AbstractsMathematics

The task of managing an investment portfolio is one that continues to challenge both professionals and private individuals on a daily basis. Contrary to popular belief, the desire of these actors is not in all (or even most) instances to generate the highest profits imaginable, but rather to achieve an acceptable return for a given level of risk. In other words, the investor desires to have his funds generate money for him, while not feeling that he is gambling away his (or his clients’) funds. The reasons for a given risk tolerance (or risk appetite) are as varied as the clients themselves – in some instances, clients will simply have their own arbitrary risk appetites, while other may need to maintain certain values to satisfy their mandates, while other may need to meet regulatory requirements. In order to accomplish this task, many measures and representations of performance data are employed to both communicate and understand the risk-reward trade-offs involved in the investment process. In light of the recent economic crisis, greater understanding and control of investment is being clamoured for around the globe, along with the concomitant finger-pointing and blame-assignation that inevitably follows such turmoil, and such heavy costs. The reputation of the industry, always dubious in the best of times, has also taken a significant knock after the events, and while this author would not like to point fingers, clearly the managers of funds, custodians of other people’s money, are in no small measure responsible for the loss of the funds under their care. It is with these concerns in mind that this thesis explores the potential for utilising the powerful tools found within the disciplines of artificial intelligence and machine learning in order to aid fund managers in the balancing of portfolios, tailoring specifically to their clients’ individual needs. These fields hold particular promise due to their focus on generalised pattern recognition, multivariable optimisation and continuous learning. With these tools in hand, a fund manager is able to continuously rebalance a portfolio for a client, given the client’s specific needs, and achieve optimal results while staying within the client’s risk parameters (in other words, keeping within the clients comfort zone in terms of price / value fluctuations).This thesis will first explore the drivers and constraints behind the investment process, as well as the process undertaken by the fund manager as recommended by the CFA (Certified Financial Analyst) Institute. The thesis will then elaborate on the existing theory behind modern investment theory, and the mathematics and statistics that underlie the process. Some common tools from the field of Technical Analysis will be examined, and their implicit assumptions and limitations will be shown, both for understanding and to show how they can still be utilised once their limitations are explicitly known. Thereafter the thesis will show the various tools from within the fields of machine learning and…