Constrained Mixture Models for Asset Returns Modelling

The estimation of asset return distributions is crucial for determining optimal trading strategies. One convenient estimation approach selects a distribution model and estimates its parameters. The advantage of this approach is the ease with which probability distributions can be calibrated and applied in post-processing. The disadvantage of assuming a particular parametric distribution is that inferences and decisions depend critically on the choice of distribution. For example, asset returns frequently feature large "outlying" values, making distributions with light tails inapplicable. Semi-parametric methods attempt to capture the advantages but not the disadvantages of a parametric specification of a returns distribution by using a more flexible functional form. Most prominent among the semi-parametric distributions are mixtures of distributions. They provide a flexible specification and, under certain conditions, can approximate distributions of any form.