This randomized phase III trial has several primary objectives. One primary objective is to compare the efficacy of 3 different endocrine therapies, the estrogen receptor down regulator fulvestrant and the aromatase inhibitor anastrozole, either alone or in combination, in reducing cancer growth before surgery (neoadjuvant) in postmenopausal women with clinical stage II-III estrogen receptor positive and HER2 negative breast cancer. Another primary objective is to evaluate whether patients who achieved a modified PEPI (Preoperative Endocrine Prognostic Index) score of 0, defined by tumor size <5 cm, N0, Ki67<2.7% (by central testing), at surgery post 6 months of neoadjuvant endocrine therapy predict excellent long term outcome, for whom chemotherapy is unnecessary.