Equity Index Options to Exploit Stock Market Volatility Spikes?

Under what conditions should speculators buy protective equity options when they expect realized stock market volatility to increase? In their September 2018 paper entitled “Being Right is Not Enough: Buying Options to Bet on Higher Realized Volatility”, Roni Israelov and Harsha Tummala analyze the relationship between: (1) long volatility return (delta-hedged options) and same-interval changes in realized volatility; and, (2) the volatility risk premium (VRP, implied volatility minus realized volatility) and same-interval changes in realized volatility. They specify long volatility as a portfolio of cash-settled equity index options, reformed monthly, that:

• On each options expiration date, buys one-third of a -25 delta put option, one-third of a +25 delta call option and one-sixth each of at-the-money put and call options. All options initially have about a month to expiration.
• Each day until expiration, hedges option deltas via equity index futures. 
• Holds the options to expiration.

They also examine sensitivity of outcome to different portfolio initiation and termination points relative to significant volatility increases. They focus on the S&P 500 Index, using VIX as implied volatility and hedging via S&P 500 Index futures, during January 1996 through December 2016. They also consider for robustness testing corresponding data for Eurostoxx 50, FTSE 100 and Nikkei 225. Using daily data as specified, they find that:

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