Free FRM Quantitative Analysis Practice Questions & Answers
400 exam-style Quantitative Analysis questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
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Question 61
Extreme Value Theory shows that the tail of many distributions converges to:
Select an option first.
Correct answer: B — The Generalised Pareto Distribution (GPD) for exceedances over a threshold, regardless of the original distribution — this is the Pickands-Balkema-de Haan theorem underlying the Peaks Over Threshold (POT) method
Explanation: B
Question 62
In a simple linear regression Y = α + βX + ε, the coefficient β represents:
Select an option first.
Correct answer: B — The expected change in Y for a one-unit increase in X
Explanation: B
Question 63
R-squared in a regression model measures:
Select an option first.
Correct answer: B — The proportion of the total variance in the dependent variable explained by the independent variable(s)
Explanation: B
Question 64
Heteroskedasticity in a regression model means:
Select an option first.
Correct answer: B — The variance of the error term is not constant across observations
Explanation: B
Question 65
A stationary time series has:
Select an option first.
Correct answer: B — A constant mean, constant variance, and autocovariance that depends only on the lag
Explanation: B
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Correct answer: B — The value at time t is correlated with values at earlier times
Explanation: B
Question 67
The F-statistic in a multiple regression tests:
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Correct answer: B — The joint null hypothesis that all slope coefficients are simultaneously equal to zero (overall model significance)
Explanation: B
Question 68
In time series analysis, a seasonal component:
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Correct answer: B — Refers to regular, periodic fluctuations that repeat over a fixed period (e.g., annually, quarterly)
Explanation: B
Question 69
OLS regression minimises:
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Correct answer: B — The sum of squared residuals
Explanation: B
Question 70
In a multiple regression, multicollinearity causes:
Select an option first.
Correct answer: B — Inflated standard errors making it difficult to determine individual variable significance
Explanation: B
Question 71
An AR(1) model X_t = φX_{t-1} + ε_t is stationary when:
Select an option first.
Correct answer: D — |φ| < 1
Explanation: D
Question 72
The Durbin-Watson test statistic close to 2 indicates:
Select an option first.
Correct answer: C — Approximately no autocorrelation in residuals
Explanation: C
Question 73
GARCH(1,1) models volatility as:
Select an option first.
Correct answer: B — A function of lagged squared returns and lagged variance, capturing volatility clustering
Explanation: B
Question 74
In a financial time series regression, heteroskedasticity-consistent (White) standard errors are used to:
Select an option first.
Correct answer: B — Correct the standard errors when heteroskedasticity is present, producing valid inference even when error variance is non-constant
Explanation: B
Question 75
The Augmented Dickey-Fuller (ADF) test tests the null hypothesis that:
Select an option first.
Correct answer: B — A time series has a unit root (is non-stationary)
Explanation: B
Question 76
A vector autoregression (VAR) model extends the AR model to:
Select an option first.
Correct answer: B — Model multiple time series simultaneously, where each variable depends on its own lags and lags of all other variables in the system
Explanation: B
Question 77
Panel data combines:
Select an option first.
Correct answer: B — Cross-sectional and time series observations — multiple entities (firms, countries) observed over multiple periods — allowing control for unobservable entity-specific effects through fixed or random effects models
Explanation: B
Question 78
In a regression with autocorrelated errors, OLS estimators are:
Select an option first.
Correct answer: B — Unbiased but inefficient, with standard errors that are biased
Explanation: B
Question 79
An ARMA(p,q) model combines:
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Correct answer: C — Both autoregressive (p lags of X) and moving average (q lags of the error term) components
Explanation: C
Question 80
Granger causality tests whether:
Select an option first.
Correct answer: A — X causes Y in a statistical sense by determining if past values of X improve the forecast of Y beyond what past values of Y alone predict
Explanation: A
Question 81
Cointegration between two non-stationary time series X and Y means:
Select an option first.
Correct answer: B — There exists a linear combination aX + bY that is stationary, even though X and Y individually are non-stationary (unit root) — implying a long-run equilibrium relationship
Explanation: B
Question 82
Market risk is best defined as:
Select an option first.
Correct answer: B — The risk of losses from adverse movements in market prices such as equity prices, interest rates, exchange rates, and commodity prices
Explanation: B
Question 83
Credit risk is:
Select an option first.
Correct answer: B — The risk that a borrower or counterparty fails to meet its contractual obligations
Explanation: B
Question 84
Operational risk is defined as:
Select an option first.
Correct answer: B — The risk of losses resulting from inadequate or failed internal processes, people, systems, or external events
Explanation: B
Question 85
Liquidity risk comprises:
Select an option first.
Correct answer: B — Both funding liquidity risk (inability to raise funds) and market liquidity risk (inability to transact at fair prices)
Explanation: B
Question 86
The risk appetite of an organisation is best described as:
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Correct answer: B — The amount and type of risk an organisation is willing to accept in pursuit of its objectives
Explanation: B
Question 87
Value at Risk (VaR) at the 99% confidence level over a one-day horizon means:
Select an option first.
Correct answer: B — The maximum loss that will not be exceeded on 99% of trading days
Explanation: B
Question 88
Expected Shortfall (ES) differs from VaR because:
Select an option first.
Correct answer: B — ES measures the average loss in the worst (1 - confidence level) scenarios, beyond the VaR threshold
Explanation: B
Question 89
Systemic risk refers to:
Select an option first.
Correct answer: B — The risk that the failure of one financial institution or market disruption could cascade across the financial system, threatening its overall stability
Explanation: B
Question 90
The risk of model error — using incorrect assumptions in a pricing or risk model — is called:
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