Analysing the optimal level of leverage in stock markets using numerical methods and agent-based modelling

Leverage offers the possibility of enhancing financial returns and, consequently, the profit and the end of period wealth. Leverage is gaining importance and has been widely adopted in the financial markets for t,VD reasons. Firstly, brokers are interested in offering margins because they can charge higher transaction fees and make profits from lending margins. Secondly, investors are also interested in taking leverage because of the ability to enhance their individual returns. The motivation of this thesis is that, even though leverage is gaining importance in modern investments, existing models in the literature models assume that the series of financial returns are normally distributed. However, financial returns present high-level of kurtosis and, hence, are not normally distributed. Thus, existing analytical models underestimate extreme returns and consequently underestimate the risk of default. I contribute to this field by proposing a new trading strategy that uses numerical methods to calculate the optimal level of leverage instead of the existing analytical models. The use of numerical methods allows me to relax the assumption of normally distributed returns, and hence minimises the risk of underestimate extreme returns and the risk. of default. I investigate whether the use of numerical methods leads to a more accurate optimal level of leverage than analytical models, and if the use of the optimal level of le'verage using numerical methods improves the investment performance. In order to test the ability of the optimal1evel of leverage using numerical methods to improve the investment performance, I employ two different approaches: back-testing and agent-based modelling. Back-testing allows me to test the optimal level of leverage using numerical methods using empirical I , evidence, and agent-based modelling allows me to test the optimal level of leverage using numerical methods in a totally controlled environment. The conclusions are that the use of numerical methods leads to a more accurate optimal level of leverage than analytical models; using daily historical data as an empirical evidence, the optimal level of leverage using numerical methods improves investment performance; and in a totally controlled environment) the ability of the optimal level of leverage to improve investment performance depends on the size of the market.EThOS - Electronic Theses Online ServiceGBUnited Kingdo