This paper is an empirical study of asset pricing with the systematic skewness in the pricing model. We adopt the Fama-French three-factor model, which incorporates the firm-size and book-to-market ratio in asset pricing as the base case, and then includes the skewness factor used by Harvey and Siddique in the pricing model. The evidence shows that systematic skewness is significant and might be important in asset pricing when portfolios are formed by industry, firm-size, book-to-market, or momentum strategies. When portfolios are constructed by momentum or coskewness strategies, lower momentum, or lower coskewness portfolios exhibit higher skewness and higher kurtosis. When portfolios are grouped by excess returns, it is seen that the average excess return is positively correlated with size and coskewness. Thus the systematic skewness is closely related to firm size. And the relationship between systematic skewness and excess return is obscured by the reverse firm-size effect.
Under the model developed by Merton (1987), the idiosyncratic risk would be important to explain the expected stock return. We follow the approach of Daniel and Titman (1998), and use the risk measure developed by Jan and Wang (2012) to examine whether idiosyncratic risk can play an important role in explaining the expected return in Taiwan stock market. We find that beta can't explain the expected return, and that idiosyncratic risk has a positive relation to expected returns for stocks with smaller beta portfolio. We also explore a weak evidence of the positive relationship between idiosyncratic risk and expected return for size-sorted portfolio.
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