Abstract
We consider an investor who trades 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 decompose the solution to the investment problem 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 under adverse market conditions are less diversified and invest on a few stocks which have low correlation with the market.
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