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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