More than half of all New Yorkers are teetering on the brink of homelessness — without enough cash in the bank to cover them in the event of a disaster or lost job, a troubling new study has found.

Nearly 60 percent of all New Yorkers don’t have enough emergency savings to cover at least three months’ worth of household expenses like food, housing and rent, according to a recent report from the Association for Neighborhood & Housing Development.