18

Reading 60

Fixed Income · Credit Risk

MODULE 60.1: CREDIT RISK

LOS 60.a

Describe credit risk and its components, probability of default and loss given default.

Credit risk is the risk of loss to a fixed-income investor arising from the borrower's failure to make timely interest or principal payments (i.e., to service their debt). A borrower that fails to service their debt is said to be in default.

Drivers of credit risk are either borrower-specific (bottom-up) or related to the broader environment (top-down). They are commonly summarized as the Cs of credit analysis.

Bottom-up factors
  • Capacity — the borrower's ability to make debt payments on time.
  • Capital — other resources available to the borrower that reduce reliance on debt.
  • Collateral — value of assets pledged to provide the lender with security in default.
  • Covenants — legal terms agreed between borrowers and lenders as part of the bond issue.
  • Character — integrity of the borrower (e.g., management quality for a corporate bond) and commitment to honor obligations.
Top-down factors
  • Conditions — the general economic environment affecting all borrowers.
  • Country — geopolitical, legal, and political environment applicable to the debt.
  • Currency — FX fluctuations that affect a borrower's ability to service foreign-denominated debt.
中文翻譯

信用風險是固定收益投資人因借款人未能按期支付利息或本金(即「履約還款」)所產生的損失風險;未能履約者稱為違約

信用風險的驅動因素分為自下而上(針對借款人本身)與自上而下(針對整體環境),通常以信用分析的「C」歸納。

自下而上因素:

  • 償付能力(Capacity):借款人按時還款的能力。
  • 資本(Capital):可降低對債務依賴的其他資源。
  • 抵押品(Collateral):提供給債權人作為違約擔保的資產價值。
  • 契約條款(Covenants):發行時雙方約定的法律條款。
  • 品格(Character):借款方(公司債則指經營層)的誠信與履約意願。

自上而下因素:

  • 經濟條件(Conditions):影響所有借款人的總體環境。
  • 國家(Country):適用於該債務的地緣政治、法律與政治環境。
  • 幣別(Currency):匯率波動對外幣計價債務償還能力的影響。

Credit risk ultimately stems from the possibility that the borrower's sources of repayment do not generate enough cash to service its debt.

  • Secured corporate debt is backed primarily by operating cash flows and investments, plus cash flows from the pledged collateral.
  • Unsecured corporate debt relies only on operating cash flows and investments, plus secondary sources such as asset sales, divestitures, or new debt/equity issuance.
  • Sovereign debt is backed by tax revenue, tariffs, and government fees; secondary sources include further debt issuance and privatizations.

Corporate credit risk may be driven by weak economic conditions, intensifying competition, low profitability, or excessive leverage. Sovereign credit risk is shaped by economic and political weakness, persistent fiscal deficits, and a high debt-to-GDP ratio.

Analysts must distinguish two states:

  • Illiquid — unable to raise enough cash to service debt at a given moment.
  • Insolvent — total assets fall below total debt.

An illiquid issuer is not necessarily insolvent, but can still default.

When default occurs, indenture clauses determine how losses are distributed:

  • Cross-default — default on one bond issue triggers default on all issues of the same issuer.
  • Pari passu — bonds of the same class rank equally in the default process.

When unsecured debt has both pari passu and cross-default provisions, a default on any one issue gives every unsecured holder a claim on the issuer's general assets. For secured debtholders, such clauses give access to both the general assets and the specifically pledged collateral. Secured bondholders only suffer credit losses when the value of pledged assets falls below the amount of pari passu secured debt.

