Every key formula for the FRM Part 1 exam, organized by domain. Covers the full 2026 GARP curriculum across all four 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. The FRM exam does not provide a formula sheet, so active recall practice is essential.
| Formula | Expression | Notes |
|---|---|---|
| CAPM | E(R) = Rf + β(Rm − Rf) | Expected return based on systematic risk only |
| Jensen's Alpha | α = Rp − [Rf + β(Rm − Rf)] | Excess return above CAPM expectation |
| Sharpe Ratio | (Rp − Rf) / σp | Return per unit of total risk |
| Treynor Ratio | (Rp − Rf) / β | Return per unit of systematic risk; use for diversified portfolios |
| Information Ratio | (Rp − Rb) / TE | Active return per unit of tracking error |
| Tracking Error | σ(Rp − Rb) | Standard deviation of active returns vs benchmark |
| Expected Loss | EL = PD × LGD × EAD | Average loss from a credit exposure |
| Formula | Expression | Notes |
|---|---|---|
| Bayes' Theorem | P(A|B) = P(B|A) × P(A) / P(B) | Updating probabilities with new evidence |
| Expected Value | E(X) = Σ xᵢ P(xᵢ) | Probability-weighted average outcome |
| Variance | Var(X) = E[(X − μ)²] | Dispersion around the mean |
| Covariance | Cov(X,Y) = E[(X − μx)(Y − μy)] | Joint variability of two variables |
| Correlation | ρ(X,Y) = Cov(X,Y) / (σx × σy) | Standardized covariance; range [−1, 1] |
| OLS Slope (β) | β = Cov(X,Y) / Var(X) | Simple linear regression slope estimator |
| Regression SE | s = √[SSE / (n − k − 1)] | Standard error of the regression; k = number of independent variables |
| t-Statistic | t = (β̂ − β₀) / SE(β̂) | Test statistic for coefficient significance |
| Confidence Interval | β̂ ± t* × SE(β̂) | Range estimate for the true parameter |
| Z-Score | Z = (X − μ) / σ | Standard normal transformation |
| Formula | Expression | Notes |
|---|---|---|
| Forward Price | F = S × e^(r−q)T | q = continuous dividend yield; set q = 0 for non-dividend assets |
| Put-Call Parity | C − P = S − Ke^(−rT) | European options on non-dividend stock |
| Black-Scholes (Call) | C = S·N(d₁) − Ke^(−rT)·N(d₂) | European call option price |
| d₁ | [ln(S/K) + (r + σ²/2)T] / σ√T | Input to Black-Scholes N() terms |
| d₂ | d₁ − σ√T | Probability of exercise (risk-neutral) |
| Macaulay Duration | D = Σ[t × CFt / (1+y)^t] / Price | Weighted average time to cash flows |
| Modified Duration | MD = D / (1 + y) | Price sensitivity per unit yield change |
| DV01 | DV01 = −MD × Price / 10,000 | Dollar change per 1 bp yield move |
| Convexity | C = Σ[t(t+1)CFt / (1+y)^(t+2)] / Price | Second-order price sensitivity to yield |
| Price Change (Duration + Convexity) | ΔP ≈ −MD × P × Δy + ½ × C × P × (Δy)² | Improved estimate including convexity adjustment |
| Formula | Expression | Notes |
|---|---|---|
| Parametric VaR (1-day) | VaR = μ − z × σ | z = standard normal quantile (e.g., 2.326 for 99%) |
| Historical Sim VaR | Sorted P&L at percentile | Non-parametric; no distributional assumption |
| Expected Shortfall | ES = E[Loss | Loss > VaR] | Average loss in the tail beyond VaR; also called CVaR |
| VaR Scaling | VaR(T) = VaR(1) × √T | Square root of time rule; assumes i.i.d. returns |
| EWMA Volatility | σ²t = λσ²(t−1) + (1−λ)r²(t−1) | Exponentially weighted; λ typically 0.94 (RiskMetrics) |
| GARCH(1,1) | σ²t = ω + αr²(t−1) + βσ²(t−1) | Mean-reverting; long-run var = ω/(1−α−β) |
| Credit Spread | s ≈ PD × LGD | Risk-neutral approximation for zero-coupon bonds |
| Recovery Rate | RR = 1 − LGD | Fraction recovered in the event of default |
| Merton Model | Equity = Call on firm assets; Debt = Risk-free bond − Put | Structural credit model; firm defaults when assets < debt at maturity |
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