In multistage randomized controlled trials it is appealing to learn how to best assign treatment to newly enrolled patients based on their attributes and previously accrued outcome data. We present a simulation study of a two-stage covariate-adjusted response adaptive randomization design. In stage 1, treatment is assigned using a balanced design, and the optimal dynamic treatment rule (ODTR) is estimated. In stage 2, treatment probabilities for new patients are determined using their covariate values and the estimated ODTR learned on stage 1. Two target parameters — the mean outcome under the ODTR and the average treatment effect (ATE) — are estimated using a doubly-robust inverse probability of treatment weighted targeted maximum likelihood estimator. Compared to a traditional fixed, balanced design, the ODTR-based adaptive design improves precision when estimating the mean outcome under the ODTR, but reduces precision when estimating the ATE. These results show how adaptive designs that optimize a specific goal reduce power for other questions (and thus target parameters) of interest. Future work could develop adaptive designs that optimize power for a set of target parameters.