Modern Portfolio Theory: Variance, Covariance, and the Mathematics of Diversification

Abstract

This paper explores how Modern Portfolio Theory, introduced by Markowitz, revolutionized investment strategy by adding a mathematical dimension to investment thought. The mathematical structures employed by investors heavily relied on variance and covariance to reduce portfolio risk by maximizing diversification. Central to this is a negative correlation among assets which can largely reduce volatility even if said assets have high risks. In addition, this paper addresses the flaws of MPT, such as performance during market downturns and its reliance on historical data. Alternatives like artificial-intelligence based strategies and Digital Portfolio Theory have an adaptability that MPT lacks. Although MPT’s concepts are still very much used and the theory remains foundational, future-oriented investing favors data-responsive and dynamic frameworks.