Robustly Modelling the Scale and Shape Dynamics of Stock Return Distributions

We explore time variation in the shape of the conditional return distribution using a model of multiple quantiles. We propose a joint model of scale (proxied by the interquartile range) and other quantiles standardised by the scale. The model allows us to capture the scale and shape of the distribution in one step without making assumptions about the distribution of the underlying conditional shocks from the outset. We find that, once we capture the dynamics of the scale effectively, the time variation in the shape allows a simpler interpretation. The method is illustrated by application to stock price and stock index data and provides evidence that the conditional return distribution becomes heavier tailed at times of market stress.