IB3K20 Financial Optimisation 2022-23
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IB3K20
Financial Optimisation
Individual Resit Assignment (15 CATS), 2022-23
Assignment Instructions
All assignments must be submitted ONLINE via my.wbs by 7pm UK time on the date displayed against this assessment.
Please ensure that you have inserted a completedassignment coversheet, which must be included as the first page of your script. This should include your Student ID number, but not your name.
Word Limit
Maximum 5 pages, including the cover page (an equivalent of 1500 words).
Word Count Policy
WBS has a school-wide policy on word counts. This is strictly enforced to ensure consistency across modules and programme. You can find more information about this policy in your Student Handbook under Academic Practice -4i. Word count policy.
This is a strict limit not a guideline: any piece submitted with more words than the limit will result in the excess not being marked.
Academic Practice
Please ensure you read the full guidelines forAcademic Practicein the Undergraduate Handbook and ensure you understand it. If in doubt, please seek clarification in advance of your submission. This includes
important information on:
• Cheating, plagiarism and collusion
• Correct referencing
• Using internet sources in assessments
• Academic writing
• English Language support
• Word count policy
When you submit this assignment online, you will be required to tick a declaration box indicating that the work involved is entirely your own. Each assignment will be put through plagiarism software to identify any collusion or inadequate referencing of materials used from different sources.
We would consider taking action if your work:
1. is too reliant on the words of particular authors (rather than presenting your ideas in your own words), if the essay uses the ideas or words of an author without referencing them or putting their words into
quotations (plagiarism).
2. suggests that you have worked very closely with another student or students (unless explicitly asked to do so by your Module Leader/Tutor) (collusion).
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Your assignment instructions begin below.
Instructions: Please read carefully!
The assignment consists of two questions. Read each question carefully and perform the following tasks.
• Modelling Tasks: For each problem, you need
o to provide the complete mathematical programming formulation in a compact form in terms of all sets of decision variables, the objective function, constraints, and parameters you use to write down the problem formulation,
o to use AMPL to solve the underlying optimisation model with appropriate solver and data,
o to provide a brief explanation of main observations if needed.
• Writing Format: Handwritten solutions are not allowed! Write your answers clearly using MS Word or LaTeX with the font size 11. The main body of the assignment should NOT exceed 5 pages (including the cover page).
o Enter your ID number at the beginning of your work. Make sure that each page (in the main document) has your ID number and the question number.
o Your AMPL codes must be named in terms of parts of the question. For example, AMPL codes of part (b) should be called as ‘ part-b.mod’, ‘ part-b.dat’, and ‘ part-b.run’ .
o Do not include your AMPL codes into the main document as the answer to any question.
• Submission and Deadline:
o A pdf version of Word or Latex document should be submitted to the ‘Individual Assignment (15 CATS)’ assessment area on my.wbs. Ensure your submission will print clearly in black and white.
o Your AMPL files should be submitted in a zip file to the ‘Individual Assignment – Zip File for Codes’ area.
o Submission must be made electronically, following electronic submission guidelines, on or before Thursday, 7th September. Late submissions are automatically marked down.
Finally, problem formulations, AMPL models as well as relevant explanations have to be your own work; any similarity between submissions (solution, writing and construction) shall be dealt with accordingly.
IB3K20: Financial Optimisation Individual Resit Assignment
Consider the following case to answer the assignment questions.
CASE: James Harrison is the fund manager of a consultancy company and would like to determine the optimal portfolio dedication strategies using only fixed income securities to pay off a series of future cash obligations over a planning horizon. He has already specified a set of government or commercial bonds that possess different payment structures and maturities. Each bond yields zero or annual coupon payments at discrete time periods up to the maturity. The principal of bonds is paid at maturity which varies from the first to the last year of the planning horizon. They assume that these bonds are widely available in the market and can be purchased in any quantities at the current market price. James needs to decide the number of securities to purchase today so that the company’s future cash requirements are met at each year. After the investment on bonds is made today, they can apply for a one-year loan at any time except the final time-period if needed. An amount of money (being borrowed as a loan at anytime t) will be paid off at the next time-period with an annual interest rate specified at time t. The company has two conflicting objectives as minimising the total cost of investment and maximising the final cash-on-hand at the end of investment horizon. In order to measure trade-off between two objectives, James would like to develop a multi-objective optimisation model by combining two objectives with weights into a single- objective optimisation model where weights attached to the objectives vary between 0 and 1.
a) Assume that all model parameters are known, and the fixed rates remain the same over a year. Introduce model parameters and decision variables. Formulate (but do not solve) a deterministic linear programming model of the portfolio dedication problem. (15 marks)
b) Now, ignore the optimisation model developed in part (a). Assume that annual interest rate at each year is uncertain. Thus, generate a scenario tree, that is showing a probabilistic representation of random rates of one-year loan over the planning horizon. Consider either one or two different events, representing realisations of random rates at each node of the scenario tree with certain probability, over the investment horizon. Modify the linear program developed in part (a) and formulate (but do not solve) a scenario based linear programming model. Briefly explain what additional variables/constraints you need to add to the model developed in part (a). (25 marks)
c) Consider an instance of the firm’s financing problem consisting of up to 10 different coupon bonds with 5-year or less than 5-year maturities over a 5-year planning horizon. Set up all other model parameters as they are known and remain the same over a year. For the scenario based stochastic programming formulation developed in part (b), generate an appropriate sample data set as input to the optimisation model. Solve the optimisation model developed in part (b) and find the optimal investment strategies by using the numerical data (to be generated) for fixing objective weights as 0, 0.25, 0.50, 0.75, and 1.0. Compare the investment strategies and briefly summarise your observations. You may use tables/figures to display your results. (60 marks)
2023-09-06