Welcome to Credit Analysis Models!

Welcome to one of the most practical chapters in the CFA Level II Fixed Income curriculum. In Level I, you learned the basics of bonds. Now, we are diving into the "detective work" of fixed income: Credit Analysis. Essentially, we are trying to answer one big question: "What is the probability that this borrower won't pay me back, and if they don't, how much will I actually lose?"

Don't worry if this seems math-heavy at first. We will break down the complex formulas into logical stories. Think of credit analysis like assessing a friend who wants to borrow $100—you look at what they own, what they owe, and how likely they are to keep their job!

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1. The Fundamentals: Expected Loss

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Before we look at complex models, we need to understand the "Big Three" components of credit risk. Everything in this chapter builds on these three variables.

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Expected Loss (EL) is the average loss a lender expects to suffer. It is calculated as:

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\( Expected \ Loss = Probability \ of \ Default \times Loss \ Given \ Default \)

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Let's break that down:

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  • Probability of Default (PD): The likelihood (0% to 100%) that the borrower fails to make full and timely payments.
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  • Loss Given Default (LGD): This is the percentage of the Exposure at Default (EAD) that you won't get back if a default happens.
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  • Recovery Rate: This is what you do get back. \( LGD = 1 - Recovery \ Rate \).
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Example: You lend a company $1,000. There is a 5% chance they will go bankrupt. If they do, you expect to recover 40 cents on the dollar ($400).
\nPD = 5%
\nRecovery Rate = 40%
\nLGD = 100% - 40% = 60%
\nExpected Loss = \( 5\% \times 60\% = 3\% \) of the total amount (or $30).

Quick Tip: Always distinguish between "Expected Loss" (the average) and "Unexpected Loss." Banks hold capital mainly to cover unexpected losses!

Key Takeaway:

Expected Loss is the product of how likely a default is and how much you lose when it happens. To minimize risk, you want both numbers to be as low as possible.

2. Credit Ratings vs. Credit Scores

While they sound similar, they are used in different contexts:

  • Credit Scores: Used for individuals and small businesses (e.g., FICO scores). They are usually based on historical behavior.
  • Credit Ratings: Used for corporate and government debt (e.g., Moody’s, S&P). These are "ordinal" rankings, meaning an 'AAA' is better than an 'AA', but it doesn't tell you exactly how much better in terms of a specific percentage.

The Limitation: Ratings can be "sticky." Rating agencies are often slow to downgrade a company even when its financials are worsening. This is why we need the Credit Models we are about to discuss!

3. Structural Models (The Merton Model)

Structural models are based on the internal "structure" of a company’s balance sheet. The most famous is the Merton Model.

The Core Idea: Think of a company's equity as a Call Option on its assets.
Imagine a company has debt of $100 due in one year.\n

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  • If the company's assets are worth $150 at the end of the year, the shareholders pay off the $100 debt and keep the remaining $50.
  • If the company's assets are only worth $80, the shareholders will "walk away" (default), leaving the assets to the bondholders. The equity is worth $0.

In this model, Default occurs when the Value of Assets < Face Value of Debt.

Key Formulas for Merton Model:

Using the Black-Scholes logic:
\( Value \ of \ Equity = Call(Assets, \ Strike=Debt) \)
\( Value \ of \ Debt = Assets - Equity \)

Distance to Default: This measures how many standard deviations the asset value is away from the default barrier (the debt level). A higher distance means a safer bond.

Advantages:
- Uses stock market data, which is updated every second.
- Provides an "Economic" view of default.

Disadvantages:
- Assumes assets are traded in a liquid market (often not true).
- Assumes debt is simple (one zero-coupon bond), but real companies have complex debt structures.

Key Takeaway:

In Structural Models, default is an internal event triggered when assets fall below a certain level. If you understand call options, you understand Merton!

4. Reduced-Form Models

If Structural Models look "inside" the company, Reduced-Form Models look "outside" at the market and the economy. They don't try to explain why a company defaults; they just try to predict when it will happen based on external data.

Key Characteristics:

  • They use Hazard Rates (the probability of default occurring in a very short time window).
  • Default is treated as a "random jump" (a Poisson process).
  • Input variables include macroeconomic data (GDP growth, interest rates) and company-specific data (credit ratings).

The Comparison Table:

Structural: Default is endogenous (internal). Assets < Debt. Hard to use for complex debt.
Reduced-Form: Default is exogenous (external/random). Easy to use with market data and varying interest rates.

Key Takeaway:

Reduced-form models are statistically flexible and reflect the reality that defaults can happen suddenly due to external shocks, not just because assets slowly declined.

5. The Term Structure of Credit Spreads

Just like the yield curve for government bonds, we have a "Credit Spread Curve." The Credit Spread is the extra yield you demand for taking on default risk.

\( Spread \approx \frac{Expected \ Loss}{Price} \)

What influences the spread?

  1. Credit Quality: Lower-rated bonds have higher spreads.
  2. Economic Cycle: Spreads widen (increase) during recessions and narrow (decrease) during booms.
  3. Liquidity: Even if a company is healthy, if its bonds are hard to trade, the spread will be higher.
  4. Broker-Dealer Capital: If banks have less capital to "make markets," spreads widen.

Memory Aid: Think of the spread as a "Risk Tax." The more dangerous the neighborhood (economy) or the shakier the house (company), the higher the tax you pay.

6. Credit Analysis of Securitized Debt

Securitized debt (like ABS or MBS) is different from corporate debt because it involves a pool of assets and a waterfall structure.

Key Concepts:

  • Tranching: Dividing the risk into layers (Senior, Mezzanine, Equity). The "Equity" tranche is the first to absorb losses.
  • Credit Enhancement: Techniques to make the senior tranches safer (e.g., overcollateralization or insurance).
  • Correlation: This is the "secret sauce." If all loans in the pool default at the same time (high correlation), the senior tranches are in trouble. If defaults are independent, the senior tranches are very safe.

Common Mistake: Students often forget that for securitized debt, you analyze the collateral pool and the structure, not the company that created the bond!

Final Quick Review

1. PD × LGD = Expected Loss.
2. Merton Model: Default = Assets < Debt. Equity is a Call Option.
3. Reduced-Form: Default is a random "jump" based on macro/market data.
4. Spreads: Widen in bad times, narrow in good times.
5. Securitization: Focus on tranches and default correlation.

Don't worry if the Merton formulas look scary! On the exam, focus on the relationships: if volatility increases, the value of the option (equity) increases, which might seem counter-intuitive, but it's a key part of the model logic! You've got this!