FRM Exam Formula Cheat Sheet
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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.
📌 Critical Numbers to Memorise
Expected Value (Discrete)
Very High YieldWeighted 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 YieldMeasures 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 YieldSquare root of variance; same units as the original variable.
Covariance
High YieldMeasures linear co-movement between two variables.
Correlation
Very High YieldNormalised 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 YieldUpdates 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 YieldStandardises 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 YieldSample 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 YieldModels linear relationship between dependent and independent variable.
OLS Beta Estimator
Very High YieldSlope coefficient that minimises sum of squared residuals.
R-Squared
Very High YieldProportion 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 YieldPenalises R² for adding more independent variables.
t-Statistic for Coefficient
Very High YieldTests 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 YieldTests overall significance of the regression model.
EWMA Volatility
Very High YieldExponentially 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 YieldGeneralised 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 YieldThe unconditional variance that GARCH(1,1) reverts to.
Volatility Scaling (Square-Root of Time)
Very High YieldScale 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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