Many investors track 13F regulatory filings to see which stocks the biggest and best investors in the world are buying and selling. Carl Icahn's filings are among the most closely watched because of the billionaire investor's activist style and stock-picking abilities.

From his 13F filing, we know that Icahn recently added to stakes in Hertz Global Holdings (NYSE:HTZ), Icahn Enterprises (NASDAQ:IEP), and Herbalife (NYSE:HLF). Here's what you should know now.

Hand holding a magnet attracting dollar bill signs.

Image source: Getty Images.

Icahn't let go

Carl Icahn more than doubled his position in Hertz after the company reported dismal earnings in November 2016. The rental-car company's results have been pressured by a double whammy of declining revenue and increased depreciation resulting from lower car prices.

A lot has happened since Icahn increased his stake. Hertz's Icahn-backed CEO, John Tague, left effective Jan. 2, and Kathryn Marinello took his place, with Icahn's public approval.

Since Marinello's appointment, Hertz's chief revenue officer stepped down in an apparent restructuring, and the company announced that it amended terms with its lenders. (On its November earnings call, analysts were worried the company would violate covenants regarding limits to its indebtedness.)

How this plays out for Hertz remains to be seen, but the company hasn't set a particularly high bar. In November, Hertz slashed its full-year 2016 earnings guidance to a range of $0.51 to $0.88 per share, down from a range of $2.75 to $3.50 that it detailed in August.

Betting on himself

Icahn's largest position is Icahn Enterprises LP, basically a publicly traded hedge fund for Icahn's investments in public and private companies. Icahn purchased more than 2.9 million shares during the fourth quarter, bringing his ownership to nearly 130 million shares, or about 92% of the company.

Icahn Enterprises famously struggled in 2015 and 2016 as the value of its energy-related stakes declined and ratings agencies slashed its ratings to junk, impairing its ability to raise cheap leverage from investors, a staple of its investment model. In a note, Moody's summed up its recent performance by noting that "valuations of its energy related investments and operating segments declined, and losses were magnified by a constant short position against the broad market."

Icahn probably increased his stake after the end of the fourth quarter. A February rights offering allowed Icahn Enterprises shareholders to increase their stakes by about 7% by purchasing shares at $53.71 per share, a discount to the then-current market price. The prospectus stated that "certain of [Carl Icahn's] affiliates intend to exercise fully all basic subscription rights and over-subscription rights allocated to them in this rights offering."

A squeeze play?

In August, it was rumored that Icahn was hunting for a buyer to purchase part of his massive Herbalife stake. We later learned that Icahn actually bought more, increasing his stake by 15% in the third calendar quarter. In the fourth quarter, Icahn again went back to the market to buy even more Herbalife, snapping up roughly 2.9 million shares, and increasing his stake by about 14% in a single calendar quarter.

It's difficult to discern between posturing and attempts to profit. During the fourth quarter, Icahn claimed that he had asked the Federal Trade Commission for permission to buy as much as 50% of Herbalife. At the time, he was limited to owning 35% of the company, and at the end of the fourth quarter, Icahn owned just over 24% of the company.

At times, Icahn's Herbalife trades appear to be part of a cat-and-mouse game with Bill Ackman, a billionaire hedge fund manager who famously made a billion-dollar bet against the value of Herbalife. When Ackman accused Icahn of attempting to sell part of his stake last year, Icahn went out to buy more, revealing his larger position on the same day as Ackman's television appearance. With short interest in the company frequently topping 40% of the public float, short sellers eager to take profits may find it difficult to locate the necessary shares to cover, given outsize holdings by large institutional investors and committed shareholders like Carl Icahn.