Reading 12: Multiple Regression and Issues in Regression A white, black, whether, related, testing

mayanfang1

Q1. 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)   evidence of multicollinearity but not serial correlation.

B)   no evidence of multicollinearity and serial correlation.

C)   evidence of multicollinearity and serial correlation.

Q2. 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)   y².

B)   3y + 2z.

C)   3.

Q3. 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 (df_numerator; df_denominator)?

A)   12; 108.

B)   108; 12.

C)   11; 120.

mayanfang1

答案和详解如下：

Q1. 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)   evidence of multicollinearity but not serial correlation.

B)   no evidence of multicollinearity and serial correlation.

C)   evidence of multicollinearity and serial correlation.

Correct answer is A )

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

Q2. 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)   y².

B)   3y + 2z.

C)   3.

Correct answer is A)

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.

Q3. 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 (df_numerator; df_denominator)?

A)   12; 108.

B)   108; 12.

C)   11; 120.

Correct answer is A)

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

k = 12

n − k − 1 = 121 − 12 − 1 = 108

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