Since the first stock exchange was opened, a lot of people are constantly thinking about when, into which stock and how much could they invest to get more money back. In the middle of the 1950 years Markowitz created his work about portfolio theory and started a scientific and economic wave. Investing in portfolios gave us the answer to how to invest in less a risky way if we are not professionals in any investment types. But less risk brings less return into the investment. The traditional Markowitz type portfolios are optimized between risk and return. But can we create investments which achieve particularly high return by using portfolios?
The log-optimal portfolio theory has a different view on portfolios by optimizing investments not on the return / risk rate, rather on the expected average growth. It uses simple machine learning algorithms to extract some hidden information from the past return rates of the stocks and optimize the distribution of our portfolio based on the estimation.
I have designed and implemented my own version of the log-optimal portfolio optimization model with self-made improvements. I have tested my model on real stock exchange data. I have collected pretty good stocks from the US markets, which could earn 17% growth in 2010 in an equally diversified portfolio. The different settings of my model achieved 26%, 32%, 34% and even 48% growth in the same period of time. The various settings of parameters perform well in different cases. The model itself has the opportunity to earn much more annual return rates; with the proper combination of the settings theoretically it could achieve 20 times more wealth until the end of 2010 than we invested in the beginning of the year.
In this thesis work I introduce the mathematical model, the design concepts and the main parts of the implementation as well as the test results and a brief analysis of the parameters for this portfolio optimization software.