For the most part, shareholder-owned corporations are allowed to run operations for themselves within the parameters of certain regulations. But not every publicly traded company falls into this category, with some experiencing significantly more government involvement in corporate decision making. Here, I'll look at four examples of shareholder -owned corporations where the government has a greater role than just as a regulatory body.

Mortgage giants
As the name implies, government sponsored entities (GSEs) have a relationship with the government that is more than the standard private corporation-to-government relationship. But after the financial crisis of 2008 and some changes to the financing terms in 2012, Fannie Mae (FNMA 1.40%) and Freddie Mac (FMCC -2.26%) are more in government control than almost any other shareholder-owned corporation.

After the set of GSE earnings, the U.S. government has recouped its full investment in the bailouts of Fannie Mae and Freddie Mac. In all fairness, the government does deserve some additional returns for taking the risk and supplying the capital as any other money lending corporation would expect had a private-sector company been willing (or even able) to supply the capital necessary to sustain the GSEs.

But the current arrangement with the government is even better for Uncle Sam. Even after returning all the funds lent by the government, Fannie and Freddie owe just as much money as they did before. This is due to an amendment put in place in 2012 that called for the sweeping of all excess profits of the GSEs into the Treasury without reducing the outstanding preferred stock owned by the Treasury. In effect, Fannie and Freddie shareholders cannot access any of the profits and, unless things change, will never be able to do so in the future.

Owners of Fannie and Freddie common and preferred stock are challenging the legality of the Sweep Amendment in court. Among those challenging the government are Bruce Berkowitz, manager of the Fairholme Fund, and Richard Perry, manager of Perry Capital. If these lawsuits are successful, Fannie and Freddie shares have the potential to increase 10 to 15 times based on both my analysis, and that of the far more recognized Bill Ackman, manager of Pershing Square.

Power to Greece
At first glance, Greece seems like the last place anyone would want to put money. Between high unemployment and ongoing government debt issues, Greece looks like the place that will balance out your capital gains. But sometimes, the most hated investments are the most profitable, and its hard to find a company more tied to both Greece and its government than Public Power Corporation.

As Greece's largest energy producer operating mines, power plants, and transmission lines, Public Power Corporation is essentially the Greek power monopoly. But this monopoly comes at a cost. The Corporation is also 51% owned by the Greek government, allowing the government to use it for promoting social and economic policy instead of seeking out maximum shareholder returns.

Upside comes from this company through two main ways. The first is a possible privatization plan. Most likely, the government would keep a minority stake, but the sale would allow the Corporation to seek out greater profits without as much focus on the effects of its policies on non-shareholders. The second way comes from an economic recovery in Greece, which would allow more electric bills to be paid, and increase total power consumption.

To buy shares of Public Power Corporation, investors will need an account allowing them to access the Frankfurt Stock Exchange or the Athens Stock Exchange.

Energy giant
Few companies have received as much increased name recognition in the past couple weeks as Gazprom (OGZPY). Unfortunately, it's not the good kind of name recognition. Gazprom is the largest energy producer in Russia, and exports oil and natural gas to Europe.

Right now, the company is at the center of the Ukrainian crisis, as it's both majority controlled by the Russian government, and supplies the commodities that western powers are threatening to put sanctions on.

As a result, fear has set in around the company. The biggest risk here is political rather than financial. It's unlikely that any giant earning as much as Gazprom would just collapse, but the Russian government could take steps that would significantly reduce the value of privately held Gazprom shares.

I view the Ukrainian crisis as an opportunity to acquire Gazprom shares at a bargain basement multiple, and begin collecting a dividend. However, anyone interested in Gazprom needs to know that they are dealing with financial, as well as political, risks.

Government discount
All four of these companies are out of favor with the investment community due to high levels of direct government involvement in their businesses. As a result, investors willing to accept these political risks can acquire otherwise strong companies at major discounts.