Deviations from Put-Call Parity and Stock Return Predictability

Abstract

Deviations from put-call parity contain information about future stock returns. Using the difference in implied volatility between pairs of call and put options to measure these deviations, we find that stocks with relatively expensive calls outperform stocks with relatively expensive puts by 50 basis points per week. We find both positive abnormal performance in stocks with relatively expensive calls and negative abnormal performance in stocks with relatively expensive puts, which cannot be explained by short sale constraints. Rebate rates from the stock lending market directly confirm that our findings are not driven by stocks that are hard to borrow. The degree of predictability is larger when option liquidity is high and stock liquidity low, while there is little predictability when the opposite is true. Controlling for size, option prices are more likely to deviate from strict put-call parity when underlying stocks face more information risk. The degree of predictability decreases over the sample period. Our results are consistent with mispricing during the earlier years of the study, with a gradual reduction of the mispricing over time.

Option-Implied Volatilities and Stock Returns: Evidence from Industry-Neutral Portfolios

“…Each week we also calculate industry SKEW (or SPREAD) by averaging the SKEW (or SPREAD) values of the firms within each industry. The mean and median values of SKEW and SPREAD of individual firms are qualitatively similar to those reported by Xing et al [2010] and Cremers and Weinbaum [2010]. The values of the industry average SKEW and SPREAD are much less volatile than those of individual firms.…”

“…In a related study, Cremers and Weinbaum [2010] examine whether volatility spread helps forecast future stock returns, where volatility spread is defined as the difference between the implied volatilities of ATM call and ATM put options. They show that stocks with relatively expensive calls significantly outperform those with relatively expensive puts.…”

Option-Implied Equity Risk and the Cross Section of Stock Returns

“…Other firm characteristic variables include the following: (1) Skew Idio , calculated by using Equation 2 of Boyer et al (2010), denotes historical estimates of idiosyncratic skewness for a firm using daily stock return data; (2) Amihud (multiplied by 10 8 ) represents the illiquidity ratio of Amihud (2002), defined as the daily ratio of the absolute return on a day to the dollar trading volume on that day averaged over the prior 12 months; 8 and (3) LagRet (lagged return, %) is the compound return over the six months ending at the beginning of the previous month. 9 We also followed Cremers and Weinbaum (2010) and Xing, Zhang, and Zhao (2010) by measuring, respectively, implied volatility spread (IV Spread ) and implied volatility skew (IV Skew ) for each stock. 10 For each firm, we averaged the daily risk-neutral (RN) skewness of one-month maturity (M) as Skew RNM .…”

“…A monthly measure of the implied volatility spread or implied volatility skew for a firm is the average of its daily estimates in each month. We referred to Cremers and Weinbaum (2010) to define the implied volatility spread as the open-interestweighted average of the difference in implied volatilities between call options and put options with the same maturity and strike price, whereas the implied volatility skew of Xing et al (2010) is defined as the difference between the implied volatilities of out-of-the-money put options and at-the-money call options. 11.…”

The relationship between the option-implied volatility smile, stock returns and heterogeneous beliefs

“…For example, Bali and Hovakimian (2009), Cremers and Weinbaum (2010), and Doran and Krieger (2010) study whether the implied volatility spread predicts future stock returns. Xing, Zhang, and Zhao (2010) finds stocks with steeper volatility smirks earn lower future stock returns and argue that this underperformance is because informed traders with negative news prefer to trade out-of-the-money put options.…”