How Useful is Statistical Skewness of Financial Data in Decision Making?

Title data

Baumann, Michael Heinrich:
How Useful is Statistical Skewness of Financial Data in Decision Making?
2024
Event: 1st CAM-Risk conference , 18.-20. Dezember 2024 , Pavia, Italy.
(Conference item: Conference , Speech )

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Statistical skewness is an important concept in the analysis of gambling and financial investment opportunities. Possibly, investors take the skewness of returns' distributions into account and, classically, search for highly skewed financial products. The concept of skewness can be used in some cases to explain or, perhaps, even predict decisions of agents. However, it is known from the literature that there are not only discrepancies between the formal definition of skewness via the third moment and the usual idea of skewness (as Pearson skewness) but also a mismatch between preference structures built on skewness and those built on expected utility. We contribute to the literature by showing via easy-to-understand, exemplary random variables that preference structures built on specific risk indicators - namely loss probabilities, worst-case losses, or value at risk - are, in general, inconsistent with those built on skewness. We illustrate the connection of risk and skewness on a basic level where we can explain the problem of mismatched preference structures avoiding unnecessarily complex mathematical models. Finally, we investigate the relationship between skewness respectively Pearson skewness and probabilities and prove mathematically that it is possible to make statements about probabilities in one special case, namely for random variables whose Pearson skewness values have different signs.