This project describes the underlying principles of Modern Portfolio Theory, the Capital Asset Pricing Model (CAPM), and multi-factor models in detail, explores the process of constructing optimal portfolios using the Modern Portfolio Theory, estimates the expected return and covariance matrix of assets using CAPM and multi-factor models, and finally, applies these models in real markets to analyze our portfolios and compare their performances.

This thesis examines the links between economic time-series innovations and statistical risk factors in the UK stock market using principal components analysis (PCA) and the general-to-specific (Gets) approach to econometric modelling. A multi-factor risk structure for the UK stock market is assumed, and it is found that the use of economic 'news' (innovations), PCA, the Gets approach, and different stock grouping criteria helps to explain the relationships between stock returns and economic variables. The Kalman Filter appears to be more appropriate than first-differencing or ARIMA modelling as a technique for estimating innovations when applying the Gets approach. Different combinations of economic variables appear to underpin the risk structure of stock returns for different sub-samples. Indications of a possible influence of firm size are found in principal components when different stock sorting criteria are used, but more definite conclusions require simultaneous sorting by market value and beta. Overall it appears that the major factor affecting the identification of specific explanatory economic variables across different sub-samples is the general economic context of investment. The influence of firm size on stock returns seems in particular to be highly sensitive to the wider economic context. There is an apparent instability in the economic underpinnings of the risk structure of stock returns (as measured by principal components) that might also be a result of changing economic conditions.