Research On Idiosyncratic Volatility

Based on the assumptions of frictionless market and rational investors, the classical capital asset pricing theory documents that only systemic risk be priced in cross-sectional stock returns, and idiosyncratic risk could be eliminated by holding well-diversified portfolios. However, firstly measuring the systemic risk with market portfolio return Beta is not reliable because the market portfolio in capital asset pricing model is not measurable, secondly investors cannot hold market portfolios because there exists market imperfection such as short sale constraints and infor-mation asymmetry. Thus, idiosyncratic risk should affect expected stock returns.Using Chinese stock market data as the samples, relying on modern econometric models and methods, through univariate portfolio-level analyses, bivariate portfolio-level analyses, firm-level cross-sectional regressions and time series regressions, I discuss how to measure idiosyncratic volatility, the relation between idiosyncratic volatility and expected stock returns, the cause of "idiosyncratic volatility puzzle" and the relation between idiosyncratic volatility and other firm-level risks in this paper.Firstly, considering the nonlinear relation between risk and return, and time-varying and non-symmetry properties of idiosyncratic volatility, I propose a nonlinear-EGARCH(1,1) model to predict stock return, and estimate the idiosyncratic volatil-ity by it.Secondly, I examine the relation between idiosyncratic volatility and expected stock returns, and the effects of idiosyncratic volatility measure method, estimate interval, sample frequency, trade limit on idiosyncratic volatility measurement and the relationship between idiosyncratic volatility and expected stock returns, and find that there is a significant negative relation between idiosyncratic volatility and expected stock returns, well-known as "idiosyncratic volatility puzzle". Compared with CAPM and Fama-French three-factor model, the puzzle investigated based on the nonlinear-EGARCH(1,1) model is significantly weakened.Thirdly, I explain the "idiosyncratic volatility puzzle" from the perspectives of investors and firm managers. From the perspective of investors speculative psychol-ogy, I find that investors prefer stocks with larger historical price change amplitude, investigate the internal connection between the investment preference and the puz-zle, and first propose price range as the proxy of investor personal preference, and find that investor personal preference has a certain degree of explanatory power for the puzzle. Besides, rather than measuring the quality of corporate information dis-closure by analysts’forecasts, I build a model for measuring information disclosure quality based on the responses of the market trading to corporate information dis-closure, and find that the quality of information disclosure positively predicts expect stock returns, but also has a certain degree of explanatory power for the puzzle.Finally, I investigate the relation between the idiosyncratic volatility as the second order moment variable and other firm-level risks such as the maximum daily return and extreme downside risk. I construct portfolios by the maximum daily return, and find low maximum daily return portfolios have higher expected returns than high maximum daily return portfolios. Due to the limit-up in China market, the cross-sectional regression result of expected stock return on maximum daily return is not significant. I propose the left tail index of return distribution as a proxy of extreme downside risk, and find extreme downside risk has stable negative explanatory ability to expected stock returns. Compared with the idiosyncratic volatility effect, extreme downside risk premia and maximum daily return effect are both secondary effect, yet idiosyncratic volatility cannot fully explain the predictive abilities of extreme downside risk and maximum daily return to expected stock return.