## _wp15140

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---

### I. Introduction: scope and objectives
- Urgent need to improve understanding of credit risk of China’s corporate sector as corporate credit exposures grow quickly.
- Main questions:
  - Applicability of standard credit risk tools to Chinese firms given China’s unique financial system, significant role of the state, absence of a full credit cycle, and potential unreliability of financial indicators.
  - Relationship of firm fundamentals, ownership (SOE vs private), and macro-financial conditions to market-based default probabilities.
  - Reliability of market indicators—equity markets or borrowing costs—for assessing stand-alone credit risk.
  - Ability to estimate default probabilities for firms that lack market data.
- Sample and approach:
  - Estimate stand-alone 1-year probability of default for a sample of about 4,500 non-financial firms.
  - Use variant of Merton (1974) structural credit model with unexpected jumps (Zhou, 1997), inclusion of non-listed firms (Jobst and Gray, 2013), and mapping to a database of actual defaults (Gray, 2009).
  - “Stand-alone” probability of default defined consistent with Standard & Poor’s (2010).

### II. Methodology overview — jump-diffusion contingent claims approach
- Structural model elements:
  - Firm market value of assets: V.
  - Default occurs if V falls to default barrier DB; operationally set DB = short-term liabilities + 1/2 long-term liabilities (Jobst and Gray, 2013).
  - Equity value E modeled as a call option on V; risky debt related via put option; V = D + E.
- Jump-diffusion specification (risk-neutral measure) with parameters:
  - θ = {μ, λ, σ, μπ, σπ}.
  - Process parameters: μ (expected rate of return), υ (expected jump), σ (instantaneous volatility conditional on no jump), dZ (Wiener), dY (Poisson intensity λ), jump size Π log-normally distributed.
  - Constraint: ensure λΔt ≤ 1 where t = 1/252 (daily frequency).
- Estimation procedure:
  - Maximize log-likelihood of empirical daily log changes in firm asset value using mixture density of Brownian and jump components.
  - Calibrate unobserved asset value V by solving equity-as-call option relationships (put-call parity) iteratively: initialize jump-diffusion parameters from equity returns; solve for V; update parameters; iterate until convergence of V, μ, σ, λ, μπ, σπ.
- Default probability calculation:
  - Follow Zhou (1997) to compute risk-neutral and stand-alone default probability; in calculation drift μ denoted by r and default barrier ξ set to 1.

### III. Rationale for jump-diffusion and empirical features
- Jump-diffusion accommodates sudden changes in firm value and default risk observed in equity markets including China.
- Empirical pattern since 2010: returns for smaller firms tended to be positively skewed (sudden price increases); jump risk can be in either direction.
- Jump-diffusion model argued to provide better default probability estimates than standard Merton model by allowing sudden upward and downward jumps.

### IV. Adjustments to convert risk-neutral to real-world probabilities
- Two adjustments (Gray, 2009) to approximate Moody’s KMV EDFTM:
  - Linear transformation of fitted asset volatility σv into σV* as in (14a); for Chinese firms authors use their own σv (derived using (9)) as input.
  - Replace risk-free rate r in (13) with drift μ* that captures time-varying price of risk: μ* = correlation between firm equity and the market × Sharpe ratio (14b).
- Parameter values used in (14):
  - γ0 = 0.05
  - γ1 = 1.37
  - ρA,M = 0.6
  - SR = 0.75
- Interpretative remarks:
  - Linear transformation approximates Moody’s North American default-history database; legal and institutional differences (e.g., China ranked 53rd in resolving insolvency vs. United States 4th and Canada 6th in the 2014 World Bank “Doing Business” survey) may limit direct comparability.
  - Public sector support (especially for SOEs) may suppress observed default frequencies; adjustment aims to estimate stand-alone default probabilities based on firm fundamentals.
  - Estimating market price of risk and Sharpe ratio ex-post is problematic in China (ex-post Sharpe ratios close to zero or negative during 2008–2013); authors use theoretically-consistent priors for μ* in (14b).

### V. Data — sample, balance sheet inputs, and asset valuation
- Panel: unbalanced, maximum of 4,483 non-financial firms between Q1-2006 and Q4-2014.
  - 2,441 listed firms with equity on a public exchange.
  - 2,042 unlisted firms that had issued bonds in the onshore bond market.
- Sample includes 1,020 local government financing vehicles (LGFVs) of which are listed firms; LGFVs identified by issuance of urban investment (Changtou) bonds.
- Balance sheet items from WIND: total assets, total liabilities, current and non-current liabilities.
- Aggregate statistic:
  - Total liabilities of sample firms about RMB53 trillion as of Q4-2014, accounting for about 45 percent of non-equity total social financing (TSF).
- Table 1 summary statistics (Billions of yuan unless otherwise specified):
  - Listed non-financial firms (Number of firms 2,411; Std. Dev. 1,390)
    - Q4 2014 Median Total assets: 2.83; Std. Dev. 68.97
    - Q4 2014 Median Total liabilities: 1.16; Std. Dev. 39.82
    - Q4 2014 Median Current liabilities: 0.92; Std. Dev. 28.03
    - Q4 2014 Median Non-current liabilities: 0.11; Std. Dev. 13.57
    - Q4 2014 Median Market cap: 3.85; Std. Dev. 32.93
    - Q3 2008 Median Total assets: 2.05; Std. Dev. 40.35
    - Q3 2008 Median Total liabilities: 1.06; Std. Dev. 18.27
    - Q3 2008 Median Current liabilities: 0.83; Std. Dev. 12.82
    - Q3 2008 Median Non-current liabilities: 0.09; Std. Dev. 5.98
    - Q3 2008 Median Market cap: 1.86; Std. Dev. 70.33
  - Non-listed non-financial firms (Number of firms 1,586; Std. Dev. 675)
    - Q4 2014 Median Total assets: 7.55; Std. Dev. 185.07
    - Q4 2014 Median Total liabilities: 4.34; Std. Dev. 111.56
    - Q4 2014 Median Current liabilities: 2.37; Std. Dev. 47.35
    - Q4 2014 Median Non-current liabilities: 1.07; Std. Dev. 75.68
    - Q3 2008 Median Total assets: 9.32; Std. Dev. 120.48
    - Q3 2008 Median Total liabilities: 5.00; Std. Dev. 56.68
    - Q3 2008 Median Current liabilities: 3.17; Std. Dev. 30.90
    - Q3 2008 Median Non-current liabilities: 1.53; Std. Dev. 29.60
  - Footnote: End-2013 and End-2008 for non-listed firms.
- Estimating market value of assets:
  - Listed firms: quarter-end levels and rolling 250-day standard deviations of log changes in equity market capitalizations from Bloomberg.
  - Dual-listed shares: market capitalization = sum of listings converted to yuan.
  - Non-listed firms: peer-group matching by sub-industry (WIND), minimize squared distance DS over standardized size (book value of assets BV) and leverage (D/E) as in (15); use median sector price-to-book to convert book equity to market proxy; solve for market asset values and jump diffusion parameters analogously to listed firms.

