CFA Level 2 Candidate Resource Questions with Answers

University:
CFA Institute
Course:
CFA Level II - Quantitative Methods
Academic year:

2023
Views:

308

Pages:

308
Author:

LabsAnonym

Brendan Dennehy Case Scenario Brendan Dennehy works for Transon Investments, PLC, a Dublin-based hedge fund with significant equity investments in technology companies in Asia, North America, and Europe. Transon is technology (IT) is Sean Malloy. number of defective assemblies per hour is a function of the outside air temperature and the speed (production rate) of the assembly lines. Malloy recalls that Dennehy has had substantial training in statistics while working on his MBA. He asks Dennehy to help him interpret the regression results supplied by Winston. Exhibit 1 Regression Results Dt = b0 + b1Airt + b2Rt + ɸt Coefficient Standard Error Constant (b0) 0.016 0.0942 Outside air temperature (b1) 0.0006 0.001 Assembly line speed (b2) 0.5984 0.3 Number of observations used in the regression 384 Critical t-value at 5% significance (two-tail test where coefficient equals zero Standard Error of the Estimate Durbinʹ Watson Statistic FStatistic Significance of F 0.414 0.333 1.89 157.699 0 DurbinʹWatson critical values (5% significance) 1.63 1.72 Dt = b0 + b1Airt + b2Rt + ɸt Coefficient Standard Error Correlation between outside air temperature and assembly line speed 0.015 Using the data provided in Exhibit 1, Dennehy tests the hypothesis that the coefficients for outside air temperature and assembly line speed are significantly different from zero, using a significance level of 5%. Dennehy also uses the results given in Exhibit 1 to evaluate the potential for multicollinearity in the data. Finally, Dennehy would like to confirm that nonstationary is not a problem. To test for this he conducts DickeyʹFuller tests for a unit root on each of the time series. The results are reported in Exhibit 2. Exhibit 2 Results of the Dickey-Fuller Tests Time Series Value of the Test Statistic Standard Error tStatistic Significance of t Defective assemblies per hour 0.0036 0.0023 1.591 0.1123 Outside air temperature ʹ0.423 0.0724 ʹ5.846 0 Assembly line speed ʹ0.586 0.043 ʹ13.510 0 Question 1 Based on Exhibit 1 and statistical tests, the best conclusion Dennehy can make is that the regression coefficient is significantly different from zero with respect to the coefficient(s) for: A. assembly line speed (b2) only. Solution A is correct. The null hypotheses are that the coefficients equal zero. The alternative hypotheses are that the coefficients do not equal zero (two-tailed tests). The appropriate test statistics, t, are calculated by dividing the estimates of the coefficients by their respective standard error. tb1 = 0.0006/0.0010 = 0.60 tb2 = 0.5984/0.30 = 1.9947 The test statistic for outside air temperature is less than the critical value of 1.96. The test statistic for assembly line speed exceeds the critical value of 1.96. Dennehy cannot reject the null hypothesis that the population regression coefficient for outside air temperature, b1, is zero. Dennehy can reject the null hypothesis that b2 is zero at the 5% level of significance. B is incorrect. Only assembly line speed is significant. C is incorrect. Outside air temperature is not significant. The most appropriate interpretation of the results reported in Exhibit 1 is that: A. the F-statistic of the regression is not significant. B. predictions of defective assemblies per hour made using the regression have only about a 41% chance of being correct. C. variations in the independent variables explain approximately 41% of the variation in the defective assemblies per hour. Solution C is correct. The R2 indicates that variations in the independent variables explain approximately 41% of the variation in the dependent variable. The F-statistic is highly significant. R2 does not inform us regarding the probability of a dependent variable prediction being correct. A is incorrect. The F-test of the regression is highly significant. B is incorrect. R2 does not inform us regarding the probability of a dependent variable prediction being correct. The results reported in Exhibit 1 are most accurately interpreted as indicating that: A. the reported R 2 is spurious. B. multicollinearity is not present. C. the regression coefficients have inflated standard errors. Solution B is correct. The pairwise correlation is low. The only case in which correlation between independent variables may be a reasonable indicator of multicollinearity occurs in a regression with exactly two independent variables, as is the case in this problem. Furthermore, the additional classic symptoms of multicollinearity (high R2 and significant F-statistic but not significant coefficients) are not present. A is incorrect. Even in the face of multicollinearity, a regression may have a high R2 . C is incorrect. At least one coefficient (b2) is different from zero. Assuming a 5% level of significance, the most appropriate conclusion that can be drawn from the DickeyʹFuller results reported in Exhibit 2 is that the: A. test for a unit root is inconclusive for the dependent variable. B. independent variables exhibit unit roots but the dependent variable does not. C. dependent variable exhibits a unit root but the independent variables do not. Solution C is correct. The DickeyʹFuller test uses the following type of regression: The null hypothesis is H0: g1 = 0 versus the alternative hypothesis Ha: g1 < 0 (a one-tail test). If g1 = 0, the time series has a unit root and is nonstationary. Thus, if the null hypothesis fails to be rejected, then the possibility exists that the time series has a unit root and is nonstationary. Based on the t ratios and their significance levels in Exhibit 2, the null hypothesis that the coefficient is zero is rejected for both outside air temperature and assembly line speed (i.e., the independent variables). But the null hypothesis is not rejected for the dependent variable, defective assemblies per hour. A is incorrect because the p-value for the DickeyʹFuller test of the dependent variable time series (11.23%) clearly fails to reject the null at 5% level of significance. B is incorrect. We reject the null hypothesis that the coefficient is zero for both outside air temperature and assembly line speed. We do not reject the null for the independent variable, defective assemblies per hour. Eduardo DeMolay Case Scenario Eduardo DeMolay, a research analyst at Mumbai Securities, is studying the time-series behavior of price-to-earnings ratios (P/Es) computed with trailing 12-month earnings (Etrailing). He and his assistant, Deepa Kamini, are reviewing the results of the ordinary least squares time series regression shown in Exhibit 1. Exhibit 1 Results of Regression of P/E on Lagged P/E (P/Et = b0 + b1P/Etʹ1 нɸt) Coefficient Standard Error t Significance of t Constant (b0) 0.143 0.153 0.935 0.176 Lagged P/E (b1) 0.991 0.003 292.958 0 R 2 Standard Error of the Estimate Durbinʹ Watson F Significance of F 0.075 1.48978 2.094 130.066 0

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