Does return persistence of individual stocks predict associated option returns? In their March 2019 paper entitled “Stock Return Autocorrelations and the Cross Section of Option Returns”, Yoontae Jeon, Raymond Kan and Gang Li investigate relationships between equity option returns and return autocorrelations of underlying stocks. They consider call options, put options and straddles (long both a call and a put with the same strike price). Each month on standard option expiration date, they:

- Measure one-step monthly stock return autocorrelations using a 36-month rolling window of monthly returns for U.S. stocks with over 20 monthly observations.
- Rank stocks (and respective options) by autocorrelation into fifths (quintiles).
- Construct a hedge portfolio that is long (short) the equal-weighted or market capitalization-weighted stocks in the top (bottom) quintile of autocorrelations, to calculate stock portfolio return as a control variable.
- Construct corresponding hedge portfolios of call options, put options or straddles, limiting choices to reasonably liquid options with moneyness closest to 1.0 and time to expiration closest to 30 days.
- Hold these portfolios until the next standard option expiration date.

They further explore out-of-sample use of results via modified mean-variance optimization of a portfolio consisting of the S&P 500 Index, the risk-free asset and equity options with bid-ask spreads no greater than 10% of price. They size individual option positions as a function of underlying stock volatility, variance risk premium and stock return autocorrelation. They assume investor utility derives from constant relative risk aversion level 3. For the frictionless case, they base option returns on the bid-ask midpoint. For the case with frictions, they assume buys (sells) occur at the ask (bid). Using specified stock and options data during January 1996 through December 2017, *they find that:*

- On average over the full sample period:
- There are 676 stocks with liquid options.
- Average one-step monthly stock return autocorrelation is -0.02.
- Average monthly gross returns of selected calls, puts and straddles are 6.1%, -13.9% and -2.5%, respectively, with average bid-ask spread 9% of option price.

- Average gross returns of selected calls, puts and straddles increase systematically across stock autocorrelation quintiles. Differences in equal-weighted (market capitalization-weighted) average gross returns between highest and lowest quintiles are:
- 4.7% (4.5%) for call options.
- 5.9% (5.8%) for put options.
- 4.8% (4.7%) for straddles.

- Results are robust to controlling for other known drivers of cross-sectional equity option returns, including idiosyncratic volatility, and to different holding periods, different ways of calculating autocorrelation, and different levels of option moneyness.
- For the modified mean-variance optimization strategy outlined above during January 2000 through December 2017:
- Average numbers of options in the portfolios range from 312 for straddles to 473 for puts per month.
- Average monthly net returns when implemented with call options, put options and straddles are 1.4%, 1.8% and 1.6%, respectively, compared to 0.4% for the S&P 500 Index.
- Corresponding monthly volatilities are 8.0%, 8.4% and 6.4%, compared to 5.6% for the S&P 500 Index
- Corresponding net monthly Sharpe ratios are 0.16, 0.20 and 0.23, compared to 0.06 for the S&P 500 Index.
- Excluding stock return autocorrelation from the process of weighting individual options substantially degrades performance, with corresponding net monthly Sharpe ratios 0.07, -0.06 and -0.02. In other words, use of stock return autocorrelation is critical.

In summary, *evidence suggests that investors may be able to exploit the power of stock return autocorrelation to predict performance of associated call and put options.*

Cautions regarding findings include:

- Regarding the out-of-sample portfolio test period (January 2000 through December 2017):
- The sample period is not long in terms of variety of market conditions and number of independent 36-month rolling autocorrelation calculation windows.
- The start date is arguably unfavorable for the S&P 500 Index, commencing with a deep bear market.
- Average monthly return for dividend-adjusted SPDR S&P 500 (SPY) over this period is 0.52%, higher than the 0.4% reported in the paper for the S&P 500 Index.

- Regarding the modified mean-variance optimization strategy used to assess practical value of findings:
- The strategies are complex and susceptible to direct and inherited data snooping bias in construction.
- Options used may have limited capacities. In other words, use of the strategy may affect option prices unfavorably and widen bid-ask spreads.
- Monthly calculations to determine weights for hundreds of options and associated portfolio reformation tasks are beyond the reach of nearly all investors, who would bear fees for delegating to a fund manager. It may be challenging for a fund manager to execute these tasks in as timely a manner as assumed.
- The portfolios with options are substantially more volatile than the S&P 500 Index, such that maximum drawdown (unreported) may be a concern.