中文翻譯

信用風險的根本原因,是借款人的還款來源可能不足以履約。

  • 有擔保公司債:主要由公司營運現金流與投資、加上抵押品所產生的現金流支撐。
  • 無擔保公司債:僅由營運現金流與投資支撐,輔以資產出售、業務剝離或新發行債券/股票等次要來源。
  • 主權債:由稅收、關稅與政府收費支撐;次要來源包括新發債務及國有資產私有化。

公司信用風險來自景氣低迷、競爭激烈、獲利偏低或槓桿過高;主權信用風險則來自經濟政治不穩、財政赤字持續,以及債務佔 GDP 比重過高。

流動性不足(illiquid)是指當下籌不到現金;資不抵債(insolvent)是指資產低於負債。流動性不足的發行人未必資不抵債,但仍可能違約。

違約時債券契約條款決定損失分配:

  • 交叉違約(cross-default):任一檔債券違約則所有檔同時違約。
  • 同等受償(pari passu):同類債券具同等清償地位。

無擔保債若同時具備上述兩條款,違約後所有無擔保債權人對一般資產享有同等求償權;有擔保債權人除一般資產外,還可主張抵押品。只有當抵押品價值低於同等順位有擔保債務金額時,有擔保投資人才會出現信用損失。

Measuring Credit Risk

Credit risk is quantified through the expected loss from a debt investment in the event of default:

$$\text{expected loss} = \text{probability of default} \times \text{loss given default}$$

  • Probability of default (POD) — the probability that the borrower fails to make interest or principal payments when due, usually expressed as an annualized rate.
  • Loss given default (LGD) — the loss the investor suffers if the issuer defaults; can be a monetary amount or a percentage.
  • Expected recovery rate — the share of the claim recovered in default.
  • Loss severity — one minus the recovery rate (i.e., the share not recovered).
  • Expected exposure / exposure at default — the difference between the amount owed (principal plus accrued interest) and the value of available collateral.

Loss given default expressed as a percentage equals expected exposure times loss severity:

$$\text{LGD\%} = \text{expected exposure} \times (1 - \text{recovery rate})$$

教授提醒

Strictly, loss given default is a monetary amount and loss severity is the corresponding rate. However, the Level I curriculum often states LGD as a rate and uses it as a rate in examples; the definition is loose. Read each question carefully. In SchweserNotes, when LGD is used as a rate it is written LGD%.

中文翻譯

信用風險的衡量:以違約時的預期損失表達:

$$\text{預期損失} = \text{違約機率} \times \text{違約損失}$$

  • 違約機率(POD):借款人未能按時付息或還本的機率,通常以年化表示。
  • 違約損失(LGD):違約時投資人實際的損失,可表達為金額或百分比。
  • 預期回收率:違約時可回收的比例。
  • 損失嚴重度:1 減回收率,即未回收比例。
  • 預期暴險/違約暴險:應收金額(本金加應計利息)與可用抵押品價值之差。

以百分比表示的違約損失:

$$\text{LGD\%} = \text{預期暴險} \times (1 - \text{回收率})$$

教授提醒:嚴格定義下,LGD 為金額、損失嚴重度才是比率,但 Level I 常把 LGD 直接當作比率使用,定義較寬鬆,作答時須仔細辨認;本講義以 LGD% 表示比率形式。

The annualized expected loss (in percentage terms) approximates the credit spread an investor should demand over a risk-free benchmark for bearing the issue's credit risk:

$$\text{credit spread} \approx \text{POD} \times \text{LGD\%}$$

  • If the actual spread exceeds this estimated spread, investors are more than fairly compensated for credit risk.
  • If the actual spread is below the estimate, investors are inadequately compensated and should avoid the bond.
EXAMPLE — Expected loss and credit spreads

A bond issuer has a 3% probability of default; one of its bonds has a recovery rate of 75%. The bond carries a 4% coupon and trades at par. A government security of similar maturity yields 2.5%. Is the credit spread adequate compensation for credit risk?

Answer

Trading at par means yield equals coupon (4%). Actual spread = 4% − 2.5% = 1.5%.

Estimated spread = POD × (1 − recovery rate) = 0.03 × (1 − 0.75) = 0.0075 = 0.75%.

The actual spread is double the fair spread, so investors are more than adequately compensated for credit risk.

