DETERMINISTIC DECISION MODELS

Optimisation parts The assignment requires you to consider three different approaches to portfolio optimisation: 1. Choosing according to asset class restrictions, and individual asset risk appetite. 2. Choosing according to portfolio size restrictions and risk appetite. 3. Choosing according to portfolio risk and return requirements. These three approaches allow exploration of three different optimisation techniques: linear programming, integer programming and non?linear programming: 1. LP model: In this approach, the aim is to achieve the maximum overall return, subject to specified requirements on risk mix (percentages in R1 to R4) and category mix (percentages in C1 to C5). These requirements may be simple – such as “no more than 10% in R1, or more complex such as “there should be as much invested in R1 as there is in R4”. Other restrictions might be of the form – “at least 25% should be in the banking sector, and no more than 20% in energy”. It is up to you to determine the restrictions that you wish to impose. I expect these to be “sensible”, respecting a sense of diversity in the portfolio, and a defendable risk acceptance approach. The only requirement is that they should respect the learning aims of this assignment and therefore they should not in any way trivialise the problem. As an example, there should be realistic range requirements for each of R1 to R4, and C1 to C5. To require all assets in the portfolio to be in risk category R1, for example, would be to trivialise the problem. Use a sensitivity analysis report to comment on how changes to the risk and category constraints might affect the optimum portfolio. 2. ILP model: In this approach, we assume that a balanced portfolio of exactly 7 stocks is to be chosen. The 5 asset categories (the C classification) have to be included. In addition, at most 2 of the assets can be in the riskiest group R4, and at least 2 must be in the least risky group R1. The goal is to achieve the maximum overall return, subject to the specified requirements. 1 bonus point: besides the above part, consider modeling of above ILP model with at least 3 asset categories (the C classification) be included (instead of 5 asset categories. 3. NLP model: In this approach, the aim is to optimise without category constraint using the methods of Module 2, topic 7 – i.e. considering the overall portfolio risk/return profile. There are three sub?problems here: a. Achieve the maximum overall return, subject to an upper limit on portfolio risk (your choice of limit). b. Achieve the minimum portfolio risk, subject to a requirement to achieve at least a specified return (your choice of required return). c. Achieve the maximum of risk adjusted return (Sharpe ratio). Summarise your report (all of above parts) in a Powerpoint, present all your results comparatively in a coherent and compelling manner, and then, based on your assessment of the various approaches, explain briefly about a strategy that you might prefer to use for portfolio optimisation. For each optimisation model, explain about the optimisation approach taken, the mathematical formulation and identify the Excel Solver to be used (explaining any particular constraints used – e.g. that a variable needs to be an integer, or binary).

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  • Uploaded By : John
  • Posted on : December 11th, 2017
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