  Stochastic portfolio theory aims at finding relative arbitrages, i.e. trading
strategies which outperform the market with probability one. Functionally
generated portfolios, which are deterministic functions of the market weights,
are an invaluable tool in doing so. Driven by a practitioner point of view,
where investment decisions are based upon consideration of various financial
variables, we generalize functionally generated portfolios and allow them to
depend on continuous-path semimartingales, in addition to the market weights.
By means of examples we demonstrate how the inclusion of additional processes
can reduce time horizons beyond which relative arbitrage is possible, boost
performance of generated portfolios, and how investor preferences and specific
investment views can be included in the context of stochastic portfolio theory.
Striking is also the construction of a relative arbitrage opportunity which is
generated by the volatility of the additional semimartingale. An in-depth
empirical analysis of the performance of the proposed strategies confirms our
theoretical findings and demonstrates that our portfolios represent profitable
investment opportunities even in the presence of transaction costs.
