  The debate between active and passive investment strategies has been ongoing
for many years and is far from being over. In this paper, we show that the
choice of an optimal portfolio management strategy depends on an investment
climate, which we measure via the parameters of the Heston model calibrated to
the real stock market data. Depending on the values of those parameters, the
passive strategy may namely outperform the active ones or vice versa. The
method is tested on three stock market indices: S\&P500, DAX and WIG20.
