Spread component costs and stock trading characteristics in the Spanish Stock Exchange. Two flexible fractional response models

This paper investigates relationships between the spread component costs (adverse selection, order processing and inventory costs) and stock trading characteristics in the Spanish Stock Exchange (SSE), taking into account the random nature of these costs. First, we analyse the statistical properties of estimated spread components in the market, which are obtained by using two statistical models to decompose the bid-ask spread. We then propose a fractional response regression model based on two flexible cross-sectional probability density functions with covariates which accommodate certain aspects of the empirical estimates, such as skewness and bounded distribution. Our model has two main advantages: (i) it can be implemented easily in a maximum likelihood framework; (ii) in contrast to linear regression models, it provides a useful estimate of the statistical significance of the parameters, and predicts costs not only at the conditional mean but also by using quantiles of the estimated conditional distribution. The empirical results corroborate the presence of statistically significant large order processing costs and smaller adverse selection and inventory costs in the SSE. These spread components have a skewed empirical distribution and the proposed fractional regression models represent the behaviour of these costs reasonably well, surpassing the linear regression model in various specification tests.