Does beta react to market conditions? Estimates of 'bull' and 'bear' betas using a nonlinear market model with an endogenous threshold parameter

The authors use a logistic smooth transition market (LSTM) model to investigate whether 'bull' and 'bear' market betas for Australian industry portfolios returns differ. The LSTM model allows the data to determine a threshold parameter that differentiates between 'bull' and 'bear' states, and it also allows for smooth transition between these two states. Their results indicate that 'bull' and 'bear' betas are significantly different for most industries, and that up-market risk is not always lower than down-market risk. LSTM models indicate that the transition between 'bull' and 'bear' states is abrupt, supporting a dual-beta market modelling framework.