Modern hedge fund industry essentially uses algorithmic trading strategies, which take long or short positions in several assets by the predefined moments of time. Strategies have to satisfy some constraints and this imply the properties we shall investigate in the paper. We found that the set of possible vectors of strategy positions is a boundary of a convex polyhedron. We detect the range for strategy profitability in terms of the vector of assets profitabilities. We deduce profit-and-loss formulae under some reasonable assumptions on strategy execution. We prove the existence of operation (exact decay) on series of strategy position vectors which makes the strategy turnover to be equal to the given value. Also we conclude with two numerical experiments which illustrate the profitability distribution and exact decay operation on the real-life strategies.