fixed-income-corporate

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Original

English

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Translation

Chinese

Fixed Income — Corporate

固定收益——公司债

Purpose

用途

Analyze corporate bonds and credit instruments including investment grade and high yield debt. This skill covers credit spread measurement (G-spread, Z-spread, OAS), credit rating frameworks, default and recovery analysis, callable bond structures, covenant analysis, and private credit fundamentals.

分析公司债券及信贷工具，包括投资级和高收益债券。本skill涵盖信用利差计量（G-spread、Z-spread、OAS）、信用评级框架、违约与回收分析、可赎回债券结构、契约条款分析以及私募信贷基础。

Layer

层级

2 — Asset Classes

2 — 资产类别

Direction

适用方向

both

双向

When to Use

使用场景

User asks about corporate debt, corporate bonds, or credit risk
User asks about credit spreads (OAS, Z-spread, G-spread)
User asks about credit ratings, rating migration, or default probabilities
User asks about investment grade vs high yield bonds
User asks about callable bonds, yield-to-call, or yield-to-worst
User asks about covenants, recovery rates, or loss given default
User asks about private credit, direct lending, or mezzanine debt
User asks about CDS (Credit Default Swaps) or market-implied default probabilities

当用户询问公司债务、公司债券或信用风险时
当用户询问信用利差（OAS、Z-spread、G-spread）时
当用户询问信用评级、评级迁移或违约概率时
当用户询问投资级与高收益债券的区别时
当用户询问可赎回债券、赎回收益率（YTC）或最差收益率（YTW）时
当用户询问契约条款、回收率或违约损失率时
当用户询问私募信贷、直接贷款或夹层债务时
当用户询问CDS（信用违约互换）或市场隐含违约概率时

Core Concepts

核心概念

Credit Spreads

信用利差

Compensation for default risk, liquidity risk, and downgrade risk above the risk-free rate. Multiple spread measures exist with increasing precision:

G-spread (Government Spread): Bond yield minus interpolated Treasury yield of the same maturity. Simple but assumes a flat term structure between benchmark maturities.

Z-spread (Zero-Volatility Spread): The constant spread added to each point on the risk-free spot rate curve such that the sum of discounted cash flows equals the bond's market price. Superior to G-spread because it accounts for the full shape of the term structure.

OAS (Option-Adjusted Spread): For bonds with embedded options, OAS = Z-spread minus the value of the embedded option. OAS represents the "true" credit compensation after removing the option component. Requires an interest rate model to compute.

是对无风险利率之上违约风险、流动性风险和降级风险的补偿。存在多种精度逐步提升的利差计量方式：

G-spread（国债利差）：债券收益率减去同期限插值后的国债收益率。计算简单，但假设基准期限之间的收益率曲线是平坦的。

Z-spread（零波动利差）：在无风险即期收益率曲线的每个时点上添加的恒定利差，使得折现后的现金流总和等于债券的市场价格。相比G-spread更优，因为它考虑了收益率曲线的完整形态。

OAS（期权调整利差）：对于含嵌入期权的债券，OAS = Z-spread - 嵌入期权价值。OAS代表剔除期权成分后的“真实”信用补偿，计算时需要用到利率模型。

Credit Ratings

信用评级

AAA/AA/A/BBB are investment grade. BB/B/CCC/CC/C/D are high yield (speculative grade). The BBB/BB boundary is the most consequential threshold — many institutional mandates prohibit sub-investment-grade holdings. A downgrade across this boundary ("fallen angel") forces selling by constrained investors.

AAA/AA/A/BBB为投资级，BB/B/CCC/CC/C/D为高收益级（投机级）。BBB/BB的分界是最关键的阈值——许多机构的投资指令禁止持有投机级债券。跨过分界的降级（“堕落天使”）会迫使受约束的投资者抛售债券。

Migration Matrix

评级迁移矩阵

A transition matrix shows the probability of moving from one rating to another over a 1-year horizon. A BBB-rated issuer has roughly 85-90% probability of remaining BBB, 4-5% chance of upgrade, 4-5% chance of downgrade, and a small probability (~0.2%) of default. Migration matrices are published annually by rating agencies.

