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Quantitative Techniques Project Instructions Dr Stephanie Thomas Due Date: Friday, 5 June 2020 at 16:00 AWST Introduction The aim of this project is to prepare, evaluate and analyse a portfolio consisting of four financial assets. It requires a deep understanding of both the statistics and the mathematics components of this unit. You should be able to do parts of this project as the unit progresses. It is recommended that you work on this on a weekly basis. Treat this as if you have been asked to complete this report by a business manager. Data Download the file Projectdata.csv from Blackboard. The file contains daily stock prices for four companies: A, B, C, and D. The Analysis 1 Part 1 [10 Points] Plot the prices of each asset over time separately using software such as Excel, Tableau, R (or any suitable other software of your choice). Succinctly describe in words the evolution of each asset over time. (limit: 100 words for each time series). 2 Part 2 [5 Points] Calculate the returns of each asset using the following formula: = Where is the asset price at time 1 . Plot the returns for each asset. 3 Part 3 [10 Points] Create a histogram for each of the returns series. Also, report the descriptive statistics in a table which includes the mean, median, variance, standard deviation, skewness and kurtosis for each series. What conclusion can you draw from examining the kurtosis in each case? 4 Part 4 [10 Points] Under the assumption that the returns of each asset are drawn from an independently and identically distributed normal distribution, are the expected returns statistically different from zero for each asset? State clearly the null and alternative hypothesis in each case. Calculate and report all the relevant values for your conclusion. ( = 1% ). 5 Part 5 [10 Points] Assume the returns of each asset are independent from each other, are the mean returns statistically different from each other? Calculate and report all the relevant values for your conclusion. = 1% (hint: You need to discuss the equality of variances first). 6 Part 6 [5 Points] Calculate the correlation matrix of the returns and discuss the directions and strength of the correlations. 7 Part 7 [20 Points] Is the assumptions of independence realistic? If not, re-test the hypotheses in Question 1.5 using appropriate test statistics. (hint: You are required to test the significance of the correlation). 8 Part 8 [30 Points] If you can only choose a maximum of two assets to hold in your portfolio, which two would you choose? What are the optimal weights and the optimal expected returns? Submission You have been assigned a Report ID be sure to include this on the first page. Two parts are required: 1. A report, which is formatted in a manner appropriate for a business context.(As if you are submitted this to the business manager) Each section of the report should be numbered appropriately All Figures and Tables must be labelled and have an appropriate caption Figures should be clear and properly labelled. Figures without proper titles, labels, and explanations, or that are poorly formatted will not be credited. The type of chart should be appropriate for the type of variable which is plotted. 2. An appendix that occurs at the end of the report. This appendix details all your calculations: mathematical, statistical, and those used to generate figures/charts. For statistical calculations and figures state the software you used as well as the formulae, commands and packages (add-ons) used to generate your results. Please do not submit the original data file. A results (numbers) should be accurate to 3 decimal places. Please proof-read your report! Do not include spelling or grammatical errors. Submit the project as a single file (the report followed by the appendix) to the Turnitin link on the Unit BlackBoard site. Rubric The submission is worth 100 Points in total. Part Plot Result Explanation Calculations Max Points 1 4 0 4 2 10 2 4 0 0 1 5 3 4 4 1 1 10 4 0 4 4 2 10 5 0 4 4 2 10 6 0 3 1 1 5 7 0 4 10 6 20 8 0 5 10 15 30 12 24 34 30 100 Total Note: Details on how points are allocated: Plot: A clear plot/chart that is appropriate for the data is presented. The plot is numbered, has an appropriate title, and the axes are labelled. Result: The results are correct and presented to three digits of accuracy. Explanation: A clear explanation and/or interpretation is given. The text is free of spelling and grammatical errors. Word limits are respected. Calculations: Steps are clear and correct. Where appropriate the statistical package is stated and the steps are given with sufficient detail to replicate the output