Is the conventional wisdom that equity index put options are effective tail risk hedges for a stock portfolio correct? In his March 2017 paper entitled “Pathetic Protection: The Elusive Benefits of Protective Puts”, Roni Israelov compares the hedging properties of put protection strategies with those of daily rebalanced stocks-cash (divested) portfolios that generate the same compound annualized return in excess of cash. He considers put protection portfolios based on: (1) the CBOE S&P 500 5% Put Protection Index (PPUT), which systematically purchases monthly put options that are 5% out of the money; and, (2) Monte Carlo simulations with and without a volatility risk premium (difference between implied and realized volatilities). For simulations, he assumes compound annualized equity return 4% with 20% annualized volatility, zero risk-free rate and dividend yield and monthly purchases of 5% out-of-the-money put options held to expiration. For simulations with a volatility risk premium, he assumes annualized implied volatility 22%. Using monthly PPUT and S&P 500 Total Return Index (SPTR) returns during July 1986 through mid-May 2016, *he finds that:*

- Over the sample period, SPTR has 5.8% compound annualized excess return.
- For PPUT as a put protection portfolio:
- PPUT has gross compound annualized excess return 2.5%, and annualized alpha -1.8% and beta 0.74 relative to SPTR, with annualized volatility 13.5%.
- Putting 36.5% in SPTR and 63.5% in cash generates the same gross compound annualized excess return as PPUT, with beta only 0.37 and annualized volatility only 6.6%.
- The divested portfolio almost always has shallower drawdowns than the protected portfolio. For example, the worst 1% peak-to-trough drawdowns over a 20-day (250-day) interval are -6.6% (-20.9%) for the divested portfolio and -9.6% (-32.1%) for the protected portfolio.
- Conversely, the protected portfolio wins rallies. For example, the best 99% trough-to-peak rally over a 20-day (250-day) interval is 5.4% (20.3%) for the divested portfolio and 11.7% (36.7%) for the protected portfolio.
- Matching the equity exposure of a divested portfolio out-of-sample based on the average expanding window of historical PPUT equity exposure results in a 60% higher gross Sharpe ratio for divested (with only modestly higher drawdowns).

- For Monte Carlo simulations of one million days with no volatility risk premium:
- The simulated put protection portfolio has annualized alpha 0.0% and beta 0.83 relative to SPTR.
- Putting 78% in SPTR and 22% in cash generates the same compound annualized return as the put protection portfolio.
- The worst 1% peak-to-trough drawdowns over a 20-day (250-day) interval are -10.5% (-32.9%) for the divested portfolio and -9.8% (-33.7%) for the protected portfolio.
- The best 99% trough-to-peak rally over a 20-day (250-day) interval is 12.3% (57.0%) for the divested portfolio and 15.0% (67.9%) for the protected portfolio.

- For Monte Carlo simulations of one million days with a volatility risk premium:
- The simulated put protection portfolio has annualized alpha -1.9% and beta 0.82 relative to SPTR, with annualized volatility 16.9%.
- Putting 29% in SPTR and 71% in cash generates the same compound annualized return as the put protection portfolio, with annualized volatility 5.8%.
- The worst 1% peak-to-trough drawdowns over a 20-day (250-day) interval are -4.0% (-13.4%) for the divested portfolio and -9.9% (-34.2%) for the protected portfolio.
- The best 99% trough-to-peak rally over a 20-day (250-day) interval is 4.4% (18.2%) for the divested portfolio and 14.7% (65.4%) for the protected portfolio.

In summary, *evidence from two testing approaches offers little support for belief that protective equity index puts are the best approach to mitigate stock portfolio drawdowns.*

Cautions regarding findings include:

- Daily rebalancing of divested (stocks-cash) portfolios may generate material trading frictions for some investors, thereby lowering returns for divested portfolios.
- The put option pricing assumptions of PPUT may understate the cost of monthly purchases of put options for some investors.
- Monthly purchases of put options for simulated put protection portfolios may generate material trading frictions for some investors, thereby lowering returns for put protection portfolios.
- The author notes in the paper: “I have no doubt that with enough effort, an enticing backtest can be constructed, but I worry about robustness and out-of-sample properties.” In other words, intensive experimentation would impound considerable data snooping bias in performance and overstate expectations.

See also “Buying and Selling Crash Insurance (Tail Risk Protection)” and “Crash Protection Strategies”.

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