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Contribution Details

Type Master's Thesis
Scope Discipline-based scholarship
Title The Relation between Implied and Realised Volatility Risk Premia
Other Titles Master Quantitative Finance
Organization Unit
Authors
  • Romain Cece
Supervisors
  • Alexandre Ziegler
Language
  • English
Institution University of Zurich
Faculty Faculty of Business, Economics and Informatics
Number of Pages 93
Date 2021
Zusammenfassung This study assessed the relevance of volatility assets as equity portfolio enhancing alter-natives. The aim was to provide the best unconditional and timing volatility strategies to retail equity investors using simple indicators and liquid assets. We focused on two types of assets allowing volatility exposure: index options and CBOE Volatility Index (VIX) futures. The main criteria for this choice were the liquidity of such assets and their ability to provide exposures to implied volatility variations for VIX futures and to both realised and implied volatilities variations for straddles. As the goal of this study was to isolate exposures to volatility while getting rid of the time decay factor, the final choice for the volatility assets traded was a rolling 2M Delta-hedged At-The-Money straddle portfolio (STR), rolled monthly and daily rebalanced with vega exposure is 1% at rolling day, and a rolling long 30 days constant-maturity VIX futures portfolio, daily rebalanced (VX30). The first step of this study was a theoretical computation of the returns of puts, calls and VIX futures, to get an intuition of their drivers and identify an hypothetical relationship between them. The models chosen were the Black Scholes model for index options and a simplified version of the work of Zhang and Gehricke1 for VIX futures. Computations allowed us to observe similarities in the drivers of both assets’ returns. Both of our assets were mainly sensible to two factors. The first factor was a positive proportionality to variation of the implied volatility (the implied volatility of the option for options; the VIX itself for its futures). The second factor was a loss proportional to a specific volatility risk premium and to time decay. We then decided to empirically investigate the hypothetical influence of these volatility risk premia on volatility trading returns. The second step of this study was the determination of the best unconditional pure volatility strategy and the best unconditional volatility strategy for an investor that would have a long stock position. In this step we chose to use an empirical study on a period as long as possible. We observed that an unconditional long volatility position was losing on the long term, we then recommend to have a short volatility position if no timing method is applied. We also noticed that shorting VX30 could bring dramatic drawdowns (loss of 99% in 2018 for example). Finally, after a try of mixed portfolios with different weightings of both long and short STR and VX30, the unconditional pure volatility strategy with the best statistics was shorting STR. Nevertheless, when adding an exposure to stock market, the best unconditional volatility strategies observed were portfolios with a high exposure to short STR and a small exposure to long VX30. For instance, a portfolio with exposures of 100% to S&P 500 futures, 10% to long VX30 and 40% to short STR doubled the Sharpe ratio of the S&P 500 futures Total Return on the period from 2007-01-01 to 2020-11-01. The third step was a determination of the best timing volatility strategy that could be used by an investor who would have a long stock exposure. This analysis was focused on indicators derived from the volatility term Structure (VTS), which is the daily plot of prices of VIX futures (resp. values of VIX indexes) with their time-to-maturity as abciss. The first indicator tested was the VIX level. It did not turn out to be a robust indicator for timing volatility exposure. The second indicator was the realised volatility risk premium, which is the difference between the VIX and the S&P 500 realised volatility. This indicator did not show a satisfying in-sample robustness. The third indicator tested was the implied volatility risk premium, which is the difference between the VX30 and the VIX. This indicator gave encouraging statistical in-sample results. After a full out-of-sample backtest, we recommend to take a short volatility exposure when V IX < V X30 and a long volatility otherwise, both with an exposure equal to the percentile rank of |V IX − V X30|. The fourth and fifth indicators were based on the convexity or concavity of the shape of the VIX futures Term Structure and the VIX indexes Term Structure. To build these indicators, we used a geometrical approach and defined angles between the 30-days, the 60-days and the 120-days maturity-constant VIX futures on the VIX Term Structure (resp. VIX, VIX3M and VIX6M for the VIX indexes Term Structure). Both of these indicators gave encouraging robustness in-sample and satisfying out-of-sample backtests. We recommend to take long volatility exposure when these curves are convex and decreasing, and to take short volatility exposure when these curves are concave and increasing. The volatility exposure should be the percentile rank of the absolute value of the difference between the 30-days and the 120-days constant maturity VIX futures (resp. of the difference between the VIX and the VIX6M for the VIX indexes Term Structure). Finally, based on the backtests results, we recommend to use the implied volatility risk premium or the shapes of the VIX futures and VIX indexes Term Structures to time volatility. Nevertheless, these strategies are flattening since 2018, especially the short volatility strategies. It is important to notice that these strategies would have allowed to hedge the crisis on March 2020 and even make high profits out of it. An investor could then consider them as a robust way of hedging an equity portfolio against market crashes.
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