Woodward_George - Does Beta React to Market Conditions...

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Does Beta React to Market Conditions?: Estimates of Bull and Bear Betas using a Nonlinear Market Model with Endogenous Threshold Parameter by George Woodward and Heather Anderson Department of Econometrics, Monash University, Clayton, Victoria 3168, Australia. ABSTRACT 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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1. INTRODUCTION The simple linear market model has long been used, in tests of the Capital Asset Pricing Model (CAPM), as a benchmark for the performance of mutual funds, and for the measurement of abnormal returns in event studies. See Fama and French (1992), Sharpe (1966) and Fama et. al. (1969) for some examples. The stability of the beta coefficient in the market model over bull and bear market conditions is therefore of considerable interest since if beta does in fact differ with market conditions the single beta estimated over an entire period can result in erroneous conclusions in each case. 1 Direct evidence of the importance of the beta/market condition relationship issue is given by the fact that investment houses regularly publish separate alphas and betas over bull and bear markets, for a range of securities, to offer differing levels of upside potential and downside risk. Many studies have investigated the relationship between beta risk and stock market conditions. These include studies of: individual securities (Fabozzi and Francis (1977), Clinball et. al. (1993) and Kim and Zumwalt (1979)), mutual funds (Fabozzi and Francis (1979) and Kao et. al. (1998)), size based portfolios (Bhardwaj and Brooks (1993), Wiggins (1992) and Howton and Peterson (1998)), risk based portfolios (Spiceland and Trapnell (1983) and Wiggins (1992)) and past performance based portfolios (Wiggins (1992) and DeBondt and Thaler (1987)). While most of these studies found evidence that beta varies with market conditions, this evidence is mixed and very weak. Furthermore most of these studies used the dual beta market (DBM) model and simple t- and F-testing method in conjunction with crude “up” and “down” market definitions of bull and bear markets to investigate this phenomenon.
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This note was uploaded on 12/08/2011 for the course CIS 625 taught by Professor Michaelkearns during the Spring '12 term at Penn State.

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Woodward_George - Does Beta React to Market Conditions...

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