  Managing investment portfolios is an old and well know problem in multiple
fields including financial mathematics and financial engineering as well as
econometrics and econophysics. Multiple different concepts and theories were
used so far to describe methods of handling with financial assets, including
differential equations, stochastic calculus and advanced statistics. In this
paper, using a set of tools from the probability theory, various strategies of
building financial portfolios are analysed in different market conditions. A
special attention is given to several realisations of a so called balanced
portfolio, which is rooted in the natural "buy-low-sell-high" principle.
Results show that there is no universal strategy, because they perform
differently in different circumstances (e.g. for varying transaction costs).
Moreover, the planned time of investment may also have a significant impact on
the profitability of certain strategies. All methods have been tested with both
simulated trajectories and real data from the Polish stock market.
