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
Quantitative Analysis · Medium difficulty
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?
A. 0.000376
B. 0.00043
C. 0.0009
D. 0.0013
The correct answer is B — 0.00043.
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.
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.