Question 6 (15 marks | Word limit: 600 words)

(a) The ‘Q6a’ tab in the Excel spreadsheet provides the summary statistics of 84 regressions based on cross-sectional data for each month between January 2001 and December 2007. The following summary statistics are shown in the spreadsheet:

• multiple R

• R-square

• adjusted R-square

• standard error

• significance of F.

Define each of the above terms and interpret each of the statistics in regards to the data over the time period from January 2001 to December 2007. (5 marks)

(b) (i) Consider the following notations:

Ri = return of stock i for a particular month

Xi1 = exposure of stock i to the constant unit of 1

Xi2 = exposure of stock i to the size

Xi3 = exposure of stock i to the momentum

Xi4 = exposure of stock i to the value

f1 = the intercept term

f2 = the regression coefficient of size

f3 = the regression coefficient of momentum

f4 = the regression coefficient of value.

Complete the formula for the specific returns (or residual term) of stock i for a particular month, Ui, given the information above and the linear regression model. What do the specific returns attempt to measure? (2 marks)

(ii) Calculate the monthly specific returns (i.e. the residuals of the regressions) for CBA, WES and BHP for the 84-month in-sample period. To do this calculation, use the formula derived from part (i), the data given in the notations in part (i), and the data in the ‘Q6b’ tab of the Excel spreadsheet.

From your Excel results, paste a copy of the specific returns for CBA, WES and BHP for the months of January 2001 and December 2007 only in the Word document of your assignment (and in the format below). (3 marks)

Month CBA WES BHP

Jan. 2001

Dec. 2007

(c) Calculate the historical variance of the monthly specific returns for CBA, WES and BHP for the 84 month in-sample period.

Note: The specific returns are assumed to be uncorrelated so that the off-diagonal elements of the covariance matrix are zero.

From your Excel results, paste a copy of the monthly specific returns covariance matrix for CBA, WES and BHP in the Word document of your assignment (and in the format below).

See the ‘Q6c-d’ tab of the Excel spreadsheet. (3 marks)

Monthly specific returns covariance matrix

CBA WES BHP

CBA

WES

BHP

(d) From your Excel results, paste a copy of the annualised specific returns volatilities for CBA, WES and BHP in the Word document of your assignment (and in the format below). See the ‘Q6c-d’ tab of the Excel spreadsheet. (2 marks)

Annualised specific returns volatility

CBA WES BHP

CBA

WES

BHP

Criteria-based marking guide for Question 6(a)–(d)

Excellent (Mark range: 11–15 marks) Satisfactory (Mark range: 6–10.5 marks) Unsatisfactory (Mark range: 0–5.5 marks)

• Correct definition of statistics

• Correct interpretation of statistics

• Correct completion of formula and correct and logical explanation of what specific returns measure attempts to measure

• Correct and complete calculation of monthly specific returns

• Correct and complete calculation of annualised historical variance • Adequate definition of statistics

• Adequate interpretation of statistics

• Correct completion of formula and correct explanation of what specific returns measure attempts to measure

• Correct and mostly complete calculation of monthly specific returns

• Correct and mostly complete calculation of annualised historical variance • Incorrect definition of statistics

• Incorrect interpretation of statistics

• Incorrect completion of formula and correct explanation of what specific returns measure attempts to measure

• Incorrect and incomplete calculation of monthly specific returns

• Incorrect and/or incomplete calculation of annualised historical variance

Insert your answers to Question 6(a)–(d) below this line

End of answers to Question 6(a)–(d)

Question 7 (14 marks | Word limit: 400 words)

Answer the questions below, providing reasons and valid arguments to demonstrate your understanding of regression limitations and how to manage them in practice.

(a) Describe the four (4) conditions that must be satisfied for a regression analysis to be valid. (2 marks)

(b) Describe two (2) ways of dealing with heteroscedasticity. (2 marks)

(c) Calculate the rolling 12-month volatility of price returns for each of the 10 stocks over the in sample period using data in the ‘Q7’ tab in the Excel spreadsheet. (2 marks)

Note: The rolling 12-month volatility at any month is the annualised standard deviation using the monthly returns of the preceding 12 months.

Save your Excel workings for part (c) as a tab labelled ‘7c’.

(d) Draw a graph of the results in part (c). Based on the graph, describe the relationship between volatilities of stocks over time. (2 marks)

(e) Explain the Durbin-Watson test and how its results should be interpreted. (2 marks)

(f) Why would a transformation of the dependent variable be used?