### VI. Distribution of estimated default probabilities and mapping to ratings
- Table 2: Distribution of Estimated DPs (Q1-2014), Jump-Diffusion Structural Credit Model:
  - 10th percentile: 1.7X10-20 (Cumulative Number of Firms 400)
  - 25th percentile: 4.3X10-9 (Cumulative Number of Firms 1,000)
  - 50th percentile: 0.0006 (Cumulative Number of Firms 1,999)
  - 75th percentile: 0.1 (Cumulative Number of Firms 2,998)
  - 90th percentile: 0.6 (Cumulative Number of Firms 3,597)
  - Max: 46.9 (Cumulative Number of Firms 3,997)
- Mapping 1-year DP to implied credit rating (Table 3; Issuer-Weighted Long-Term Average; Lower Limit; Upper Limit):
  - AAA: 0.00; 0.00; 0.01
  - AA: 0.02; 0.01; 0.05
  - A: 0.07; 0.05; 0.14
  - BBB: 0.21; 0.14; 0.51
  - BB: 0.80; 0.51; 2.46
  - B: 4.11; 2.46; 15.49
  - CCC/C: 26.87; 15.49; 100.00
- Observed implication: mapping suggests 89 percent of firms were investment grade at end-Q1-2014 based on estimated DPs; upper quartile firm at end-Q1-2014 had DP of just 0.1 percent.
- Caveat: structural models tend to under-predict short-horizon default probabilities (about one year) and for investment-grade debt; downward bias may reflect suppressed actual default rates due to third-party support and technical calibration limits (e.g., limited capture of volatility clustering).

### VII. Case studies (illustrative firm-level dynamics)
- Shanghai Chaori Solar Energy Science and Technology Ltd (Chaori)
  - First domestic bond-market default in China.
  - IPO November 2010 raised 2.38 billion yuan.
  - Model detected 1-year DP rising from near zero to over 10 percent in July 2013 as stock price fell; DP dipped to 3–5 percent then spiked to over 25 percent by end-2013.
  - Implied ratings moved from AAA-AA to B and finally to CCC.
  - Drivers: declining distance-to-default from falling market value of assets, rising asset volatility, increased downward jump risk. Chaori missed a coupon payment in March 2014 on a 5-year 1 billion yuan bond issued in May 2012.
- Vanke China Ltd
  - 1-year DP rose significantly during 2008 (asset value decline, asset volatility increase); low through recovery 2009–early 2013; rose to between 2–4 percent as property market slowed since early 2013 due to gradual asset value declines and rising volatility.

### VIII. Aggregate and sectoral findings
- Time coverage: Q1-2006 to Q4-2014; 1-year DPs estimated each quarter.
- Distributional patterns:
  - DPs rose significantly during the Global Financial Crisis (GFC) but remained stable and low since 2012.
  - Despite increased liabilities, rising asset values and remarkably low equity price volatilities since 2012 have kept DPs low.
- Sectoral vulnerability (median to 75th percentile skew):
  - Construction, real estate, retail and wholesale, and utilities skewed toward sub-investment grade relative to full sample.
  - Comparison of 90th percentile firms by sector at Q4-2008, Q4-2013, Q4-2014: rising equity valuations lowered default risks recently, but construction, real estate, and retail and wholesale remain most vulnerable.
- Ownership and listing status (Q4-2014):
  - Distribution of default risk similar for listed and non-listed firms.
  - Stand-alone default risk higher for SOEs, particularly locally-owned SOEs, compared to LGFVs and privately-owned firms.
    - Implied credit rating range for local SOE firms between the 75th and 90th percentile: close to A–BB.
    - Range for LGFVs is almost all investment grade (AAA to BB).

