Optimization-based Tail Risk Hedging

Abstract

This thesis presents a mixed risk-return optimization framework for selecting long put option positions to hedge the tail risk of investments. We formulate tractable optimization models by utilizing hypothetical portfolios that roll put options on a constant basis. Variance and sample Conditional Value-at-Risk (CVaR) are used as risk measures. Firstly, the tail risk hedging for a single asset such as the S 500 ETF is considered. Our proposed models are tested against the out-of-sample historical S 500 index values as well as the values of the index paired with long put options of varying strike prices. The optimized hedged portfolios could provide sufficient protection in market downturns while not losing significant returns in a longer investment horizon without explicitly predicting future market behavior. This is achieved by dynamically adjusting the positions of put options with different protection levels according to the market trends. Allocations to different put options are analyzed under various market trends and investor risk aversion levels. Then our framework is extended to multiple underlying assets and put options associated with them by constructing a hypothetical portfolio consisting of a combination of each put option and the associated underlying asset. The optimized strategies overcome traditional drawbacks associated with protective put strategies, as well as outperform the strategies of investing directly in the underlying assets and holding constant long positions in put options.