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.

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This study investigates the eå ects of perceived mathematics ability (PMA) on the learning process with special reference to 147 undergraduates following an elementary statistics (ES) course. A model incorporating PMA together with aptitude, eå ort put in, expected grade, motivation to do well and interest in the subject, which are deemed to be either directly or indirectly associated with performance, is developed. PMA itself is not a good predictor of ES performance, rather its eå ect may be channelled through interest, expected grade and motivation to do well in ES. Low perception in mathematics ability impedes eå ort put forth when learning ES. The in¯uence of PMA on ES performance is likely to be the consequence of the belief that mathematics is essential to learn ES.

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