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Financial Mathematics

Financial Mathematics: Portfolio Analysis, Risk and Volatility Modelling

This Financial Mathematics coursework focuses on the quantitative analysis of financial assets, portfolio construction, investment risk and volatility modelling. Students are required to work with historical daily share-price data for five stocks previously selected in their portfolio. The data should cover a sufficiently long period, with at least one year of observations, and should provide positive average returns. Students must briefly describe each selected company and the nature of its business before conducting the financial analysis. The first part of the coursework requires students to calculate the expected return and volatility of each of the five companies and analyse the correlations between their asset returns. These calculations provide the foundation for evaluating the risk and return characteristics of the individual assets and their potential contribution to a diversified portfolio. The second part focuses on portfolio optimisation. Students must use an appropriate Solver function to determine portfolio risk and the percentage investment allocated to each asset for a selected target return. The process must be repeated for different target returns to generate an efficient frontier curve. This analysis demonstrates the relationship between expected portfolio returns and the associated levels of portfolio risk. The third part requires students to calculate Sharpe ratios for a range of expected portfolio returns and volatilities obtained through the portfolio analysis. Using a risk-free investment with a guaranteed return of 1.5%, students must determine the equation of the Capital Market Line and discuss its economic significance in relation to investment decisions and portfolio performance. The fourth part applies linear regression analysis to calculate the beta of each asset in the portfolio and discuss the significance of beta as a measure of systematic risk. Students must also estimate the portfolio's Value at Risk at the 5% level and discuss the contribution of each individual asset to the estimated portfolio VaR. The fifth part focuses on financial volatility modelling using R. Students must estimate the volatility of a selected individual asset using ARCH/GARCH models and their extensions, identify the most appropriate model and provide an explanation supporting the model selection. Finally, students must present their findings in non-technical language suitable for a potential investor. The conclusion should identify the implications of the analysis for selecting an efficient portfolio and discuss other relevant performance measurements. The coursework requires clear explanations of the methods and formulae used in Excel worksheets and R outputs, while unnecessary explanations of portfolio theory and the Capital Asset Pricing Model should be avoided.

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Operations and Supply Chain Management 1,987 words

Supply Chain Analytics and Quantitative Data Analysis for Organisational Decision-Making

This postgraduate individual report focuses on the application of quantitative data analysis to Operations, Logistics and Supply Chain Management decision-making. Students are required to select an organisation from the private, public or third sector and investigate a relevant operational or supply-chain issue using quantitative data. The purpose is to demonstrate how data can be collected, prepared, analysed and interpreted to generate evidence-based insights that may support managerial decision-making. The selected dataset must relate to the organisation's operations or supply chain and may include variables such as revenues, product orders, sales, transportation costs, procurement expenditure, inventory levels or other appropriate quantitative measures. The dataset must contain at least 60 observations, and the analysis must involve at least two variables. Data may be obtained directly from organisations or from recognised secondary-data platforms and databases. The assessment consists of two equally weighted components. Part A – Motivation and Justification for the Analysis requires students to formulate relevant analytical questions and explain their practical importance by linking them to Operations and Supply Chain Management theory and business practice. Appropriate academic, industry and practitioner evidence should be used to justify the selected issue. Research questions may also be translated into testable hypotheses where appropriate. Part B – Execution of the Analysis requires students to answer the identified questions through appropriate statistical techniques. Potential methods include tables, charts, summary statistics, t-tests and regression analysis. Data may first need to be cleaned, transformed and structured before analysis. The results must then be interpreted clearly for a managerial audience such as the organisation's board, owner or CEO. The statistical analysis is expected to be conducted using Stata, with all data-cleaning, manipulation and analytical commands recorded in a reproducible do-file. The report must also demonstrate explicit links between theory and practice and contain a suitable mixture of academic and professional evidence, including at least five academic journal articles. Harvard referencing is required throughout. The resulting work demonstrates practical competence in business analytics, statistical interpretation, supply-chain decision support, reproducible analysis and evidence-based managerial communication. Overview word count: approximately 370 words.

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