### IX. Determinants of default probabilities — regression analysis
- Objective: link market-based DPs to firm-specific accounting ratios and macro-financial conditions via pooled logit regression (equation (16)).
- Sample for regressions: unbalanced panel of 2,409 listed firms with equity market data; firm-specific variables lagged one period and winsorized at 1st and 99th percentiles; OLS with robust standard errors.
- Firm-specific explanatory variables (Table 4) — median; standard deviation; expected sign:
  - Profitability (EBIT/TA): Median: -0.06; Std. Dev.: 0.08; Expected sign: –
  - Profitability (RE/TA): Median: -0.14; Std. Dev.: 0.27; Expected sign: –
  - Leverage (TA/TL): Median: 1.73; Std. Dev.: 0.66; Expected sign: +
  - Liquidity (WC/TA): Median: -0.16; Std. Dev.: 0.31; Expected sign: –
  - Debt maturity (CL/NCL): Median: 2.30; Std. Dev.: 30.36; Expected sign: –
  - Relative size (TA / median TA): Median: 0.57; Std. Dev.: 8.87; Expected sign: +/–
  - Age (months since listing): Median: 112.37; Std. Dev.: 68.54; Expected sign: +
- Macroeconomic explanatory variables (Table 5) and expected signs:
  - Official manufacturing PMI — Expected sign: +
  - M2 y/y growth deflated by CPI inflation — Expected sign: +
  - Average lending rate deflated by CPI inflation — Expected sign: –
  - Price-to-book ratio of Shanghai Composite index — Expected sign: +
- Key regression results (examples from Table 6 and specifications):
  - ln(1-EBIT/TA): correctly signed (negative), statistically significant (example: -3.43** in Table 6, specification 1).
  - ln(1-RE/TA): negative, statistically significant and larger effect than Altman et al. (2011) (example: -8.78** in Table 6, specification 1).
  - 1+ln(TA/TL) (leverage): positive, statistically significant and robust (example: 9.77** in Table 6, specification 1).
  - Liquidity, debt structure, size, and age: mixed significance; often insignificant or not robust across specifications.
- Economic significance examples:
  - For an A-rated firm with 1-year estimated DP of 0.07 percent:
    - Fall in asset-to-liabilities ratio from 5 to 4 (25 percent increase in liabilities) would increase DP to 0.19 percent.
    - Decline in profitability measured as 10ppts fall in EBIT-assets ratio would increase DP to 0.09 percent.
- Ownership effects:
  - State ownership increases stand-alone DP (as measured from equity investor perspective excluding likelihood of state financial support).
  - Dummy variable coefficients for central SOE, local SOE, and LGFV are negative in regression tables (interpreted as positive relation with DP) and statistically significant.
  - Using specification 5 in Table 6: for an A-rated privately-owned firm with DP of 0.07 percent:
    - Central SOE: DP would be 0.06ppt higher (one notch lower from A to A-minus).
    - Local SOE: DP would rise by 0.1ppt (two notches lower to BBB).
    - LGFV: DP would rise by 0.17ppt (implied rating close to BBB-minus).
  - SOE shareholding variable: negative and statistically significant; specification 5 implies DP rises by 0.02ppt for every 10ppt increase in public ownership for an A-rated firm.
  - Wald tests reject null that ownership variables have no impact on DP (Chi-squared statistics reported; examples include 23.20**, 121.59**, 48.44**; Wald test statistics 46.86** and 106.79**).
- Subsample of SOEs and LGFVs:
  - Coefficients on firm-specific variables remain significant and with expected signs.
  - Central SOEs have lower DPs than local SOEs, which have lower DPs than LGFVs (same qualitative ordering as full-sample specifications).
- Macro-financial variables:
  - Coefficients correctly signed and statistically significant in some specifications but less robust than firm fundamentals.
  - Most robust macro finding: rise in PMI lowers DP.
  - Example: specification 5 in Table 8 — for an A-rated firm with DP of 0.07 percent, a two standard deviation (2pt) decline in PMI would raise DP by about 0.09ppt (pushing rating two notches lower to BBB).
  - Aggregate financial variables’ effects sensitive to inclusion of market sentiment indicators (PBV).
- Model fit and robustness:
  - Firm-specific variables provide greater in-sample explanatory power than macro variables.
  - Adjusted R-squared ranged from 16-23 percent across pooled regressions (noted lower than Altman et al. (2011) but comparable to Benito et al. (2004) and Bonfim (2009)).
  - Panel regressions with fixed effects: similar quantitative results; adjusted R-squared rises to about 33 percent.
  - Excluding SOEs and LGFVs: firm fundamentals still dominant; monetary conditions become less significant.
- Excluding state-owned firms (Table 10):
  - Sample: 28,823 observations; reported R-squared values include 17.7%, 17.9%, 18.0%, 23.9%, 18.5%, 20.1%.
  - Key coefficients for firm fundamentals remain significant in many specifications.

### X. Borrowing costs versus market-implied DPs
- Alternative dependent variable: firm borrowing rate (gross interest expense / total interest-bearing liabilities) converted into DP assuming zero recovery; reduced sample to 1,969 firms.
- Findings (Table 11):
  - Borrowing-rate based specifications yield coefficients often incorrectly signed, smaller, or statistically insignificant relative to market-based DP regressions.
  - Examples: profitability has little effect; higher leverage implies lower DP in borrowing-rate regressions; public ownership tends to lower DP when borrowing-costs are dependent variable.
  - Comparative R-squared:
    - Borrowing-rate models (columns 1-4): 0.078, 0.158, 0.160, 0.160.
    - Market-based models (columns 5-8): 0.096, 0.143, 0.144, 0.144.
- Interpretation:
  - Equity market-based DPs better indicate stand-alone default risk in China than borrowing costs.
  - Reason: implicit guarantees benefit creditors (banks, non-bank lenders, bondholders) more than equity holders; equity investors less protected by implicit guarantees and expect limited equity value recovery from bailouts (which can dilute equity).

### XI. Conclusion — implications and caveats
- Actual bond-market defaults are rare in China and provide limited guidance; credit spreads and borrowing costs often reflect creditor focus on implicit guarantees rather than stand-alone creditworthiness.
- Structural credit models estimating stand-alone 1-year DP can be usefully applied in China, particularly at individual stock level, despite equity market volatility.
- Empirical support:
  - Market-based DPs signaled increased stress for some firms, including the first onshore corporate bond default.
  - Probabilities respond intuitively to changes in firm fundamentals (profitability, balance sheet strength).
- Caveats:
  - Macroeconomic and financial conditions appear to have less impact than might be expected; investor speculation about “policy stimulus” can offset deterioration in broad conditions.
  - Forward-looking models beneficial but equity valuations may overshoot; structural models tend to under-predict short-horizon default frequencies for investment-grade firms.

*Source: _wp15140 - REFERENCES*

### REFERENCES .............................................................................................................

### _wp15140 - REFERENCES

### I. Introduction: scope and objectives
- Urgent need to improve understanding of credit risk of China’s corporate sector as corporate credit exposures grow quickly.
- Main questions:
  - Can standard credit risk tools be applied to Chinese firms given China’s unique financial system, significant role of the state, absence of a full credit cycle, and potential unreliability of financial indicators?
  - Are firm fundamentals, ownership (SOE vs private), and macro-financial conditions related to market-based default probabilities?
  - Which market indicators—equity markets or borrowing costs—are more reliable for assessing stand-alone credit risk?
  - Can the model estimate default probabilities for firms that lack market data?
- Sample and approach:
  - Estimate stand-alone 1-year probability of default for a sample of about 4,500 non-financial firms.
  - Use a variant of Merton’s (1974) structural credit model with unexpected jumps (Zhou, 1997), inclusion of non-listed firms (Jobst and Gray, 2013), and mapping to a database of actual defaults (Gray, 2009).
  - Definition of “stand-alone” probability of default consistent with Standard & Poor’s (2010).

