Citadel LLC is among the 30 largest hedge funds in the United States. During 2012, when the average hedge fund returned just 5.5%, Citadel managed a 26% return, which was more than double what the S&P 500 returned.

Though we Fools like to see such returns spanning more than just a year, it's worth kicking the tires on Citadel's recent purchases to see if we can get any good ideas. During the third quarter, Citadel made purchases in more than 3,000 different stocks, but today I'm going to focus on three of the biggest positions.

Elan (ELN)

Elan is a biotechnology outfit headquartered in Dublin. One of the company's drugs, multiple-sclerosis treatment Tysabri, has been a major success, while several other drugs for the treatment of mood disorders are currently in clinical trials.

During the third quarter, Citadel initiated a position in Elan by purchasing roughly 6.5 million shares, which are now worth about $100 million. Hopefully for Citadel, it purchased shares of the company before Perrigo (PRGO 2.43%) formally announced it would be acquiring Elan in a stock-and-cash deal that is expected to close before the end of the year. Should Citadel choose to hold its shares of Perrigo after the deal closes, it would own approximately 500,000 shares of New Perrigo, the name of the combined entity.

Dow Chemical (DOW)

Source: Brian Reading, via Wikimedia Commons.

This global company has its hand in several different industries, ranging from plastics to electronics to energy. But no segment has received as much attention lately as Dow AgroSciences, which manufactures pesticides, herbicides, and genetically modified seeds.

During the third quarter, Citadel initiated a position in Dow by buying 1.7 million shares worth approximately $64 million. So far, that move looks like a solid investment, as the stock is up 21% since the start of July.

There are several reasons why Citadel was excited about Dow's prospects. With natural-gas prices still relatively low, Dow is hoping to take advantage by building petrochemical plants along the Gulf Coast. And the increasing prevalence of genetically modified seeds can't be ignored as a growth outlet, either.

Finisar (FNSR)Between July and September, Citadel purchased 2.7 million shares of Finisar worth about $61 million. With any luck, Citadel purchased the shares in early July, as Finisar has seen its stock appreciate 25% since then.

Finisar certainly fits into the "growth" category for Citadel. The company makes optical subsystems and components that allow large amounts of data to efficiently travel between electrical devices, like server storage devices. Currently, it trades for almost 71 times earnings.

Finisar has had an up-and-down year. Throughout the first half of the year, investors were excited by stronger-than-expected sales of its Ethernet transceivers. But more recently, weakness from Cisco, Finisar's single largest customer, has investors worried that demand could come in below expectations over the next few quarters.