Investor Composition and Liquidity Component: Li & Yu (2026)

What this is. The paper’s core results, the directed-search model with two-sided heterogeneity, and the key equations that connect investor composition to the liquidity component of corporate bond credit spreads: enough to understand what it found and how, without reading all 52 pages. To replicate or extend it, read the full source at the original.

TL;DR

Building on Bao, Pan, and Wang (2011), who find that illiquidity explains a significant part of common credit spread variation, the paper documents that from 2005 to 2019 the loading of U.S. corporate bond credit spreads on bid-ask spreads more than doubled, driven by the rapid entry of mutual funds and ETFs into the bond market. The authors document this trend and use a 10-year time-to-maturity discontinuity in fund mandates as an instrument to show causally that bonds held by more short-term investors have higher trading activity and a stronger credit-spread sensitivity to secondary-market frictions. A directed-search model with heterogeneous investors (differing in liquidity shock frequency) and heterogeneous bonds (differing in maturity and default probability) shows that declining risk-free rates induce more short-term investors to reach for yield in the illiquid bond market, amplifying the effect of secondary-market frictions on prices through two channels: a direct channel (more frequent trading means each unit of transaction cost is incurred more often) and an indirect channel (bid-ask spreads are correlated with seller-buyer ratios, so trade delays are priced into credit spreads). The calibrated model matches the observed 2.5 to 2.8x growth in the liquidity component and shows the indirect channel accounts for more than half of the total sensitivity by the end of the sample.

Core results

Magnitudes and significance are as reported; \*, \*\*, \*\*\* = 5%, 1%, 0.1%. Locators point into the source PDF.

#	Result	Locator	Magnitude
R1	The loading of credit spreads on bid-ask spreads (beta) has increased significantly for both investment-grade and high-yield bonds since 2005	Figure 1, p. 880; Figure A3, p. 910	IG: loading rose from ~10-20 bp/100 bp BA to ~60 bp/100 bp BA by 2019; HY: from ~60 bp/100 bp BA to ~250 bp/100 bp BA; for the full sample, beta rose from 0.54 to 1.2
R2	The median liquidity component (loading x BA / CS) grew from roughly 10% to 30% of credit spreads, a ~2.8x increase	Figure 2, p. 882; §I.B, p. 881-882	Median liq. component grew ~2.8x from pre-GFC to 2019 (11.3% in first three years of sample; 31.4% in last three years); model predicts 6.77% in 2005 and 16.62% in 2019, a 2.5x model increase
R3	Bonds held by more short-term investors have significantly higher investor composition measures and significantly more trades (IV first stage and second stage)	Table I, cols. (1)-(6), p. 886	First stage: 1_{ttm>10} coefficient on Inv_Comp = -0.00581*** (t=-5.86, full) and -0.00692*** (t=-7.24, subsample). Second stage: 1 s.d. increase in Inv_Comp raises log No. of Trades by 75.02*** (t=8.02) and 61.62*** (t=9.69)
R4	Higher investor composition (more short-term investors) significantly increases the loading of credit spreads on bid-ask spreads (Inv_Comp x Bid_Ask interaction)	Table II, cols. (2) and (4), p. 887	Inv_Comp x Bid_Ask: 48.65*** (t=6.61, full sample) and 55.86*** (t=3.93, subsample); a 1 s.d. increase in investor composition (0.03) is associated with ~1.44 increase in the loading coefficient
R5	The model generates positive assortative matching: short-term investors endogenously hold short-maturity and high-default-probability bonds (Proposition 1)	§III, p. 895; Figure 3, p. 884	Theoretical result (Prop. 1): theta’(delta+d) > 0 in equilibrium; empirically confirmed by monotone relationships in Figure 3 across 20 investor-composition bins
R6	As the risk-free rate declines, more short-term investors enter the illiquid bond market, reducing the seller-buyer ratio in all submarkets (Proposition 3)	§III, p. 898; Figure 4, p. 898	Proposition 3 result; numerically verified: cutoff theta increases from 0.688 in 2005 to 0.766 in 2019 in calibration (Table IV, p. 903)
R7	The calibrated model matches the key empirical moments; the indirect channel (bid-ask spreads correlated with seller-buyer ratios) accounts for more than 50% of the total sensitivity by 2019	Table III and Table V, pp. 903-905	beta_exo (direct component): 0.27 in 2005, 0.35 in 2019; beta_endo (indirect component): 0.65 in 2005, 1.7 in 2019; total empirical beta: 0.54 in 2005, 1.2 in 2019
R8	The change in investor composition amplifies the effect of a dealer regulation change for short-term bonds but alleviates it for long-term bonds, highlighting the dual liquidity-provision role	§IV, p. 907; Appendix A	Qualitative result from calibration: for short-term bonds, more short-term investors amplify dealer regulation frictions; for long-term bonds, investor inflows provide liquidity that dampens the regulation effect