### II. Market-based default probabilities for Chinese firms — Methodology overview
- Structural model foundation:
  - Firm market value of assets: V.
  - Default occurs if V falls to a default barrier DB (practically between total liabilities and current liabilities; authors set DB = short-term liabilities + 1/2 long-term liabilities following Jobst and Gray (2013)).
  - Equity value E at maturity modeled as a call option on V with strike DB (equation (1)).
  - Risky debt value described as DB minus a put option with strike DB (equation (2)).
  - Firm value relation: V = D + E (CCA balance sheet).
- Jump-diffusion specification (under risk-neutral measure):
  - Asset value V follows a jump diffusion process as in equation (3) with parameters:
    - μ (expected rate of return),
    - υ (expected jump),
    - σ (instantaneous volatility conditional on no jump),
    - dZ (Wiener process),
    - dY (Poisson process with intensity λ),
    - jump size Π log-normally distributed (equation (4)).
  - Expected value of jump size expressed as in equation (5).
- Estimation approach:
  - Estimate parameters θ = {μ, λ, σ, μπ, σπ} by maximizing a log-likelihood function using the empirical distribution of daily log changes in firm asset value.
  - For small λΔt, jump probability approximated as Bernoulli; density of Δx during Δt is a weighted mixture (equation (6)).
  - Brownian component density given in (7); jump component density given in (8).
  - Constraint on λ: ensure λΔt ≤ 1 where t = 1/252 (equation (9) constraint ensures probability that asset value jumps once in Δt is ≤ 1).
- Calibration of unobserved asset value V:
  - Equity value equals value of a European call on firm assets with strike DB (call pricing given in (10)).
  - Use put-call parity C = e^{-rT}DB - P + ??? (put-call parity invoked in (11) with call C, put P, DB).
  - Put option premium computed via formula in (12).
  - Iterative procedure:
    - Initialize jump diffusion parameters from equity return distribution.
    - Solve for V using option relationships and Newton method or put-call parity.
    - Update parameters and iterate until convergence of V, μ, σ, λ, μπ, and σπ.
- Default probability calculation:
  - Follow Zhou (1997) to calculate risk-neutral and stand-alone default probability, denoting drift μ by r, using equation (13) with default barrier ξ set to 1.

### III. Rationale for jump-diffusion and empirical features
- Incorporation of jump diffusion accommodates sudden changes in firm value and default risk, a common feature in equity markets including China (Figure 1).
- Observed empirical pattern since 2010: returns for smaller firms have tended to be positively skewed (sudden price increases) — jump risk can be in either direction.
- Claim: jump-diffusion model can provide a better estimate of default probability than a standard Merton model because it allows for sudden jumps both upward and downward.

### IV. Model inputs and practical settings (as described)
- Default barrier DB operational choice: DB = short-term liabilities + 1/2 long-term liabilities (Jobst and Gray, 2013).
- Time step used in jump constraint: t = 1/252 (daily frequency).
- Default barrier for probability calculation: ξ = 1 in equation (13).
- Parameters estimated per firm: μ, σ, λ, μπ, σπ.

*Source: _wp15140 - REFERENCES (content excerpt from the referenced PDF).*

### 2. Distribution of skewness of daily returns

### _wp15140 - 2. Distribution of skewness of daily returns

### Adjusting to real-world probabilities
- Risk-neutral default probabilities used the risk-free rate r as the Brownian motion drift in (13) and theoretical distributions for firm values; these can differ materially from real-world probabilities due to investor risk aversion and firms’ real-world corrective actions.
- Two adjustments adopted (Gray, 2009) to approximate Moody’s KMV EDFTM and convert risk-neutral to actual probabilities:
  - Linear transformation of fitted asset volatility σv into σV* as in (14a) to better match EDFTM behavior; for Chinese firms the authors use their own estimate σv (derived using (9)) as the independent variable in (14a).
  - Replace the risk-free rate r in (13) with a drift μ* that captures the time-varying price of risk, calculated as the product of the correlation between firm equity and the market and the Sharpe ratio as in (14b).
- Parameter values used in (14):
  - γ0 = 0.05
  - γ1 = 1.37
  - ρA,M = 0.6
  - SR = 0.75
- Interpretative remarks for China:
  - The linear transformation approximates Moody’s North American-based default-history database; legal and institutional differences (e.g., China ranked 53rd in resolving insolvency vs. United States 4th and Canada 6th in the 2014 World Bank “Doing Business” survey) may limit direct comparability.
  - Public sector support (especially for SOEs) may suppress observed default frequencies; the adjustment aims to estimate stand-alone default probabilities based on firm fundamentals.
  - Estimating market price of risk and Sharpe ratio ex-post is problematic in China (ex-post Sharpe ratios close to zero or negative during 2008–2013); the authors use theoretically-consistent priors for μ* in (14b) to reflect forward-looking investor expectations.

### Data — Sample of firms
- Panel: unbalanced, maximum of 4,483 non-financial firms between Q1-2006 and Q4-2014.
  - 2,441 listed firms with equity on a public exchange.
  - 2,042 unlisted firms that had issued bonds in the onshore bond market.
- Sample includes 1,020 local government financing vehicles (LGFVs) of which are listed firms; LGFVs identified by issuance of urban investment (Changtou) bonds.
- Survivor bias: few de-listings; survivor bias likely minimal.

### Data — Firms’ balance sheet items
- All balance sheet data from the WIND database: total assets, total liabilities, current and non-current liabilities.
- Reporting frequency:
  - Listed firms: variables reported shortly after each calendar quarter.
  - Non-listed bond issuers: financial statements disclosed for three years prior to issuance and annually thereafter; some report quarterly.
- Default barrier includes all liabilities (current and non-current) because of material size and contingent-claim status.
- Aggregate statistic:
  - Total liabilities of sample firms about RMB53 trillion as of Q4-2014, accounting for about 45 percent of non-equity total social financing (TSF).

