Jensen's alpha measured and decomposed under skew symmetric semi-parametric model for error terms in the market model

Navruzbek Karamatov and Ryozo Miura

No 99, DSSR Discussion Papers from Graduate School of Economics and Management, Tohoku University

Abstract: A simple estimation method, namely the Ordinary Least Squares (LS) is applied for nearly all empirical analysis to estimate ?A. However, Jensen (1968) made clear that CAPM is not able to explain abnormal returns and is used to account for this unobserved factors. More importantly Jensen's Alpha is obtained as a mean value of residuals from a simple regression. Nonetheless, LS is sensitive to outliers and this could make estimators to be vulnerable. As empirical studies states, observed residuals are not symmetrically distributed. Can asymmetry in error term distribution explain Jensen's Alpha? This research tries to find the answer by applying robust Rank statistics, in comparison with Least Squares, to fit a simple linear regression into Nikkei 225, FTSE 100 and S&P 500 stocks. Furthermore, the Generalized Lehmann's Alternative Model (GLAM) is applied to observed residuals to analyze the location and asymmetry of the residuals distribution. We found that residuals are, indeed, noticeably skewed. GLAM model shows that ma- jority of stocks in all three markets experience asymmetry, especially during the financially stressful periods in 2008. In addition, our asymmetry parameter ?A possesses a statistically significant relation to ?? and to the skew effect which is defined as a difference between ?? and location (?E). Furthermore, in order to obtain the underlying F distribution we fitted t distribution with varying degrees of freedom. Our results show that most of the stocks experience smaller degrees of freedom meaning that R estimate is more effcient than its counterpart LS. Moreover we found that R approach is suitable even in the case of high degrees of freedom (close to normal) but large ?A values. Next, we also found that LS underestimates ?? and ?A for majority of stocks with smaller degrees of freedom.

Pages: 67 pages
Date: 2019-07
New Economics Papers: this item is included in nep-fmk
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