By law, Carl Icahn and other large investors have to disclose their investments four times a year in what's known as a form 13F filing. Based on information in the recently filed 13F, we know that Icahn increased his stake in AIG (AIG 0.56%) and Hertz Global Holdings (HTZG.Q), while building a new position in Xerox (XRX).

A battle over an insurance giant
No surprise, one of Icahn's largest buys in the fourth quarter was AIG, an insurance company Icahn believes is "too big to succeed" and should be broken up. He's identified the company as a bloated insurance conglomerate that, if shaken up, would be more likely to embrace much-needed cost cuts.

Last quarter, Icahn increased his stake to more than 42.2 million shares, adding 40.9 million shares in the period ended Dec. 31, 2015, an increase of 30 times his third-quarter holdings.

In early February, the billionaire investor agreed to cease his public feud with the company, promising "a year of peace," in the words of The Wall Street Journal, in exchange for two board seats -- one for Icahn, and one for fellow investor John Paulson.

Recent results from AIG were unspectacular. The company reported that it would boost reserves for losses by $3.6 billion, which resulted in a fourth-quarter loss of $1.3 billion. In something of a "double-whammy," investment income also fell about 20% year over year. If nothing else, it further strengthens the case that change may be very necessary to get AIG back on track.

Doubling down on car rentals
Icahn also made a sizable increase in his stake in car rental company, Hertz Global Holdings. Hertz is a relatively longtime holding. He reportedly held about 51.9 million shares at the end of 2014, and has continued to add to his position as the company's share price languishes. He now holds about 63.7 million shares after adding roughly 11.8 million shares in the fourth quarter of 2015.

Hertz has been an activist stock for a long time. Known activist investor Jana Partners also held shares of the company, though it has slowly reduced its stake. (Jana Partners further reduced its holdings in the fourth quarter of 2015.)

In a recent presentation aptly titled "Achieving Full Potential," Hertz identified $300 million in annual expense cuts, noting that it already realized $150 million in "cost inefficiencies" through the third quarter of 2015. It believes right-sizing its fleet may help drive margin expansion by 6 to 8 percentage points in the next two to three years. The company is also planning to spin out its equipment leasing business to investors in 2016. Plenty of changes are under way. It's only fitting that Carl Icahn is along for the ride. 

A new bet on an old business
There was once a time when papers weren't just photocopied; they were Xeroxed. Carl Icahn remembers those days, initiating a new position in the business services and technology company in the fourth quarter.

Icahn's stake was relatively small at the end of the fourth quarter at about 86.4 million shares, amounting to less than $1 billion, but his influence has been anything but. The company announced in late January that it would separate into two independent publicly traded companies. Xerox's "Document Technology" and "Business Procession Outsourcing" business lines will have to stand on their own as independent businesses.

In a recurring theme of Icahn's portfolio, Xerox hopes that cost cuts will further drive its share prices after the companies are split up. It hopes to deliver $2.4 billion in expense cuts over the next three years, with $700 million in annualized savings in 2016.

Investors who like to follow Icahn will appreciate that he's squarely in the driver's seat. After the spin-off, the Business Process Outsourcing company will feature a nine-member board, of which two directors may come from Xerox's current board, and three will be selected by Icahn. He'll also get the opportunity to oversee the selection of a CEO for the new company.

One of Wall Street's favorite "corporate raiders" was particularly active last quarter. And while it'd be inadvisable to buy any stock just because a legendary investor is buying it, Carl Icahn's recent buys may be a great place to start shopping for a new stock to add to your portfolio.