- Table 1 summary statistics (Billions of yuan unless otherwise specified):
  - Listed non-financial firms (Number of firms 2,411; Std. Dev. 1,390)
    - Q4 2014 Median Total assets: 2.83; Std. Dev. 68.97
    - Q4 2014 Median Total liabilities: 1.16; Std. Dev. 39.82
    - Q4 2014 Median Current liabilities: 0.92; Std. Dev. 28.03
    - Q4 2014 Median Non-current liabilities: 0.11; Std. Dev. 13.57
    - Q4 2014 Median Market cap: 3.85; Std. Dev. 32.93
    - Q3 2008 Median Total assets: 2.05; Std. Dev. 40.35
    - Q3 2008 Median Total liabilities: 1.06; Std. Dev. 18.27
    - Q3 2008 Median Current liabilities: 0.83; Std. Dev. 12.82
    - Q3 2008 Median Non-current liabilities: 0.09; Std. Dev. 5.98
    - Q3 2008 Median Market cap: 1.86; Std. Dev. 70.33
  - Non-listed non-financial firms (Number of firms 1,586; Std. Dev. 675)
    - Q4 2014 Median Total assets: 7.55; Std. Dev. 185.07
    - Q4 2014 Median Total liabilities: 4.34; Std. Dev. 111.56
    - Q4 2014 Median Current liabilities: 2.37; Std. Dev. 47.35
    - Q4 2014 Median Non-current liabilities: 1.07; Std. Dev. 75.68
    - Q3 2008 Median Total assets: 9.32; Std. Dev. 120.48
    - Q3 2008 Median Total liabilities: 5.00; Std. Dev. 56.68
    - Q3 2008 Median Current liabilities: 3.17; Std. Dev. 30.90
    - Q3 2008 Median Non-current liabilities: 1.53; Std. Dev. 29.60
  - Footnote: End-2013 and End-2008 for non-listed firms.

### Estimating the market value of assets
- Listed firms:
  - Asset values and volatilities estimated using quarter-end levels and rolling 250-day standard deviations of log changes in equity market capitalizations from Bloomberg.
  - Dual-listed shares: market capitalization = sum of listings converted to yuan at prevailing exchange rates (including H shares).
- Non-listed firms:
  - Peer-group matching (Jobst and Gray, 2013):
    - Group non-listed firms by sub-industry (WIND database).
    - Minimize squared distance DS between non-listed firm i and listed firms j = 1...N in same sub-industry over standardized characteristics: size (book value of assets BV) and leverage (debt-to-equity D/E) as in (15).
    - Use median price-to-book ratio of the same sector to convert book value of equity to market value proxy; then solve for non-listed firms’ market asset values and jump diffusion parameters using the same process as for listed firms.

### Default Probability Under-Prediction
- Structural credit models, including the calibrated jump-diffusion model here, tend to under-predict default probabilities at short horizons (about one year) and for investment-grade debt.
- Despite jump-risk inclusion and the linear transformation (14a), estimated default probabilities can appear unreasonably low, possibly due to:
  - Actual default rates being suppressed by third-party financial support.
  - Technical shortcomings of the jump diffusion calibration (limited ability to capture volatility clustering).
- Table 2: Distribution of Estimated DPs (Q1-2014), Jump-Diffusion Structural Credit Model:
  - 10th percentile: 1.7X10-20 (Cumulative Number of Firms 400)
  - 25th percentile: 4.3X10-9 (Cumulative Number of Firms 1,000)
  - 50th percentile: 0.0006 (Cumulative Number of Firms 1,999)
  - 75th percentile: 0.1 (Cumulative Number of Firms 2,998)
  - 90th percentile: 0.6 (Cumulative Number of Firms 3,597)
  - Max: 46.9 (Cumulative Number of Firms 3,997)
- Mapping to credit ratings suggests 89 percent of firms were investment grade at the end of Q1-2014 based on these default probabilities; the upper quartile firm at end-Q1-2014 had a default probability of just 0.1 percent.

### Default Probability–Implied Credit Ratings
- Method: map estimated 1-year default probability to actual default rates by published credit rating from Standard & Poor’s (2014); rating intervals determined by mid-points of averages of adjacent ratings.
- Table 3: 1-Year Default Probability to Implied Credit Rating Mapping (Issuer-Weighted Long-Term Average; Lower Limit; Upper Limit)
  - AAA: 0.00; 0.00; 0.01
  - AA: 0.02; 0.01; 0.05
  - A: 0.07; 0.05; 0.14
  - BBB: 0.21; 0.14; 0.51
  - BB: 0.80; 0.51; 2.46
  - B: 4.11; 2.46; 15.49
  - CCC/C: 26.87; 15.49; 100.00
- Mapping provides an alternative reporting metric but does not correct for downward bias.

### Case Studies
- A. Shanghai Chaori Solar Energy Science and Technology Ltd (Chaori)
  - First domestic bond-market default in China.
  - IPO November 2010 raised 2.38 billion yuan.
  - Model detected rising 1-year DP from near zero to over 10 percent in July 2013 as stock price fell; DP dipped to 3–5 percent then spiked to over 25 percent by end-2013.
  - Implied ratings moved from AAA-AA to B and finally to CCC.
  - Drivers: declining distance-to-default from falling market value of assets, rising asset volatility, increased jump risk (downward skew). Chaori missed a coupon payment in March 2014 on a 5-year 1 billion yuan bond issued in May 2012.
- B. Vanke China Ltd
  - One of the largest property developers; rapid turnover growth until late 2013.
  - Model: 1-year DP rose significantly during 2008 (asset value decline, asset volatility increase); low through recovery 2009–early 2013; rose to between 2–4 percent as property market slowed since early 2013 due to gradual asset value declines and rising volatility.

