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QBA ASSIGNMENT PROJECT
Semester 2, 2014.
This assignment has several parts of unequal value. Some parts are technical, and are designed to help you understand the connection between Mathematics and Econometric Regression Analysis.
You must type or neatly hand-write such answers in the spaces provided.
Other parts are applied, and are designed to help you develop practical econometric skills. You will apply regression analysis as done by finance professionals using real world data. These parts will test your econometric modelling skills using multiple regression and Eviews.
For these parts you may be required to report your Eviews output in the spaces below.
This assignment may be done in groups of up to five students. Your group members do not need to be part of the same tutorial group. When you hand in your assignment you must include this cover sheet. No names may be added to the group lists apart from the names that appear below at hand-in. Submit only one assignment for each group. DO NOT hand in a separate assignment for each group member. Late assignments will require a Special Consideration application and will otherwise not be accepted.
Due Time/Date: 12:00pm on Wednesday 29-10-2014
ALL STUDENTS: Deposit your assignment script into your assigned tutor’s assignment box on Level 3, Building 5 in Finance and Economics at the CITY campus on the due date by the indicated time.
Tutorial Day and Time:
Date stamp or tutor’s signature and date
Group Work Protocol
Group work and group assignments are an important part of business education. The purpose of group work goes beyond the requirements of the group project itself. Group work is also intended to develop awareness of the dynamics of teamwork and your role in a team environment. In undertaking group work it is expected that each team member will communicate with other team members in a professional and courteous manner. Resolving any conflict or difficulties that arise within the team is also part of the group dynamics that may emerge during the project. It is expected that each team member will take responsibility for managing and reducing any conflict that may arise. If the team members are unable to resolve tensions or conflicts then this MUST be discussed with the lecturer/tutor as soon as it becomes obvious that a resolution within the team cannot be agreed.
In the learning environment of group work we are seeking to ensure that you develop and demonstrate both academic skills and important group work skills such as:
Commitment to working with others (eg, undertaking a fair share of the work, sharing ideas, doing the tasks allocated, attending meetings)
Collaboration and inclusiveness (eg encouraging and supporting others, respecting others; recognising the skills and valuing the contribution of others, helping resolve conflicts)
Contribution to establishing and working towards a common outcome (eg establishing and supporting team goals, plans, rules, roles, decisions)
Group Work Declaration Form
Individuals must sign a declaration form, otherwise the project report will not be marked. Complete only Part 1 or Part 2. Do not complete both. This sheet should be completed and handed in along with your group assignment.
I believe that all members of the group have contributed fairly to this assignment, and each member should receive the same mark for the assignment.
Group member names:
I believe that not all members of the group have contributed fairly to this assignment. I believe the proportion of the total workload that each has contributed is indicated below.
Group member names: Proportion of Workload:
Total = 100%
Please note that if you have signed Part 2 you must attach a statement explaining:
Why you believe a group member/group members have not contributed their fair share to the project
A breakdown of tasks you and others have completed in the project
An estimate of the time you think each of those tasks has taken.
Any other positive or negative contributions made by you and others
This information will be shown to other group members so that they have an opportunity to respond.
While each group member’s comments will be taken into consideration, the final decision on how the marks are awarded will remain the right of the course coordinator.
The capital asset pricing model (CAPM) is used in finance to determine a theoretically appropriate required rate of return of an asset, where that asset is to be added to an already well-diversified portfolio, given that asset’s non-diversifiable risk. Traditionally, applications of the CAPM use only one variable to describe the returns of a portfolio or stock with the returns of the market as a whole:
In contrast, the Fama–French model uses three variables:
is the stock’s rate of return, is the risk-free return rate, and is the return of the whole stock market. The parameter is the stock’s ‘alpha’. It measures how much the stock outperforms its ‘theoretical’ predicted returns under the CAPM and is the stock’s ‘beta’, which measures the stock’s exposure to the overall market. Different stocks will have different parameters.
