How do you calculate Expected Loss from PD, LGD, and EAD, and why does each component matter separately?

Understanding the three pillars of expected loss is essential for FRM Part II credit risk — and for real-world credit risk management. Let me break down each component and then tie them together. **The Expected Loss Formula:** $$\text{EL} = \text{PD} \times \text{LGD} \times \text{EAD}$$ **Why Separate Estimation Matters** Banks estimate PD, LGD, and EAD independently because each is driven by different factors and requires different modeling approaches. Lumping them together would obscure where the risk actually lives. **1. Probability of Default (PD)** - The likelihood that a borrower defaults within a given time horizon (typically 1 year for regulatory purposes). - Drivers: borrower's financial health, credit rating, macroeconomic conditions, industry sector. - **Example:** Harborview National Bank rates its commercial borrowers on a 10-grade internal scale. A BBB-equivalent borrower might have a 1-year PD of 0.45%, while a B-equivalent borrower has a PD of 4.2%. **2. Loss Given Default (LGD)** - The percentage of exposure that is actually lost once default occurs. LGD = 1 − Recovery Rate. - Drivers: collateral type and quality, seniority of the claim, jurisdiction (bankruptcy laws), economic conditions at time of default. - **Example:** A secured commercial real estate loan with a 60% loan-to-value ratio might have an LGD of 25% (75% recovery from selling the property). An unsecured revolving credit facility to the same borrower might have an LGD of 65%. **3. Exposure at Default (EAD)** - The total amount the bank is exposed to at the moment of default. - For term loans, EAD ≈ outstanding balance. For revolving facilities, borrowers tend to draw down more as they approach default (this is called the **credit conversion factor**). - **Example:** A borrower has a $5M revolving facility with $2M currently drawn. Historical data shows distressed borrowers draw an additional 60% of the undrawn amount before defaulting. EAD = $2M + 0.60 × $3M = **$3.8M**. **Full Portfolio Example:** Harborview National Bank's commercial loan book: | Borrower | PD | LGD | EAD | Expected Loss | |---|---|---|---|---| | Oakridge Manufacturing | 0.45% | 25% | $12.0M | $13,500 | | Westfield Retail Corp | 2.10% | 55% | $8.5M | $98,175 | | Summit Logistics LLC | 4.20% | 65% | $3.8M | $103,740 | | **Portfolio Total** | | | **$24.3M** | **$215,415** | The bank should hold $215,415 in provisions to cover expected losses on this portfolio. **Unexpected losses** (the tail risk beyond EL) are covered by regulatory capital — that's where the UL calculation and Basel requirements come in. **Key Distinctions for the Exam:** - **EL is a cost of doing business** — it's priced into loan spreads and provisioned for. - **UL is what capital is for** — it covers the volatility around EL. - **PD and LGD are positively correlated** in downturns (downturn LGD) — Basel requires banks to use through-the-cycle or downturn estimates, not point-in-time benign conditions. AcadiFi's FRM Part II course walks through the full Basel IRB framework with dozens of exam-style scenarios. Worth checking out if credit risk modeling is where you need the most practice.