Beta Risk and Regime Shift in Market Volatility

Beta Risk and Regime Shift in Market Volatility - Beta Risk...

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Beta Risk and Regime Shift in Market Volatility Roland Shami * and Don U.A. Galagedera Department of Econometrics and Business Statistics Monash University Abstract In this paper, we relate security returns in the thirty securities in the Dow Jones index to regime shifts in the market portfolio (S&P500) volatility. We model market volatility as a multiple-state Markov switching process of order one and estimate non-diversifiable security risk (beta) in the different market volatility regimes. We test the significance of the premium of the beta risk associated with the different market regimes and find evidence of a relationship between security return and beta risk when conditional on the up and down market movement. Key words: Markov regime-switching, market volatility, beta risk. JEL Classification: G12, G15 1. Introduction When testing the validity of asset pricing models, especially the capital asset pricing model (CAPM 1 ), many studies examine models conditional on market movements. A common method to capture market movements is to define up and down markets based on some arbitrarily chosen Correspondence to: Roland Shami, Department of Econometrics and Business Statistics, Monash University, PO Box 197, Caulfield East, Victoria 3145, Australia. email: [email protected] 1 CAPM conveys the notion that securities are priced so that their expected return will compensate investors for their expected risk. Symbolically, CAPM is expressed as ( )( ) [ ] f m i f i R R E R R E + = β where, is the return on security i , is the return on risk-free asset, is the return on the market portfolio and i R f R m R i is the measure of security i ’s non-diversifiable risk relative to that of the market portfolio.
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threshold value. For example, Kim and Zumwalt (1979) used three threshold levels, namely, average monthly market return, average risk-free rate and zero. Several studies have investigated the risk-return relationship in the tails of the market return distribution. For example, Crombez and Vander Vennet (2000) defined three regimes for market movements, namely, substantially upward moving, neutral, and substantial bear. They used the following threshold points: (i) the average positive market return and average negative market return, (ii) the average positive market return plus half the standard deviation of positive market returns and average negative market return less half the standard deviation of negative market returns, and (iii) the average positive market return plus three-quarters of the standard deviation of positive market returns and average negative market return less three-quarters of the standard deviation of negative market returns. Crombez and Vander Vennet (2000) assessed the robustness of the regime classification on the conditional beta risk-return relationship by varying the width of the neutral interval. They found the relationship to be stronger as the classification of up and down markets became more pronounced.
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This note was uploaded on 01/29/2012 for the course ECONOMICS 101 taught by Professor Tikk during the Spring '11 term at University of Toronto.

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Beta Risk and Regime Shift in Market Volatility - Beta Risk...

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