Rule Atlas
Basel III: VaR and Expected Shortfall: Core Risk Measures
Under Basel III (GARP / Basel Committee), vaR and Expected Shortfall: Core Risk Measures establishes the authoritative rules tested on the GARP FRM® Part I. This lesson explores Value at Risk (VaR) and Expected Shortfall (ES) as key measures of financial risk, comparing parametric and historical simulation approaches and evaluating their coherence. VoraPrep verifies every threshold, worked table, and practice question below against the current GARP FRM® Part I blueprint.
Core Statutory Concepts
| Axiom | Description | VaR Status | ES Status |
|---|---|---|---|
| 1. Monotonicity | If portfolio A always has worse outcomes than portfolio B, then the risk of A must be greater than or equal to the risk of B. (ρ(X) ≤ ρ(Y) if X ≥ Y) | Satisfied | Satisfied |
| 2. Subadditivity | The risk of a combined portfolio should not be greater than the sum of the risks of its individual components. This encourages diversification. (ρ(X + Y) ≤ ρ(X) + ρ(Y)) | Often violated* | Satisfied |
| 3. Positive Homogeneity | Scaling the size of a portfolio by a positive factor scales its risk by the same factor. (ρ(cX) = cρ(X) for c > 0) | Satisfied | Satisfied |
| 4. Translation Invariance | Adding a sure amount to a portfolio reduces its risk by that same amount. (ρ(X + a) = ρ(X) - a for a sure amount 'a') | Satisfied | Satisfied |
A large internationally active bank is developing its internal model for market risk capital requirements under Basel III. The regulators require that any risk measure used for capital calculation must be 'coherent' to ensure prudent and consistent risk aggregation. Which of the following is a fundamental property that a risk measure must satisfy to be considered coherent, especially in the context of regulatory capital frameworks like Basel III?
Practitioner Application: VaR and Expected Shortfall: Core Risk Measures
A risk manager at a large investment bank is tasked with calculating the daily market risk for a diverse multi-asset portfolio. Management requires a clear, single number to represent potential losses, but the regulator (aligned with Basel III principles) emphasizes the need for a robust measure that accounts for 'fat tails' and extreme events. The manager must decide between Value at Risk (VaR) and Expected Shortfall (ES) and choose an appropriate estimation method, while being mindful of their underlying assumptions and limitations.
- Financial institutions utilize various risk measures to quantify potential losses from market movements. The FRM curriculum, consistent with GARP FRM Learning Objectives and implicitly supporting Basel Accords for capital adequacy, focuses heavily on Value at Risk (VaR) and Expected Shortfall (ES).
- Value at Risk (VaR) VaR quantifies the maximum potential loss over a specific time horizon at a given confidence level. For example, a 1-day 99% VaR of $1 million means there is a 1% chance the portfolio will lose more than $1 million over the next day.
Common GARP FRM® Part I Distractors on Basel III
- 1⚠️ Exam trap: Confusing VaR with ES. VaR is the threshold loss at a given confidence level; ES is the average loss beyond that threshold. ES will always be greater than or equal to VaR for the same confidence level.
- 2⚠️ Exam trap: Incorrectly applying coherence properties. Remember that VaR can violate subadditivity, especially with portfolios containing options or assets with non-normal returns. This is a critical distinction that often appears on the exam.
- 3VaR (Value at Risk): Maximum potential loss over a horizon at a confidence level. Does not tell you how much you lose if the VaR threshold is breached.
- 4Parametric VaR: Assumes a distribution (often normal). Fast, but poor for non-normal returns or non-linear instruments.
- 5Historical Simulation VaR: Uses past data. Good for 'fat tails' and non-linearities, but backward-looking and data-intensive.
Frequently Asked Questions: Basel III
What is the core rule under Basel III (VaR and Expected Shortfall: Core Risk Measures)?
Under Basel III (GARP / Basel Committee), vaR and Expected Shortfall: Core Risk Measures establishes the authoritative rules tested on the GARP FRM® Part I. This lesson explores Value at Risk (VaR) and Expected Shortfall (ES) as key measures of financial risk, comparing parametric and historical simulation approaches and evaluating their coherence. VoraPrep verifies every threshold, worked table, and practice question below against the current GARP FRM® Part I blueprint.
How is Basel III tested on the GARP FRM® Part I?
⚠️ Exam trap: Confusing VaR with ES. VaR is the threshold loss at a given confidence level; ES is the average loss beyond that threshold. ES will always be greater than or equal to VaR for the same confidence level. ⚠️ Exam trap: Incorrectly applying coherence properties. Remember that VaR can violate subadditivity, especially with portfolios containing options or assets with non-normal returns. This is a critical distinction that often appears on the exam.
Where can I practice GARP FRM® Part I questions on VaR and Expected Shortfall: Core Risk Measures?
Test yourself instantly with the free playable GARP FRM® Part I question on this page, or launch VoraPrep's full GARP FRM® Part I adaptive question bank, interactive lessons, and 1:1 exam simulator at voraprep.com/frm.