Robust pricing models often suffer from being overly conservative. This is due to lack of asymmetry information within the set of possible valuation distributions. However, even when information on asymmetry is available incorporating it within pricing models makes the characterization of pricing policies very difficult. Our main results address this challenge by providing an explicit characterization of the worst-case prior under the extended information setting that includes semivariance as a measure of asymmetry on top of mean and variance. We illustrate the gain from having the asymmetry information captured via semivariance.