Why Credit Risk Dominates FRM Part II
Credit risk is the single largest source of risk for most financial institutions and accordingly receives heavy weight on the FRM Part II exam. The curriculum spans theoretical models (how do we think about default?), practical measurement (how do we estimate loss parameters?), and risk management (how do we price and hedge credit exposure?). This guide connects those pieces into a coherent framework.
Structural Models: The Merton Framework
Robert Merton's insight was that a company's equity can be viewed as a European call option on the firm's assets, with the strike price equal to the face value of debt. If the firm's asset value exceeds its debt at maturity, equity holders keep the residual; otherwise, the firm defaults and equity is worthless.
Under this framework, default probability depends on three factors: the distance between the current asset value and the default point (face value of debt), the volatility of the firm's assets, and the time to maturity. These inputs combine into the 'distance to default,' which maps directly to a default probability through the standard normal distribution.
The practical implementation (commercialized as the KMV model by Moody's) estimates asset value and volatility from observable equity prices and the firm's capital structure. Firms with low distance to default — highly leveraged companies with volatile assets — have the highest default probabilities.
Strengths of the structural approach: it is grounded in economic theory, provides an intuitive link between firm fundamentals and default, and generates implied credit spreads that can be compared to market prices. Limitations: it assumes a simple capital structure (one class of debt), treats default as occurring only at maturity, and tends to underestimate short-term default probabilities.
Reduced-Form Models
Reduced-form models take a fundamentally different approach: rather than modeling the economics of default, they treat default as an unpredictable event governed by a stochastic intensity (hazard rate). The hazard rate can vary over time and depend on observable variables like credit spreads, macroeconomic indicators, or credit ratings.
The probability of surviving from time zero to time T without defaulting equals the exponential of the negative integral of the hazard rate over that interval. For a constant hazard rate of 2% per year, the one-year survival probability is approximately 98.02% and the five-year survival probability is approximately 90.48%.
Reduced-form models are calibrated directly to market prices of credit-sensitive instruments (corporate bonds, CDS spreads), making them the standard for pricing and trading applications. Their weakness is the lack of economic intuition — the model does not explain why a firm defaults, only the statistical pattern of when.
The Three Pillars: PD, LGD, and EAD
Probability of Default (PD)
PD can be estimated from internal rating models (using financial ratios, industry factors, and behavioral data), external credit ratings (mapping agency ratings to historical default rates), or market-implied approaches (extracting default probabilities from CDS spreads or bond spreads).
For regulatory purposes under Basel, banks must estimate through-the-cycle PDs that reflect long-run average default rates for each rating grade, smoothing out cyclical fluctuations. For economic capital and pricing, point-in-time PDs that reflect current conditions are preferred.
Loss Given Default (LGD)
LGD represents the fraction of exposure that is actually lost when default occurs. If a loan has an exposure of $10 million and the bank recovers $3.5 million through collateral liquidation and workout, the LGD is 65%.
LGD depends on collateral type and quality (secured loans have lower LGD), seniority (senior secured debt recovers more than subordinated unsecured), industry (asset-heavy industries tend to have higher recovery), and the economic cycle (recovery rates drop during recessions, creating a correlation between PD and LGD known as wrong-way risk).
The Basel framework prescribes LGD floors for different exposure types and requires banks to estimate downturn LGD that reflects stressed conditions.
Exposure at Default (EAD)
For term loans, EAD is straightforward: it equals the outstanding balance. For revolving credit facilities, EAD is more complex because borrowers tend to draw down unused lines before defaulting. EAD equals the current drawn amount plus a credit conversion factor (CCF) times the undrawn commitment.
Estimating the CCF requires analyzing historical drawdown behavior of defaulting obligors. Typical CCFs range from 40% to 75%, meaning a borrower with a $5 million undrawn line might be expected to draw an additional $2 million to $3.75 million before defaulting.
Expected Loss vs. Unexpected Loss
Expected Loss (EL) equals PD times LGD times EAD. It represents the average loss over a full credit cycle and should be covered by loan pricing (credit spreads) and provisions. A loan with a 2% PD, 45% LGD, and $1 million EAD has an EL of $9,000 per year.
Unexpected Loss (UL) is the volatility around the expected loss — the risk that actual losses deviate from the average. UL depends not only on individual loan parameters but critically on the correlation between defaults in the portfolio. Higher default correlation (which increases during economic downturns) leads to fatter tails in the portfolio loss distribution and higher UL.
Capital is held against unexpected loss. The Basel IRB formula calculates required capital as a function of PD, LGD, EAD, maturity, and a supervisory asset correlation parameter that increases with lower PD (reflecting the observation that higher-quality borrowers are more sensitive to systematic risk).
Credit Valuation Adjustment (CVA)
CVA quantifies the market value of counterparty credit risk in derivative transactions. It represents the difference between the risk-free portfolio value and the portfolio value accounting for the possibility that the counterparty defaults.
Conceptually, CVA equals the sum over all future time periods of the probability of counterparty default in that period, times the expected exposure at that time, times the LGD. The calculation requires modeling the future exposure profile of the derivative (using Monte Carlo simulation) and the counterparty's default probability term structure.
Debit Valuation Adjustment (DVA) is the mirror image: the benefit that arises from your own default risk. While controversial (you profit from your own credit deterioration), DVA is required under both IFRS and US GAAP accounting standards.
Wrong-way risk arises when the counterparty's credit quality is negatively correlated with your exposure to them. The classic example is a credit default swap where the protection seller's creditworthiness deteriorates precisely when you need the protection most. Wrong-way risk increases CVA beyond what standard models predict.
Credit Derivatives
Credit default swaps (CDS) are the most liquid credit derivatives. The protection buyer pays a periodic premium (the CDS spread) and receives a contingent payment if the reference entity defaults. The CDS spread reflects the market's assessment of the reference entity's default risk and LGD.
For a single-name CDS, the fair spread equates the present value of premium payments (the premium leg) with the present value of the expected default payment (the protection leg). This equilibrium spread is approximately equal to PD times LGD divided by (1 minus PD times LGD) for short maturities, though the full calculation requires discounting and term structure modeling.
Credit index products (CDX in North America, iTraxx in Europe) provide exposure to a basket of reference entities. Index tranches (equity, mezzanine, senior) offer different risk-return profiles based on attachment and detachment points in the portfolio loss distribution.
Exam Preparation Strategy
FRM Part II credit risk questions test both conceptual understanding and calculation. Be prepared to derive default probabilities from CDS spreads, calculate expected loss for a loan portfolio, explain the difference between structural and reduced-form models, compute CVA for a simple derivative position, and analyze backtesting results for credit risk models.
The most common conceptual error is confusing expected and unexpected loss or failing to recognize the role of default correlation in portfolio risk. The most common calculation error is mishandling the relationship between hazard rates and survival probabilities.
Practice with our FRM credit risk question bank, or discuss modeling approaches with fellow candidates in the community Q&A.