Market efficiency is, formally, the statement that discounted asset prices are martingales. This implies a sharp restriction: a variable reflecting only relative trading activity should carry no information about how a stock’s options are priced. In my tests, I investigate this restriction using the option-to-stock volume ratio (O/S) of Roll, Schwartz, and Subrahmanyam [2], asking whether O/S predicts the gap between implied and realized volatility-the variance risk premium-in the cross-section of U.S. equity options over 2019-2023. Portfolio sorts and Fama-MacBeth regressions reject the no-predictability restriction: lower O/S predicts a systematically larger premium, with t-statistics up to 11, and the relationship replicates out of sample on a disjoint 2014-2018 window. By the joint-hypothesis problem the rejection does not establish inefficiency; I argue the regularity most plausibly reflects an illiquidity premium rather than easy cash.