Systemic Risk of Optioned Portfolios: Controllability and Optimization

TL;DR

This paper explores how adding options to stock portfolios can control systemic risk measured by CoVaR, improve return-risk trade-offs, and be efficiently optimized using SOCP, supported by simulations and empirical tests.

Contribution

It demonstrates that options are essential for controlling systemic risk in portfolios and introduces an SOCP-based optimization method for such portfolios.

Findings

Pure stock portfolios have uncontrollable systemic risk.

Options enable controllability of systemic risk through hedging.

The proposed optimization method is computationally efficient.

Abstract

We investigate the portfolio selection problem against the systemic risk which is measured by CoVaR. We first demonstrate that the systemic risk of pure stock portfolios is essentially uncontrollable due to the contagion effect and the seesaw effect. Next, we prove that it is necessary and sufficient to introduce options to make the systemic risk controllable by the correlation hedging and the extreme loss hedging. In addition to systemic risk control, we show that using options can also enhance return-risk performance. Then, with a reasonable approximation of the conditional distribution of optioned portfolios, we show that the portfolio optimization problem can be formulated as a second-order cone program (SOCP) that allows for efficient computation. Finally, we carry out comprehensive simulations and empirical tests to illustrate the theoretical findings and the performance of our method.