An empirical analysis of controlled risk and investment performance using risk measures: a study of risk controlled environment

In this thesis, I study the performance behaviour of hedge funds and mutual funds. I study a basket of various risk statistics that are widely used to measure the fluctuation of asset prices. Those risk statistics are used to rank the performance of the assets. The linear dependence relation of these risk measures in ranking assets is investigated and the set of risk measures is reduced by excluding risk measures that produce linearly dependent ranking vectors to other risk measures. The ranks within each of the selected remaining risk statistics are standardised and then linearly transformed into a new set of linearly independent factors where principal component analysis is carried out as a variable reduction technique to remove the noise while preserve the main variation of the original data. The transformed factors are sorted in descending order according to their contribution to the variation of the original data. The factor loadings of the first two principal components PC1 and PC2 are reviewed and interpreted as styles (PC1 as consistency and PC2 as aggression). The universe of a set of hedge funds is classified according to these styles as BL=(low consistency, low aggression), BR=(high consistency, low aggression), TL=(low consistency, high aggression) and TR=(high consistency, high aggression). I examine the performance behaviour of the four different classified classes whereby this classification method provides an indication on returns and management styles of hedge funds. A three-factor prediction model for asset returns is introduced by regressing 12 weeks’ forward rank of return on the historical ranks of risk statistics. The first few principal components, which explain the main variation of information captured by risk statistics, are used in the prediction model. The robustness of the model is tested by applying the model to the following 12-week period using the set of independent factors. An investment strategy is constructed based on the prediction model using the set of independent factors. I discover high evidence of predictability and I test for out-of-sample forecasting performance. I then examine the use of subsets of risk statistics from the basket rather than using the set of all risk statistics. I further study the use of the so-called s2/µ risk measure in predicting the market “turning point” of performance of a portfolio of hedge funds. Risk measure quantity s2/µ replaces the traditional variance s2 in the Black-Scholes option valuation formula when it is evaluated for hedge funds.