American billionaire Wilbur Ross bet the Greek economy was finally improving in April last year when he joined a group investing €1.33 billion ($1.55 billion) in lender Eurobank Ergasias SA.

The value of the investment has since fallen by a third, as markets have been shaken by Greek Prime Minister Antonis Samaras’s failure to win a parliamentary majority to elect a new president. That has triggered a snap general election on Jan. 25, which may open the door to left-wing firebrand Alexis Tsipras, who is leading in the polls....