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36 multiple-choice questions and 29 flashcards on Quantitative Methods, about 9% of the CFA Level II bank. Every one carries a written rationale.
Quantitative Methods is one of 10 chapters in CoStudy's CFA Level II bank, and it holds 36 of the bank's 401 multiple-choice questions — roughly 9% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.
Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.
9 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.
A quarterly inflation series is modeled as an AR(1) process: x_t = 0.5 + 0.5x_{t-1} + ε_t. The correct basis for concluding the series is covariance stationary is that:
Answer: D — The series is stationary because the absolute value of the lag coefficient (0.5) is less than 1
A) Misidentifies the stationarity condition — it is the lag coefficient, not the intercept, whose magnitude must be below 1; the intercept can take any value without affecting stationarity. B) The coefficients happening to be numerically equal is irrelevant to stationarity; this is a spurious pattern-match rather than the actual test. C) Comparing the mean-reverting level to the lag coefficient is not the stationarity test — this fabricates a comparison that doesn't determine stationarity. D) Correct — a covariance-stationary AR(1) process requires the absolute value of the lag coefficient to be below 1, which holds here (0.5 < 1); the series reverts to a mean-reverting level of 0.5/(1−0.5) = 1.0.
Time series: stationarity required because:
Answer: A — Non-stationary series have time-varying
A) Correct — this identifies Non-stationary series have time-varying mean/variance. B) Multicollinearity effect on standard errors — related concept, not the definition. C) Serial correlation of regression residuals — related concept, not the definition. D) Heteroskedasticity effect on inference — related concept, not the definition.
An analyst tests two time series for cointegration using the Engle-Granger procedure: she regresses Y on X and then tests the residuals for stationarity. The residuals are stationary. The MOST appropriate conclusion is:
Answer: D — Y and X are cointegrated
A) Underfitting the sample data — related concept, not the definition. B) Sample selection bias effect — related concept, not the definition. C) Robust Newey-West correction — related concept, not the definition. D) Correct — this identifies Y and X are cointegrated.
A linear regression of fund returns on benchmark returns yields a Durbin-Watson statistic of 1.05 (n = 96; dL = 1.62, dU = 1.71). The analyst should conclude that residuals exhibit:
Answer: D — Positive serial correlation
A) Underfitting the sample data — related concept, not the definition. B) Sample selection bias effect — related concept, not the definition. C) Robust Newey-West correction — related concept, not the definition. D) Correct — this identifies Positive serial correlation.
An analyst wants to model potential future values of a pension plan's asset portfolio under thousands of randomly generated economic scenarios drawn from an assumed multivariate distribution of risk factors, rather than relying solely on the plan's historical return history. This approach is BEST described as:
Answer: A — Monte Carlo simulation, which generates scenarios from a specified probability distribution rather than resampling actual historical observations
A) Correct. B) Right concept, wrong scenario — historical simulation resamples actual historical data rather than generating scenarios from a specified theoretical distribution. C) Right concept, wrong scenario — bootstrap resampling also draws from the empirical dataset, not a specified distribution. D) True but irrelevant — sensitivity analysis varies one input at a time, a different technique from generating many joint random scenarios.
A Breusch-Pagan test on residuals from a cross-sectional regression returns a chi-square statistic of 17.2 with 4 degrees of freedom (critical value at 5% is 9.49). The analyst should:
Answer: D — Reject the null of homoskedasticity and use
A) Multicollinearity effect on standard errors — related concept, not the definition. B) Serial correlation of regression residuals — related concept, not the definition. C) Heteroskedasticity effect on inference — related concept, not the definition. D) Correct — this identifies Reject the null of homoskedasticity and use.
A 95% confidence interval for a regression coefficient is reported as [0.10, 0.42]. The MOST accurate interpretation of this interval is that:
Answer: A — If the sampling and estimation procedure were repeated many times, 95% of such constructed intervals would be expected to contain the true population coefficient
A) Correct. B) Common practitioner misconception — the frequentist interpretation doesn't assign a probability to the fixed true parameter for this one realized interval; that reading is a widely held but incorrect shortcut. C) Misconception — confuses the coefficient's confidence interval with the distribution of the underlying raw observations, an unrelated concept. D) Plausible-but-incomplete — excluding zero supports significance at the 5% level (since it's a 95% interval), but claiming 1% significance requires a narrower 99% interval, which wasn't provided.
A regression model's R² value is 0.65. This means:
Answer: C — 65% of the variation in the dependent variable is per calc
A) 71.50% per calc approx (rounded) ≈ value est. (calc) — off-by-percent numeric trap. B) 58.50% per calc approx (rounded) ≈ value est. (calc) — off-by-percent numeric trap. C) Correct — the computed value is 65% of the variation in the dependent variable is. D) 78.00% per calc approx (rounded) ≈ value est. (calc) — off-by-percent numeric trap.
A regression's residuals appear to have variance proportional to the square of an explanatory variable x. The MOST appropriate remediation is:
Answer: D — Apply weighted least squares with weights 1/x²
A) Multicollinearity effect on standard errors — related concept, not the definition. B) Serial correlation of regression residuals — related concept, not the definition. C) Heteroskedasticity effect on inference — related concept, not the definition. D) Correct — this identifies Apply weighted least squares with weights 1/x².
4 cards from the 29 in this chapter.
What is mean reversion in time series?
Tendency of a series to return to its long-run mean. AR(1) model: stationary if |b₁| < 1. Mean = b₀/(1−b₁).
What is the standard error of the mean?
σ / √n. Standard deviation of the sampling distribution of the sample mean. Decreases as sample size increases.
In a vignette: PM uses BL model. How are 'views' incorporated?
Investor expresses views as expected returns (absolute or relative) with confidence (variance). BL combines with implied equilibrium returns weighted by confidence.
In evaluating a machine learning model's out-of-sample performance, what is the difference between a validation set and a test set?
The validation set is used iteratively during model development to tune hyperparameters and select among competing specifications; the test set is held out entirely until final evaluation, providing an unbiased estimate of generalization performance uncontaminated by the tuning process.
These are a sample. The full Quantitative Methods chapter runs 65 items with per-chapter progress tracking, on the web and in the iOS app.
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