2024 Curriculum CFA Program Level II Fixed Income

Credit Analysis Models

Available to members

## Introduction

Credit analysis plays an important role in the broader fixed-income space. Our coverage will go over important concepts, tools, and applications of credit analysis. We first look at modeling credit risk. The inputs to credit risk modeling are the expected exposure to default loss, the loss given default, and the probability of default. We explain these terms and use a numerical example to illustrate the calculation of the credit valuation adjustment for a corporate bond and its credit spread over a government bond yield taken as a proxy for a default-risk-free rate (or default-free rate).

We then discuss credit scoring and credit ratings. Credit scoring is a measure of credit risk used in retail loan markets, and ratings are used in the wholesale bond market. We explain two types of credit analysis models used in practice—structural models and reduced-form models. Both models are highly mathematical and beyond the scope of our coverage. Therefore, we provide only an overview to highlight the key ideas and the similarities and differences between them. We then use the arbitrage-free framework and a binomial interest rate tree to value risky fixed-rate and floating-rate bonds for different assumptions about interest rate volatility. We also build on the credit risk model to interpret changes in credit spreads that arise from changes in the assumed probability of default, the recovery rate, or the exposure to default loss. We also explain the term structure of credit spreads and finally compare the credit analysis required for securitized debt with the credit analysis of corporate bonds.

## Learning Outcomes

The member should be able to:

• explain expected exposure, the loss given default, the probability of default, and the credit valuation adjustment;
• explain credit scores and credit ratings;
• calculate the expected return on a bond given transition in its credit rating;
• explain structural and reduced-form models of corporate credit risk, including assumptions, strengths, and weaknesses;
• calculate the value of a bond and its credit spread, given assumptions about the credit risk parameters;
• interpret changes in a credit spread;
• explain the determinants of the term structure of credit spreads and interpret a term structure of credit spreads;
• compare the credit analysis required for securitized debt to the credit analysis of corporate debt.

## Summary

This reading has covered several important topics in credit analysis. Among the points made are the following:

• Three factors important to modeling credit risk are the expected exposure to default, the recovery rate, and the loss given default.

• These factors permit the calculation of a credit valuation adjustment that is subtracted from the (hypothetical) value of the bond, if it were default risk free, to get the bond’s fair value given its credit risk. The credit valuation adjustment is calculated as the sum of the present values of the expected loss for each period in the remaining life of the bond. Expected values are computed using risk-neutral probabilities, and discounting is done at the risk-free rates for the relevant maturities.

• The CVA captures investors’ compensation for bearing default risk. The compensation can also be expressed in terms of a credit spread.

• Credit scores and credit ratings are third-party evaluations of creditworthiness used in distinct markets.

• Analysts may use credit ratings and a transition matrix of probabilities to adjust a bond’s yield-to-maturity to reflect the probabilities of credit migration. Credit spread migration typically reduces expected return.

• Credit analysis models fall into two broad categories: structural models and reduced-form models.

• Structural models are based on an option perspective of the positions of the stakeholders of the company. Bondholders are viewed as owning the assets of the company; shareholders have call options on those assets.

• Reduced-form models seek to predict when a default may occur, but they do not explain the why as do structural models. Reduced-form models, unlike structural models, are based only on observable variables.

• When interest rates are assumed to be volatile, the credit risk of a bond can be estimated in an arbitrage-free valuation framework.

• The discount margin for floating-rate notes is similar to the credit spread for fixed-coupon bonds. The discount margin can also be calculated using an arbitrage-free valuation framework.

• Arbitrage-free valuation can be applied to judge the sensitivity of the credit spread to changes in credit risk parameters.

• The term structure of credit spreads depends on macro and micro factors.

• As it concerns macro factors, the credit spread curve tends to become steeper and widen in conditions of weak economic activity. Market supply and demand dynamics are important. The most frequently traded securities tend to determine the shape of this curve.

• Issuer- or industry-specific factors, such as the chance of a future leverage-decreasing event, can cause the credit spread curve to flatten or invert.

• When a bond is very likely to default, it often trades close to its recovery value at various maturities; moreover, the credit spread curve is less informative about the relationship between credit risk and maturity.

• For securitized debt, the characteristics of the asset portfolio themselves suggest the best approach for a credit analyst to take when deciding among investments. Important considerations include the relative concentration of assets and their similarity or heterogeneity as it concerns credit risk.