Optimization-based tail risk hedging of the S&P 500 index

Abstract

In this paper, we present a mixed risk-return optimization framework for selecting long put option positions for hedging the tail risk of investments in the S&P 500 index. A tractable formulation is developed by constructing hypothetical portfolios that are constantly rolling put options. Variance and sample CVaR are used as risk measures. The models are tested against out-of-sample historical S&P 500 index values as well as the values of the index paired with long put options of varying strike prices. The optimized hedged portfolio could provide sufficient protection in market downturns while not losing significant return the long horizons. This is achieved by dynamically adjusting the put option compositions to market trends in a timely manner. Allocations to different put options are analyzed in various market trends and investor risk aversion levels. The strategy overcomes the traditional drawbacks of protective put strategies and outperforms both directly investing in the underlying asset and holding a constant long position in a particular put option.

Additional information

Funding

This work was supported by Prof. Kwon's NSERC Discovery Grant 455963.

Notes on contributors

Yuehuan He

Yuehuan He received his M.A.Sc. in operations research from the University of Toronto in 2021. He received his B.Sc. in mathematics and applied mathematics from the Beijing Normal University in 2019. His research interests include mathematical optimization and its application in financial engineering, risk management, and data science.

Roy Kwon

Roy H. Kwon is a professor in the Department of Mechanical and Industrial Engineering at the University of Toronto. He obtained his Ph.D. in operations research at the University of Pennsylvania. His primary focus is in the field of mathematical optimization with applications in financial engineering, risk management, and operations management. He is also a member of the faculty in the Mathematical Finance Program (MMF) at the University of Toronto. Dr. Kwon has extensive consulting and collaboration with industry in the use of financial optimization.