In this study, we investigate the ability of three higher-order risk-neutral return cumulants to predict short maturity (weekly) returns of oil futures. Our data includes weekly West Texas Crude Oil futures options that expire in 7 days (7DTE). Using a model-free approach, we estimate these risk-neutral return cumulants at the beginning of each options expiration cycle. Our results suggest that the third risk-neutral return cumulant consistently predicts the returns of various oil futures (including WTI, Brent, Dubai, Heating Oil, and RBOB Gasoline). We compare our findings with 14 other predictors and offer a theoretical explanation for the negative coefficient observed for the 7DTE third risk-neutral return cumulant. Our theory connects higher-order risk-neutral return cumulants with the risk premiums of oil futures. Furthermore, our quantitative investment strategy favors the predictability of oil futures returns.