Overall (paper’s conclusion). Where Wu (2020) attributes similar trends to dealer regulation changes, this paper shows that investor composition is an independent quantitative explanation even for investment-grade bonds where dealer regulation may matter less. The massive growth of mutual funds and ETFs in the corporate bond market is quantitatively important in explaining the rising sensitivity of credit spreads to secondary-market frictions. The model shows this operates through two amplification channels (direct trading frequency, indirect trade-delay pricing) and that investor composition can interact with dealer regulatory changes in complex ways depending on bond maturity.

Theory / model

The paper builds a directed-search model with two-sided heterogeneity: investors differ in their liquidity shock frequency $\theta$ and bonds differ in their maturity intensity $\delta$ and default intensity $d$. Time is continuous. All agents are infinitely lived and risk-neutral.

Investors. Each period measure $m_I$ of new investors enter with discount rate $\rho$. Investor $j$ faces liquidity shocks arriving at Poisson rate $\theta_j \in [\bar{\theta}, +\infty)$, a permanent feature with CDF $F(\cdot)$ and PDF $f(\cdot)$. Upon a liquidity shock an investor becomes impatient and values flow coupon at a discount $\Delta$ units less. The effective flow to an impatient investor is thus $r_i - \Delta$ (p. 889, §II.A).

Bonds. There is a continuum of bonds indexed by $i \in I$. Bond $i$ has face value 1, coupon $r_i$ (determined in equilibrium), matures at rate $\delta_i$, and defaults at Poisson intensity $d_i$ with recovery $s_i$. Bonds are ordered so that $\delta_i + d_i \leq \delta_j + d_j$ for $i \leq j$ (p. 889, §II.A.2).

Secondary market and bid-ask spread. In each submarket (indexed by bond type and price), sellers search for buyers via a Cobb-Douglas matching function (p. 890, II.A.2):

$$m(\alpha_{s,i},\, \alpha_{b,j}) = \eta \cdot \alpha_{s,i}^{\gamma} \cdot \alpha_{b,j}^{1-\gamma}, \quad \eta > 0,\; \gamma \in (0,1)$$

Following the reduced-form bid-ask spread specification of Lester, Rocheteau, and Weill (2015), which micro-founds the bid-ask spread as a fraction of the trade surplus in directed search, the bid-ask spread decomposes into an endogenous component $\xi$ (proportional to the trade surplus) and an exogenous component $\epsilon_{\xi}$ capturing dealers’ balance sheet conditions:

$$P_{b,i,t} - P_{s,i,t} = \xi_i + \epsilon_{\xi,i} \tag{9}$$ $$\text{Assumption 1:} \quad \xi_i = \kappa \bigl(V_{h,i}(\theta) - V_{b,i}(\theta) - V_{s,i}\bigr), \quad \kappa \in (0,1) \tag{14}$$

Value functions. The HJB equation for a patient bondholder of type $\theta$ holding bond $i$ is (eq. 10, p. 891):

$$\rho \, V_{h,i}(\theta) = r_i + \delta_i \bigl(1 - V_{h,i}(\theta)\bigr) + d_i \bigl(s_i - V_{h,i}(\theta)\bigr) + \theta \bigl(V_{s,i} - V_{h,i}(\theta)\bigr) \tag{10}$$

The seller’s HJB is (eq. 11, p. 892):

$$\rho \, V_{s,i} = r_i - \Delta + \delta_i \bigl(1 - V_{s,i}\bigr) + d_i \bigl(s_i - V_{s,i}\bigr) + \mu_s\!\bigl(\lambda(i, P_s)\bigr) \bigl(P_s - V_{s,i}\bigr) \tag{11}$$

The buyer’s HJB for type $\theta$ searching in bond $i$‘s submarket is (eq. 12, p. 892):

$$\rho \, V_{b,i}(\theta) = \mu_b\!\bigl(\lambda(i, P_s)\bigr) \bigl(V_{h,i}(\theta) - V_{b,i}(\theta) - P_{b,i}\bigr) \tag{12}$$

where $\mu_b(\lambda) = \eta \lambda^{\gamma}$ and $\mu_s(\lambda) = \eta \lambda^{\gamma-1}$ are the buyer and seller meeting intensities given Cobb-Douglas matching.

