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LANGNAN CHEN WEI XIONG
(
Sun Yat-Sen University
)
Abstract We investigate the determinants of the idiosyncratic volatility by utilizing the regression and employing the daily data from Shanghai Stock Exchange from 1997 to 2010.
First of all, we measure the idiosyncratic volatility by utilizing the nonparametric method of Campbell, Lettau, Malkiel and Xu (or CLMX, 2001) and the parametric method of Malkiel and Xu (2003) and Ang, Hodrick, Xing and Zhang (2009). The nonparametric method is based on the fact that the weighted average of all betas in the stock market with respect to the market factor is equal to 1. Thus, we can derive a weighted average volatility at the market level. And then, we calculate the stock return volatilities each month with daily data and divide the total volatility into three parts: market volatility, industry volatility and firm-specific volatility. The parametric method is based on the residuals of the CAPM model. We regress the daily excess returns of stock i against the daily market returns and use the variance of the daily regression residuals each month as the idiosyncratic volatility of stock i in that month.
Secondly, we derive an empirical model to test the determinants of the idiosyncratic volatility. We examine the determinants of idiosyncratic volatility by incorporating the cross-term of idiosyncratic volatility, current unexpected earnings, lagged unexpected earnings and future unexpected earnings into the regression against excessive stock return.
where, r i, t is the excess stock return, IV i, t is the idiosyncratic volatility of firm i in year t, ΔE i, t+τ is the unexpected earnings, which is the difference between the current earnings and the earnings last year divided by the size of the firm. We use the stock return next year as a control variable to reduce the measure errors in the unexpected earnings (Collins et al., 1994). asset i, t is the firm size, which is the log value of the outstanding shares multiply by the stock price. We add three more control variables: the standard deviation of firm's earnings in the past three years, which reflects the information transparency of a firm; the ratio of shares held by the second to ten largest shareholders to that of the largest shareholder, which measures the power balance with shareholder structure; and the ratio of fixed assets to total assets, which represents the timeliness of release of financial statements (Beaver and Ryan, 1993).
We estimate the model by utilizing the Fama-MacBeth regression method. First, we run the regression each year and get a time series of the estimated coefficients. Second, we derive the mean values of the coefficients throughout the time period and their Newy-West t-values to see whether it is statistically significant. The coefficient of the lagged unexpected earnings ΔE i, t-1 (λ -1 ) and the coefficient of the future unexpected earnings ΔE i, t+1 (λ 1 ) reflect the post earnings announcement drift and prices lead earnings effect in the market respectively. To find the determinants of the idiosyncratic volatility, we focus on the coefficients of the cross-terms, β τ (τ=-1, 0, 1), which indicates the relationship between the unexpected earnings and stock returns in each period is affected by the idiosyncratic volatility.
Finally, this paper presents the important findings. The coefficient of the lagged earnings is positive, suggesting the existence of the post earnings announcement drift effect, but is not significant. The coefficient of the earnings next period is positive and significant, suggesting that the prices lead earnings effect does exist in the Chinese stock market. The coefficient of the cross-term of idiosyncratic volatility and lagged unexpected earnings is positive though it is insignificant, while the coefficient of the cross-term of idiosyncratic volatility and future unexpected earnings is negative and insignificant. These findings contradict the firm-specific information hypothesis, which arguing that the market returns should incorporate the information content of a firm's current earning more quickly and reflect future earnings to greater extent as the idiosyncratic volatility goes up. The evidence clearly indicates that the market efficiency reflecting firm-specific information does not improve as the idiosyncratic volatility increases. Therefore, we can conclude that the idiosyncratic volatility is driven by noise trading, rather than firm-specific information.
Key words Idiosyncratic Volatility, Market Efficiency, Firm-specific Information, Noise Trading