The information frown in option prices

In the S&P 500 options market, the information content of implied volatilities differs by strike in a frown pattern that is a rough mirror image of the implied volatility smile. Implied volatilities calculated from moderately high strike price options are both unbiased and efficient predictors of future volatility. Implied volatilities calculated from low and at-the-money strikes are biased and less efficient. This bias cannot be explained by market imperfections but is consistent with the hedging pressure argument of Bollen and Whaley [J. Finan. 59 (2004) 711] and Ederington and Guan [J. Derivat. 10 (2002) (Winter) 9]. We also find that a serious estimation bias results when the relations are estimated using panel data.