Answer: SGD 7.5 million

The **1-year unexpected loss (UL)** at the 99% confidence level for this loan portfolio is the portion of potential losses that exceeds the **expected loss (EL)**. Banks provision for EL through reserves (e.g., loan loss allowances), while UL requires **economic capital** as a buffer against volatility in credit losses. In credit risk contexts (a core FRM Part 1 topic in the Valuation and Risk Models book), UL at a specific confidence level is typically calculated as: **UL = Credit VaR (or loss quantile at the confidence level) − EL** Here, the problem directly provides the **year 99% VaR** as SGD 9.6 million. This represents the **99% Credit VaR** (the loss level not exceeded with 99% probability over one year, including both expected and unexpected components). ### Step 1: Calculate Expected Loss (EL) EL is the average or "anticipated" credit loss over the period. **Formula**: EL = Principal (Exposure) × Portfolio Default Rate (PD) × Loss Given Default (LGD) - LGD = 1 − Recovery rate = 1 − 30% = 70% (or 0.70) - Principal = SGD 120 million - PD = 2.5% (or 0.025) **EL = 120,000,000 × 0.025 × 0.70 = 120,000,000 × 0.0175 = SGD 2.1 million** This SGD 2.1 million is what the bank "expects" on average and should cover via provisions. ### Step 2: Calculate Unexpected Loss (UL) at 99% Confidence **UL = 99% VaR − EL = 9.6 million − 2.1 million = SGD 7.5 million** This is the volatility or "surprise" loss component at the 99% level. ### Explanations for Each Option **A: SGD 7.5 million** — **Correct**. This matches the standard FRM definition and calculation: 99% Credit VaR minus EL. It isolates the unexpected portion of losses that requires economic capital. The recovery rate is used only to derive LGD for EL; the given VaR already reflects portfolio-level loss modeling (including correlations, etc.). **B: SGD 11.7 million** — **Incorrect**. This appears to be a common distractor, perhaps from mistakenly subtracting something else (e.g., 9.6 + 2.1 or misapplying LGD directly to VaR without proper EL). It does not align with UL = VaR − EL. **C: SGD 12.7 million** — **Incorrect**. This might result from errors like using the wrong LGD (e.g., subtracting only 30% recovery incorrectly from VaR) or adding/subtracting numbers without the proper EL formula (e.g., 9.6 + something or 14.8 − 2.1). It overstates or miscalculates the unexpected component. **D: SGD 16.9 million** — **Incorrect**. This could come from using the **Expected Shortfall (ES)** instead of VaR (14.8 + 2.1 = 16.9), or adding EL to ES. While ES (also called CVaR or TailVaR) is a more conservative tail-risk measure (average loss in the worst 1% of cases), the question specifically asks for UL at the 99% confidence level using the provided **VaR**. ES is provided as a red herring. UL is not typically ES − EL in this context unless specified. **Note on ES (SGD 14.8 million)**: ES is useful for capturing severity beyond VaR (coherent risk measure), but the question asks for UL based on the 99% VaR figure. In some advanced contexts, economic capital might reference ES, but standard FRM Part 1 credit risk UL uses the VaR − EL approach. ### Reference Answer The correct answer is **A: SGD 7.5 million**. For exam prep tip: Always compute EL first using EAD × PD × LGD, then subtract it from the given quantile (VaR) to isolate UL. Watch for distractors involving ES or misapplied recovery rates. This concept links directly to economic capital allocation (capital covers UL, provisions cover EL). Practice similar calculations with the binomial or Vasicek models for deeper understanding.