Relationship between systematic-risk measured in the second-order and third-order co-moments in the downside framework

The difference between systematic risk measured in terms of the third-order and second-order co-moment of returns in the downside framework is influenced by a factor associated with the market portfolio returns. Empirical evidence reveals that the smaller the spread in the returns in the market portfolio, the greater the influence of this factor. When measuring systematic risk in the downside, the choice of the order of co-moment is influenced by the variation in abnormal returns in the portfolios.