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...

Our modest research goal has been to define a durable investor utility framework, dismissing the decades old – expected-utility (EUT) maximizing economic agent assumption. This has enabled us to properly re-define and re-quantify risk, and part from a reliance upon explanatory ex post analysis...

We show that the Cumulative Distribution Function (CDF) is represented by the ratio of the lower partial moment (LPM) ratio to the distribution for the interval in question. The addition of the upper partial moment (UPM) ratio enables us to create probability density functions (PDF) for any...

Nonlinear nonparametric statistics (NNS) algorithm offers new tools for curve fitting. A relationship between k-means clustering and NNS regression points is explored with graphics showing a perfect fit in the limit. The goal of this paper is to demonstrate NNS as a form of unsupervised...

We derive conditional means from partial moment quadrants of the joint distribution. Restricting quadrants enables scenario analysis without the need for an underlying correlation assumption. Weighting of these conditional means permits more generalized scenarios with embedded dependence...

NNS stands for Nonlinear Nonparametric Statistics, henceforth "NNS". What is NNS clustering analysis? NNS clustering is a method of partitioning the joint distribution into partial moment quadrants (clustering), and assigning identifiers to observations (classification). NNS clustering is very...

We identify the necessary conditions to define causation between two variables. We compare this to Granger causality and the convergent cross mapping method to illustrate the theoretical differences. Our proposed method avoids the reciprocal Granger and nonlinearity concerns. We loosely share a...

This note serves as a hands-on supplement to: Viole, F. and Nawrocki, D. (2012), "Deriving Nonlinear Correlation Coefficients from Partial Moments" "https://ssrn.com/abstract=2148522" https://ssrn.com/abstract=2148522