Beyond Correlation: Using the Elements of Variance for Conditional Means and Probabilities

Abstract

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 structures. The resulting analysis simultaneously considers multiple correlation assumptions and demonstrates that correlation is not necessary to derive expected values, rather merely a probability of that expected value for a given condition. Extending the analysis to mean/variance optimization identifies a major philosophical inconsistency with its treatment of correlation, and offers an alternative to the use of correlation in constructing portfolios.

Keywords: Partial Moments, Correlation, Dependence, Conditional Means

JEL Classification: C00