Credit risk and portfolio strategies - Credit migration LGD ...

Learning Outcomes

After reading this article, you will be able to calculate expected loss on credit exposures, apply credit migration matrices, and interpret the significance of loss given default (LGD). You will also understand the concepts of exposure at default, probability of default, and credit valuation adjustment (CVA), and learn to use these tools for portfolio credit risk assessment and strategy selection.

CFA Level 2 Syllabus

For CFA Level 2, you are required to understand the quantitative assessment of credit risk within a portfolio context. Efficient revision should focus on these key syllabus areas:

• Explain and calculate expected loss, loss given default (LGD), exposure at default (EAD), and probability of default (PD)
• Use credit migration (transition) matrices to estimate portfolio credit risk and expected loss
• Describe the use of LGD and credit migration in credit valuation adjustment (CVA)
• Analyze the impact of credit risk metrics on portfolio strategies and risk management approaches

Test Your Knowledge

Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision.

1. Which formula is most accurate to calculate expected credit loss for a loan over one period?
   1. Expected Loss = EAD × LGD × PD
   2. Expected Loss = Notional × Coupon × Recovery Rate
   3. Expected Loss = EAD – (LGD × PD)
   4. Expected Loss = Market Value × Recovery Rate

2. If a corporate bond migrates from A to BB in one year and the probability of this transition is 3%, what role does a credit migration matrix play in expected loss estimation?

3. Define loss given default (LGD). Why is it important for risk managers?

4. What impact does an increase in the probability of default (PD) have on a portfolio’s total expected credit loss, assuming LGD and EAD remain constant?

Introduction

Credit risk management requires understanding the components and calculation of expected loss for individual credit exposures and portfolios. This includes quantifying the likelihood and severity of losses due to default events, measuring risk with inputs such as probability of default, exposure at default, loss given default, and interpreting the effect of credit migration. You must be able to use these measures to estimate portfolio risk, inform allocation, and support disciplined credit portfolio strategies.

Key Term: Expected Loss (EL)
The average monetary loss an investor or bank expects to incur on a credit exposure, calculated as EL = EAD × LGD × PD.

Key Term: Loss Given Default (LGD)
The percentage of an exposure not recovered in the event of default, expressed as (1 – recovery rate).

Key Term: Probability of Default (PD)
The likelihood that a borrower fails to meet its debt obligations over a specified period, usually one year.

Key Term: Exposure at Default (EAD)
The total value at risk in the event the counterparty defaults, often equivalent to the outstanding loan principal or current market value.

Key Term: Credit Migration (Transition) Matrix
A matrix presenting probabilities of a credit instrument moving between different rating categories over a specified time horizon.

Key Term: Credit Valuation Adjustment (CVA)
The present value of expected credit losses on a financial instrument due to the counterparty’s possible default.

CREDIT RISK COMPONENTS

Credit risk reflects both the chance that a borrower will default and the extent of any resulting financial loss. The core formula for expected loss (EL) combines three elements:

• Probability of Default (PD): The likelihood of default during the period assessed.
• Loss Given Default (LGD): The fraction of exposure not recovered if default occurs.
• Exposure at Default (EAD): The monetary value exposed to loss at the moment of default.

The formula is:

Worked Example 1.1

A bank holds a $500,000 unsecured loan to a company with a one-year probability of default of 1.2%. If the estimated recovery rate in the event of default is 35%, what is the expected loss?

Answer:
LGD = 1 – 0.35 = 0.65
Expected Loss = $500,000 × 0.65 × 0.012 = $3,900

RELATIONSHIP BETWEEN PD, LGD, AND EXPECTED LOSS

Higher PD or LGD increase EL, while a higher recovery rate reduces it. Portfolio strategies may focus on reducing PD (better underwriting), improving recovery processes (increasing recovery rates), or limiting EAD (reducing exposure to any one borrower).

CREDIT MIGRATION AND TRANSITION MATRICES

Borrowers’ credit quality may change over time. A credit migration matrix (or transition matrix) shows the probabilities of moving from one credit rating to another—including default—within a set period, typically one year.

