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CFA InstituteCourse
CFA Chartered Financial AnalystPages
10
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2023
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CFA Level 2 - Quantitative Analysis Session 3 - Reading 12 (Practice Questions, Sample Questions) 1. Consider the following estimated regression equation, with calculatedt-statistics of the estimates as indicated:AUTOt = 10.0 + 1.25 PIt + 1.0 TEENt – 2.0 INStwith 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 ofsigniﬁcance, which of the independent variables signiﬁcantly diﬀerentfrom 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 anda 5% level of signiﬁcance are ± 2.028. Therefore, only TEEN isstatistically signiﬁcant.] 2. Consider the following estimated regression equation, with thestandard errors of the slope coeﬃcients as noted:Sales i = 10.0 + 1.25 R&Di + 1.0 ADVi – 2.0 COMPi + 8.0 CAPiwhere 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 , thestandard error for the estimated coeﬃcient on COMP is 0.63, and thestandard error for the estimated coeﬃcient on CAP is 2.5.
The equation was estimated over 40 companies. Using a 5% level ofsigniﬁcance, which of the estimated coeﬃcients are signiﬁcantlydiﬀerent 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 anda 5% level of signiﬁcance are ± 2.03.The calculated t-values are:t for R&D = 1.25 / 0.45 = 2.777t for ADV = 1.0/ 2.2 = 0.455t for COMP = -2.0 / 0.63 = -3.175t 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 CAPiwhere Sales is dollar sales in millions, R&D is research and developmentexpenditures in millions, ADV is dollar amount spent on advertising inmillions, COMP is the number of competitors in the industry, and CAPis the capital expenditures for the period in millions of dollars.Which of the following is NOT a correct interpretation of this regressioninformationA) If a company spends $1 million more on capital expenditures (holdingeverything else constant), Sales are expected to increase by $8.0 million.B) One more competitor will mean $2 million less in Sales (holdingeverything else constant).
C) If R&D and advertising expenditures are $1 million each, there are5 competitors, and capital expenditures are $2 million, expected Salesare $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 COMPiwhere Sales is dollar sales in millions, R&D is research and developmentexpenditures in millions, ADV is dollar amount spent on advertising inmillions, and COMP is the number of competitors in the industry.Which of the following is NOT a correct interpretation of this regressioninformation?A) One more competitor will mean $3 million less in sales (holdingeverything else constant).B) If R&D and advertising expenditures are $1 million each and there are5 competitors, expected sales are $9.5 million. C) If a company spends $1 more on R&D (holding everything elseconstant), sales are expected to increase by $1.5 million. [Explanation: If a company spends $1 million more on R&D (holdingeverything 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. Whichof the following would NOT be an indication of multicollinearity? X isclosely related to:A) 3y + 2z. B) y2. C) 3.
[Explanation: If x is related to y2, the relationship between x and y is notlinear, so multicollinearity does not exist. If x is equal to a constant (3), itwill 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 toattempt to eliminate highly correlated variables.] 7. Which of the following statements regarding multicollinearity is leastaccurate? A) Multicollinearity may be present in any regression model. B) Multicollinearity may be a problem even if the multicollinearity is notperfect.C) If the t-statistics for the individual independent variables areinsigniﬁcant, yet the F-statistic is signiﬁcant, this indicates the presenceof multicollinearity.[Explanation: Multicollinearity is not an issue in simple linearregression.] 8. An analyst runs a regression of portfolio returns on three independentvariables. These independent variables are price-to-sales (P/S),price-to-cash ﬂow (P/CF), and price-to-book (P/B). The analyst discoversthat 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 theindividual independent variables are not signiﬁcant. What violation ofregression analysis has occurred?A) conditional heteroskedasticity.B) serial correlation. C) multicollinearity. [Explanation: An indication of multicollinearity is when the independentvariables individually are not statistically signiﬁcant but the F-testsuggests that the variables as a whole do an excellent job of explainingthe variation in the dependent variable.] 9. When two or more of the independent variables in a multipleregression 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 moreof the independent variables, or linear combinations of the independentvariables, in a multiple regression are highly correlated with each other.This condition distorts the standard error of estimate and the coeﬃcientstandard errors, leading to problems when conducting t-tests forstatistical signiﬁcance of parameters.] 10. When utilizing a proxy for one or more independent variables in amultiple regression model, which of the following errors is most likely tooccur?A) Multicollinearity.B) Heteroskedasticity.