Equilibrium conditions. In equilibrium buyers are indifferent between primary and secondary markets:

$$V_{h,i}(\theta) - 1 = V_{b,i}(\theta) \tag{15}$$

The investor participation decision features a cutoff strategy: investors with $\theta < \bar{\theta}(r_f)$ hold risk-free assets; those with $\theta \geq \bar{\theta}$ participate in the bond market. As $r_f$ decreases, the cutoff falls and more short-term investors enter (Proposition 3, p. 898).

Equilibrium characterization. Unlike Amihud and Mendelson (1986), where investors sort on exogenous bid-ask spreads, here bid-ask spreads are endogenous and investors sort on maturity and default probability. Under Assumption 1 and $\epsilon_{\xi} = 0$, Proposition 1 (p. 895) establishes positive assortative matching: $\theta'(\delta+d) > 0$. Proposition 2 (p. 896) characterizes the full equilibrium as a system of ODEs in $\bar{\delta} = \delta + d$ (eq. 24, p. 896):

$$\begin{cases} \lambda'(\bar{\delta}) = \dfrac{\lambda \left[\frac{1-\gamma}{\alpha_b}\,\lambda - \frac{\gamma}{\alpha_b}\,\theta'\!\left(\frac{1}{\alpha_b} + (1-\gamma)\!\left(\frac{1}{\rho} + \frac{1}{\alpha_b}\right)\right)\right]}{\gamma(1-\gamma)(\rho + \bar{\delta} + \theta)} \\[10pt] \theta'(\bar{\delta}) = \dfrac{\bar{\delta} + \rho\,\alpha_s / (\rho + \mu_s + \bar{\delta} + d)}{m_I\, f(\theta)} \end{cases} \tag{24}$$

with boundary conditions $\theta(\bar{\delta} + \bar{d}) = \bar{\theta}$ and $\theta(\bar{\delta}_{\text{end}} + \bar{d}) = \bar{\theta}_{\text{end}}$.

Interest rate and credit spread sensitivity. In equilibrium the interest rate for bond $j$ is (Lemma 2, eq. 26, p. 899):

$$r = \frac{\rho}{\rho + \delta + \theta} + \frac{d(1-s)}{\rho + \delta + \theta} + \frac{\theta\,\Delta}{\rho + \delta + \theta} + [\text{exo and endo bid-ask spread terms}] \tag{26}$$

The sensitivity of the interest rate to exogenous bid-ask spread changes is (Corollary 2, eq. 27, p. 900):

$$\frac{dr}{d\epsilon_{\xi}} = \frac{\dfrac{\theta}{\rho+\delta+\theta}\cdot\dfrac{\gamma}{\lambda} - \dfrac{\rho+\delta}{\rho}\cdot(1-\gamma)}{\left(\dfrac{1}{\mu_s} + \dfrac{1-\kappa}{\rho+\delta+\theta}\right)\dfrac{\gamma}{\lambda} + \left(\dfrac{1-\kappa}{\rho} + \dfrac{1}{\mu_b}\right)(1-\gamma)} \tag{27}$$

When $r_f$ decreases (more short-term investors enter), $dr/d\epsilon_{\xi}$ increases for all bonds.

Method

The paper applies two complementary methods: reduced-form panel regressions with an instrumental variables (IV) design, and a calibrated structural model solved via ordinary differential equations (ODEs).

Reduced-form evidence. The baseline cross-sectional regression is (eq. 1, p. 880):

$$\text{CS}_{i,t} = \alpha_t + \beta_t \cdot \text{BA}_{i,t} + \gamma_t^T X_{i,t} + \epsilon_{i,t} \tag{1}$$

Run quarter by quarter; $X_{i,t}$ includes bond characteristics (bond age, time-to-maturity, coupon, offering amount, rating) and firm characteristics (leverage, size, profitability, equity volatility, total asset value) and industry fixed effects. Standard errors are clustered at the firm level.