Key Term: Credit Migration (Transition) Matrix
Probabilities for rating upgrades, downgrades, or default, used to project future rating distributions and quantify expected losses across the portfolio.

Probabilities from the matrix allow calculation of expected portfolio value, expected loss, and scenario analysis (e.g., the impact of a mass downgrade of BBB-rated bonds).

Worked Example 1.2

An analyst examines a $2 million portfolio of BBB-rated bonds. The one-year transition matrix gives a 4% probability of downgrade to BB (with LGD of 60%) and 1% probability of default (with LGD of 70%). What is the expected loss due to these two outcomes in a year?

Answer:
Loss from downgrade to BB: $2,000,000 × 0.04 × 0.60 = $48,000
Loss from default: $2,000,000 × 0.01 × 0.70 = $14,000
Total expected loss from transitions: $48,000 + $14,000 = $62,000

APPLICATIONS TO CREDIT PORTFOLIO STRATEGIES

In credit portfolio management, expected loss (EL) serves as a basis for risk-based pricing, loss forecasting, and capital allocation.

Portfolio strategies may include:

• Diversifying to manage exposure concentrations.
• Adjusting exposures to credits with changing transition (migration) probabilities.
• Pricing facilities to cover EL plus a premium for unexpected loss (economic capital).
• Using credit derivatives or insurance to offset PD or LGD risk where justified by CVA analysis.

CREDIT VALUATION ADJUSTMENT (CVA)

When valuing derivatives or other bilateral exposures, the credit valuation adjustment (CVA) represents the present value of all expected credit losses due to the counterparty’s potential default.

Key Term: Credit Valuation Adjustment (CVA)
The monetary difference between the risk-free value and the actual value of an instrument that accounts for potential counterparty default.

CVA is determined by applying PD, LGD, and EAD to projected cash flows over each period, discounting expected losses to present value.

Worked Example 1.3

A $10 million notional, five-year derivative contract has annual PD of 2%, LGD of 55%, and annual expected positive exposure of $2 million. Using simple annual periods and discounting at 0%, estimate the total expected credit loss for CVA.

Answer:
Annual expected loss = $2,000,000 × 0.55 × 0.02 = $22,000
Total CVA over 5 years (undiscounted) = 5 × $22,000 = $110,000
(If discounting is required, present value each year's expected loss.)

Exam Warning

A frequent error is to omit compounding or not to adjust PD when using multi-year horizons. For multi-year periods, cumulative PD must reflect survival (i.e., non-default) up to each year. Always multiply period survival probabilities by hazard rates.

Revision Tip

When evaluating portfolio credit risk, always check that LGD and EAD are appropriate for the instrument type (secured vs. unsecured, amortizing vs. bullet, etc.), and apply transition matrices to forecast rating migrations, not only defaults.

Summary

Expected credit loss (EL) measures the average loss for a given portfolio and is essential for pricing, provisioning, and capital allocation. Credit migration matrices provide probabilities required for predicting losses from rating downgrades or default. LGD quantifies the severity of loss upon default, while EAD is the sum at risk. These quantitative tools are central to best practice in credit risk and portfolio management.

Key Point Checklist

This article has covered the following key knowledge points:

• Expected loss equals EAD × LGD × PD
• LGD is the percentage not recovered after default: LGD = 1 – recovery rate
• Credit migration matrices provide probabilities of rating upgrades, downgrades, and defaults
• Credit valuation adjustment (CVA) uses expected loss to discount deal values for counterparty risk
• Portfolio strategies balance diversification, risk pricing, and use of LGD, PD, and EAD
• Use transition matrices to forecast portfolio-wide expected loss, not just point-in-time PDs

Key Terms and Concepts

• Expected Loss (EL)
• Loss Given Default (LGD)
• Probability of Default (PD)
• Exposure at Default (EAD)
• Credit Migration (Transition) Matrix
• Credit Valuation Adjustment (CVA)