What FRM Part 1 Quantitative Analysis actually tests
Quantitative Analysis is 20% of the Part 1 exam:
| Area | What it covers |
|---|---|
| Probability Fundamentals | Conditional probability, Bayes' theorem, counting rules |
| Probability Distributions | Normal, lognormal, Student's t, chi-square, F, Poisson, binomial |
| Statistical Inference | Estimators, confidence intervals, hypothesis testing, Type I/II errors |
| Linear Regression | OLS assumptions, R-squared, heteroskedasticity, multicollinearity, autocorrelation |
| Time-Series Analysis | Stationarity, unit root tests, AR/MA/ARMA processes, cointegration |
| Simulation Methods | Monte Carlo, variance reduction (antithetic and control variates) |
| Volatility Modeling | EWMA, GARCH(1,1), implied volatility |
| Correlation & Copulas | Pearson, Spearman, Kendall, tail dependence, correlation breakdown in stress |
Why EWMA is worth mastering cold
EWMA is the simplest of the volatility models FRM tests, but it's tested in both directions — "given yesterday's variance and today's return, compute today's variance" and "explain why a higher lambda makes the estimate less reactive to recent shocks." Confusing the direction of the decay factor is the single most common EWMA mistake.
Sample question: EWMA Volatility
Yesterday's EWMA variance estimate was 0.0004 (daily). Today's return was 3%. Using a decay factor (λ) of 0.94, what is today's updated EWMA variance estimate?
EWMA: σ²ₜ = λ·σ²ₜ₋₁ + (1−λ)·r²ₜ = 0.94×0.0004 + 0.06×(0.03)² = 0.000376 + 0.000054 = 0.00043. Choice A stops after just the first (decayed prior variance) term — a common error that forgets to add the new-information term entirely.
The 2026 Quantitative Analysis syllabus, reading by reading
Pinnacle runs on a syllabus graph — named readings with explicit prerequisites, each one mapped against GARP's official 2026 FRM Study Guide. It is the same map the free diagnostic reasons over, not a marketing summary of it. These are the six confirmed Quantitative Analysis readings, and what each one covers:
Probability & Distributions
Probability fundamentals — sample spaces, mutually exclusive events, conditional probability, Bayes' theorem, the law of total probability — and the named distributions used in risk: uniform, Bernoulli, binomial, Poisson, normal, lognormal, Student's t, chi-square, F, and beta.
Statistical Inference
Sample moments and the population-versus-sample distinction; the properties of estimators — bias, efficiency, consistency; and hypothesis testing with confidence intervals.
Linear Regression
OLS assumptions and parameter interpretation, R-squared and the F-statistic, residual analysis — heteroskedasticity, multicollinearity, autocorrelation and Durbin-Watson — and multiple regression in risk modelling.
Time Series & Volatility
Stationarity and unit-root tests, AR, MA and ARMA processes, cointegration and forecasting; volatility modelling with realised volatility, EWMA and GARCH(1,1); and measuring returns, volatility and correlation for normally and non-normally distributed variables.
Simulation & Bootstrapping
Monte Carlo methods: generating scenarios, pseudorandom numbers, and variance reduction via antithetic variates, control variates, and importance sampling.
Machine Learning Foundations
Preparing data for machine-learning applications, distinguishing the types of model, the leading supervised models for classification and prediction, and machine learning as an alternative to traditional model-building in finance.
Every practice question in the bank is tagged to one of these readings — which is how the diagnostic can name the specific concept underneath a wrong answer, not just the topic area it sat in.
Reading names follow GARP's published 2026 FRM Study Guide, referenced for accuracy. Pinnacle is an independent adaptive learning platform. FRM® is a registered trademark of the Global Association of Risk Professionals (GARP). Pinnacle is not affiliated with, endorsed by, or connected to that organisation.