Hedge funds once dove into the warm waters of the reinsurance business. Now, two prominent investors who took that plunge — Daniel Loeb and David Einhorn — find that their own reinsurers have chilled, even as the rest of the industry is heating up from a long-awaited upturn in pricing.

Loeb is behind Third Point Reinsurance; his Third Point hedge fund manages investments for the Bermuda-based reinsurer. Einhorn is chairman of Greenlight Capital Re, while his Greenlight Capital runs investments for the Cayman Islands reinsurer. Einhorn and Loeb are large shareholders in their companies.