Learning zero-cost portfolio selection with pattern matching.

We replicate and extend the adversarial expert based learning approach of Györfi 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 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. We argue that the strategies are on the boundary of profitability when considered in the context of their application to intraday quantitative trading but demonstrate that patterns in financial time-series on the JSE could be systematically exploited in collective and that they are persistent in the data investigated. We do not suggest that the strategies can be profitably implemented but argue that these types of patterns may exists for either structural of implementation cost reasons.