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FRM Formula Cheat Sheet

Every critical formula, exam tip, and calculation shortcut across all 10 FRM topics. Printable, searchable, and designed to maximise your score on exam day.

76+ formulas 36+ exam tips 15 critical numbers

📌 Critical Numbers to Memorise

95% VaR z-score (one-tail)1.645
99% VaR z-score (one-tail)2.326
95% two-tail z-score1.960
99% two-tail z-score2.576
Basel III minimum CET14.5%
Basel III minimum Tier 16.0%
Basel III minimum Total Capital8.0%
Capital Conservation Buffer2.5%
LCR minimum100%
NSFR minimum100%
Basel Leverage Ratio minimum3.0%
EWMA λ (RiskMetrics daily)0.94
EWMA λ (RiskMetrics monthly)0.97
Basel VaR scaling period10 days
BIA operational risk α15%

Expected Value (Discrete)

Very High Yield

Weighted average of all possible outcomes.

Exam Tip: Know the difference between population and sample mean. The exam loves to test whether you divide by n or n−1.

Variance

Very High Yield

Measures dispersion of a random variable around its mean.

Exam Tip: Sample variance divides by (n−1), NOT n. This is a classic exam trap.

Standard Deviation

Very High Yield

Square root of variance; same units as the original variable.

Covariance

High Yield

Measures linear co-movement between two variables.

Correlation

Very High Yield

Normalised covariance, bounded between −1 and +1.

Exam Tip: Correlation = 0 does NOT mean independence (only for normal distributions). The exam tests this distinction.

Bayes' Theorem

Very High Yield

Updates prior probability given new evidence.

Exam Tip: Appears heavily in credit-risk contexts: updating PD given new information. Write out numerator and denominator separately to avoid errors.

Normal Distribution Z-Score

Very High Yield

Standardises any normal variable to N(0,1).

Exam Tip: Key z-values: 1.65 (95% one-tail), 1.96 (95% two-tail), 2.33 (99% one-tail), 2.58 (99% two-tail).

Central Limit Theorem

High Yield

Sample mean approaches normal distribution regardless of the population distribution.

Exam Tip: Works even for non-normal populations when n ≥ 30. The exam may ask when CLT fails (e.g., infinite variance distributions).

Simple Linear Regression

Very High Yield

Models linear relationship between dependent and independent variable.

OLS Beta Estimator

Very High Yield

Slope coefficient that minimises sum of squared residuals.

R-Squared

Very High Yield

Proportion of variance explained by the model.

Exam Tip: R² always increases with more variables. Use Adjusted R² for model comparison. The exam tests this distinction.

Adjusted R-Squared

High Yield

Penalises R² for adding more independent variables.

t-Statistic for Coefficient

Very High Yield

Tests whether a regression coefficient is statistically significant.

Exam Tip: If |t| > 2 (roughly), the coefficient is significant at the 5% level. Watch for one-tail vs two-tail questions.

F-Statistic

High Yield

Tests overall significance of the regression model.

EWMA Volatility

Very High Yield

Exponentially Weighted Moving Average volatility. Recent returns get more weight.

Exam Tip: RiskMetrics uses λ = 0.94 for daily data. EWMA is a special case of GARCH(1,1) where ω = 0. This is an extremely common exam question.

GARCH(1,1)

Very High Yield

Generalised model with mean-reverting long-run variance.

Exam Tip: Long-run variance = ω/(1−α−β). Stationarity requires α+β < 1. When α+β = 1, it degenerates to IGARCH (similar to EWMA).

GARCH Long-Run Variance

High Yield

The unconditional variance that GARCH(1,1) reverts to.

Volatility Scaling (Square-Root of Time)

Very High Yield

Scale daily volatility to T-day horizon assuming i.i.d. returns.

Exam Tip: Only valid under i.i.d. assumption. If returns are autocorrelated, this breaks down. Exam loves to test this assumption.

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