Idiosyncratic Volatility Of Stock Returns

The relationship between risk and return is the core content of the financial theory. The classical asset pricing theory assumes that capital markets are efficient and investors can hold diversified portfolios to avoid idiosyncratic risk, so only market risk should be priced into the returns of assets. But recent papers find capital markets are not efficient and many investors can hardly hold perfectly diversified portfolios because of incomplete information and the limitations of short-selling mechanism. Whether idiosyncratic risk should be priced becomes the core of financial research.In the paper, daily data and monthly data of stock market for January 1,2000 to March 31,2011 as research sample, use Fama-French three factor regression and EGARCH(1,1) model to estimate idiosyncratic risk. With portfolio analysis and the cross-sectional regression analysis method, the relationship between idiosyncratic risk and the return of stocks is analyzed. Using Fama-French three factor regression to estimate idiosyncratic risk, a strongly statistically significant positive relationship between idiosyncratic risk and the return of stocks is found. Using EGARCH(1,1)model to estimate idiosyncratic risk, I find that under single factor portfolio analysis, there is a strongly statistically significant positive relationship between idiosyncratic risk and the weighted return of stocks, while under double factor portfolio analysis, there is not a strongly statistically significant relationship between idiosyncratic risk and the weighted return of stocks. Using EGARCH(1,1)model to estimate idiosyncratic risk, under the cross-sectional regression analysis method, there is a strongly statistically significant negative relationship between idiosyncratic risk and the weighted return of stocks. Moreover, size, turnover, illiquidity and return of stocks is positively correlated, the momentum and return of stocks is negatively correlated. Book to market ratio and return of stocks is generally positively correlated.