kasinkei

Which of the following statements regarding serial correlation that might be encountered in regression analysis is least accurate?

A) Negative serial correlation causes a failure to reject the null hypothesis when it is actually false.

B) Serial correlation occurs least often with time series data.

C) Positive serial correlation typically has the same effect as heteroskedasticity.

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Serial correlation, which is sometimes referred to as autocorrelation, occurs when the residual terms are correlated with one another, and is most frequently encountered with time series data.

kasinkei

Alex Wade, CFA, is analyzing the result of a regression analysis comparing the performance of gold stocks versus a broad equity market index. Wade believes that serial correlation may be present, and in order to prove his theory, should use which of the following methods to detect its presence?

A) The Durbin-Watson statistic.

B) The Breusch-Pagan test.

C) The Hansen method.

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The Durbin-Watson statistic is the most commonly used method for the detection of serial correlation, although residual plots can also be utilized. For a large sample size, DW ≈ 2(1-r), where r is the correlation coefficient between residuals from one period and those from a previous period. The DW statistic is then compared to a table of DW statistics that gives upper and lower critical values for various sample sizes, levels of significance and numbers of degrees of freedom to detect the presence or absence of serial correlation.

kasinkei

An analyst is estimating whether a fund’s excess return for a month is dependent on interest rates and whether the S&P 500 has increased or decreased during the month. The analyst collects 90 monthly return premia (the return on the fund minus the return on the S&P 500 benchmark), 90 monthly interest rates, and 90 monthly S&P 500 index returns from July 1999 to December 2006. After estimating the regression equation, the analyst finds that the correlation between the regressions residuals from one period and the residuals from the previous period is 0.145. Which of the following is most accurate at a 0.05 level of significance, based solely on the information provided? The analyst:

A) cannot conclude that the regression exhibits either serial correlation or heteroskedasticity.

B) can conclude that the regression exhibits serial correlation, but cannot conclude that the regression exhibits heteroskedasticity.

C) can conclude that the regression exhibits heteroskedasticity, but cannot conclude that the regression exhibits serial correlation.

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The Durbin-Watson statistic tests for serial correlation. For large samples, the Durbin-Watson statistic is equal to two multiplied by the difference between one and the sample correlation between the regressions residuals from one period and the residuals from the previous period, which is 2 × (1 − 0.145) = 1.71, which is higher than the upper Durbin-Watson value (with 2 variables and 90 observations) of 1.70. That means the hypothesis of no serial correlation cannot be rejected. There is no information on whether the regression exhibits heteroskedasticity.

kasinkei

An analyst is estimating whether a fund’s excess return for a month is dependent on interest rates and whether the S&P 500 has increased or decreased during the month. The analyst collects 90 monthly return premia (the return on the fund minus the return on the S&P 500 benchmark), 90 monthly interest rates, and 90 monthly S&P 500 index returns from July 1999 to December 2006. After estimating the regression equation, the analyst finds that the correlation between the regressions residuals from one period and the residuals from the previous period is 0.199. Which of the following is most accurate at a 0.05 level of significance, based solely on the information provided? The analyst:

A) can conclude that the regression exhibits serial correlation, but cannot conclude that the regression exhibits multicollinearity.

B) cannot conclude that the regression exhibits either serial correlation or multicollinearity.

C) can conclude that the regression exhibits multicollinearity, but cannot conclude that the regression exhibits serial correlation.

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The Durbin-Watson statistic tests for serial correlation. For large samples, the Durbin-Watson statistic is approximately equal to two multiplied by the difference between one and the sample correlation between the regressions residuals from one period and the residuals from the previous period, which is 2 × (1 − 0.199) = 1.602, which is less than the lower Durbin-Watson value (with 2 variables and 90 observations) of 1.61. That means the hypothesis of no serial correlation is rejected. There is no information on whether the regression exhibits multicollinearity.

kasinkei

Which of the following is least accurate regarding the Durbin-Watson (DW) test statistic?

A) If the residuals have negative serial correlation, the DW statistic will be greater than 2.

B) In tests of serial correlation using the DW statistic, there is a rejection region, a region over which the test can fail to reject the null, and an inconclusive region.

C) If the residuals have positive serial correlation, the DW statistic will be greater than 2.

