Electronic Thesis and Dissertation Repository


Master of Science


Applied Mathematics


Dr. Matt Davison

2nd Supervisor

Dr. Adam Metzler

Joint Supervisor


The purpose of this thesis is to conduct a sensitivity analysis of the investment allocation decisions made, not within a modern portfolio theory, but within a capital asset pricing model framework. For analytic tractability, we made the simplification (of some current practical interest) that investors have the objective of minimizing the variance of their portfolios without reference to the expected returns to be obtained from these portfolios. Our analytic results reveal how the minimum variance portfolio composition, expected return and risk would change with respect to the changes of the underlying asset correlations and volatilities. We give the investors instructions on how to build the minimum variance portfolio and keep the portfolio risk minimized with variable market data. We also specifically discuss the two-asset portfolio, which is analytically tractable and we find many interesting results. Finally, we analyze the risk that is not covered when the investor makes estimation errors about the market data using our model. We show the portfolio minimum variance is stable.