We adopt an agent-based computational model to consider the market microstructure, the behavioural aspect of the financial market. By keeping a record of artificial traders’ behaviour, which is determined by a choice of the error function, allows us to address a question of how agents’ performance (defined in terms of profitability) depends upon the loss function adopted for making forecasting and trading decisions.

The analysis presented in this paper reveals strong relationships between the error criterion, used to train the artificial neural network and economic performances of trading strategies, developed with this network. Our experiments have identified moderate relationships between the order of the loss function used in minimisation and the statistical characteristics of the resulted forecasts or trading strategies. Trading mechanisms, based on L⁶ error criterion demonstrate robust relationships with profitability, unlike those based on L² and L¹ cost functions minimisation.

Setting up the performance surface with appropriate loss function minimisation is thus an essential factor in the development of a computational model. Learning the mapping of forecasts into trading strategies establishes the predictive density that determines agents’ actions. Measures of trading strategies’ predictive power might significantly differ from criteria leading to its profit maximisation. The choice of evaluation criterion, combining statistical qualities and economic profitability, is viewed as essential for an adequate analysis of economic structures.

When profits are not observable, the ‘performance index’ (based on the relative performance of the artificial neural network and the ‘naive’ prediction) is proposed as an evaluation criterion for an economic prediction, due to its robust relationship with annualised returns. If conventional least squares are to be considered inadequate, an alternative estimation technique for economic behaviour might use a combination of measures, demonstrated to have stable relationships with profitability; the ‘performance index’ has been identified so far.

The presence of at least two objectives (statistical and economic) to be satisfied at the same time might be considered in a multi-objective optimisation problem in future investigations. It seems that evolutionary algorithms, capable generating the Pareto optimal set in a single run, could be particularly appropriate for this task. A natural path is thus to apply a genetic algorithm and extend the model to a multi-assets environment.

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