### Aggregate results
- Time coverage: Q1-2006 to Q4-2014; 1-year default probabilities estimated each quarter for all firms using (1)–(14).
- Distributional findings:
  - Default probabilities rose significantly during the Global Financial Crisis (GFC) but remained stable and low since 2012.
  - Despite increased liabilities, rising asset values and remarkably low equity price volatilities since 2012 have kept default probabilities low.
- Sectoral patterns (Figure 4 summary):
  - From median to 75th percentile, construction, real estate, retail and wholesale, and utilities are skewed toward sub-investment grade relative to the full sample.
  - Comparison of 90th percentile firms by sector at Q4-2008, Q4-2013, Q4-2014: rising equity valuations lowered default risks recently, but construction, real estate, and retail and wholesale remain most vulnerable.
- Ownership and listing status (Figure 5 summary):
  - At end-Q4-2014, distribution of default risk similar for listed and non-listed firms.
  - Stand-alone default risk higher for SOEs, particularly locally-owned SOEs, compared to LGFVs and privately-owned firms.
    - Implied credit rating range for local SOE firms between the 75th and 90th percentile: close to A–BB.
    - Range for LGFVs is almost all investment grade (AAA to BB).

*Source: WIND database; Bloomberg; authors’ calculations (from the provided IMF working paper content).*

### 1. Listing Status and Ownership, Q4-2014

### 1. Listing Status and Ownership, Q4-2014

### Summary findings
- During Q4-2014, default probabilities were depressed by lower asset volatilities.
- The weak tails of the distribution of both central and local SOEs have lower volatilities than other privately-owned firms, offsetting generally higher leverage among these firms.
- The leverage of local SOEs and LGFVs has continued to rise while that of other firms has been more stable.
- Lower default probabilities for LGFVs may be attributable to lower asset volatility and leverage.

### Evidence and comparisons
- Time markers and snapshots referenced:
  - 2014Q4
  - 2013Q4
  - 2008Q4
- Rating categories shown in figures: CCC, BBB, BBB, A, AA, AAA (preserved as presented).
- Axis/scale markers presented in figures: -1 2 3 4 and -1 2 3 4 5 6 7 (preserved as presented).
- Firm groups analyzed:
  - Central SOE
  - Local SOE
  - LGFV
  - Others
  - Listed
  - Non-listed

### Interpretive points
- Lower asset volatility is identified as a primary driver of reduced default probabilities in Q4-2014.
- For central and local SOEs, reduced asset volatility in the distribution tails helps offset higher leverage, thereby lowering measured default risk relative to privately-owned firms.
- Rising leverage among local SOEs and LGFVs suggests a diverging leverage trend versus more stable leverage among other firms.
- The combination of lower asset volatility and lower leverage is offered as an explanation for relatively lower default probabilities observed for LGFVs.

### Visual material referenced
- Figure 6. Leverage and Asset Volatility by Ownership Q4-2014 vs 2008
- Sub-caption/headline: 90th Percentile Firms by Listing/ Ownership
- Data sources cited: Wind; Bloomberg; and authors’ calculations.

*Source: _wp15140 - 1. Listing Status and Ownership, Q4-2014*

### 1. Asset Volatility by Ownership

### 1. Asset Volatility by Ownership

### V. DETERMINANTS OF DEFAULT PROBABILITIES IN CHINA
- Objective: establish empirical link between market-based assessments of default probabilities and explanatory variables including firm-specific accounting ratios and economic and financial conditions.
- Research question: are market-based measures of default probability in China affected by factors that should intuitively influence credit risk, and are standard credit risk assessment methods justified for China?

### A. Previous Literature
- Methodological precedent: follow Altman et al. (2011) who used a logit model with risk-neutral default probability estimated from a structural credit model (inputs: equity market capitalizations, equity price volatilities, distress barrier = short-term liabilities + one-half of long-term liabilities).
- Explanatory variables typically include profitability, leverage, liquidity, growth, firm size, and age (Altman Z-score variables).
- Key prior findings:
  - Altman et al. (2011): accounting-based measures explain about 40 percent of total in-sample variation in market-based default probabilities; all Z-score variables correctly signed and statistically significant.
  - Zhang, Han, and Chan (2014) for China: Altman Z-score variables accounted for about half of estimated variation in default probabilities.
  - Jacobson, Lindé, and Rozbach (2013) (Sweden): firm-specific variables important for relative default likelihood; macro variables exert much greater influence on average economy-wide default risk.
  - Bonfim (2009) (Portugal) and Benito, Delgado, and Pagés (2004) (Spain): firm-specific variables are important; macroeconomic variables contribute to systematic shocks but tend to exert less influence than firm-specific factors.

### B. Methodology and Data
- Model specification: standard logit pooled regression (equation (16)):
  - For each time t and firm i: α common intercept; β (k x 1) parameters for firm-specific X_it-1 (k x 1) vector lagged one period; γ (l x 1) parameters for macro Z_t-1 (l x 1) vector lagged one period; ζ (m x 1) parameters for D (m x 1) dummy variables; λ_t time effect; residuals ε_it assumed independent across firms after controlling for common factors.
  - Firm-specific variables winsorized at the 1st and 99th percentiles.
  - Estimation: OLS with robust standard errors.
  - Sample: unbalanced panel of 2,409 listed firms with firm-specific equity market data.
- Firm-specific explanatory variables (Table 4) — median, standard deviation, expected sign:
  - Profitability: ratio of earnings before interest and taxes to total assets — Median: -0.06; Standard Deviation: 0.08; Expected sign: –
  - Profitability: ratio of retained earnings to total assets — Median: -0.14; Standard Deviation: 0.27; Expected sign: –
  - Leverage: ratio of total assets to total liabilities — Median: 1.73; Standard Deviation: 0.66; Expected sign: +
  - Liquidity: ratio of working capital to total assets — Median: -0.16; Standard Deviation: 0.31; Expected sign: –
  - Debt maturity structure: ratio of current liabilities to non-current liabilities — Median: 2.30; Standard Deviation: 30.36; Expected sign: –
  - Relative size: ratio of total assets to median of total assets of all sample firms — Median: 0.57; Standard Deviation: 8.87; Expected sign: +/–
  - Age: number of months since listing — Median: 112.37; Standard Deviation: 68.54; Expected sign: +
- Macroeconomic explanatory variables (Table 5) and expected signs:
  - Economic outlook: Official manufacturing PMI — Expected sign: +
  - Monetary conditions: M2 year-on-year growth deflated by CPI inflation — Expected sign: +
  - Monetary conditions: Average lending rate deflated by CPI inflation — Expected sign: –
  - Market valuation: Price-to-book ratio of Shanghai Composite index — Expected sign: +
- Dummies included: quarterly (time-effect), CSRC industry classification, ownership dummies (centrally state owned, locally state owned, LGFV, privately owned).
- Underlying assumption: equity payoffs of Chinese firms are not implicitly guaranteed; equity market-based estimate of default risk reflects impact of state ownership on firm’s ability to service obligations from its own resources rather than probability of public sector financial support.

