CFA Level 2 - Quantitative Analysis Session 3 - Reading 12

CFA Level 2 - Quantitative Analysis Session 3 - Reading 12 (Practice Questions, Sample Questions) 1. Consider the following estimated regression equation, with calculated t-statistics of the estimates as indicated: AUTOt = 10.0 + 1.25 PIt + 1.0 TEENt – 2.0 INSt with a PI calculated t-statstic of 0.45, a TEEN calculated t-statstic of 2.2, and an INS calculated t-statstic of 0.63. The equation was estimated over 40 companies. Using a 5% level of significance, which of the independent variables significantly different from zero? A) PI and INS only. B) PI only. C) TEEN only. [Explanation: The critical t-values for 40-3-1 = 36 degrees of freedom and a 5% level of significance are ± 2.028. Therefore, only TEEN is statistically significant.] 2. Consider the following estimated regression equation, with the standard errors of the slope coefficients as noted: Sales i = 10.0 + 1.25 R&Di + 1.0 ADVi – 2.0 COMPi + 8.0 CAPi where the standard error for the estimated coefficient on R&D is 0.45, the standard error for the estimated coefficient on ADV is 2.2 , the standard error for the estimated coefficient on COMP is 0.63, and the standard error for the estimated coefficient on CAP is 2.5. The equation was estimated over 40 companies. Using a 5% level of significance, which of the estimated coefficients are significantly different from zero? A) R&D, COMP, and CAP only. B) R&D, ADV, COMP, and CAP. C) ADV and CAP only. [Explanation: The critical t-values for 40-4-1 = 35 degrees of freedom and a 5% level of significance are ± 2.03. The calculated t-values are: t for R&D = 1.25 / 0.45 = 2.777 t for ADV = 1.0/ 2.2 = 0.455 t for COMP = -2.0 / 0.63 = -3.175 t for CAP = 8.0 / 2.5 = 3.2] 3. Consider the following regression equation: Sales i = 10.0 + 1.25 R&Di + 1.0 ADVi – 2.0 COMPi + 8.0 CAPi where Sales is dollar sales in millions, R&D is research and development expenditures in millions, ADV is dollar amount spent on advertising in millions, COMP is the number of competitors in the industry, and CAP is the capital expenditures for the period in millions of dollars. Which of the following is NOT a correct interpretation of this regression information A) If a company spends $1 million more on capital expenditures (holding everything else constant), Sales are expected to increase by $8.0 million. B) One more competitor will mean $2 million less in Sales (holding everything else constant). C) If R&D and advertising expenditures are $1 million each, there are 5 competitors, and capital expenditures are $2 million, expected Sales are $8.25 million. [Explanation: Predicted sales = $10 + 1.25 + 1 – 10 + 16 = $18.25 million.] 4. Consider the following regression equation: Sales i = 20.5 + 1.5 R&Di + 2.5 ADVi – 3.0 COMPi where Sales is dollar sales in millions, R&D is research and development expenditures in millions, ADV is dollar amount spent on advertising in millions, and COMP is the number of competitors in the industry. Which of the following is NOT a correct interpretation of this regression information? A) One more competitor will mean $3 million less in sales (holding everything else constant). B) If R&D and advertising expenditures are $1 million each and there are 5 competitors, expected sales are $9.5 million. C) If a company spends $1 more on R&D (holding everything else constant), sales are expected to increase by $1.5 million. [Explanation: If a company spends $1 million more on R&D (holding everything else constant), sales are expected to increase by $1.5 million. Always be aware of the units of measure for the different variables.] 5. A variable is regressed against three other variables, x, y, and z. Which of the following would NOT be an indication of multicollinearity? X is closely related to: A) 3y + 2z. B) y2. C) 3. [Explanation: If x is related to y2, the relationship between x and y is not linear, so multicollinearity does not exist. If x is equal to a constant (3), it will be correlated with the intercept term.] 6. Which of the following is a potential remedy for multicollinearity? A) Omit one or more of the collinear variables. B) Take first differences of the dependent variable. C) Add dummy variables to the regression. [Explanation: The first differencing is not a remedy for the collinearity, nor is the inclusion of dummy variables. The best potential remedy is to attempt to eliminate highly correlated variables.] 7. Which of the following statements regarding multicollinearity is least accurate? A) Multicollinearity may be present in any regression model. B) Multicollinearity may be a problem even if the multicollinearity is not perfect. C) If the t-statistics for the individual independent variables are insignificant, yet the F-statistic is significant, this indicates the presence of multicollinearity. [Explanation: Multicollinearity is not an issue in simple linear regression.] 8. An analyst runs a regression of portfolio returns on three independent variables. These independent variables are price-to-sales (P/S), price-to-cash flow (P/CF), and price-to-book (P/B). The analyst discovers that the p-values for each independent variable are relatively high. However, the F-test has a very small p-value. The analyst is puzzled and tries to figure out how the F-test can be statistically significant when the individual independent variables are not significant. What violation of regression analysis has occurred? A) conditional heteroskedasticity. B) serial correlation. C) multicollinearity. [Explanation: An indication of multicollinearity is when the independent variables individually are not statistically significant but the F-test suggests that the variables as a whole do an excellent job of explaining the variation in the dependent variable.] 9. When two or more of the independent variables in a multiple regression are correlated with each other, the condition is called: A) serial correlation. B) multicollinearity. C) conditional heteroskedasticity. [Explanation: Multicollinearity refers to the condition when two or more of the independent variables, or linear combinations of the independent variables, in a multiple regression are highly correlated with each other. This condition distorts the standard error of estimate and the coefficient standard errors, leading to problems when conducting t-tests for statistical significance of parameters.] 