Carlyle Group LP posted a wider fourth-quarter loss than in the year-earlier period, hurt by costs from a hedge fund division it has all but exited. Investment funds at nearly all of the Washington, D.C.-based asset manager's business lines rose in value, including 4% appreciation in the private-equity funds for which Carlyle is best known. But the firm's results continued to reflect fallout from struggles in its hedge fund business, which it has largely shuttered following poor performance. In the three months ended Dec. 31, Carlyle lost $8.9 million, or 16 cents a share, versus a loss of $4.6 million,...