Quantitative Techniques in Finance and Investments

The model below is for an APT (arbitrage pricing theory)-type multiple regression analysis and it investigates what influences the rate of return on a company’s shares.
ERCOMPANYt = ?+?1ERSFTSEt+ ?2TERMt + ?3EXCHANGEt+ ?4INFLATIONt + ?5DMONEYt+ ?6OILt +?t (1) The dependent variable (ERCOMPANY) is the company’s excess return based on its
share price {labelled as COMPANY in the Excel data spreadsheet}. Note that you are expected to construct this variable yourself, knowing that excess return means the additional return on top of risk-free rate proxy, i.e., TBILLSHORT as explained below.
The explanatory variables are: I. ERSFTSE: excess rate of return based on the FTSE ALL SHARE index in
London Stock Exchange {labelled as FTSE in the Excel data spreadsheet}. II. TERM: The difference between annual returns on 20-year government bonds and 3-month treasury bills {labelled as TBILLLONG and TBILLSHORT,
respectively, in the Excel data spreadsheet}.
III. EXCHANGE: exchange rate between US dollar and UK sterling {labelled as
EXCHANGE in the Excel data spreadsheet}.IV. INFLATION: inflation rate based on producer price index {labelled as PPI in the
Excel data spreadsheet}. V. MONEY: narrow definition of money supply, i.e., M1, in billion £ {labelled as MONEY in the Excel data spreadsheet}. VI. OIL: crude oil price in $US (labelled as OILPRICE in the Excel data
spreadsheet}.

In order to employ a set of regression analyses, the dataset is provided in Canvas (file name: Data for Assignment 2016.xlsx). The dataset is real data, with monthlyfrequency for the period September 1986 to August 2013. The explanatory variables on the right hand side are the same for all students. However, each student is allocated a different company; hence, the dependent variable of each assignment will be different. Check your student number to find out which company is allocated to you in the ‘company share price’ spreadsheet. Then, copy/paste the share price of the company allocated to you in column B of the spreadsheet named ‘Macroeconomic data’ in the same file.

APT assumes that it is the unexpected changes in financial and macroeconomic factors that exert influence on company returns. Therefore, before analysing data with regressions, you are advised to read the core textbook and module notes to identify how to use the raw data to transform series into variables that will eventually be included in the regression model.

Required:
1. Conduct the OLS regression analysis and comment on the results. Do the
estimates give any direct or indirect support to the APT?
(25 marks)
2. Refer to the OLS assumptions and conduct the diagnostic tests with respect to heteroscedasticity, normality, and autocorrelation. If there is any violation of the OLS assumptions, what can be done as remedies to these misspecifications? Namely, explain how to address regression models that fail these diagnostic tests in your analysis. (35 marks) 3. Is the functional form of the model actually linear as suggested by equation (1) and does it suffer from the multicollinearity problem? Provide the necessary tests.
(15 marks)
4. Test for the parameters’ stability by considering two or more sub-samples, e.g., the time between September 1986 and December 1999; and the time between January 2000 and August 2013. You can think of other periods such as the 2007-08 financial crisis. (15 marks) 5. Are there any other diagnostic tests that you might have considered? Provide them if the answer is ‘yes’.(10 marks)

NOTES:
– Word limit: 2,500 to 3,000 words (excluding references and appendices)
– Submission deadline: 15 December 2016, by 4 p.m. (It is suggested that students should submit by around 3 p.m. to avoid the possibility of late submissions due to technical reasons. See Canvas, module handbook for
further details).- You are expected to refer to and use academic journal articles for any section above. – You may have sections in your assignment. e.g., section 1 introduction; section 2 background about APT; section 3 Diagnostics tests,…. etc. Then, the last
section can be conclusion.

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