是一个转换矩阵，显示1年内评级从一个级别迁移至另一个级别的概率。BBB评级的发行人约有85-90%的概率维持BBB评级，4-5%的概率升级，4-5%的概率降级，违约概率极低（约0.2%）。评级机构每年会发布迁移矩阵。

Default Probability, Loss Given Default, and Recovery Rate

违约概率、违约损失率与回收率

PD = Probability of Default over a given horizon
LGD = Loss Given Default (percentage of exposure lost)
Recovery Rate (RR) = 1 - LGD
Expected Loss: EL = PD × LGD × EAD (Exposure at Default)

Recovery rates vary by seniority: senior secured (60-65%), senior unsecured (40-50%), subordinated (20-30%).

PD = 特定时间段内的违约概率
LGD = 违约损失率（违约时损失的敞口比例）
回收率（RR）= 1 - LGD
预期损失：EL = PD × LGD × EAD（违约时敞口）

回收率因债务优先级不同而差异显著：优先有担保债务（60-65%）、优先无担保债务（40-50%）、次级债务（20-30%）。

Callable Bonds

可赎回债券

The issuer can redeem the bond early. Call schedules specify prices and dates. Yield-to-call (YTC) is calculated using the call date and call price. Yield-to-worst (YTW) is the minimum of YTM and all possible YTCs. For callable bonds, OAS is the appropriate spread measure (not G-spread or Z-spread).

发行人可提前赎回债券。赎回条款会明确赎回价格和日期。赎回收益率（YTC）基于赎回日期和赎回价格计算。最差收益率（YTW）是到期收益率（YTM）与所有可能的YTC中的最小值。对于可赎回债券，应使用OAS作为合适的利差计量指标（而非G-spread或Z-spread）。

Covenants

契约条款

Maintenance covenants: Tested periodically (e.g., quarterly). Issuer must maintain financial ratios at all times. Common in bank loans.

Incurrence covenants: Tested only when the issuer takes a specific action (e.g., issues new debt). Common in bond indentures. Key covenants include leverage ratio (Debt/EBITDA), interest coverage (EBITDA/Interest), and restricted payments.

维持性条款：定期测试（如按季度）。发行人必须始终维持特定财务比率。常见于银行贷款。

触发型条款：仅当发行人采取特定行动（如发行新债务）时才会触发测试。常见于债券契约。关键条款包括杠杆率（债务/EBITDA）、利息覆盖率（EBITDA/利息支出）以及限制性支付。

Private Credit

私募信贷

Direct lending by non-bank lenders to middle-market companies. Offers an illiquidity premium of 150-400bp over comparable syndicated loans. Typically features stronger covenant protection than public market deals. Valuations are mark-based (quarterly), which smooths reported volatility.

由非银行贷款人直接向中型企业提供的贷款。相比可比的银团贷款，可获得150-400个基点的流动性溢价。通常比公开市场交易具有更强的契约保护。估值采用按市值计价（按季度），可平滑报告的波动率。

CDS (Credit Default Swaps)

CDS（信用违约互换）

A derivative where the protection buyer pays a periodic spread and receives payment upon a credit event. CDS spreads can be used to derive market-implied default probabilities. CDS spreads are often more responsive to credit deterioration than bond spreads.

一种衍生品，保护买方定期支付利差，在发生信用事件时获得赔付。CDS利差可用于推导市场隐含的违约概率。CDS利差通常比债券利差更早对信用恶化做出反应。

Key Formulas

核心公式

Formula	Expression	Use Case
G-spread	Bond Yield - Interpolated Treasury Yield	Simple spread measure
Z-spread	Constant spread s: P = sum CF_t / (1+s_t+s)^t	Full curve spread
OAS	Z-spread - Option Cost	Spread for callable bonds
Expected Loss	EL = PD × LGD × EAD	Credit loss estimation
Recovery Rate	RR = 1 - LGD	Recovery from default
Yield-to-Worst	min(YTM, YTC_1, YTC_2, ...)	Conservative yield measure