中文翻譯

以百分比表示的年化預期損失,可作為投資人對信用風險所要求的相對於無風險基準的合理信用利差

$$\text{信用利差} \approx \text{違約機率} \times \text{LGD\%}$$

  • 實際利差大於估計值:投資人獲得超額補償。
  • 實際利差小於估計值:補償不足,應避免投資。

例題:違約機率 3%、回收率 75%、票面利率 4% 平價交易、同期公債殖利率 2.5%。

  • 實際利差 = 4% − 2.5% = 1.5%
  • 估計利差 = 0.03 × (1 − 0.75) = 0.75%
  • 實際是合理利差的兩倍,投資人對信用風險獲得超額補償。

To assess required returns from credit-risky bonds, an analyst must estimate POD for the issuer and LGD for the specific issue.

Probability of default can be assessed via quantitative measures of capacity to repay. A high-credit-quality issuer (low POD) typically shows:

  • Strong profitability (high EBIT margin)
  • High interest coverage ratio (EBIT / interest)
  • Low leverage multiples (e.g., debt / EBITDA)
  • High cash flow to net debt

Loss given default depends on whether the bond is secured or unsecured and on its seniority in the capital structure. More senior, secured debt typically has a smaller LGD than junior, unsecured debt.

Investment grade issuers have a lower POD than high-yield issuers due to greater financial strength. However, high-yield bonds are often secured with secondary repayment sources, so high-yield secured debt can have a lower LGD than unsecured investment-grade debt. The dominant risk for unsecured investment-grade investors is therefore not rising LGD but a rising POD as the issuer's financial condition deteriorates.

教授提醒

The terms investment grade and high yield are formally defined in terms of credit ratings, covered next.

中文翻譯

分析師需估計發行人之違約機率與該檔債券的違約損失。

違約機率可由償付能力的量化指標衡量。優質信用發行人通常具備:高 EBIT 利潤率、高利息保障倍數、低槓桿(債務/EBITDA 低)、現金流對淨債務比率高。

違約損失取決於是否有擔保以及在資本結構中的順位:順位高、有擔保的債權違約損失較小。

投資等級發行人因財務體質佳,違約機率低於非投資等級。但非投資等級往往為有擔保債並具次要還款來源,因此其 LGD 可能低於投資等級之無擔保債。對於投資等級無擔保投資人而言,主要風險不是 LGD 上升,而是發行人體質惡化導致違約機率上升。

教授提醒:「投資等級」與「非投資等級(高收益)」是依信用評等正式定義的,下節說明。

LOS 60.b

Describe the uses of ratings from credit rating agencies and their limitations.

Credit rating agencies assign forward-looking ratings to both bond issuers and individual bond issues, based on qualitative and quantitative credit risk factors.

Common uses of credit ratings include:

  • Comparing credit risk across issuers, industries, and bond types, and tracking changes in credit conditions over time.
  • Assessing credit migration risk — the risk that a rating downgrade reduces bond value and may trigger contractual clauses.
  • Meeting regulatory, statutory, or contractual requirements (e.g., investment mandates that restrict holdings to investment grade).
中文翻譯

信評機構針對發行人與個別債券發行給予前瞻性評級,綜合質化與量化信用風險因素。

信用評級的常見用途:

  • 跨發行人、跨產業、跨債券類別比較信用風險,並追蹤信用情況變化。
  • 評估信用遷移風險:評等下調將降低債券價值,並可能觸發合約條款。
  • 滿足監管、法規或合約要求(例如僅允許投資等級的投資授權)。
Figure 60.1: Credit Rating Categories
Investment Grade Non-investment Grade (High-Yield)
Moody'sS&P / Fitch Moody'sS&P / Fitch*
AaaAAABa1BB+
Aa1AA+Ba2BB
Aa2AABa3BB−
Aa3AA−B1B+
A1A+B2B
A2AB3B−
A3A−Caa1CCC+
Baa1BBB+Caa2CCC
Baa2BBBCaa3CCC−
Baa3BBB−CaCC
CC
CD

*Fitch omits +/− symbols for the CCC rating.

