METHODS AND APPARATUS EMPLOYING HIERARCHICAL CONDITIONAL VALUE AT RISK TO MINIMIZE DOWNSIDE RISK OF A MULTI-ASSET CLASS PORTFOLIO AND IMPROVED GRAPHICAL USER INTERFACE

The traditional Markowitz mean-variance-optimization (MVO) framework that uses the standard deviation of the possible portfolio returns as a measure of risk does not accurately measure the risk of multi-asset class portfolios whose return distributions are non-Gaussian and asymmetric. A scenario-based conditional value-at-risk (CVaR) approach for minimizing the downside risk of a multi-asset class portfolio is addressed that uses Monte-Carlo simulations to generate the asset return scenarios. These return scenarios are incorporated into a modified Rockafellar-Uryasev based convex programming formulation to generate an optimized hedge. One example addresses hedging in an equity portfolio with options. Testing shows that a hierarchical CVaR approach generates portfolios with better predicted worst case loss, downside risk, standard deviation, and skew.