公式	表达式	适用场景
G-spread	债券收益率 - 插值后的国债收益率	简单利差计量
Z-spread	恒定利差s：P = Σ CF_t / (1+s_t+s)^t	全曲线利差计量
OAS	Z-spread - 期权成本	可赎回债券利差
预期损失	EL = PD × LGD × EAD	信用损失估算
回收率	RR = 1 - LGD	违约后回收计算
最差收益率	min(YTM, YTC_1, YTC_2, ...)	保守型收益率计量

Worked Examples

示例演算

Example 1: Compare Z-spread vs G-spread

示例1：比较Z-spread与G-spread

Given: A 7-year corporate bond yields 5.8%. The 7-year interpolated Treasury yield is 4.5%. The Z-spread (computed using the full spot curve) is 118bp. Calculate: G-spread and compare to Z-spread Solution: G-spread = 5.8% - 4.5% = 1.30% = 130bp Z-spread = 118bp The G-spread (130bp) exceeds the Z-spread (118bp) by 12bp. This difference arises because the G-spread uses a single interpolated benchmark point while the Z-spread properly accounts for the shape of the entire yield curve. In a steep curve environment, G-spread tends to overstate the true spread.

已知： 一只7年期公司债券收益率为5.8%。7年期插值后的国债收益率为4.5%。基于完整即期曲线计算的Z-spread为118个基点。 计算： G-spread并与Z-spread比较 解答： G-spread = 5.8% - 4.5% = 1.30% = 130个基点 Z-spread = 118个基点 G-spread（130个基点）比Z-spread（118个基点）高出12个基点。这种差异源于G-spread使用单一插值后的基准点，而Z-spread恰当地考虑了整个收益率曲线的形态。在收益率曲线陡峭的环境中，G-spread往往会高估真实利差。

Example 2: Expected Loss Calculation

示例2：预期损失计算

Given: PD = 2% (annual), LGD = 60%, EAD = $1,000,000 Calculate: Expected annual loss Solution: EL = PD × LGD × EAD EL = 0.02 × 0.60 × $1,000,000 EL = $12,000

The expected annual credit loss is $12,000, or 1.2% of the exposure. This represents the actuarial cost of credit risk — the spread must at least cover this expected loss, with additional compensation for unexpected losses and risk aversion.

已知： PD = 2%（年化），LGD = 60%，EAD = 1,000,000美元 计算： 年化预期损失 解答： EL = PD × LGD × EAD EL = 0.02 × 0.60 × 1,000,000美元 EL = 12,000美元

年化预期信用损失为12,000美元，即敞口的1.2%。这代表信用风险的精算成本——利差至少需要覆盖该预期损失，同时还要为非预期损失和风险厌恶提供额外补偿。

Common Pitfalls

常见误区

Using G-spread for callable bonds — use OAS instead, which removes the option component
Ignoring liquidity premium in spread analysis — part of the spread compensates for illiquidity, not just default risk
Rating agency lag vs market-implied credit quality — CDS spreads often move before rating actions
Assuming recovery rates are constant — they vary significantly by seniority and economic cycle (lower in recessions)

对可赎回债券使用G-spread——应改用OAS，因为它剔除了期权成分
在利差分析中忽略流动性溢价——利差的一部分是对流动性不足的补偿，而非仅针对违约风险
评级机构滞后与市场隐含信用质量——CDS利差往往在评级调整之前就已变动
假设回收率恒定——回收率因债务优先级和经济周期（衰退期更低）而存在显著差异

Cross-References

交叉引用

Layer 2:
```
fixed-income-sovereign
```
for the Treasury curve used as the risk-free benchmark
Layer 2:
```
fixed-income-structured
```
for CLOs and structured credit products
Layer 2:
```
alternatives
```
for private credit as an alternative investment
Layer 3:
```
portfolio-construction
```
for credit allocation in multi-asset portfolios

层级2：
```
fixed-income-sovereign
```
（作为无风险基准的国债曲线）
层级2：
```
fixed-income-structured
```
（担保债务凭证（CLO）及结构化信贷产品）
层级2：
```
alternatives
```
（作为另类投资的私募信贷）
层级3：
```
portfolio-construction
```
（多资产组合中的信贷配置）

Reference Implementation

参考实现

See

scripts/fixed_income_corporate.py

for computational helpers.

计算辅助工具请参见

scripts/fixed_income_corporate.py

。