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Abstract. The skewness of the Weibull family of distributions is discussed for all values of the shape parameter. This class includes unimodal probability densities for which the coefficient of skewness μ3/o3 is positive, but the order of the mean, median and mode is μ < m < M. For values of the shape parameter used in practice the distributions are skewed to the right by a well accepted definition of skewness.

AbstractBond skewness and coskewness (i.e., bond return comovement with market volatility) are both time varying, with cross‐sectional variation driven by maturity and credit rating. Other things being equal, longer maturity bonds have lower skewness, and lower coskewness with respect to the bond market index; lower quality bonds have lower skewness, and higher coskewness with respect to the bond market index. Three‐moment bond alphas (which account for coskewness effects) are time varying and predictable by market default spread. They are significantly different from, and often are closer to zero than, two‐moment alphas (which ignore coskewness effects).

This paper introduces some new elements to measure the skewness of a probability distribution, suggesting that a given distribution can have both positive and negative skewness, depending on the centred sub‐interval of the support set being observed. A skewness function for positive reals is defined, from which a bivariate index of positive–negative skewness is obtained. Certain interesting properties of this new index are studied, and they are also obtained for some common discrete distributions. We show the advantages of their use as a complement to the information derived by traditional measures of skewness.

AbstractSkewness in returns is relevant to option investors. Because options possess positively skewed distributions, the traditional maxim of diversification, which can destroy positive skewness, is not necessarily consistent with investment objectives. The results indicate that the majority of skewness in option portfolios is diversified with a relatively small portfolio size, suggesting a strategy of antidiversification for option investors. Even though the investment performance of options is inferior to stocks on a risk‐return basis, the data indicate the suitability of option portfolios in an environment where an investor's utility is measured by the return, risk, and skewness of the return distribution.