The liquidity component is defined following Dick-Nielsen, Feldhutter, and Lando (2012) as (eq. 2, p. 881):

$$\text{liquidity\_component}_{i,t} = \frac{\beta_t \times \text{BA}_{i,t}}{\text{CS}_{i,t}} \tag{2}$$

Investor composition measure. Fund-level net transaction rate (eq. 3, p. 882):

$$\text{net\_transaction}_{j,t} = \frac{\left|\sum_i \text{holding}_{i,j,t} - \sum_i \text{holding}_{i,j,t-1}\right|}{\sum_i \text{holding}_{i,j,t-1}} \tag{3}$$

Smoothed over four quarters (eq. 4, p. 883):

$$\text{NT}_{j,t} = \frac{1}{4} \sum_{t'=1}^{4} \text{net\_transaction}_{j,t-t'} \tag{4}$$

Bond-level investor composition (eq. 5, p. 883):

$$\text{investor\_comp}_{i,t} = \frac{\sum_j \text{holding}_{i,j,t} \times \text{NT}_{j,t}}{\sum_j \text{holding}_{i,j,t}} \tag{5}$$

Instrumental variables design. Exploiting the 10-year time-to-maturity threshold in intermediate-term bond fund mandates documented by Bai, Li, and Manela (2022) as a sharp discontinuity, using the two-stage specification (eqs. 6-7, pp. 885-886):

First stage: $\text{Inv\_Comp}_{i,t} = \alpha + \beta_1 \cdot \mathbf{1}_{\text{ttm}>10} + \gamma^T X_{i,t} + \epsilon_{i,t}$

Second stage: $Y_{i,t} = \alpha + \beta_1 \cdot \widehat{\text{Inv\_Comp}}_{i,t} + \gamma^T X_{i,t} + \epsilon_{i,t}$

with optimal bandwidth around the 10-year cutoff (Calonico, Cattaneo, and Titiunik 2014). Also instruments the interaction term $\text{Inv\_Comp} \times \text{BA}$ with $\mathbf{1}_{\text{ttm}>10} \times \text{BA}$ for the credit-spread loading regression (eq. 8, p. 886):

$$\text{CS}_{i,t} = \alpha + \beta_1 \cdot \text{BA}_{i,t} + \beta_2 \cdot \widehat{\text{Inv\_Comp}}_{i,t} + \beta_3 \cdot \text{BA}_{i,t} \times \widehat{\text{Inv\_Comp}}_{i,t} + \gamma^T X_{i,t} + \epsilon_{i,t} \tag{8}$$

Standard errors are clustered by industry and time; estimation uses demeaned bid-ask spreads for interpretability.

Calibration. The structural model is calibrated to annual-level moments for bonds with 2 to 15 years to maturity ($\bar{\delta} \in [1/15,\, 0.5]$). Parameters are set to match six moments in 2005 and 2019: bond turnover rates, the loading coefficient on bid-ask spreads, average credit spreads, average bid-ask spreads, and the ratio of residualized standard deviations (Table III, p. 903). The model is then simulated for $N = 1{,}000$ bonds and the following regression run on simulated data to obtain the model-implied $\beta$:

$$\text{CS}_i = \beta_0 + \beta \cdot \text{BA}_i + \beta_M \cdot \delta_i + \epsilon_i \tag{32}$$

The mechanism decomposition separates the loading into an exogenous component (eq. 34, p. 904):

$$\text{CS}_i = \beta_0 + \beta_{\text{exo}} \cdot \epsilon_{\xi,i} + \beta_M \cdot \delta_i + \epsilon_i \tag{34}$$

and an endogenous component (eq. 35, p. 905):

$$\text{CS}_i = \beta_0 + \beta_{\text{endo}} \cdot \text{BA}_{\text{endo},i} + \beta_M \cdot \delta_i + \epsilon_i \tag{35}$$

where $\text{BA}_{\text{endo},i}$ is the endogenous part of bid-ask spreads with $\epsilon_{\xi}$ set to zero.

Empirical specifications

All regressions are quarterly, 2005Q2 to 2019Q2, on U.S. corporate debentures with fixed coupon, nonconvertible, nonputtable, and nonexchangeable. The primary sample excludes bonds that have more than 95% of days with no trading. Bonds with ratings below CCC- are excluded.

