Do realized betas exhibit up/down market tendencies?

In this paper we employ the STAR (smooth transition autoregressive) model to investigate potential nonlinearities, cyclical behaviour and duration dependence in the realized monthly betas of 39 US industry portfolios. Tests reject linearity for all but eight industries. The estimated nonlinear models suggest that industry betas are characterised by asymmetric cycles, with the speed of transition between the bull and bear market regimes being relatively slow for seven industries. We find duration dependence in industry betas since the probability of transition between regimes does depend on how long the market has been in an up or a down state.