F71AH/PT Sample Coursework Assignment 2
Project description
You are given the historical data on the weekly rate of returns of four stocks (Tesco, Experian, DLG, HSBC) and FTSE 100 index (the data are available on vision). Your task is to conduct quantitative analysis under the mean-variance framework on the following four questions. We only consider investments over a single time period and assume that short-selling is allowed.
(1) Use the unbiased estimator introduced in the lecture to estimate the expected rate of returns, variances and covariances of the four stocks and index and provide a comparison for the four stocks. In particular, if the investor wishes to assign all investment to a single stock, which one would you suggest? Explain your suggestion.
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(2) Now the investor would like to invest in the four stocks simultaneously. Using “solve” and Lagrangian method in the lecture to find the composition of efficient (in the sense of mean-variance) portfolios P with expected return given as 0.5%. Compare the efficient portfolio with your suggestion in (1) and illustrate the improvement.
(3) Assume there is a risk-free rate of 0.01% (F) available in the market. Following the same approach as was used in (2), find the new efficient portfolio P ′ including the risk- free rate that has expected return at 0.1%, compare it with the efficient portfolio in (2) and illustrate the improvement.
(4) Using the same risk-free rate in (3) and taking FTSE 100 as the market portfolio M, sketch the equation of Capital Market Line. [Hint: use “abline” in R for plotting] Compare the efficient portfolios in (2) and (3) with M. According to the analysis you have conducted so far, do your results support the Efficient Market Hypothesis? Explain your answer. [Hint: can P ′ beat the efficient portfolio written on M and F ?]
Your findings should be presented in the form of a report, which should:
[7 marks] [Total 15 marks]
• have a clear and logical structure;
• includedetailofyourmathematicalcalculationssothatyourresultscouldbereproduced
by another statistician;
• include clearly labelled and correctly referenced tables and diagrams, as appropriate;
• include the R code you used in an appendix (you do not need to explain individual R commands but some comments should be included to indicate the purpose of each section of code);
• include citation and referencing for any material (books, papers, websites etc.) used. Notes
• This assignment counts for 15% of the course assessment.
• You may have discussions with me or your colleagues, but your report must be your own work. Plagiarism is a serious academic offence and carries a range of penalties, some very serious. Copying a friend’s report or code, or copying text into your report from another source (such as a book or website) without citing and referencing that source, is plagiarism. Collusion is also a serious academic offence. You must not share a copy of your report (as a hard copy or in electronic form) or your computer code with anyone else. Penalties for plagiarism or collusion can include voiding of your mark for the course.
• Your report should be submitted through Turnitin by 1st-April 6.00 p.m., 2022. Assignments submitted late (but within 5 working days of the deadline) will have their mark reduced by 30%. Projects submitted more than 5 working days late will not be marked.
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