# Best Portfolio Management Strategies For Synthetic and Real Assets

## TL;DR

This paper analyzes various portfolio management strategies for both synthetic and real assets using probability tools, highlighting their performance differences across market conditions and investment horizons.

## Contribution

It provides a comparative analysis of portfolio strategies, especially balanced portfolios, under different market scenarios and transaction costs, using both simulated and real data.

## Key findings

- No universal strategy performs best in all conditions.
- Strategy performance varies with transaction costs and investment duration.
- Balanced portfolios based on 'buy-low-sell-high' principle show specific advantages.

## Abstract

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.