Triple A (AAA / Aaa) is the highest rating. Bonds rated Baa3 / BBB− or higher are investment grade; bonds rated Ba1 / BB+ or lower are non-investment grade, also called high-yield or junk bonds. Bonds in default are rated D by S&P and Fitch and fall in Moody's lowest category, C.

中文翻譯

信用評級對照(圖60.1):三大機構(Moody's、S&P、Fitch)的評級從最高 AAA/Aaa 起依序遞降。

  • 投資等級:Baa3/BBB− 以上。
  • 非投資等級(高收益/垃圾債):Ba1/BB+ 以下。
  • 違約:S&P/Fitch 評為 D;Moody's 歸入最低類 C。
  • Fitch 對 CCC 等級不使用 +/− 符號。

Relying on rating agency ratings carries risks:

  1. Ratings lag market pricing. Market prices and credit spreads can move much faster than ratings. Two bonds with the same rating may trade at different yields — ratings focus on expected loss, while distressed-debt prices focus more on default timing and expected recoveries.
  2. Some risks are hard to assess. Litigation, natural disasters, environmental risks, acquisitions, and debt-funded equity buybacks are difficult to predict and may not be captured in ratings. Different agencies may take different views, producing split ratings.
  3. Agencies make mistakes. Subprime mortgage securities famously received ratings far above what they deserved before the 2008–2009 global financial crisis. Corporate fraud has also caused highly rated firms to default suddenly.

Investors should perform their own due diligence and not rely solely on ratings. Investors who trade in anticipation of rating changes will outperform those who trade in reaction to them.

中文翻譯

過度依賴評級存在以下風險:

  1. 評級落後市場:市場價格與信用利差變化遠快於評等。同一評等的兩檔債券可能因市場聚焦違約時點與回收差異而以不同殖利率交易。
  2. 部分風險難以評估:訴訟、天災、環境、併購、舉債回購等事件難以預測,不同機構看法不同會產生分歧評等(split ratings)。
  3. 評級機構也會犯錯:2008–2009 金融危機前次貸證券獲得遠高於實質風險的評等;企業舞弊亦曾使高評等公司突然違約。

投資人應自行盡職調查;能預判評級變動者績效遠優於僅事後反應者。

LOS 60.c

Describe macroeconomic, market, and issuer-specific factors that influence the level and volatility of yield spreads.

Credit spread risk is the risk that yield spreads widen due to deteriorating conditions, causing prices of credit-risky bonds to fall. For investment-grade investors this is the primary credit concern, since outright default is unlikely to be sudden — the realistic worry is spread widening as conditions worsen. Spread risk arises from macroeconomic, issuer-specific, and market (trading-related) factors.

Macroeconomic factors

Credit risk follows the economic cycle: in expansions, POD falls and spreads contract; in recessions, POD rises and spreads widen. Typical patterns:

  • Investment-grade issuers have lower yield spreads than high-yield issuers because expected loss is lower.
  • Yield spreads usually increase with maturity because POD rises over longer horizons, producing upward-sloping credit spread curves (spread vs. maturity).
    • In contractions, both investment-grade and high-yield curves rise and flatten as near-term default risk increases. The high-yield curve may even invert (slope downward) at this stage.
    • In expansions, both curves fall and steepen as near-term default risk decreases. Curves are at their lowest and steepest near the cycle peak.
  • Across issuers, the dispersion of high-yield spreads is wider than that of investment-grade spreads.
  • High-yield spreads fluctuate more than investment-grade spreads as conditions change. In crises, high-yield spreads can widen sharply during a flight to quality, and bid-offer spreads on (less liquid) high-yield debt may widen more than on investment-grade debt.
教授提醒

Two different "spreads" appear here:

  • Yield spread — extra yield over a risk-free benchmark.
  • Bid-offer spread — difference between dealer buy and sell prices.

