Now, however, war has erupted as Elliott has nominated five directors to replace the company’s board. The activist investor has called for Mr. Kleinfeld to be fired and replaced by Elliott’s own handpicked chief executive, Larry Lawson, who led Spirit AeroSystems Holdings.

How did things get so bad?

From the public record, Elliott’s grievance appears to lie entirely with Mr. Kleinfeld. The hedge fund paints him as a dilettante who is more interested in being at the World Economic Forum in Davos, Switzerland, or meeting with President Trump than in running a business.

Arconic, meanwhile, has disappointed on quarterly results both as a spinoff and before. Elliott complains of high corporate spending, like a corporate marketing campaign that plays off the 1960s cartoon “The Jetsons” and an expensive headquarters in Lever House on Park Avenue in Manhattan. (The company inherited the building in the split.) While Arconic is spending too much, Elliott says the new Alcoa is busy cutting costs.

The hedge fund also contends that Mr. Kleinfeld has overspent on acquisitions that have not borne fruit, while ignoring the development of a domestic Chinese aluminum market as a competitor. And Arconic’s margins are lower than a competitor, Precision Castparts.

Arconic has a response and its own set of facts. In investor presentations and elsewhere, the company has argued that Mr. Kleinfeld took over a troubled company and created the Arconic business through acquisitions. Moreover, this business is dependent on personal relationships that he has established through his global profile.

As for those pesky margins, Arconic says it is focused on increasing profit margins and has a plan, while comparisons with Precision Castparts are inapt because Arconic is an array of different businesses.

In addition, all the directors of Arconic currently support Mr. Kleinfeld, including the three Elliott-nominated directors. And finally, Arconic’s stock has been on a tear since the spinoff last November — up more than 54 percent. To be sure, some of that may be a result of the “Trump bump” rally in the stock market, but as Arconic argues, “the separation has enhanced the respective businesses and unlocked substantial value for shareholders.”