A mean-variance optimized portfolio constructed for investment in a reference security, for an investor with a preference towards an accepted set of securities

TL;DR

This paper develops a mean-variance portfolio optimization method for investors who prefer a set of accepted securities similar to a reference security, but cannot invest directly in it due to constraints.

Contribution

It introduces a framework for constructing portfolios that approximate a reference security using an accepted set, incorporating similarity measures and performance metrics.

Findings

Optimal portfolios can be derived using mean-variance criteria.

The approach considers the Sharpe Ratio for performance evaluation.

The method accommodates investor-specific constraints.

Abstract

We consider a reference security, understood to be an attractive investment, with the caveat that an investor is not willing to directly invest in the security, for presence of constraints, either investor specific or pertaining to the security itself. The investor, however, is open to a portfolio constructed with an accepted set of securities, where returns could be considered similar to the reference security. We demonstrate, under a measure of similarity, such a portfolio could be selected with a mean-variance characterization, as defined by Markowitz. Furthermore, we consider the performance relative to the reference security, with the Sharpe Ratio. The objective of the paper is to derive an optimal portfolio to address an investor preference for the accepted set of securities.