Does nominal stock price matter for associated option returns? In their May 2020 paper entitled “Cheap Options Are Expensive”, Assaf Eisdorfer, Amit Goyal and Alexei Zhdanov evaluate option returns across the range of U.S. stock prices. For each stock each month, they:
- Pick a single call option and a single put option closest to at-the-money and expiring the third Friday of the month, excluding those with zero open interest or zero trading volume to ensure liquidity.
- Sort options into tenths (deciles) based on underlying stock price.
- Construct equal-weighted delta-hedged call and put portfolios and hold to option expiration, computing returns from option quote midpoints (zero effective bid-ask spread).
Using price and characteristics data for 257,107 call options and 204,123 put options on a broad sample of U.S. common stocks during 1996 through 2017, they find that:
- Average stock prices across deciles range from $7.31 in the lowest to $141.66 in the highest. Decile 1 stocks generally have higher book-to-market ratios, lower past returns, lower profitabilities, higher idiosyncratic volatilities and more positive return skewnesses than decile 10 stocks. Decile 1 options generally have greater implied-to-historical volatility gaps than decile 10 options.
- Options on stocks with low prices tend to be more expensive than those on stocks with high prices. For example:
- Gross average weekly excess return on a portfolio that is each month long (short) delta-hedged calls on decile 10 (1) stocks 0.54%. The corresponding return for delta-hedge put options is 0.34%.
- Adjusting raw returns based on an 8-factor model of option returns produces gross weekly alpha 0.44% (0.29%) for delta-hedged call (put) options, or 28.1% (22.9%) annualized.
- Findings are robust to double-sorting tests that control for various stock and option characteristics, to different ways of computing option returns, and to option moneyness and time to expiration.
- Findings are much stronger during the first half of the sample period, consistent with increasing options market efficiency. For example, gross weekly 8-factor alpha for call options is 0.71% (0.22%) during 1996-2006 (2007-2017).
- Long-short option portfolios are profitable, with statistically significant 8-factor alphas only for trading frictions less than 25% of bid-ask spreads.
- Effects of stock splits and mini-indexes corroborate direct findings. For example, call (put) options are:
- 13% (9%) more expensive before stock splits than during the three-day window after.
- 0.5% (1.2%) more expensive on mini-indexes than main indexes.
- Institutional ownership of underlying stocks dampens option mispricing related to stock price. Retail investors tend to buy options on low-priced stocks.
In summary, evidence suggests that retail investor demand for low-priced options makes options on low-priced stocks relatively expensive.
Conversely, selling options may be more attractive for low-priced than high-priced stocks, depending on option bid-ask spreads.
Cautions regarding findings include:
- As noted, reported returns and alphas are gross, not net. The breakeven level of trading frictions appears difficult to achieve.
- Long-only approaches to exploitation of findings are likely unattractive, but short-only may be attractive.
- Construction/maintenance of delta-hedged option portfolios is beyond the reach of most investors, who would bear fees for delegating the work to a fund manager.
