Three essays on stock market volatility

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Fu, Chengbo
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This dissertation consists of three essays on stock market volatility. In the first essay, we show that investors will have the information in the idiosyncratic volatility spread when using two different models to estimate idiosyncratic volatility. In a theoretical framework, we show that idiosyncratic volatility spread is related to the change in beta and the new betas from the extra factors between two different factor models. Empirically, we find that idiosyncratic volatility spread predicts the cross section of stock returns. The negative spread-return relation is independent from the relation between idiosyncratic volatility and stock returns. The result is driven by the change in beta component and the new beta component of the spread. The spread-relation is also robust when investors estimate the spread using a conditional model or EGARCH method. In the second essay, the variance of stock returns is decomposed based on a conditional Fama–French three-factor model instead of its unconditional counterpart. Using time-varying alpha and betas in this model, it is evident that four additional risk terms must be considered. They include the variance of alpha, the variance of the interaction between the time-varying component of beta and factors, and two covariance terms. These additional risk terms are components that are included in the idiosyncratic risk estimate using an unconditional model. By investigating the relation between the risk terms and stock returns, we find that only the variance of the time-varying alpha is negatively associated with stock returns. Further tests show that stock returns are not affected by the variance of time-varying beta. These results are consistent with the findings in the literature identifying return predictability from time-varying alpha rather than betas. In the third essay, we employ a two-step estimation method to separate the upside and downside idiosyncratic volatility and examine its relation with future stock returns. We find that idiosyncratic volatility is negatively related to stock returns when the market is up and when it is down. The upside idiosyncratic volatility is not related to stock returns. Our results also suggest that the relation between downside idiosyncratic volatility and future stock returns is negative and significant. It is the downside idiosyncratic volatility that drives the inverse relation between total idiosyncratic volatility and stock returns. The results are consistent with the literature that investor overreact to bad news and underreact to good news.
Stock Market Volatility, Stock Returns
Fu, C. Alpha Beta Risk and Stock Returns—A Decomposition Analysis of Idiosyncratic Volatility with Conditional Models. Risks 2018, 6, 124.