Aggregate trend (R1, R2). Regression (1) run quarter by quarter on all bonds using WRDS bid-ask spreads; standard errors clustered at the firm level (Figure 1, p. 880). The aggregate loading $\beta_t$ and the liquidity component median are the key time-series outcomes.

Cross-sectional analysis, investor composition effects (R3). Table I (p. 886) reports the first-stage and second-stage IV regressions using the 10-year maturity threshold as an instrument, with bandwidth 1.699 for the full sample and 2.282 for the subsample with maturity > 10 years at issuance. Controls include time-to-maturity, age, coupon, log amount outstanding, firm total assets, fraction of long-term debt, leverage ratio, profitability, equity price volatility, slope and level of Treasury yields, and rating x industry x date fixed effects.

Credit spreads and bid-ask spreads interaction (R4). Table II (p. 887) reports four specifications of regression (8): full sample OLS, full sample IV, subsample OLS, subsample IV. Investor composition is instrumented with $\mathbf{1}_{\text{ttm}>10}$; the interaction $\text{Inv\_Comp} \times \text{BA}$ is instrumented with $\mathbf{1}_{\text{ttm}>10} \times \text{BA}$. Standard errors are clustered by industry and time. The key finding is the significant positive coefficient on $\text{Inv\_Comp} \times \text{Bid\_Ask}$ (48.65*** OLS full sample; 55.86*** IV subsample).

Structural equilibrium and calibration (R5-R7). The model is simulated in 2005 and 2019 with calibrated parameters (Table IV, p. 903). The mechanism decomposition (Table V, p. 905) shows $\beta_{\text{exo}} = 0.27/0.35$ (2005/2019) vs empirical $\beta = 0.54/1.2$, confirming the indirect channel (via seller-buyer ratio correlation) must explain the remainder. The indirect loading $\beta_{\text{endo}} = 0.65/1.7$ matches the total pattern.

Datasets used

Dataset	Role in paper	Wiki page
TRACE (Enhanced, FINRA)	Corporate bond transaction prices and volumes for bid-ask spread calculation, number of trades, bond turnover; filtered following Dick-Nielsen (2014)	TRACE (licensed)
WRDS Bond Return database + Mergent FISD	Bond characteristics: maturity, coupon, rating, offering amount, issuance date; credit spreads calculated from reported yields minus matched Treasury yield	WRDS (licensed)
CRSP equity returns	Equity price volatility for bond issuers	WRDS / CRSP (licensed)
Compustat annual fundamentals	Firm characteristics: leverage, size, profitability, total asset value, fraction of long-term debt	WRDS / Compustat (licensed)
Lipper eMaxx (Thomson Reuters)	Quarterly investor holdings of corporate bonds at the CUSIP level for insurance companies, mutual funds, ETFs, and annuities; covers 40-50% of total bonds outstanding	[no page yet]
Flow of Funds (Federal Reserve)	Aggregate corporate and foreign bond holdings by investor type for benchmarking eMaxx coverage	[no page yet]
Gurkaynak, Sack & Wright (2007) Treasury yield curve	Used to calculate credit spreads by subtracting matched Treasury yields	[no page yet]

Sample: 2005Q2 to 2019Q2 (58 quarters, quarterly). Primary analysis covers U.S. corporate debentures with fixed coupon; 15,256 unique bonds, 3,217 unique firms (cross-sectional sample with eMaxx coverage > 20%).

When to read the full paper

Use the original if you are: investigating the corporate bond liquidity premium and its time-series variation; building or calibrating a model of OTC bond markets with heterogeneous investors; studying how the growth of mutual funds and ETFs affects bond market fragility; evaluating the interaction between investor-side and dealer-side regulatory changes; or replicating the regression discontinuity design around the 10-year maturity threshold. The locators above point to the exact tables and figures.

Attribution and rights

Source: peer-reviewed, The Journal of Finance 81(2), April 2026. This distillation was extracted by an LLM on 2026-06-01 and is not human-verified or independently reproduced. The article is paywalled; redistribution is extract-only. Access the original at https://doi.org/10.1111/jofi.70024.

Li, Jian, and Haiyue Yu. “Investor Composition and the Liquidity Component in the U.S. Corporate Bond Market.” The Journal of Finance 81, no. 2 (April 2026): 871-922. DOI: 10.1111/jofi.70024. (c) 2026 the American Finance Association.