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Word Limit

Maximum 5 pages, including the cover page.

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:

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•    Correct referencing

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•    English Language support

•    Word count policy

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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).

3.    includes unreferenced work that you have previously submitted for any accredited course of study (unless explicitly asked to do so by your Module Leader/Tutor) (self-plagiarism).

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Self-certification is a university-wide policy whereby you are permitted an automatic extension of 5 working days on eligible written assessed work without the need for evidence. WBS permits self-certification for all types of written, assessed works such as essays and dissertations. It is not permitted for exams, course tests, or presentations.

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see:https://my.wbs.ac.uk/-/academic/20778/item/id/1244460/.

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Your assignment instructions begin below.

Questions 1 (60% of marks)

CASE A:

The  portfolio  manager  of  a telecommunication  company  is  currently  considering  different fixed  income securities such as government and commercial bonds (labelled as i = 1,2, … , n) to pay off a series of future cash obligations over a four-year planning horizon. They now need to decide the number of securities to purchase today so that the future cash requirements Ct  (£) in year t for t = 1, . . . , 4 are met. The portfolio manager  assumes that these securities are widely available  in the  market  and can  be  purchased  in any quantities at the given price. Moreover, he considers only securities with 1, 2, 3, and 4-year maturities.

Let pi(£) denote the current market price of security i . Each security i yields annual coupon payment of qi(£) up to its maturity. The principal Fi(£) of security i is paid out at maturity. After an initial investment on bonds is made at t = 0, they can also apply for a one-year loan or borrow a certain amount of money at any time if they need, but do not wish to consider another reinvestment opportunities. An amount of money can be borrowed from year t to year t+1 with annual rate of bt(%) at each time-period. Similarly, a loan to be received at each time-period will be paid-off at the next time-period with annual interest rate Tt(%) from year t to the next year  t+1. Moreover, there is no cash reinvestment, loan or borrowing at the end of planning horizon.  The  portfolio  manager  would  like  to  determine  an  optimal  portfolio  dedication  strategy  that maximizes the final cash on hand at the end of investment horizon and minimizes the total cost of investment.

a) Assume that all model parameters are known, and the fixed rates remain the same over a year. Formulate (but do not solve) a deterministic linear programming model of the portfolio dedication problem. (10 marks)

b) Now, ignore the optimization model developed in part (a). They assume that both rates ̃Tt   and t are uncertain. Thus, they generate a scenario tree, that is showing a probabilistic representation of random rates of one-year loan and annual borrowing over the five-year period. They observe either one or two different events, representing realizations of random rates at each node of 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 that maximizes the total expected cash on hand at the final time-period and minimizes the total cost of investment. Briefly explain what additional variables/constraints you need to add to the model developed in part (a). (20 marks)

c) Consider an instance of the firm’s financing problem consisting of up to 10 securities. For the scenario based stochastic programming formulation developed in part (b), generate an appropriate sample data  set  as  input to the optimisation  model.  Find the  optimal  investment  strategy  by  using the numerical data (to be generated). Briefly summarize your observations. (30 marks)