Read each question carefully, especially when the question links the liquidity component of yield spread to the size of bid-offer spreads.

中文翻譯

信用利差風險是指因情勢惡化導致利差擴大、信用風險債券價格下跌的風險;對投資等級投資人而言,違約少見且突然,主要顧慮就是利差擴大造成的價格損失。

總體經濟因素:信用風險隨景氣循環變化。擴張時違約機率下降、利差收窄;衰退時違約機率上升、利差擴大。典型樣態:

  • 投資等級利差低於高收益。
  • 利差通常隨期限拉長而上升,形成向上傾斜的信用利差曲線。
    • 衰退期:兩種曲線均上移並趨平坦,高收益曲線甚至可能倒掛(向下傾斜)。
    • 擴張期:兩種曲線均下移並更陡峭,景氣高峰時最低且最陡。
  • 跨發行人之間,高收益利差離散度大於投資等級。
  • 高收益利差波動度大於投資等級;危機時資金避險(flight to quality)使高收益利差急劇擴大,且因流動性差,買賣價差也擴大得更多。

教授提醒:注意兩種利差不要混淆——殖利率利差(yield spread)是相對於無風險基準的額外殖利率;買賣價差(bid-offer spread)是交易商買賣價格差異。題目可能用買賣價差判斷殖利率利差中的流動性成分。

Holding high-yield debt is riskier in spread terms (more volatile spreads) but offers higher yield. Other reasons investors take this exposure:

  • Diversification — high-yield prices have low or negative correlation with investment-grade prices, diversifying a fixed-income portfolio.
  • Capital appreciation — larger spread tightening during recoveries produces larger price gains than for investment-grade.
  • Equity-like returns — empirical data suggests high-yield offers equity-like returns with lower volatility than equities.

Other systematic forces that can push yield spreads higher:

  • Tighter regulation of broker-dealers and corporate bond market makers raises the cost of funding bond positions.
  • Funding stresses across markets can heighten risk aversion.
  • Heavy new bond issuance may not be matched by investor demand.
中文翻譯

持有高收益債的利差波動較大但殖利率也較高。其他誘因:

  • 分散:與投資等級相關性低甚至為負,可分散固定收益組合。
  • 資本利得:景氣復甦時利差大幅收窄帶來較大價格漲幅。
  • 類股票報酬:實證上提供類似股票的報酬但波動較低。

會推升利差的其他系統性因素:

  • 對經紀自營商與做市商加強監管,提高債券融資部位成本。
  • 市場資金壓力升高使風險規避增強。
  • 新債發行供給過大,需求未能跟上。
Issuer-specific factors

The financial performance of the issuer materially affects the level and volatility of its bond spreads. Investors compare an issuer's spread to the average for its rating cohort: an issuer with debt-service problems will trade wider than the average for its rating.

Market factors

Market liquidity risk reflects the cost of trading a bond, often assessed via the dealer's bid-offer spread. A wider bid-offer spread means higher trading costs and higher liquidity risk.

  • Issuers with more debt outstanding or higher credit ratings tend to have more actively traded bonds (narrower bid-offer spreads, lower liquidity risk).
  • Liquidity risk is higher for less actively traded bonds, lower-quality issuers, and issuers with little debt outstanding.
  • Bid-offer spreads can widen sharply for high-yield issuers during financial stress; rising risk aversion may then spill over to investment-grade names too.

Dealer bid-offer spreads can be used to isolate the liquidity component of yield spread: compute the yield at the bid price and at the offer price; the difference is treated as the liquidity spread, and the remaining spread is attributed to credit risk.

