Optimal portfolio management under only mean and variance/covariance measures in Markowitz (J Finance 7(1):77–91, 1952; J Polit Econ:152–158, 1952) and Tobin (Rev Econ Stud 25:65–86, 1958; Econometrica 26(1):24–36, 1958) framework, is inefficient in real stock markets, as investors do not have quadratic utility functions, and returns are not normally, independently, and identically distributed. Hence alternative forms of utility functions with further higher moments such as the power utility should be used, but these do not provide closed form solutions towards a good feasible portfolio selection. A variety of innovative heuristics have been put forward recently. Hence implementing empirical data, we test and compare different heuristic techniques for portfolio management with power utility as well as contrasting the differences between power utility maximised portfolios and quadratic utility maximised portfolios.