We consider an investor whose objective is to trade off tail risk and expected growth of the investment. We measure tail risk through portfolio's expected losses conditioned on the occurrence of a systemic event: financial market loss being exactly at, or at least at, its VaR level and investor's portfolio losses being above their CoVaR level. We obtain a closed-form solution to the investment problem, and decompose it in terms of the Markowitz mean--variance portfolio and an adjustment for systemic risk. We show that VaR and CoVaR confidence levels control, respectively, the relative sensitivity of the investor's objective function to portfolio--market correlation and portfolio variance. Our empirical analysis demonstrates that the investor attains higher risk-adjusted returns, compared to well known benchmark portfolio criteria, during times of market downturn. Portfolios that perform best in adverse market conditions are less diversified and concentrate on few stocks which have low correlation with the market.

Bio: Alexey Rubtsov is an Assistant Professor of Mathematical Finance at Ryerson University, a Senior Research Associate at the Global Risk Institute in Financial Services, and an Academic Advisor at Borealis AI. Prior to this, he was a PostDoctoral Fellow at Ryerson and Aarhus Universities where he worked on applications of Stochastic Control to Portfolio Management. He holds PhD in Operations Research and MSc in Financial Mathematics from North Carolina State University. His areas of research are Machine Learning, Stochastic Control, Systemic Risk, and Portfolio Optimization.