Every key formula for the FRM Part 2 exam, organized by domain. Covers the full 2026 GARP curriculum across all six tested areas. No signup required.
Formulas are organized by exam domain and subtopic. Use this sheet alongside practice questions to verify recall — don't treat it as a substitute for understanding the underlying concepts. Part 2 emphasizes application over computation, so focus on when and why each formula is used, not just the mechanics.
| Formula | Expression | Notes |
|---|---|---|
| Parametric VaR | VaR = μ − zσ | z = standard normal quantile (e.g., 2.326 for 99%); σ = portfolio std dev |
| Component VaR | CVaRᵢ = βᵢ × VaR_portfolio | Contribution of position i to total portfolio VaR; Σ CVaRᵢ = VaR_total |
| Marginal VaR | MVaRᵢ = β × VaR / Portfolio_value | Change in portfolio VaR per unit change in position i |
| Expected Shortfall | ES = E[L | L > VaR] | Average loss in the tail beyond VaR; also called CVaR. Coherent risk measure |
| Delta-Normal VaR | VaR_option ≈ |Δ| × VaR_underlying | Linear approximation for option VaR using delta; ignores gamma/convexity |
| Delta (Δ) | Δ = ∂V/∂S | Rate of change of option value with respect to underlying price |
| Gamma (Γ) | Γ = ∂²V/∂S² | Rate of change of delta; measures convexity of option payoff |
| Vega (ν) | ν = ∂V/∂σ | Sensitivity of option value to implied volatility |
| Theta (Θ) | Θ = ∂V/∂t | Time decay; rate of change of option value as time passes |
| Rho (ρ) | ρ = ∂V/∂r | Sensitivity of option value to risk-free interest rate |
| Formula | Expression | Notes |
|---|---|---|
| PD (TTC vs PIT) | PD_TTC = long-run avg; PD_PIT = current cycle | Through-the-cycle smooths over business cycle; point-in-time reflects current conditions |
| LGD | LGD = 1 − Recovery Rate | Loss given default; fraction of exposure lost if borrower defaults |
| EAD (Revolving) | EAD = Drawn + CCF × (Limit − Drawn) | CCF = credit conversion factor; captures undrawn commitments likely to be drawn at default |
| Expected Loss | EL = PD × LGD × EAD | Average anticipated loss; basis for loan loss provisioning |
| CVA | CVA = LGD × Σ EE(tᵢ) × PD(tᵢ₋₁, tᵢ) × DF(tᵢ) | Credit valuation adjustment; market value of counterparty credit risk |
| Wrong-Way Risk | CVA_wwr > CVA_standard | Exposure increases when counterparty credit quality deteriorates; positive correlation between EE and PD |
| Vasicek Model | PD_stressed = Φ([Φ⁻¹(PD) + √ρ × Φ⁻¹(q)] / √(1−ρ)) | Single-factor model; ρ = asset correlation, q = quantile for economic scenario |
| Credit Spread | s ≈ PD × LGD | Risk-neutral approximation; actual spreads include liquidity and risk premium |
| Formula | Expression | Notes |
|---|---|---|
| LDA | Loss = Frequency × Severity | Loss Distribution Approach; frequency (Poisson) and severity (lognormal/Pareto) modeled separately, then convolved |
| Basic Indicator | K_BIA = α × GI (α = 15%) | Capital charge = 15% of avg positive gross income over prior 3 years |
| Standardized Approach | K_SA = Σ (βⱼ × GIⱼ) | Capital by business line; β ranges from 12% (retail banking) to 18% (corporate finance, trading) |
| OpVaR | OpVaR = F⁻¹(confidence) from aggregate loss dist | Operational VaR from the convolution of frequency and severity distributions |
| Power Law (Tail) | P(X > x) ≈ Cx⁻ᵅ | Heavy-tailed severity; α = tail index. Lower α → fatter tail → more extreme losses |
| Expected OpLoss | E[L] = E[N] × E[X] | Expected number of events × expected loss per event; used for provisioning |
| Formula | Expression | Notes |
|---|---|---|
| LCR | LCR = HQLA / Net cash outflows₃₀ | Liquidity Coverage Ratio; must be ≥ 100%. HQLA = Level 1 + haircut-adjusted Level 2 assets |
| NSFR | NSFR = ASF / RSF | Net Stable Funding Ratio; must be ≥ 100%. ASF = available stable funding, RSF = required stable funding over 1 year |
| Liquidity-Adjusted VaR | LVaR = VaR + Liquidity cost | Adds liquidation cost to standard VaR; Liquidity cost = ½ × spread × position value |
| Bid-Ask Spread | Spread = (Ask − Bid) / Mid | Relative spread; primary measure of market liquidity. Wider spread → less liquid |
| Exogenous LVaR | LVaR = VaR + ½(μ_spread + z × σ_spread) × V | Accounts for uncertainty in liquidation cost via spread volatility |
| Cash Flow at Risk | CFaR = Expected CF − CF at confidence level | Liquidity-focused metric; maximum cash flow shortfall at a given confidence level |
| Formula | Expression | Notes |
|---|---|---|
| Portfolio VaR | VaR_p = √(w′Σw) × z × V | w = weight vector, Σ = covariance matrix; captures diversification via correlations |
| Risk Budgeting | Σ CVaRᵢ = VaR_total | Component VaRs sum to total; each position's risk contribution is its budget allocation |
| Tracking Error | TE = σ(Rp − Rb) | Standard deviation of active returns; measures deviation from benchmark |
| Information Ratio | IR = (Rp − Rb) / TE | Active return per unit of tracking error; measures active management skill |
| Factor Model | Rᵢ = αᵢ + Σ βᵢⱼFⱼ + εᵢ | Multi-factor decomposition; isolates systematic risk exposures from idiosyncratic risk |
| Risk Parity | wᵢσᵢ(∂σp/∂wᵢ) = wⱼσⱼ(∂σp/∂wⱼ) for all i, j | Equal risk contribution from each asset; alternative to equal-weight or mean-variance |
| Surplus at Risk | SaR = E[Surplus] − Surplus at confidence | Maximum shortfall of assets vs liabilities at a given confidence level; for pension/insurance |
Current Issues is a reading-based domain that changes each year. The 2026 curriculum covers topics like climate risk modeling, AI/ML in risk management, digital asset regulation, and emerging systemic risks. Questions test your understanding of qualitative concepts, regulatory frameworks, and real-world implications — not formulas. Focus on reading the assigned papers carefully and understanding the key arguments and conclusions.
Knowing formulas is only half the battle. Test your ability to apply them with our practice questions, or start building real exam readiness with PrepAscend.
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