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COSKEWNESS
Coskewness can be defined as the statistical measure that calculates the symmetry of a variable's probability distribution in relation to another variable's probability distribution symmetry. A positive co skewness can be defined as the first variable's probability distribution which is skewed to the right of the second variable's distribution.
Coskewness can be used as a supplement to the covariance calculation of risk estimation and so usually the co skewness is calculated using a security's historic price data as the first variable and the second variable is market's historic price data. So by calculating like this, it provides an estimation of the security's risk in relation to market risk.
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An investor would prefer a positive co-skewness because this is used to represent a higher probability of extreme positive returns in the security over market returns. Recent asset pricing studies demonstrate the relevance of incorporating co skewness in asset pricing models and it is used to illustrate how this component helps to explain the time variation of ex-ante market risk premiums.
The role of co-skewness in mutual fund performance evaluation and funds adds a co-skewness factor which is economically and statistically significant. It also explains that co skewness is sometimes managed and shows the persistence of the co skewness policy over time and one of the most striking results is that many negative (positive) alpha funds measured relative to the CAPM risk adjustments.
It would be reclassified as positive (negative) alpha funds using a model with co skewness and therefore performance ranking is based on risk-adjusted returns. It is without considering co skewness which could generate an erroneous classification and moreover, some fund characteristics such as the turnover ratio or category are related to the likelihood of managing co-skewness.
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The co skewness helps to explain the time-variation of ex-ante market risk premiums and it is found that the effects of adding co skewness to evaluate the performance are significant. The factors are based on size and book-to-market as well as momentum.
Practical implications are the omission of a co skewness factor which may lead to erroneous evaluations of a fund's performance and therefore issues such as the persistence of performance should be revised.
Originality/value which are the effects of incorporating a co skewness factor in the analysis of investment performance in an unconditional and a conditional framework is by using SDF models.