10. When utilizing a proxy for one or more independent variables in a multiple regression model, which of the following errors is most likely to occur? A) Multicollinearity. B) Heteroskedasticity. C) Model misspecification. [Explanation: By using a proxy for an independent variable in a multiple regression analysis, there is some degree of error in the measurement of the variable.] 11. When constructing a regression model to predict portfolio returns, an analyst runs a regression for the past five year period. After examining the results, she determines that an increase in interest rates two years ago had a significant impact on portfolio results for the time of the increase until the present. By performing a regression over two separate time periods, the analyst would be attempting to prevent which type of misspecification? A) Incorrectly pooling data. B) Using a lagged dependent variable as an independent variable. C) Forecasting the past. [Explanation: The relationship between returns and the dependent variables can change over time, so it is critical that the data be pooled correctly. Running the regression for multiple sub-periods (in this case two) rather than one time period can produce more accurate results.] 12. Which of the following is least likely to result in misspecification of a regression model? A) Transforming a variable. B) Using a lagged dependent variable as an independent variable. C) Measuring independent variables with errors. [Explanation: A basic assumption of regression is that the dependent variable is linearly related to each of the independent variables. Frequently, they are not linearly related and the independent variable must be transformed or the model is misspecified. Therefore, transforming an independent variable is a potential solution to a misspecification. Methods used to transform independent variables include squaring the variable or taking the square root.] 13. An analyst is building a regression model which returns a qualitative dependant variable based on a probability distribution. This is least likely a: A) probit model. B) discriminant model. C) logit model. [Explanation: A probit model is a qualitative dependant variable which is based on a normal distribution. A logit model is a qualitative dependant variable which is based on the logistic distribution. A discriminant model returns a qualitative dependant variable based on a linear relationship that can be used for ranking or classification into discrete states.] 14. Which of the following questions is least likely answered by using a qualitative dependent variable? A) Based on the following company-specific financial ratios, will company ABC enter bankruptcy? B) Based on the following subsidiary and competition variables, will company XYZ divest itself of a subsidiary? C) Based on the following executive-specific and company-specific variables, how many shares will be acquired through the exercise of executive stock options? [Explanation: The number of shares can be a broad range of values and is, therefore, not considered a qualitative dependent variable.] 15. Which of the following is NOT a model that has a qualitative dependent variable? A) Logit. B) Event study. C) Discriminant analysis. [Explanation: An event study is the estimation of the abnormal returns--generally associated with an informational event—that take on quantitative values.] 16. A high-yield bond analyst is trying to develop an equation using financial ratios to estimate the probability of a company defaulting on its bonds. Since the analyst is using data over different economic time periods, there is concern about whether the variance is constant over time. A technique that can be used to develop this equation is: A) multiple linear regression adjusting for heteroskedasticity. B) logit modeling. C) dummy variable regression. [Explanation: The only one of the possible answers that estimates a probability of a discrete outcome is logit modeling.] 17. What is the main difference between probit models and typical dummy variable models? A) There is no difference--a probit model is simply a special case of a dummy variable regression. B) A dummy variable represents a qualitative independent variable, while a probit model is used for estimating the probability of a qualitative dependent variable. C) Dummy variable regressions attempt to create an equation to classify items into one of two categories, while probit models estimate a probability. [Explanation: Dummy variables are used to represent a qualitative independent variable. Probit models are used to estimate the probability of occurrence for a qualitative dependent variable.] 18. An analyst has run several regressions hoping to predict stock returns, and wants to translate this into an economic interpretation for his clients. Return = 3.0 + 2.0Beta – 0.0001Market Cap (in billions) + ε A correct interpretation of the regression most likely includes: A) a billion dollar increase in market capitalization will drive returns down by 0.01%. B) a stock with zero beta and zero market capitalization will return precisely 3.0%. C) prediction errors are always on the positive side. [Explanation: The coefficient of MarketCap is 0.01%, indicating that larger companies have slightly smaller returns. Note that a company with no market capitalization would not be expected to have a return at all. Error terms are typically assumed to be normally distributed with a mean of zero] 19. Mary Steen estimated that if she purchased shares of companies who announced restructuring plans at the announcement and held them for five days, she would earn returns in excess of those expected from the market model of 0.9%. These returns are statistically significantly different from zero. The model was estimated without transactions costs, and in reality these would approximate 1% if the strategy were effected. This is an example of: A) statistical significance, but not economic significance. B) statistical and economic significance. C) a market inefficiency. [Explanation: The abnormal returns are not sufficient to cover transactions costs, so there is no economic significance to this trading strategy. This is not an example of market inefficiency because excess returns are not available after covering transactions costs.]