中文翻譯

發行人因素:發行人財務體質直接影響其債券利差水準與波動。投資人會將其利差與同評等平均比較;履約困難者通常較同評等平均更

市場因素:市場流動性風險反映交易成本,常以買賣價差衡量;買賣價差越寬代表流動性風險越高。

  • 債務存量大或評等高的發行人交易較活躍(買賣價差較窄)。
  • 交易冷清、信用差、發行量小者流動性風險較高。
  • 金融壓力期間,高收益買賣價差急劇擴大;風險規避甚至會擴散到投資等級。

可用買賣價差分離利差中的流動性成分:用買價計算殖利率與用賣價計算殖利率,兩者之差視為流動性利差,剩餘部分視為信用利差。

EXAMPLE — Decomposing yield spread into liquidity and credit spreads

A 10-year bond pays an annual coupon of 5% and is quoted bid/offer at 99.5/100.5. The benchmark 10-year yield is 3%. Decompose the yield spread.

Answer

Mid price = (99.5 + 100.5) / 2 = 100. At par, yield = coupon = 5%. Yield spread over benchmark = 5% − 3% = 2%.

Yield at bid (PV = −99.5, PMT = 5, FV = 100, N = 10) → I/Y ≈ 5.065%.

Yield at offer (PV = −100.5, PMT = 5, FV = 100, N = 10) → I/Y ≈ 4.935%.

Liquidity spread = 5.065% − 4.935% = 0.13%.

Credit spread = 2% − 0.13% = 1.87%.

The price impact of a change in spread can be estimated using the bond's duration and convexity, replacing the yield change with the spread change:

$$\Delta(\text{full price}) \approx -\text{ModDur} \cdot \Delta\text{Spread} + \tfrac{1}{2}\,\text{convexity}\,(\Delta\text{Spread})^2$$

中文翻譯

例題(分解利差):10 年期債券,5% 年息,買賣報價 99.5/100.5,基準殖利率 3%。

  • 中價 = (99.5 + 100.5) / 2 = 100;平價時殖利率 = 票息 = 5%;殖利率利差 = 5% − 3% = 2%。
  • 買價殖利率 ≈ 5.065%;賣價殖利率 ≈ 4.935%。
  • 流動性利差 = 5.065% − 4.935% = 0.13%。
  • 信用利差 = 2% − 0.13% = 1.87%。

利差變動對全價的影響可用存續期間與凸性近似(將殖利率變動換為利差變動):

$$\Delta(\text{全價}) \approx -\text{ModDur} \cdot \Delta\text{Spread} + \tfrac{1}{2}\,\text{凸性}\,(\Delta\text{Spread})^2$$

Module Quiz 60.1
1. The two components of expected loss are:
  • A. default risk and yield spread.
  • B. probability of default and loss severity.
  • C. loss severity and yield spread.
B — Expected loss is composed of probability of default and loss severity. Yield spread reflects credit risk but is a result of expected loss, not a component of it. (LOS 60.a)
2. Expected loss can decrease with an increase in a bond's:
  • A. probability of default.
  • B. loss severity.
  • C. recovery rate.
C — A higher recovery rate means lower loss severity, which decreases expected loss. (LOS 60.a)
3. Which of the following factors in credit analysis is least likely a top-down factor?
  • A. Capital.
  • B. Conditions.
  • C. Currency.
A — Top-down factors are country, conditions, and currency. Capital is a bottom-up factor relating to the issuer's reliance on debt and other funding sources. (LOS 60.b)
4. Higher credit risk is indicated by a higher:
  • A. cash flow / debt ratio.
  • B. debt / EBITDA ratio.
  • C. EBITDA / interest expense ratio.
B — A higher debt / EBITDA ratio indicates higher leverage and higher credit risk. Higher cash flow / debt and EBITDA / interest expense ratios indicate lower credit risk. (LOS 60.a)
5. Compared to other firms in the same industry, an issuer with a credit rating of AAA is most likely to have a lower:
  • A. cash flow / debt ratio.
  • B. operating margin.
  • C. debt / capital ratio.
C — A low debt / capital ratio indicates low leverage. An AAA issuer would typically have a high operating margin and a high cash flow / debt ratio compared to peers. (LOS 60.a)
6. Credit spreads tend to widen as:
  • A. the credit cycle improves.
  • B. economic conditions worsen.
  • C. broker-dealers become more willing to provide capital.
B — Credit spreads widen as economic conditions worsen. Spreads narrow as the credit cycle improves and as broker-dealers commit more capital to bond markets. (LOS 60.c)
7. Compared to shorter-duration bonds, longer-duration bonds:
  • A. have smaller bid-ask spreads.
  • B. are less sensitive to credit spreads.
  • C. have less certainty regarding future creditworthiness.
C — Longer-duration bonds usually have longer maturities and so carry more uncertainty about future creditworthiness. (LOS 60.c)
Key Concepts — Reading 60
LOS 60.a

