CoursHeroTranscribedText: ACTL2131/5101 Assignment Submission deadline: Friday, 27 May, 11am sharp via Turnitin Start body copy here. Please use any style within the Arial Font Family. This assignment deals with analysing data, and consists of a mix of practical questions. There are two main tasks in this assignment. Both have components of knowledge and problem solving and will be used to assess your communication skills. Background You are an analyst working in an investment fund. Your manager has a set of bivariate data of daily logreturns and would like to conduct some analysis. The first column represents log-returns of an equity index and the second column represents an individual stock returns. The total number of observation is 2500, which corresponds to 10 years of data (assuming 250 trading days per year). The returns are daily and reported in percentage terms, i.e. 0.02 means 0.02% daily return. Note: for all the tasks below, if you require to set a significance level for the tests, please use 5%. Task 1 Your first task is to analyse the log-returns on both the index and the stock. It is accepted by many researchers and practitioners that log-returns of indices or stocks follow a normal distribution. However, recent literature suggests that a Student-t distribution may be more appropriate (see e.g. Hurst and Platen (1997), Granger (2003) and Platen and Rendek (2008)). 1. Carefully investigate the manager's conjecture that whether the data (both series) follow Studentt distribution (rather than normal) is appropriate or not. You should use appropriate tests and graphical illustrations to support your conclusions. [32 marks] 1 2. The fund manager is also interested in the performance of the stock, compared to the index. Assist the fund manager in completing this task by comparing for example the annualised means, variances and other appropriate statistics for the index and the stock. [23 marks] 1 Task 2 It is reasonable to expect that stock returns have some degree of correlation with the index returns. In this task, you will analyse the relationship between the log-returns of the index and the stock. The manager postulates a linear model to describe the relationship between the index return and the stock return: Rt = + Rtm + t , (1) where Rt is the return on the stock, Rtm is the market return (i.e. index return) and is an error term with zero mean. Furthermore at a recent conference, the manager heard about the so-called out-of-sample procedure can be used to validate the predictive power of the model and want you to use it here. The out-of-sample procedure assumes that the estimation of the model is performed in-sample (e.g. for 2000 observations), and the remaining sub-sample (e.g. 500 observations) is treated as an out-of-sample period, which is used to validate the quality of the predictive power of the model. 1. Perform a detailed statistical analysis on whether the linear model in Equation (1) is reasonable to describe the relationship between the index and the stock returns. [24 marks] 2. Help the manager validate the quality of the predictive power of the model in Equation (1) by using the out-of-sample procedure. [21 marks] Format This is an individual assignment. You can perform your analysis in Excel or R. The assignment should be typed with the main tables, charts and results presented throughout the assignment to highlight your responses to the assignment questions. Marks will be awarded for neatness, conciseness and clarity of answers; refer to the assessment rubric. Maximum number of pages: 4 (excluding the title page and references). The first 3 pages must be a self-contained report, and the fourth page can be used as a technical appendix describing the detailed methodology used. Be as concise as you can, while clearly addressing each question. 2 If the length exceeds 4 pages, the pages beyond page 4 will not be marked. Format of each page: Please use at least font size 11; single line spacing; and at least 1.27cm page margins from the left, right, top and bottom. As a requirement for the assessment to be marked, you must submit your excel spreadsheet or R code. We will refer to your excel spreadsheet or R code if necessary. Assignment should be submitted via Turnitin on Moodle. Plagiarism awareness Students are reminded that the work they submit must be their own. While we have no problem with students working together on the assignment problems, the material students submit for assessment must be their own. This means that: Students should make sure they understand what plagiarism iscases of plagiarism have a very high probability of being discovered. For issues of collective work, having different persons marking the assignment does not decrease this probability. Students should consult the Turnitin section of the website accessible to all ACTL students well in advance, as this gives a (non exhaustive list) of things that could go wrong and explains how the policies above are implemented. References 1. Granger, C. (2003). Time series concept for conditional distributions. Oxford Bulletin of Economics and Statistics, 65, 689-701. 2. Hurst, S. and Platen, E. (1997). The marginal distributions of returns and volatility. IMS Lecture Notes. Monograph Series. Hayward, CA: Institute of Mathematical Statistics, 31, 301-314. 3. Platen, E. and Rendek, R. (2008). Empirical evidence on Student-t log-returns of diversified world stock indices. Journal of Statistical Theory and Practice, 2, 233-251. 3