Excel "IF" "AND" statement not returning desired result

My excel statement should identify the year I want the date to be associated with.

• If my date in column E is less than 11/1/2015, then column F reads 2015
• If the date in column E is between 10/31/2015 and 11/1/2016, then column F reads 2016
• If the date in column E is greater than 10/31/2016, then column F reads 2017

However, they are all reading 2015.

=IF(E2<"11/01/2015","2015",IF(AND(E2<"11/1/2016",E2>"10/31/2015"),"2016",IF(E2>"10/31/2016","2017")))