### C. Results
- General: firm-specific variables largely in line with expectations and similar to or somewhat larger than Altman et al. (2011).
- Key coefficient findings (Specification 1 and comparisons):
  - ln(1-EBIT/TA): correctly signed (negative), statistically significant across specifications (example: -3.43** in Table 6, specification 1).
  - ln(1-RE/TA): correctly signed (negative), statistically significant and larger effect in this model than Altman et al. (2011) (example: -8.78** in Table 6, specification 1). Retained earnings negative for about one-fifth of sample observations; interaction with negative DV included.
  - 1+ln(TA/TL) (leverage): correctly signed (positive), statistically significant and robust (example: 9.77** in Table 6, specification 1).
  - Indicators of liquidity (WC/TA), debt structure (ln(CL/NCL)), size, and age: either statistically insignificant, economically insignificant, or not robust across specifications (mixed results).
- Economic significance example calculations:
  - For an A-rated firm with 1-year estimated default probability of 0.07 percent:
    - Fall in asset-to-liabilities ratio from 5 to 4 (25 percent increase in liabilities) would increase default probability to 0.19 percent.
    - Decline in profitability measured as a 10ppts fall in the EBIT-assets ratio would increase default probability to 0.09 percent.
- Ownership effects:
  - State ownership appears to increase stand-alone default probability (measured from equity investor perspective, excluding likelihood of state financial support).
  - Dummy variable coefficients for centrally-owned SOE, locally-owned SOE, and LGFV were negative in the regression tables (interpreted as positive relation with default probability) and statistically significant and robust.
  - Quantitative context (using specification 5 in Table 6):
    - For an A-rated privately-owned firm with default probability of 0.07 percent:
      - Central SOE: default probability would be 0.06ppt higher (equivalent to one notch lower from A to A-minus).
      - Local SOE: default probability would rise by 0.1ppt (equivalent to two notches lower to BBB).
      - LGFV: default probability would rise by 0.17ppt (implied rating close to BBB-minus).
  - Estimated SOE shareholding variable: negative and statistically significant. Using specification 5, for an A-rated firm, default probability would rise by 0.02ppt for every 10ppt increase in public ownership.
  - Wald tests reject null that ownership variables have no impact on default probability (Table 8): Chi-squared statistics reported (e.g., 23.20**, 121.59**, 48.44** for individual constraints; Wald test statistic 46.86** and 106.79** in two reported columns).
- Subsample: SOEs and LGFVs (Table 9)
  - Coefficients on firm-specific variables remain significant with expected signs.
  - Central SOEs have lower default probabilities than local SOEs, which in turn have lower default probabilities than LGFVs. Rating differences similar to specification 5 in Table 8.
- Economic and financial conditions (γ coefficients):
  - Coefficients on macroeconomic/financial variables are correctly signed and statistically significant in some specifications but much less robust than firm-specific fundamentals.
  - Market price-to-book ratio (PBV) inclusion strongly affects estimates for some macro variables.
  - Most robust macro finding: rise in PMI of manufacturing activity lowers probability of default.
  - Example: using specification 5 in Table 8, for an A-rated firm with 1-year default probability of 0.07 percent, a two standard deviation (2pt) decline in PMI would raise default probability by about 0.09ppt (pushing rating two notches lower to BBB).
  - Aggregate financial variables' effects are less robust and highly sensitive to inclusion of market sentiment indicators (PBV).
- Model fit and robustness:
  - Firm-specific variables contribute more to in-sample predictive power than macro variables.
  - Adjusted R-squared ranged from 16-23 percent across estimations (noted as lower than Altman et al. (2011) but comparable to Benito et al. (2004) and Bonfim (2009)).
  - Excluding SOEs and LGFVs: firm-specific variables still dominate predictive power; predictive power of monetary conditions becomes less significant, suggesting these firms may be more sensitive to monetary policy (easier access to credit).
  - Potential missing variables: unobservable market sentiment and adverse shocks to market value of assets (information asymmetry).
  - Panel regressions with fixed effects (not shown): similar quantitative results; sizes of significant firm-specific and macro variables somewhat lower and higher respectively; adjusted R-squared rises to about 33 percent.
- Excluding state-owned firms (Table 10):
  - Sample: 28,823 observations; various specifications report R-squared values of 17.7%, 17.9%, 18.0%, 23.9%, 18.5%, 20.1%.
  - Key coefficients remain significant for firm-specific fundamentals in many specifications (examples preserved in table).

### Borrowing costs as dependent variable
- Alternative test: use firm-specific borrowing rate (gross interest expense / total interest-bearing liabilities) converted into default probability assuming zero recovery rate; reduced sample to 1,969 firms for availability of borrowing costs.
- Findings (Table 11):
  - Borrowing rate-based specifications yield estimated coefficients that are often incorrectly signed, smaller in size, or statistically insignificant compared with market-based default probability regressions.
  - Examples: profitability has little effect; higher leverage implies lower default probability in borrowing-rate regressions; public ownership tends to lower default probability when borrowing-costs are dependent variable.
  - Comparison (Table 11): R-squared for borrowing rate-based models in columns 1-4 are 0.078, 0.158, 0.160, 0.160; for market-based models in columns 5-8 are 0.096, 0.143, 0.144, 0.144.
- Interpretation and conjecture:
  - Equity market-based default probabilities are more effective indicators of stand-alone default risk in China than borrowing costs.
  - Reasoning: implicit guarantees provided by the state benefit creditors (banks, non-bank lenders, bondholders) more than equity holders; equity holders do not benefit as much from implicit guarantees and expect that third-party support will do little to boost equity value in distress; bailouts that increase public ownership can dilute existing equity holders.

