Vibrating sample magnetization (VSM) measurements have been made on round Fe-clad monocore MgB 2 wire fabricated by a powder-in-Fe-tube technique. Magnetization, AC loss, and transport measurements are reported. The M-H and loss measurements were made with a field sweep amplitude of 17 kOe over a temperature range of 4-40 K. In a round monocore wire the superconducting core was completely shielded against an external field of +/-2 kOe; at higher fields a fixed ΔH was observed (partial shielding). It was found that the signal picked up by the VSM was itself also partially shielded, i.e. reduced in magnitude during its 'return passage' through the sheath, leading to a low field dip in the magnetization. FEM calculations of this latter effect are presented. The fact that the field which reaches the inside of the conductor is less than the external field leads to a real loss suppression, even at moderate fields. The low field dip caused by a suppression of the signal emanating from the superconducting core leads to an apparent loss suppression, i.e., the magnetically measured loss is less than the real (e.g., calorimetric) loss. The difference between real and apparent loss is estimated by FEM calculation, and the field sweep amplitude dependence of these two components was computed neglecting the effects of partial flux penetration.