Portfolio Optimization from a Risk-Management Perspective A Mathematical Approach to Portfolio Optimization in Risk Management

Abstract

In finance, we have the mantra of “high-risk, high-return”. However, the aim of Modern Portfolio Theory is to minimize risk for a given level of return or conversely, to maximize return given a certain amount of risk. Taking the Markowitz Mean-Variance framework as a starting point, this paper addresses how you can create risk-minimizing portfolios in order to outperform the market. The use of variance as a risk measure in the Markowitz model is clearly outdated and therefore different measures will be introduced into the model to create better risk-adjusted portfolios. The modifications in the theoretical framework will be tested with historical data, and performance will be compared to that of the benchmark indices and the original Markowitz model.