Abstract: The risk-return trade-off is an important and classical issue in finance. This paper proposes a new model: double absolute autoregressive (DAAR) model, to characterize this relationship. It is an alternative to the GARCH-in-mean model in the literature, which has been used in empirical applications. While it is very difficult to establish asymptotics of the estimation in GARCH-in-mean model. This hinders applications of the latter in practice. For our DAAR model, statistical inference becomes easy. In this talk, we study the QMLE with its asymptotics for the stationary augmented DAAR model. Further, nonstationary first-order DAAR model is also studied entirely. Simulation studies are conducted to assess the performance of the QMLE and two real examples are analyzed to illustrate the usefulness of DAAR models in characterizing risk-return trade-off.