Describe what sorts of transformations are commonly used. (2 marks)

(g) Explain four (4) steps in a backward elimination stepwise regression approach. (2 marks)

Criteria-based marking guide for Question 7(a)–(g)

Excellent (Mark range: 10.5–14 marks) Satisfactory (Mark range: 6–10 marks) Unsatisfactory (Mark range: 0–5.5 marks)

• Clear and accurate description of four (4) conditions for valid regression analysis

• Full and accurate description of two (2) ways of dealing with heteroscedasticity

• Correct and complete calculations of price returns for each of 10 stocks

• Logical, full and correct description of the relationship between volatilities of stocks over time and at any specific month

• Correct, logical and full description of the Durbin Watson test and explanation of how its results should be interpreted

• Correct and full explanation of why a transformation of the dependent variable would be used and clear descriptions of transformations used

• Four complete and correct steps explained in a backward elimination stepwise regression approach • Adequate and accurate description of four (4) conditions for valid regression analysis

• Adequate and accurate description of two (2) ways of dealing with heteroscedasticity

• Correct and complete calculations of price returns for each of 10 stocks

• Adequate and correct description of the relationship between volatilities of stocks over time and at any specific month

• Mostly correct and full description of the Durbin Watson test and explanation of how its results should be interpreted

• Mostly correct explanation of why a transformation of the dependent variable would be used and adequate descriptions of transformations used

• Four steps explained in a backward elimination stepwise regression approach • Inaccurate and unclear description of less than four (4) conditions for valid regression analysis

• Unclear and/or inaccurate description of ways of dealing with heteroscedasticity

• Incorrect and/or incomplete calculations of price returns for most stocks

• Unclear and/or incorrect description of the relationship between volatilities of stocks over time and at any specific month

• Poor and/or incorrect description of the Durbin-Watson test and explanation of how its results should be interpreted

• Poor and/or incorrect explanation of why a transformation of the dependent variable would be used and unclear or no descriptions of transformations used

• Poor, incomplete and/or incorrect steps explained in a backward elimination stepwise regression approach

Insert your answers to Question 7(a)–(g) below this line

End of answers to Question 7(a)–(g)

Question 8 (8 marks | Word limit: 400 words)

Use Figure 1 to answer the questions below.

Figure 1

(a) (i) What does Figure 1 depict and what is the financial name or description given to the diagram? (2 marks)

(ii) Which portfolio (A or B) would be preferred and why? (2 marks)

(b) Explain how volatility is measured with respect to Figure 1. (1 mark)

(c) (i) A portfolio manager decides to allocate superannuation funds of their recent clients who are more risk averse than average. What would the portfolio manager need to do to achieve this outcome? (2 marks)

(ii) Briefly state where this portfolio of assets would be represented with respect to Figure 1. (1 mark)

Criteria-based marking guide for Question 8(a)–(c)

Excellent (Mark range: 6–8 marks) Satisfactory (Mark range: 3.5–5.5 marks) Unsatisfactory (Mark range: 0–3 marks)

• Clear and accurate description of the figure and portfolios

• Correct interpretation of volatility

• Clear and accurate explanation of risk aversion and portfolio construction • Adequate description of the figure and portfolios

• Mostly correct interpretation of volatility

• Fair explanation of risk aversion and portfolio construction • Poor description of the figure and portfolios

• Incorrect interpretation of volatility

• Poor explanation of risk aversion and portfolio construction

Insert your answers to Question 8(a)–(c) below this line

End of answers to Question 8(a)–(c)

Question 9 (12 marks | Word limit: 400 words)

Assume that we have estimated the following AR(1) model:

Xt = 0.0825 + 0.7654Xt – 1 + et

Furthermore, assume that the current level of X is 0.4968.

(a) Forecast the value of X at time 1 (X1) and time 4 (X4). (2 marks)

(b) Which of these two forecasts is likely to be more reliable? Why? (2 marks)

(c) What is serial correlation? How do we test for its presence in this model? (4 marks)

(d) What is the mean reverting level of this model? What does this mean? (4 marks)

Criteria-based marking guide for Question 9(a)–(d)

Excellent (Mark range: 8–12 marks) Satisfactory (Mark range: 4.5–7.5 marks) Unsatisfactory (Mark range: 0–4 marks)

• Correct calculation and interpretation of model forecast

• Clear and accurate description of serial correlation

• Correct and full explanation of the appropriate test of serial correlation

• Correct calculation and interpretation of the mean reverting level

• All relevant workings shown • Mostly correct calculation and interpretation of model forecast

• Adequate description of serial correlation

• Mostly correct explanation of the appropriate test of serial correlation

• Mostly correct calculation and interpretation of the mean reverting level

• Most relevant workings shown • Incorrect calculation and interpretation of model forecast

• Poor description of serial correlation

• Incorrect and full explanation of the appropriate test of serial correlation

• Incorrect calculation and interpretation of the mean reverting level

• Little or no working shown

Insert your answers to Question 9(a)–(d) below this line

End of answers to Question 9(a)–(d)

End of Assi

(a) The ‘Q6a’ tab in the Excel spreadsheet provides the summary statistics of 84 regressions based on cross-sectional data for each month between January 2001 and December 2007. The following summary statistics are shown in the spreadsheet:

• multiple R

• R-square

• adjusted R-square

• standard error

• significance of F.