C) Model misspeciﬁcation. [Explanation: By using a proxy for an independent variable in a multipleregression analysis, there is some degree of error in the measurement ofthe variable.] 11. When constructing a regression model to predict portfolio returns,an analyst runs a regression for the past ﬁve year period. A erexamining the results, she determines that an increase in interest ratestwo years ago had a signiﬁcant impact on portfolio results for the time ofthe increase until the present. By performing a regression over twoseparate time periods, the analyst would be attempting to prevent whichtype 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 dependentvariables can change over time, so it is critical that the data be pooledcorrectly. Running the regression for multiple sub-periods (in this casetwo) rather than one time period can produce more accurate results.] 12. Which of the following is least likely to result in misspeciﬁcation of aregression 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 dependentvariable 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 amisspeciﬁcation. Methods used to transform independent variablesinclude squaring the variable or taking the square root.] 13. An analyst is building a regression model which returns a qualitativedependant variable based on a probability distribution. This is leastlikely a:A) probit model. B) discriminant model. C) logit model.[Explanation: A probit model is a qualitative dependant variable which isbased on a normal distribution. A logit model is a qualitative dependantvariable which is based on the logistic distribution. A discriminantmodel returns a qualitative dependant variable based on a linearrelationship that can be used for ranking or classiﬁcation into discretestates.] 14. Which of the following questions is least likely answered by using aqualitative dependent variable?A) Based on the following company-speciﬁc ﬁnancial ratios, willcompany ABC enter bankruptcy?B) Based on the following subsidiary and competition variables, willcompany XYZ divest itself of a subsidiary? C) Based on the following executive-speciﬁc and company-speciﬁcvariables, how many shares will be acquired through the exercise ofexecutive stock options?
[Explanation: The number of shares can be a broad range of values andis, therefore, not considered a qualitative dependent variable.] 15. Which of the following is NOT a model that has a qualitativedependent variable?A) Logit. B) Event study. C) Discriminant analysis.[Explanation: An event study is the estimation of the abnormalreturns--generally associated with an informational event—that take onquantitative values.] 16. A high-yield bond analyst is trying to develop an equation usingﬁnancial ratios to estimate the probability of a company defaulting on itsbonds. Since the analyst is using data over diﬀerent economic timeperiods, there is concern about whether the variance is constant overtime. 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 aprobability of a discrete outcome is logit modeling.] 17. What is the main diﬀerence between probit models and typicaldummy variable models?A) There is no diﬀerence--a probit model is simply a special case of adummy variable regression.
B) A dummy variable represents a qualitative independent variable,while a probit model is used for estimating the probability of aqualitative dependent variable. C) Dummy variable regressions attempt to create an equation to classifyitems into one of two categories, while probit models estimate aprobability.[Explanation: Dummy variables are used to represent a qualitativeindependent variable. Probit models are used to estimate the probabilityof occurrence for a qualitative dependent variable.] 18. An analyst has run several regressions hoping to predict stockreturns, and wants to translate this into an economic interpretation forhis 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 returnsdown by 0.01% . B) a stock with zero beta and zero market capitalization will returnprecisely 3.0%.C) prediction errors are always on the positive side.[Explanation: The coeﬃcient of MarketCap is 0.01%, indicating thatlarger companies have slightly smaller returns. Note that a companywith no market capitalization would not be expected to have a return atall. Error terms are typically assumed to be normally distributed with amean of zero] 19. Mary Steen estimated that if she purchased shares of companies whoannounced restructuring plans at the announcement and held them for
ﬁve days, she would earn returns in excess of those expected from themarket model of 0.9%. These returns are statistically signiﬁcantlydiﬀerent 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 covertransactions costs, so there is no economic signiﬁcance to this tradingstrategy. This is not an example of market ineﬃciency because excessreturns are not available a er covering transactions costs.]
CFA Level 2 - Quantitative Analysis Session 3 - Reading 12
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