The Fama-French model contains two additional factors to explain stock returns. “Small market capitalization Minus Big “; measures the historic excess returns of small cap stocks over big caps. “High book-to-market ratio (BtM) Minus Low book-to-market ratio” measures the historic excess returns of value stocks (small BtM ratio) over growth stocks (High BtM ratio). These factors are calculated with combinations of portfolios composed by ranked stocks (BtM ranking, Capitalisation ranking) and available historical market data. Historical values are available on Kenneth French’s web page for American stocks. We have supplied Australian data from the ASX in the spreadsheet AssgtData.xls not available there.
The variables are as follows:
= Monthly return on BHP stock as observed on the ASX.
= Monthly return on market index, here the All Ordinaries Index, AOI.
= Small market capitalization Minus Big market capitalization factor.
= High book-to-market ratio Minus Low book-to-market ration
You are to assume a risk-free rate of per month. Your task is to estimate the Fama-French three factor model using the given data. and determine whether it is any better at explaining the BHP stock returns compared to the market excess returns given by only the All Ordinaries Index.
Please enter all your answers into the provided spaces below.
Part 1: Deriving the Least Squares Estimators
Recall, in Linear Least Squares, we have to estimate the ‘line of best fit’ which minimizes the ‘sum of squared deviations’ of the data. This is equivalent to choosing parameters which minimises the function of two variables (namely SSR):
You will use calculus to show that is minimized for the choices:
where and .
You may assume the following summation properties in your solution (see Lecture 5):
If k is a constant, .
Given and for , then .
Differentiating a summation (the ‘derivative of the sums’ equals ‘the sum of the derivatives’):
Q1 (1 mark): In lectures we saw that the ‘total deviation about the mean’is always zero, i.e. . Expand the summation across the brackets and apply this result to the to prove that: .
Q2 (1 mark) Prove that
Q3 (2 marks): By differentiating the summation, show that when .
Q4 (1 mark): Differentiate the summation with respect to to get a summation expression for .
Q5 (2 marks): Prove that by choosing b0 and b1 to minimize you obtain the least squares estimators, namely:
Q6. (1 marks): Read the supplied data into Eviews. Generate two new variables and , which are the stock and market‘excess returns’ respectively, assuming . Use these to estimate the model given by Equation (1):
Paste your Eviews output below
Q7. (1 mark) Comment on the sign of the estimated coefficient , and state whether this is what you expect.
Q8 (1 mark) Formulate and carry out an appropriate hypothesis test, to test whether the excess market returns explain the excess returns of BHP shares. Use the t-statistic approach, at the a=0.05 level. Assume the large sample approximation applies.
Q9 (1 mark) Formulate and carry out an appropriate hypothesis test for testing whether BHP’s ‘beta’ is greater than one at the a=0.05 level
Q10. (1 mark): Use the data to estimate the Fama-French 3-Factor model given by Equation (2):
Paste your Eviews output below
Q11 (2 marks) In the Fama-French 3-factor model you estimated, test the following hypotheses about the coefficients B2 and B3. Clearly specify the rejection region if you are using critical values, and clearly state your conclusions. When using p‑values, calculate and compare your p-values to the test size then state your conclusion. (Hint, assume the Central Limit Theorem Holds)
(a) H0: , H1:, with a=0.05 using the critical-value approach.
(b) H0:, H1:, with a=0.05 using the critical-value approach.
(c) H0: , H1:, with a=0.05using the p-value approach.
(d) H0: , H1:, with a=0.05using the p-value approach.
Q12 (3 marks) Formulate a joint-hypothesis test to test whether the Fama-French 3-Factor model explains the stock returns better than the model given by Equation (1). Perform the hypothesis test by calculating the homoskedasticity-consistent F-Statistic, using the relevant formula.
Verify your conclusion by performing the Wald test in Eviews and considering p-values. What is your conclusion?
Q13 (3 marks) A Financial Analyst believes that the effect of book-to-market values (HML) on stock returns is twice as great as the effect of market capitalization (SMB). Formulate an appropriate hypothesis test and use re-parametrisation to convert it to a simple t-test to test the assertion. Perform the required regression and paste your Eviews output below. State your conclusion at the 5% level.
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