Research Topics: Statistical Modelling

Financial Mathematics and Statistical Modelling Coursework

Instructions This coursework tests your basic financial mathematics and statistical modelling, using spreadsheet software (Excel – financial maths, graphical features, the Data Analysis and Solver tools). Your answers are to be presented in a report (essay) format, for which you will use a word processor. In writing your reports, please: ·        state and explain all assumptions, on which your answers are based; ·        include selected printouts of formulae underlying computed values, indicating the cells to which these formulae refer.   Your coursework should be presented readably on A4 paper, single sided, stapled at the top left corner – no binders – and maximum of 9 pages (including any Appendix, penalties will be applied for excess – you are required to develop your judgement). Ten per cent of the total mark is allowed for quality of the presentation and these marks are equally distributed among the questions.   Note that there are penalties for late submissions. Please, take backups often, because last-minute file corruption is not an acceptable excuse for a late submission.   The coursework is to be handed to the Undergraduate Course Office (3rd Floor, Drysdale Building) by 12 pm on Wednesday, 4 April 2007.   This coursework is your own (individual) work.  Any student found guilty of plagiarism will be penalised.   Question 1:                                                                                                                 (35%)   In order to provide for future education costs, a family considers two methods of savings:   1.      An annual deposit of £6,000 to be made at the beginning of each year, starting from next year and to be compounded yearly for a total of five years. 2.      Sixty monthly deposits of £500 to be made at the start of each month (same starting date as above), which will then be compounded monthly.   There is uncertainty concerning the interest rate, which is to be applicable over the whole period of the investment. The family has been advised that expected interest rates and their respective probabilities are as follows:   Interest (% p.a.) 5.5 6 6.5 7 Probability 0.15 0.4 0.3 0.15   ·        How much would the family expect to save according to each method? ·        Which method should they choose? Why? They estimate that they will not require the accumulated amount at once and were advised to spend ¾ of the accumulated amount on an annuity. In the worst scenario, they estimate that a discount rate of 7.5% p.a. compounded monthly will apply. Assuming that the annuity will pay monthly, for 36 months starting one month after it is bought: ·        How much should they expect the monthly payment to be, if they had chosen the better of the two saving alternatives?   Question 2:                                                                                                                 (25%)   B&L Electronics supplies each of four computer manufacturers with a particular chip that can be produced at any of their three factories. As these factories are located in different areas, it costs 93 pence to produce a chip at Factory 1, 105 pence at Factory 2 and 102 at Factory 3. The monthly production capacity at each factory is: 90,000 chips at Factory 1, 100,000 chips at Factory 2 and 80,000 chips at Factory 3. Sales forecasts project a monthly demand from each computer manufacturer respectively to be equal to: 51000, 72000, 80000 and 58000.   The company would like to find out how many chips should be made at each factory to transport to each of the computer manufacturers. The transportation costs in pence per chip are tabulated below: Computer Manufacturer Factory A B C D 1 6 5 4 6 2 8 6 5 9 3 5 7 5 7   ·        Formulate and solve this problem. Finally, advise B&L on the production plan that will minimize its costs.   Question 3:                                                                                                                 (15%)   The travel expenses of 17 employees from a marketing department and 17 employees from a research and development department (R&D) are provided in the “QMCoursework-data” spreadsheet.   ·        Summarize and compare the distributions. ·        Does the R&D’s mean travel expenses exceed that of the marketing department? (Choose an appropriate test and significance level, when answering this question.)   Question 4:                                                                                                               (15%)   During the year of 2001, in the US residential lenders were saturated in refinancing.  The total mortgage packages approved exceeded .5 trillion. However, refinancing was not homogeneous across the US.  Twenty major mortgage institutions were randomly selected, and the total refinancing was recorded for 2001 and 2000 (data are in the “QMCoursework-data” spreadsheet). ·        Do the data support the hypothesis that there is a linear relationship between the amounts in each year? ·        Is any observation influential? Credit:ivythesis.typepad.com

Financial Mathematics and Statistical Modelling Coursework

Instructions This coursework tests your basic financial mathematics and statistical modelling, using spreadsheet software (Excel – financ...