Notional portfolios and normalized linear returns

TL;DR

This paper introduces notional portfolios and normalized linear returns to address the mismatch between actual portfolio returns and the assumptions of the mean-variance model, enabling better application to compound return data.

Contribution

It proposes a novel approach using notional portfolios and normalized linear returns to adapt the mean-variance framework for compound returns.

Findings

Addresses the non-convexity of compound return vectors.

Provides a method to apply mean-variance analysis to real-world data.

Enhances the theoretical foundation of portfolio selection models.

Abstract

The vector of periodic, compound returns of a typical investment portfolio is almost never a convex combination of the return vectors of the securities in the portfolio. As a result the ex post version of Harry Markowitz's "standard mean-variance portfolio selection model" does not apply to compound return data. We propose using notional portfolios and normalized linear returns to remedy this problem.