Credit Risk

Fixed Income

Sources of Credit Risk

Learning Outcome Statement:

describe credit risk and its components, probability of default and loss given default

Summary:

Credit risk refers to the risk that a borrower will default on any type of debt by failing to make required payments. The main components of credit risk include the probability of default (POD) and loss given default (LGD). Credit risk can be influenced by several factors including the borrower's financial health, economic conditions, and the nature of the lending agreement.

Key Concepts:

Probability of Default (POD)

POD is the likelihood that an issuer will fail to make full and timely payments of principal and interest. It is typically an annualized measure and reflects the borrower's financial stability and external economic conditions.

Loss Given Default (LGD)

LGD represents the investor's loss conditional on an issuer event of default. It combines the severity of loss under a default scenario with the amount of the investor’s claim at the time of default. LGD is calculated as the product of expected exposure and (1 - recovery rate).

Recovery Rate (RR)

RR is the percentage of an outstanding debt claim recovered when an issuer defaults. It affects the LGD as the unrecovered portion of the claim.

Expected Loss (EL)

EL is the probability-weighted potential loss for a given period, calculated as the product of POD and LGD. It represents the expected economic loss under a potential borrower default over the life of the contract.

Credit Spread

Credit spread is the yield difference between a corporate bond and a risk-free government bond, reflecting the compensation investors demand for bearing credit risk. It is approximated by the product of POD and LGD.

Formulas:

Expected Loss

EL = POD \times LGD

This formula calculates the expected loss by multiplying the probability of default by the loss given default.

Variables:

$EL$ :: Expected Loss
$POD$ :: Probability of Default
$LGD$ :: Loss Given Default

Units: percentage or monetary value

Loss Given Default

LGD = EE \times (1 - RR)

This formula calculates the loss given default by multiplying the expected exposure by the unrecovered portion of the claim.

Variables:

$LGD$ :: Loss Given Default
$EE$ :: Expected Exposure
$RR$ :: Recovery Rate

Units: percentage or monetary value

Credit Rating Agencies and Credit Ratings

Learning Outcome Statement:

describe the uses of ratings from credit rating agencies and their limitations

Summary:

Credit rating agencies such as Moody's, S&P, and Fitch play a crucial role in assessing issuer credit risk and providing ratings that indicate the potential risk of default. These ratings are used by investors for comparability and risk assessment, and are subject to regulatory and contractual requirements. However, ratings can lag market conditions, may not capture all risks, and have been criticized for past inaccuracies, such as during the 2008 financial crisis.

Key Concepts:

Credit Rating Agencies

Agencies like Moody's, S&P, and Fitch provide independent assessments of the credit risk associated with bond issuers and their issues, using both quantitative and qualitative analyses.

Credit Ratings

Symbol-based measures provided by rating agencies that indicate the likelihood of default and potential loss. These ratings range from high-quality (e.g., AAA) to speculative grades (e.g., BB or lower).

Uses of Credit Ratings

Ratings facilitate the comparison of creditworthiness across issuers and industries, influence the pricing of bonds, and are used to meet regulatory and contractual obligations.

Limitations of Credit Ratings

Ratings may not promptly reflect market conditions, might overlook certain risks like litigation or environmental issues, and have historically failed in predicting major defaults, leading to financial crises.

Credit Rating Considerations

Investors are advised to conduct their own analysis rather than solely relying on ratings, as ratings can lag market pricing of credit risk and may not fully capture all relevant financial risks.

Formulas:

Expected Loss (EL)

EL = POD \times LGD

This formula calculates the expected loss by multiplying the probability of default by the loss given default.

Variables:

$POD$ :: Probability of Default
$LGD$ :: Loss Given Default

Units: percentage

Factors Impacting Yield Spreads

Learning Outcome Statement:

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

Summary:

Yield spreads, the difference in yields between different types of bonds, are influenced by macroeconomic factors, market factors, and issuer-specific factors. These factors affect the level and volatility of yield spreads, impacting the risk and return profile of bonds.

Key Concepts:

Macroeconomic Factors

Macroeconomic conditions such as economic growth, interest rates, and the credit cycle influence yield spreads. For example, during economic expansions, credit spreads typically narrow as the perceived credit risk decreases.

Market Factors

Market liquidity, the bid-ask spread, and overall market sentiment towards risk influence yield spreads. For instance, during financial distress, investors might prefer safer assets, causing spreads on riskier bonds to widen.

Issuer-Specific Factors

Factors such as an issuer's financial performance, credit rating changes, and the specifics of the bond issuance (like coupon rate and maturity) directly affect the yield spread of an issuer's bonds.

Price Impact of Spread Changes

Changes in yield spreads directly impact bond prices. An increase in spreads leads to a decrease in bond prices and vice versa. This relationship is quantified using bond duration and convexity metrics.

Formulas:

Price Impact of Spread Change

\%\Delta PV_{Full} = -(AnnModDur \times \Delta Spread) + \frac{1}{2} AnnConvexity \times (\Delta Spread)^2

This formula estimates the percentage change in the full price of a bond given a change in its yield spread. It incorporates both the first-order effect (duration) and the second-order effect (convexity).

Variables:

$AnnModDur$ :: Annualized Modified Duration
$AnnConvexity$ :: Annualized Convexity
$Delta Spread$ :: Change in Spread

Units: percentage

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