Policy makers periodically consider using student assignment policies to improve educational outcomes by altering the socio-economic and academic skill composition of schools. We exploit the quasi-random reassignment of elementary and middle-school students across schools in the Wake County Public School System to estimate the academic and behavioral effects of being reassigned to a different school and, separately, of shifts in peer characteristics. We restrict our identification of peer effects to those students whom the district does not select to switch schools. We rule out all but substantively small effects of transitioning to a different school as a result of reassignment on test scores, course grades and chronic absenteeism. In contrast, increasing the achievement levels of students' peers improves students' math and ELA test scores but harms their ELA course grades. Test score benefits accrue primarily to students from higher-income families, though students with lower family-income or lower prior performance still benefit. Our results suggest that student assignment policies that relocate students to avoid the over-concentration of lower-achieving students or those from lower-income families can accomplish equity goals (despite important caveats); though these gains may reduce achievement for students from higher-income backgrounds.