Define each of the above terms and interpret each of the statistics in regards to the data over the time period from January 2001 to December 2007. (5 marks)

(b) (i) Consider the following notations:

Ri = return of stock i for a particular month

Xi1 = exposure of stock i to the constant unit of 1

Xi2 = exposure of stock i to the size

Xi3 = exposure of stock i to the momentum

Xi4 = exposure of stock i to the value

f1 = the intercept term

f2 = the regression coefficient of size

f3 = the regression coefficient of momentum

f4 = the regression coefficient of value.

Complete the formula for the specific returns (or residual term) of stock i for a particular month, Ui, given the information above and the linear regression model. What do the specific returns attempt to measure? (2 marks)

(ii) Calculate the monthly specific returns (i.e. the residuals of the regressions) for CBA, WES and BHP for the 84-month in-sample period. To do this calculation, use the formula derived from part (i), the data given in the notations in part (i), and the data in the ‘Q6b’ tab of the Excel spreadsheet.

From your Excel results, paste a copy of the specific returns for CBA, WES and BHP for the months of January 2001 and December 2007 only in the Word document of your assignment (and in the format below). (3 marks)

Month CBA WES BHP

Jan. 2001

Dec. 2007

(c) Calculate the historical variance of the monthly specific returns for CBA, WES and BHP for the 84 month in-sample period.

Note: The specific returns are assumed to be uncorrelated so that the off-diagonal elements of the covariance matrix are zero.

From your Excel results, paste a copy of the monthly specific returns covariance matrix for CBA, WES and BHP in the Word document of your assignment (and in the format below).

See the ‘Q6c-d’ tab of the Excel spreadsheet. (3 marks)

Monthly specific returns covariance matrix

CBA WES BHP

CBA

WES

BHP

(d) From your Excel results, paste a copy of the annualised specific returns volatilities for CBA, WES and BHP in the Word document of your assignment (and in the format below). See the ‘Q6c-d’ tab of the Excel spreadsheet. (2 marks)

Annualised specific returns volatility

CBA WES BHP

CBA

WES

BHP

Criteria-based marking guide for Question 6(a)–(d)

Excellent (Mark range: 11–15 marks) Satisfactory (Mark range: 6–10.5 marks) Unsatisfactory (Mark range: 0–5.5 marks)

• Correct definition of statistics

• Correct interpretation of statistics

• Correct completion of formula and correct and logical explanation of what specific returns measure attempts to measure

• Correct and complete calculation of monthly specific returns

• Correct and complete calculation of annualised historical variance • Adequate definition of statistics

• Adequate interpretation of statistics

• Correct completion of formula and correct explanation of what specific returns measure attempts to measure

• Correct and mostly complete calculation of monthly specific returns

• Correct and mostly complete calculation of annualised historical variance • Incorrect definition of statistics

• Incorrect interpretation of statistics

• Incorrect completion of formula and correct explanation of what specific returns measure attempts to measure

• Incorrect and incomplete calculation of monthly specific returns

• Incorrect and/or incomplete calculation of annualised historical variance

Insert your answers to Question 6(a)–(d) below this line

End of answers to Question 6(a)–(d)

Question 7 (14 marks | Word limit: 400 words)

Answer the questions below, providing reasons and valid arguments to demonstrate your understanding of regression limitations and how to manage them in practice.

(a) Describe the four (4) conditions that must be satisfied for a regression analysis to be valid. (2 marks)

(b) Describe two (2) ways of dealing with heteroscedasticity. (2 marks)

(c) Calculate the rolling 12-month volatility of price returns for each of the 10 stocks over the in sample period using data in the ‘Q7’ tab in the Excel spreadsheet. (2 marks)

Note: The rolling 12-month volatility at any month is the annualised standard deviation using the monthly returns of the preceding 12 months.

Save your Excel workings for part (c) as a tab labelled ‘7c’.

(d) Draw a graph of the results in part (c). Based on the graph, describe the relationship between volatilities of stocks over time. (2 marks)

(e) Explain the Durbin-Watson test and how its results should be interpreted. (2 marks)

(f) Why would a transformation of the dependent variable be used?

