Quantitative Analysis

FRM® Part I, published weight 20%. Probability, hypothesis testing, regression, time series, volatility, simulation.

What the outline covers

Probability, Bayes’ rule, random variables and common distributions
Sample moments and hypothesis testing
Linear regression; multiple regression and regression diagnostics
Stationary and non-stationary time series
Measuring volatility and correlation
Simulation methods and bootstrapping
Machine learning and prediction

Sample questions

These 5 questions are free in the app too. Try each one before opening the answer.

Question 1

A test for a rare condition has 95% sensitivity and 95% specificity. The condition affects 1% of the population. Given a positive result, the probability the condition is present is closest to:

P(D) = 1% · sensitivity 95% · specificity 95%

A. 16%
B. 48%
C. 85%
D. 95%

Show the answer

A. P(D

+) = (0.95 × 0.01)/[(0.95 × 0.01) + (0.05 × 0.99)] = 0.0095/0.0590 = 16.1%. Base rates dominate when the event is rare.

Reading: Quantitative Analysis — Bayes’ Rule

Question 2

A GARCH(1,1) model is estimated with α = 0.08 and β = 0.90. Persistence and the implication for volatility are:

α = 0.08 · β = 0.90

A. 0.98 — volatility mean-reverts slowly
B. 0.98 — volatility mean-reverts quickly
C. 0.82 — the model is non-stationary
D. 1.00 — the model reduces to EWMA

Show the answer

A. Persistence is α + β = 0.98, close to one, so shocks decay slowly and volatility mean-reverts only gradually. At exactly 1.00 it becomes EWMA.

Reading: Quantitative Analysis — Measuring Volatility

Question 3

An analyst regresses one random walk on an unrelated random walk and obtains an R² of 0.78 with a significant t-statistic. The correct conclusion is that:

A. A genuine economic relationship exists
B. The regression is spurious because both series are non-stationary
C. The sample size is too small
D. Heteroskedasticity is present

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B. Regressing non-stationary series produces spuriously high R² and significant t-statistics with no underlying relationship. Difference the series first.

Reading: Quantitative Analysis — Stationary and Non-Stationary Time Series

Question 4

Lowering the significance level of a hypothesis test from 5% to 1% will:

A. Reduce Type I error and reduce Type II error
B. Reduce Type I error and increase Type II error
C. Increase Type I error and reduce Type II error
D. Leave both error rates unchanged

Show the answer

B. A stricter threshold makes rejection harder, cutting false rejections (Type I) but raising failures to reject a false null (Type II).

Reading: Quantitative Analysis — Hypothesis Testing

Question 5

Compared with GARCH(1,1), the EWMA model:

A. Includes a long-run variance term and mean-reverts
B. Omits the long-run variance term and does not mean-revert
C. Requires a normality assumption GARCH does not
D. Cannot be estimated from historical returns

Show the answer

B. EWMA is GARCH(1,1) with ω = 0 and α + β = 1, so there is no long-run variance to revert to.

Reading: Quantitative Analysis — Measuring Volatility and Correlation

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