The Mathematical Formulation and Practical Implementation of Markowitz 2.0

Abstract: Standard Deviation is a commonly used risk measures in risk management and portfolio optimization. Optimal portfolios have normally been computed using standard deviation as the measure of choice for risk. However, ever since the Great Recession, it has come up short in capturing tail risk leading practitioners and investors alike to look for alternative measures such as Value-at-Risk (VaR) and conditional Value-at-Risk (CVaR). Further, given that it is a coherent risk measure and that it allows for a simplification of the portfolio optimization process, CVaR is preferable to VaR. This thesis analyzes the financial model referred to as Markowitz 2.0 which adopts CVaRas the risk measure of choice. Tapping into the extensive literature on portfolio optimization using CVaR and VaR, we give historical context to the model and make a mathematical formulation of the model. Moreover, we present a practical implementation of the model using data drawn from the Dow Jones Industrial Average, generate optimal portfolios and draw the efficient frontier. The results obtained are compared with those obtained through the Mean-Variance optimization framework.