### VI. CONCLUSION
- Bond market actual defaults are rare in China and provide limited guidance; credit spreads and borrowing costs largely unaffected by firm fundamentals, with creditors focusing on implicit guarantees.
- Financial account descriptive statistics are backward looking and do not provide probability of default.
- Conclusion: structural credit models estimating stand-alone 1-year probability of default can be usefully applied in China, particularly at the individual stock level, despite volatility in Chinese equity markets.
- Empirical support:
  - Market-based default probabilities provided signals of increased financial stress for some firms, including the first onshore corporate bond default.
  - Probabilities respond intuitively and quantitatively to changes in firm fundamentals (profitability, balance sheet strength).
- Caveats:
  - Macroeconomic and financial conditions appear to have less impact than might be expected; investor speculation about “policy stimulus” can offset deterioration in broad economic and financial conditions.
  - Forward-looking nature of models can be beneficial but equity valuations may overshoot.

*Source: _wp15140 - 1. Asset Volatility by Ownership (authors’ estimates, tables and text as provided).*

### REFERENCES

### REFERENCES

### Foundational theoretical models and books
- Altman, Edward, 1968, “Financial Ratios, Discriminant Analysis, and the Prediction of Corporate Bankruptcy,” Journal of Finance, Vol. 23, pp. 189-209.
- Merton, Robert C., 1974, “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,” Journal of Finance, Vol.29, pp. 449-470.
- Damodoran, Aswath, 1996, Investment Valuation, John Wiley & Sons, New York.
- Leland, Hayne E., 2006, “Predictions of Default Probabilities in Structural Models of Debt,” in The Credit Market Handbook - Advanced Modeling Issues, Ed. H. Gifford Fong, John Wiley & Sons, Inc., Hoboken, New Jersey.
- Altman, Edward, and Edith Hotchkiss, 2006, “Corporate Financial Distress and Bankruptcy” John Wiley and Sons, New York, 3rd edition.

### Contingent claims analysis, KMV, and market-implied approaches
- Crosby, Peter, and Jeff Bohn, 2003, Modeling Default Risk, Moody’s KMV Company.
- Gray, Dale, 2009, “Understanding Moody’s KMV (MKMV) Application of Contingent Claims Analysis (CCA) for Financial Institutions and Corporates and Use in Stress Testing,” unpublished transcript.
- Chan-Lau, Jorge A., 2006, “Market-Based Estimation of Default Probabilities and Its Application to Financial Market Surveillance,” IMF Working Paper No. 06/104.
- Sun, Zhao, David Munves and David T. Hamilton, 2012, “Public Firm Expected Default Frequency (EDFTM) Credit Measures: Methodology, Performance, and Model Extensions”, Moody’s Analytics – Capital Market Research.
- Altman, Edward, Neil Fargher and Egon Kalotay, 2011, “A Simple Empirical Model of Equity-Implied Probabilities of Default” Journal of Fixed Income, Vol. 20 (3), pp. 71-85.
- Jobst, Andreas A. and Dale Gray, 2013, “Systemic Contingent Claims Analysis – Estimating Market-Implied Systemic Risk,” IMF Working Paper 13/54.

### Jump-diffusion and advanced asset-pricing models
- Kou, S.G, 2008, “Jump-Diffusion Models for Asset Pricing in Financial Engineering,” Chapter 2 in Handbooks in Operational Research and Management Science, Eds. J.R. Birge and V. Linetsky, Vol. 15, Elsevier.
- Zhou, Chunsheng, 1997, “A Jump-Diffusion Approach to Modeling Credit Risk and Valuing Defaultable Securities,” Finance and Economics Discussion Series 1997-15, Board of Governors of the Federal Reserve System.
- Ardia, David, David, Juan, Arango, Ospina, and Gómez, Norman Diego Giraldo, 2011, “Jump-Diffusion Calibration Using Differential Evolution,” Wilmott, pp. 76–79.

### Empirical studies on default risk, credit spreads, and firm-level indicators
- Bonfim, Diana, 2009, “Credit risk drivers: Evaluating the contribution of firm level information and of macroeconomic dynamics”, Journal of Banking & Finance, Vol. 33, pp. 281–299.
- Hui, Cho-Hoi, Wong, Tak-Chuen, Lo, Chi-Fai, and Huang, Ming-Xi, 2005, “Benchmarking Model of Default Probabilities of Listed Companies,” Journal of Fixed Income, Vol. 15, No. 2, pp. 76-86.
- Chen, Yan and Guanglei Chu, 2014, “Estimation of Default Risk Based on KMV Model – An Empirical Study for Chinese Real Estate Companies,” Journal of Financial Risk Management, Vol. 3, pp. 40-49.
- Huang, Jing-Zhi and Ming Huang, 2012, “How Much of the Corporate-Treasury Yield Spread Is Due to Credit Risk?” Review of Asset Price Studies, Vol. 2 (2), pp. 153-202.
- Jacobson, Tor, Jesper Lindé and Kasper Roszbach, 2013, “Firm Default And Aggregate Fluctuations,” Journal of the European Economic Association, European Economic Association, Vol. 11 Issue.4, pp. 945-972.
- Benito, Andrew, Javier Delgado and Martínez Pagés, 2004, "A synthetic indicator of financial pressure for Spanish firms", Banco de España Working Paper, No.411.
- Zhang, Wenlang, Gaofeng Han and Steven Chan, 2014, “How Strong are the Linkages between Real Estate and Other Sectors in China?,” HKIMR Working Paper, No. 11.

### Rating agency studies and credit transition/default statistics
- Standard & Poor’s Rating Services, 2014, Default, Transition, and Recovery: 2013 Annual Global Corporate Default Study And Rating Transitions.
- Standard & Poor’s Rating Services, 2010, General Criteria: Stand-Alone Credit Profiles: One Component Of A Rating, (October).

### Methodological and econometric techniques
- Newey, W., and K. West, 1987, “A Simple, Positive Semidefinite, Heteroscedasticity and Autocorrelation Consistent Covariance Matrix,” Econometrica, Vol. 55, pp. 703-708.

### IMF and policy-related technical notes
- International Monetary Fund, 2011, “United Kingdom: Stress Testing the Banking Sector Technical Note,” Country Report No. 11/222 (Washington, D.C.: International Monetary Fund).

*Source: _wp15140 - REFERENCES*

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