  We consider and extend the adversarial agent-based learning approach of
Gy{\"o}rfi {\it et al} to the situation of zero-cost portfolio selection
implemented with a quadratic approximation derived from the mutual fund
separation theorems. The algorithm is applied to daily sampled sequential
Open-High-Low-Close data and sequential intraday 5-minute bar-data from the
Johannesburg Stock Exchange (JSE). Statistical tests of the algorithms are
considered. The algorithms are directly compared to standard NYSE test cases
from prior literature. The learning algorithm is used to select parameters for
agents (or experts) generated by pattern matching past dynamics using a simple
nearest-neighbour search algorithm. It is shown that there is a speed advantage
associated with using an analytic solution of the mutual fund separation
theorems. It is argued that the expected loss in performance does not undermine
the potential application to intraday quantitative trading and that when
transactions costs and slippage are considered the strategies can still remain
profitable when unleveraged. The paper demonstrates that patterns in financial
time-series on the JSE can be systematically exploited in collective but that
this does not imply predictability of the individual asset time-series
themselves.