Describe what sorts of transformations are commonly used. (2 marks)

(g) Explain four (4) steps in a backward elimination stepwise regression approach. (2 marks)

Criteria-based marking guide for Question 7(a)–(g)

Excellent (Mark range: 10.5–14 marks) Satisfactory (Mark range: 6–10 marks) Unsatisfactory (Mark range: 0–5.5 marks)

• Clear and accurate description of four (4) conditions for valid regression analysis

• Full and accurate description of two (2) ways of dealing with heteroscedasticity

• Correct and complete calculations of price returns for each of 10 stocks

• Logical, full and correct description of the relationship between volatilities of stocks over time and at any specific month

• Correct, logical and full description of the Durbin Watson test and explanation of how its results should be interpreted

• Correct and full explanation of why a transformation of the dependent variable would be used and clear descriptions of transformations used

• Four complete and correct steps explained in a backward elimination stepwise regression approach • Adequate and accurate description of four (4) conditions for valid regression analysis

• Adequate and accurate description of two (2) ways of dealing with heteroscedasticity

• Correct and complete calculations of price returns for each of 10 stocks

• Adequate and correct description of the relationship between volatilities of stocks over time and at any specific month

• Mostly correct and full description of the Durbin Watson test and explanation of how its results should be interpreted

• Mostly correct explanation of why a transformation of the dependent variable would be used and adequate descriptions of transformations used

• Four steps explained in a backward elimination stepwise regression approach • Inaccurate and unclear description of less than four (4) conditions for valid regression analysis

• Unclear and/or inaccurate description of ways of dealing with heteroscedasticity

• Incorrect and/or incomplete calculations of price returns for most stocks

• Unclear and/or incorrect description of the relationship between volatilities of stocks over time and at any specific month

• Poor and/or incorrect description of the Durbin-Watson test and explanation of how its results should be interpreted

• Poor and/or incorrect explanation of why a transformation of the dependent variable would be used and unclear or no descriptions of transformations used

• Poor, incomplete and/or incorrect steps explained in a backward elimination stepwise regression approach

Insert your answers to Question 7(a)–(g) below this line

End of answers to Question 7(a)–(g)

Question 8 (8 marks | Word limit: 400 words)

Use Figure 1 to answer the questions below.

Figure 1

(a) (i) What does Figure 1 depict and what is the financial name or description given to the diagram? (2 marks)

(ii) Which portfolio (A or B) would be preferred and why? (2 marks)

(b) Explain how volatility is measured with respect to Figure 1. (1 mark)

(c) (i) A portfolio manager decides to allocate superannuation funds of their recent clients who are more risk averse than average. What would the portfolio manager need to do to achieve this outcome? (2 marks)

(ii) Briefly state where this portfolio of assets would be represented with respect to Figure 1. (1 mark)

Criteria-based marking guide for Question 8(a)–(c)

Excellent (Mark range: 6–8 marks) Satisfactory (Mark range: 3.5–5.5 marks) Unsatisfactory (Mark range: 0–3 marks)

• Clear and accurate description of the figure and portfolios

• Correct interpretation of volatility

• Clear and accurate explanation of risk aversion and portfolio construction • Adequate description of the figure and portfolios

• Mostly correct interpretation of volatility

• Fair explanation of risk aversion and portfolio construction • Poor description of the figure and portfolios

• Incorrect interpretation of volatility

• Poor explanation of risk aversion and portfolio construction

Insert your answers to Question 8(a)–(c) below this line

End of answers to Question 8(a)–(c)

Question 9 (12 marks | Word limit: 400 words)

Assume that we have estimated the following AR(1) model:

Xt = 0.0825 + 0.7654Xt – 1 + et

Furthermore, assume that the current level of X is 0.4968.

(a) Forecast the value of X at time 1 (X1) and time 4 (X4). (2 marks)

(b) Which of these two forecasts is likely to be more reliable? Why? (2 marks)

(c) What is serial correlation? How do we test for its presence in this model? (4 marks)

(d) What is the mean reverting level of this model? What does this mean? (4 marks)

Criteria-based marking guide for Question 9(a)–(d)

Excellent (Mark range: 8–12 marks) Satisfactory (Mark range: 4.5–7.5 marks) Unsatisfactory (Mark range: 0–4 marks)

• Correct calculation and interpretation of model forecast

• Clear and accurate description of serial correlation

• Correct and full explanation of the appropriate test of serial correlation

• Correct calculation and interpretation of the mean reverting level

• All relevant workings shown • Mostly correct calculation and interpretation of model forecast

• Adequate description of serial correlation

• Mostly correct explanation of the appropriate test of serial correlation

• Mostly correct calculation and interpretation of the mean reverting level

• Most relevant workings shown • Incorrect calculation and interpretation of model forecast

• Poor description of serial correlation

• Incorrect and full explanation of the appropriate test of serial correlation

• Incorrect calculation and interpretation of the mean reverting level

• Little or no working shown

Insert your answers to Question 9(a)–(d) below this line

End of answers to Question 9(a)–(d)

End of Assi

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