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A value of 2 indicates no correlation, a value greater than 2 indicates negative correlation, and a value less than 2 indicates a positive correlation. There is a range of values in which the DW test is inconclusive.

kasinkei

Miles Mason, CFA, works for ABC Capital, a large money management company based in New York. Mason has several years of experience as a financial analyst, but is currently working in the marketing department developing materials to be used by ABC’s sales team for both existing and prospective clients. ABC Capital’s client base consists primarily of large net worth individuals and Fortune 500 companies. ABC invests its clients’ money in both publicly traded mutual funds as well as its own investment funds that are managed in-house. Five years ago, roughly half of its assets under management were invested in the publicly traded mutual funds, with the remaining half in the funds managed by ABC’s investment team. Currently, approximately 75% of ABC’s assets under management are invested in publicly traded funds, with the remaining 25% being distributed among ABC’s private funds. The managing partners at ABC would like to shift more of its client’s assets away from publicly-traded funds into ABC’s proprietary funds, ultimately returning to a 50/50 split of assets between publicly traded funds and ABC funds. There are three key reasons for this shift in the firm’s asset base. First, ABC’s in-house funds have outperformed other funds consistently for the past five years. Second, ABC can offer its clients a reduced fee structure on funds managed in-house relative to other publicly traded funds. Lastly, ABC has recently hired a top fund manager away from a competing investment company and would like to increase his assets under management.ABC Capital’s upper management requested that current clients be surveyed in order to determine the cause of the shift of assets away from ABC funds. Results of the survey indicated that clients feel there is a lack of information regarding ABC’s funds. Clients would like to see extensive information about ABC’s past performance, as well as a sensitivity analysis showing how the funds will perform in varying market scenarios. Mason is part of a team that has been charged by upper management to create a marketing program to present to both current and potential clients of ABC. He needs to be able to demonstrate a history of strong performance for the ABC funds, and, while not promising any measure of future performance, project possible return scenarios. He decides to conduct a regression analysis on all of ABC’s in-house funds. He is going to use 12 independent economic variables in order to predict each particular fund’s return. Mason is very aware of the many factors that could minimize the effectiveness of his regression model, and if any are present, he knows he must determine if any corrective actions are necessary. Mason is using a sample size of 121 monthly returns. In order to conduct an F-test, what would be the degrees of freedom used (dfnumerator; dfdenominator)?

A) 108; 12.

B) 11; 120.

C) 12; 108.

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Degrees of freedom for the F-statistic is k for the numerator and n − k − 1 for the denominator.

k = 12n − k − 1 = 121 − 12 − 1 = 108

(Study Session 3, LOS 12.e)

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In regard to multiple regression analysis, which of the following statements is most accurate?

A) Adjusted R2 always decreases as independent variables increase.

B) Adjusted R2 is less than R2.

C) R2 is less than adjusted R2.

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Whenever there is more than one independent variable, adjusted R2 is less than R2. Adding a new independent variable will increase R2, but may either increase or decrease adjusted R2.

R2 adjusted = 1 − [((n − 1) / (n − k − 1)) × (1 − R2)]Where:
n = number of observations
K = number of independent variables
R2 = unadjusted R2

(Study Session 3, LOS 12.f)

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Which of the following tests is used to detect autocorrelation?

A) Durbin-Watson.

B) Residual Plot.

C) Breusch-Pagan.

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Durbin-Watson is used to detect autocorrelation. Breusch-Pagan and the residual plot are methods to detect heteroskedasticity. (Study Session 3, LOS 12.i)

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One of the most popular ways to correct heteroskedasticity is to:

A) adjust the standard errors.

B) use robust standard errors.

C) improve the specification of the model.

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Using generalized least squares and calculating robust standard errors are possible remedies for heteroskedasticity. Improving specifications remedies serial correlation. The standard error cannot be adjusted, only the coefficient of the standard errors. (Study Session 3, LOS 12.i)

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Which of the following statements regarding the Durbin-Watson statistic is most accurate? The Durbin-Watson statistic:

A) can only be used to detect positive serial correlation.

B) is approximately equal to 1 if the error terms are not serially correlated.

C) only uses error terms in its computations.

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The formula for the Durbin-Watson statistic uses error terms in its calculation. The Durbin-Watson statistic is approximately equal to 2 if there is no serial correlation. A Durbin-Watson statistic less than 2 indicates positive serial correlation, while a Durbin-Watson statistic greater then 2 indicates negative serial correlation. (Study Session 3, LOS 12.i)

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If a regression equation shows that no individual t-tests are significant, but the F-statistic is significant, the regression probably exhibits:

A) multicollinearity.

B) heteroskedasticity.

C) serial correlation.

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Common indicators of multicollinearity include: high correlation (>0.7) between independent variables, no individual t-tests are significant but the F-statistic is, and signs on the coefficients that are opposite of what is expected. (Study Session 3, LOS 12.j)

kasinkei

An analyst is testing to see whether a dependent variable is related to three independent variables. He finds that two of the independent variables are correlated with each other, but that the correlation is spurious. Which of the following is most accurate? There is:

A) no evidence of multicollinearity and serial correlation.

B) evidence of multicollinearity but not serial correlation.

C) evidence of multicollinearity and serial correlation.

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Just because the correlation is spurious, does not mean the problem of multicollinearity will go away. However, there is no evidence of serial correlation.

kasinkei

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.

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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.

kasinkei

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.

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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.

kasinkei

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.

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Multicollinearity is not an issue in simple linear regression.