Does Beta React to Market Conditions?: Estimates of Bull and Bear Betas using a Nonlinear Market Model with Endogenous Threshold Parameter

We apply a logistic smooth transition market model (LSTM) to a sample of returns on Australian industry portfolios to investigate whether bull and bear market betas differ. Unlike other studies, our LSTM model allows for smooth transition between bull and bear states and allows the data to determine the threshold value. The estimated value of the smoothness parameter was very large for all industries implying that transition is abrupt. Therefore we estimated the threshold as a parameter along with the two betas in a DBM framework using a sequential conditional least squares (SCLS) method. Using Lagrange Multiplier type tests of linearity, and the SCLS method our results indicate that for all but two industries the bull and bear betas are significantly different. This research was supported in part by a Monash Graduate School scholarship (MGS). We are grateful to Clive Granger and Timo Teräsvirta for their helpful suggestions. We would also like to thank the Financial Derivatives Centre for their support.