Credit risk is the chance that a borrower fails to pay scheduled interest or principal.

Bottom-up factors: capacity, capital, collateral, character, covenants. Top-down factors: country, conditions, currency.

Credit risk is measured by expected loss, the product of probability of default (POD) and loss given default (LGD). As a percentage, expected loss approximates the credit spread investors should demand:

$$\text{credit spread} \approx \text{POD} \times \text{LGD\%}$$

LGD as a rate is also called loss severity = 1 − recovery rate.

A profitable issuer with high EBIT margin, high interest coverage, low leverage, and high cash flow to net debt has low POD. More senior, secured debt has lower LGD than junior, unsecured debt.

LOS 60.b

Credit ratings reflect an issuer's or issue's overall creditworthiness and the likelihood of full repayment. Investment grade = BBB− / Baa3 and above; non-investment grade (high-yield) = BB+ / Ba1 and below.

Investors should not rely solely on agency ratings because:

  • Agencies cannot always judge credit risk accurately.
  • Firms face unforeseen events that ratings do not reflect.
  • Market prices often adjust faster than ratings.
LOS 60.c

An issue's yield spread over its benchmark reflects both credit risk and liquidity risk.

Spread level and volatility are influenced by the credit and business cycles, broker-dealer capital availability, supply and demand for new issues, and issuer financial performance.

Spreads narrow when the credit cycle improves, the economy is expanding, and demand for new issues is strong; they widen when the credit cycle, economy, and markets weaken, when supply is heavy, or when dealer capital is scarce.

The liquidity spread can be estimated as the bond's bid-yield minus offer-yield; the remainder of the yield spread is the credit spread.

Given an expected change in spread, duration and convexity estimate the price impact:

$$\Delta(\text{full price}) \approx -\text{ModDur}\,\Delta\text{Spread} + \tfrac{1}{2}\,\text{convexity}\,(\Delta\text{Spread})^2$$

中文翻譯 — 重點整理

【LOS 60.a】信用風險=借款人未能按時付息/還本之風險。自下而上:償付能力、資本、抵押品、品格、契約條款;自上而下:國家、經濟條件、幣別。預期損失 = 違約機率 × 違約損失;信用利差 ≈ POD × LGD%。LGD 作為比率即為損失嚴重度(1 − 回收率)。獲利強、利息保障倍數高、槓桿低、現金流/淨債務高者違約機率低;順位高、有擔保的債券違約損失低。

【LOS 60.b】BBB−/Baa3 以上為投資等級;BB+/Ba1 以下為非投資等級(高收益/垃圾債)。不應僅依賴信評:①機構並非永遠正確;②不可預測事件未被反映;③市場價格往往比評等更快調整。

【LOS 60.c】殖利率利差包含信用風險與流動性風險。受景氣/信用循環、經銷商資金供給、新債供需與發行人體質影響。景氣好、需求強時利差收窄;景氣差、供給多、做市資金不足時利差擴大。流動性利差 = 買價殖利率 − 賣價殖利率;剩餘部分為信用利差。利差變動對全價影響可用 ModDur 與凸性近似。

0% 0:00 / 0:00
0%