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In this paper, we relate the returns in the thirty securities in the Dow Jones index to regime shifts in stock market volatility. We apply a Markov switching process of order one to market volatility and examine the variation in the securities' returns in different volatility regimes. We test the significance of the risk premium in different market regimes and we find evidence of relationship between market volatility and securities beta risk.

Beta Risk and Regime Shift in Market Volatility