Quantitative Methods - 3 - Free MCQ Practice Test with solutions, CFA Level

An analyst runs a multiple regression of monthly portfolio excess returns on four independent variables. The regression output is presented below:

The critical t-value at the 5% significance level (two-tailed) is 1.96. Based solely on this output, which coefficients are statistically significant at the 5% level?

An analyst regresses annual earnings growth on firm size (total assets) and leverage ratio for a cross-section of 120 firms. She plots the regression residuals against firm size and observes that the spread of residuals increases systematically as firm size increases. Which type of heteroskedasticity is most likely present, and what is the most appropriate corrective measure?

An analyst estimates a regression of quarterly GDP growth on two lagged macroeconomic indicators. The Durbin-Watson (DW) statistic is 0.85. The critical bounds at the 5% significance level are d_L = 1.50 and d_U = 1.75. Which of the following is the most accurate interpretation, and which corrective method is most appropriate?

An analyst estimates a multiple regression model with three independent variables. The pairwise correlation between two of the independent variables is 0.92. The analyst observes that the overall F-statistic is highly significant (p < 0.01), yet none of the individual slope coefficients has a statistically significant t-statistic. The most likely consequence of the high pairwise correlation is:

A regression model with two independent variables has R² = 0.72 and adjusted R² = 0.66 (n = 80). An analyst adds two additional predictors; R² rises to 0.73 while adjusted R² falls to 0.63. Which of the following best characterizes the impact of adding the two new predictors?

An analyst models quarterly revenue as a function of macroeconomic conditions. To capture seasonality, she creates four dummy variables: D_Q1, D_Q2, D_Q3, and D_Q4, each equal to 1 if the observation falls in the respective quarter and 0 otherwise. She includes all four dummies along with an intercept in the regression. The most likely problem with this specification is:

A financial analyst estimates the following AR(1) model for monthly commodity price index values:

x_t = 0.30 + 0.75 × x_t−1

The mean-reverting level of this series is closest to:

An analyst applies the Dickey-Fuller test to a time series of monthly interest rate spreads. The test statistic is −1.42 and the critical value at the 5% significance level is −2.89. The analyst fails to reject the null hypothesis of the Dickey-Fuller test. The most appropriate conclusion is:

An analyst estimates the following AR(2) model for a quarterly earnings series:

x_t = 0.50 + 0.60 × x_t−1 + 0.20 × x_t−2

Given that x_t−1 = 10 and x_t−2 = 8, the one-period-ahead forecast for x_t is closest to:

An analyst regresses daily equity index returns on a set of macroeconomic factors. After estimating the model, the analyst tests the squared residuals for autocorrelation and finds statistically significant positive autocorrelation. Large return shocks in one period are followed by elevated residual variance in subsequent periods. This pattern is most likely an indication that:

An analyst is building a predictive model for credit default using 50 candidate predictor variables, most of which are suspected to be irrelevant. She applies LASSO regression and observes that 35 of the 50 coefficients are shrunk to exactly zero. Compared to ridge regression, LASSO is preferred in this context primarily because:

A quantitative analyst splits a dataset of 1,000 monthly observations into five equal folds and uses each fold as a hold-out validation set in turn while training the model on the remaining four folds. The analyst then averages the out-of-sample error across all five iterations. The primary purpose of this k-fold cross-validation procedure is to:

A binary classifier model is evaluated on a test set. The confusion matrix results are as follows:

The precision of the classifier is closest to:

An analyst estimates a regression of stock returns on trading volume and market capitalization. Unknown to the analyst, investor sentiment is a relevant determinant of returns and is positively correlated with trading volume. Investor sentiment is excluded from the model. The most likely consequence for the OLS estimates is:

A portfolio manager employs a machine learning algorithm that groups equity securities into distinct clusters based on patterns in historical return data, price momentum, and volatility metrics. No predefined category labels or target outputs are provided to the algorithm. This approach is best described as:

An analyst runs a Breusch-Pagan test on a cross-sectional regression. The resulting chi-square statistic is significant at the 1% level, confirming the presence of conditional heteroskedasticity. Rather than re-specifying the model, the analyst recalculates inference using White-corrected standard errors. This approach is best described as:

An analyst estimates a time-series regression of monthly inflation rates on two lagged independent variables using 90 observations. The Durbin-Watson (DW) statistic is 1.98. The critical bounds at the 5% significance level are d_L = 1.55 and d_U = 1.75. The most appropriate interpretation is:

An analyst is evaluating a multiple regression model. The current model with two independent variables has R² = 0.68 and adjusted R² = 0.66. Adding a third independent variable causes R² to increase to 0.69 while adjusted R² falls to 0.64. Which conclusion is best supported by this evidence?

An analyst examines a time series of corporate bond yield spreads. When spreads rise above their historical average, they subsequently tend to decline back toward that average, and when spreads fall below the average, they tend to rise. This behavior is best characterized as:

A risk analyst builds a regression model with five independent variables. Two of the variables-GDP growth and industrial production growth-have a pairwise correlation of 0.95. The model produces an R² of 0.81, but the t-statistics for GDP growth (t = 1.10) and industrial production growth (t = 1.22) are both statistically insignificant at the 5% level. The most likely explanation is:

An analyst builds a regression model for daily trading volumes and creates four dummy variables-D_Mon, D_Tue, D_Wed, D_Thu, and D_Fri-for each weekday, then includes all five dummies plus an intercept in the model. The regression software returns a singularity error and cannot estimate the model. The most likely cause is:

A quantitative analyst estimates the following AR(1) model for a monthly interest rate series:

x_t = 1.20 + 0.40 × x_t−1

The mean-reverting level of this series is closest to:

An analyst applies LASSO regression to a dataset with 20 candidate predictors. After optimization, 12 of the 20 coefficients are exactly equal to zero. The analyst notes that ridge regression applied to the same dataset retains all 20 non-zero coefficients, though many are very small. The most accurate explanation for LASSO's behavior is:

An analyst tests a monthly equity return series using the Dickey-Fuller test. The computed test statistic is −3.45 and the critical value at the 5% significance level is −2.89. The null hypothesis is rejected at the 5% significance level. The most appropriate conclusion is:

A credit analyst evaluates a machine learning classifier used to predict corporate bond defaults. The confusion matrix is as follows:

The F1 score of the classifier is closest to:

An econometrics instructor asks students to distinguish between conditional and unconditional heteroskedasticity. Which of the following statements most accurately captures the distinction as defined under the CFA curriculum?

An analyst regresses monthly hedge fund returns on four risk factors. The regression output is summarized below:

The most appropriate interpretation of the F-statistic result is:

An analyst models daily equity index volatility over a five-year period. She observes that large absolute return shocks-whether positive or negative-are systematically followed by periods of elevated volatility, and calm periods tend to follow calm periods. This empirical pattern is most consistent with:

An analyst compares two competing regression models for forecasting equity risk premiums. Using 5-fold cross-validation, Model A achieves an average out-of-sample root mean squared error (RMSE) of 2.1, while Model B achieves an average out-of-sample RMSE of 3.4. Model B has a higher in-sample R² than Model A. Based on this analysis, the analyst should most likely:

An analyst is selecting a regularization method for a predictive model of sovereign credit spreads. The dataset contains 200 candidate macroeconomic and financial predictors. Economic theory suggests that only a small subset of these predictors are genuinely relevant to spread determination. Which of the following best identifies the most appropriate regularization approach and the key reason for its selection?