Complete the formula for the specific returns

Reference no: EM131002953 , Length: 1800 Words

1800 words + calculation work, please follow all the guidelines properly

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:

• multipleR

• 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:

R_i = return of stock i for a particular month

X_i₁= exposure of stock i to the constant unit of 1

X_i₂= exposure of stock i to the size

X_i₃= exposure of stock i to the momentum

X_i₄= 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,U_i, 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 forthe months of January 2001 and December 2007onlyin 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 tomeasure

Correct and complete calculation of monthly specific returns

Correct and complete calculation of annualised historicalvariance

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 specificreturns

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 10stocks

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

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 ofthe 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 10stocks

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 beinterpreted

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 questionsbelow.

Figure 1

Adobe Systems

(a) (i) What does Figure 1 depict and what is the financial name or description given tothediagram? (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 portfolioconstruction

Adequate description of the figure and portfolios

Mostly correct interpretation ofvolatility

Fairexplanation of risk aversion and portfolioconstruction

Poor description of the figure andportfolios

Incorrect interpretation ofvolatility

Poorexplanation of risk aversion and portfolioconstruction

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:

X_t= 0.0825 + 0.7654X_t_{- 1}+ e_t

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)

(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 serialcorrelation

Mostly correct calculation and interpretation of the mean reverting level

Most relevant workings shown

Incorrect calculation and interpretation of model forecast

Poor description of serialcorrelation

Incorrect and full explanation ofthe appropriate test of serialcorrelation

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)

Attachment:- FIN201_AS_v3.zip

Reference no: EM131002953

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