? Journal of Financial Economics 92(2):153–181.

Hasbrouck, J. 2009. Trading costs and returns for US equities: Estimating effective costsfrom daily data. Journal of Finance 64(3):1445–1477.

Holden, C. W. 2009. New low-frequency spread measures. Journal of Financial Market-s 12(4):778–813.

Lesmond, D. A., J. P. Ogden, and C. A. Trzcinka. 1999. A new estimate of transaction costs.Review of Financial Studies 12(5):1113–1141.

Pastor, L., and R. F. Stambaugh. 2003. Liquidity risk and expected stock returns. Journalof Political Economy 111(3):642–685.

Roll, R. 1984. A simple implicit measure of the effective bid-ask spread in an efficient market.Journal of Finance 39(4):1127–1139.

Schestag, R., P. Schuster, and M. Uhrig-Homburg. 2016. Measuring liquidity in bond mar-kets. Review of Financial Studies 29(5):1170–1219.

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determinants of short-term corporate yield spreads

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