This paper investigates how the precision and stability of a teacher's value-added estimate relates to the characteristics of the teacher's students. Using a large administrative data set and a variety of teacher value-added estimators, it finds evidence of heteroskedastic measurement error and finds that the stability over time of teacher value-added estimates based on one year of data can depend on the previous achievement level, racial characteristics, and socio-economic status of a teacher's students. The differences are large in magnitude and statistically significant. In some cases the year to year correlation of teacher value-added estimates is twice as large for teachers serving certain groups compared to other teachers serving other groups. In addition, some differences are detected even when the number of student observations is artificially set to the same level and the data are pooled across two years to compute teacher value-added. This implies that teachers who face students with certain characteristics may be differentially likely to be the recipient of negative or positive sanctions in a high stakes policy based on value-added estimates and more likely to see their estimates vary from year to year due to low stability.