Estimation error and partial moments

David Nawrocki and Fred Viole

International Review of Financial Analysis, 2024, vol. 95, issue PB

Abstract: While partial moments like semivariance, lower and upper partial moments have seen acceptance by both academics and investment professionals, there are some who consider these measures to be ad hoc measures of investment performance. This paper seeks to provide the academic foundation for the use of partial moments as a field of nonparametric statistics. The basic foundation is Chebyshev's inequality which underlies Markowitz's mean-variance modern portfolio theory. The semivariance exhibits a strong boundary equivalence to Chebyshev's inequality based on a proof provided by Berck and Hihn (1982). From this, we infer that partial moments provides a strong statistical analysis of risk and return for modern portfolio theory without assuming the underlying probability distribution of a security. The same probability statements can be made with partial moments as can be made with the normal distribution.

Keywords: Partial moments; Nonparametric statistics; Portfolio theory; Strong boundary equivalence to Chebychev's inequality (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:finana:v:95:y:2024:i:pb:s1057521924003752

DOI: 10.1016/j.irfa.2024.103443

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