AbstractUsing a sample of firms with consecutive earnings growth for more than 20 quarters (earnings strings), I assess the relationship between earnings persistence and the extent to which investors are able to anticipate breaks of earnings strings. I find that firm‐specific earnings persistence exhibits a concave trend during earnings strings. Stock returns are significantly and positively associated with earnings persistence. Upon breaks of earnings strings, investors’ reactions are more negative for firms with higher earnings persistence—especially those with smaller institutional holdings and analyst coverage, and those with insider selling activities—before the break. Additional analyses show that variations in firms’ economic performance (fundamentals) explain the varying earnings persistence during earnings strings. Copyright © 2015 ASAC. Published by John Wiley & Sons, Ltd.