Systemic risk of optioned portfolio: Controllability and optimization

Abstract

Diversification plays an important role in financial theory and lays the foundation for financial risk management. However, its role is greatly weakened for the portfolio only containing underlying assets when systemic risk events occur. In this paper, we study portfolio selection against systemic risk from the perspective of individual investors. With the typical systemic risk measure CoVaR, we first demonstrate that the systemic risk of pure stock portfolio can not be well controlled by diversification due to the contagion effect caused by the relatively high correlations between stocks and the seesaw effect caused by distresses of different stocks. Next, we illustrate that the introduction of options into the portfolio can alleviate these two adverse effects and make the systemic risk become controllable. Then, we show that the optimization problem of optioned portfolio can be reformulated as a second-order cone program (SOCP) that allows for efficient computation. Finally, we carry out simulations and empirical tests to illustrate the theoretical findings.