Statistical Methods in Finance 2018

Abstract

Investment curves and linear separation in a mean-lower partial moment framework

by Dipankar Mondal

Linear combinations of a risk-free asset and some arbitrary risky portfolio form an investment curves in a mean-risk space. The curves are not always linear when the risk is measured by lower partial moment (LPM). Due to the non-linearity, two fund linear separation is not guaranteed in a mean-LPM (MLPM) space. As a result, an investor who mistakenly assumes the separation holds will face excess portfolio risk in this space. This paper addresses to solve this issue. We first introduce some analytical properties of investment frontiers in the MLPM framework and solve a conjecture proposed by \cite{2008}. Moreover, by using the properties, we develop a necessary and sufficient criteria for obtaining two fund linear separation. The criteria helps the investors to determine whether a target admits linear separation or not.

---

---