Portfolio Optimization via a Surrogate Risk Measure: Conditional Desirability Value at Risk (CDVaR)

Abstract

A risk measure that specifies minimum capital requirements is the amount of cash that must be added to a portfolio to make its risk acceptable to regulators. The 2008 financial crisis highlighted the demise of the most widely used risk measure, Value-at-Risk. Unlike the Conditional VaR model of Rockafellar & Uryasev, VaR ignores the possibility of abnormal returns and is not even a coherent risk measure as defined by Pflug. Both VaR and CVaR portfolio optimizers use asset-price return histories. Our novelty here is introducing an annual Desirability Value (DV) for a company and using the annual differences of DVs in CVaR optimization, instead of simply utilizing annual stock-price returns. The DV of a company is the perpendicular distance from the fundamental position of that company to the best separating hyperplane $H_0$ that separates profitable companies from losers during training. Thus, we introduce both a novel coherent surrogate risk measure, Conditional-Desirability-Value-at-Risk (CDVaR) and a direction along which to reduce (downside) surrogate risk, the perpendicular to $H_0$. Since it is a surrogate measure, CDVaR optimization does not produce a cash amount as the risk measure. However, the associated CVaR (or VaR) is trivially computable. Our machine-learning-fundamental-analysis-based CDVaR portfolio optimization results are comparable to those of mainstream price-returns-based CVaR optimizers.