Icahn, who is known for taking large positions in companies and pushing for corporate management changes told the Reuters Global Investment Outlook Summit last week that his style of activist investing works since so many U.S. companies are badly managed.

The study by Icahn Enterprises LP showed those who invested in the companies when Icahn secured a board seat and held their stake during the director's tenure would have reaped the 28 percent gain over the period from November 15, 2008 to November 15, 2013.

The return beat the 18 percent annualized return of the Standard & Poor's 500 stock index and doubled the 14 percent return of Warren Buffett's Berkshire Hathaway Inc over the specified time period, the study showed.

The 20 publicly listed companies included Herbalife Ltd, Chesapeake Energy Corp, and Motorola Solutions Inc.

Herbalife, the weight-loss supplements company, was the biggest winner on the list with a 200 percent annualized return since Icahn won a board seat on April 25. His firm owned about 16.8 percent of Herbalife's shares as of September 30, according to regulatory filings.

"We don't micro manage and interestingly we get invited back because we're not a disturbance or a disruption," Icahn said.

Icahn has taken a position on Herbalife opposite that of activist hedge fund manager Bill Ackman of Pershing Square Capital Management, who called Herbalife a "pyramid scheme" and revealed a $1 billion short bet against the company nearly a year ago.

Despite Ackman's claims, Herbalife shares are up over 114 percent this year. Ackman told Bloomberg Television on November 22 he has lost up to $500 million on his bet that the shares would fall.

Icahn's firm sustained losses in four of the 20 companies over the duration of his firm's board memberships, the study showed. Investors who followed Icahn in Dynegy Inc and Voltari Corp would have lost 81 percent and 59 percent, respectively.

Take Two Interactive Software Inc was included in the study. The company said Tuesday it was buying back all of Icahn's shares and that three directors nominated by Icahn have resigned.

Shares of Icahn Enterprises have risen nearly 154 percent this year. The stock rose nearly 1 percent to $114.43 in Nasdaq trading on Tuesday.

(Editing by Jennifer Ablan and Jeffrey Benkoe)

By Sam Forgione