Just as we examine companies each week that may be rising past their fair values, we can also find companies trading at what may be bargain prices. While many investors would rather have nothing to do with stocks wallowing at 52-week lows, I think it makes a lot of sense to determine whether the market has overreacted to a company's bad news, just as we often do when the market reacts to good news.

Here's a look at three fallen angels trading near their 52-week lows that could be worth buying.

A much needed merger
Sometimes the potential for a big reward comes with a big risk. That's why I'm giving you a warning right away that this week's first pick, Portugal Telecom (OTC:PTGCY), is not for the faint of heart.

Source: Marjan Lazarevski, Flickr.

Portugal Telecom has been battered in recent weeks after it failed to disclose a $1.2 billion commercial debt purchase from Espirito Santo Financial Group prior to confirming merger agreements with Brazilian telecom company Oi. As Foolish contributor Jason Ditz notes, because some of Espirito Santo's holding companies are under investigation in Luxembourg, and because Oi was unaware of Portugal Telecom's purchase of this debt, investors are concerned that the merger may be delayed or may end up being more costly than previously anticipated.

Ultimately, both companies greatly need this merger. Portugal Telecom has the cash flow and cash balance to help Oi expand its mobile operations in Brazil, while Oi offers Portugal Telecom the opportunity to stick its nose in an emerging market with rapid growth potential. It'll also create a Portuguese-speaking telecom giant with roughly 100 million subscribers across three continents (Portugal Telecom has assets in Africa as well) and no antitrust issues. I suspect it could yield as much as $1 billion in annual free cash flow within a few years.  

The deal isn't wholly without risks, as Spain's struggling economy and Oi's near-term profitability weakness could lengthen the time it takes for these two companies to experience fruitful synergies from their upcoming merger. However, with the expectation that both companies will remain healthfully profitable on an annual basis and generate ample cash flow to cover existing debt, I believe Portugal Telecom could be worth the risk here.

Drilling for dollars
If socially responsible investing isn't part of your strategy but you enjoy life's basic necessities, then perhaps it's time you took a closer look at Rex Energy (NASDAQ:REXX), an oil and gas exploration and production company operating in the Appalachian and Illinois Basins.

Rex Energy shares have been in a slump recently due to delays that have constrained its production. Specifically, in its second-quarter production update Rex reiterated that high pressure in some of its new wells in the Butler Operated Area won't be solved until field compression has been added. However, the company also stood behind its full-year production guidance of 143 MMcfe per day to 149 MMcfe per day despite its Q2 production forecast only coming in at 128 MMcfe/d.

Rex Energy Annual Report, production by year. Source: Rex Energy

Rex Energy certainly won't appear cheap if you look solely at its trailing 12-month P/E, or if you take into account that it has missed Wall Street's EPS estimates in two of the past three quarters. However, if you look at the company's history of boosting its production, you'll understand that even with minor production snafus, Rex Energy is on pace to deliver big gains for investors. As you can see from its production figures (and taking into account the midpoint of its 2014 production forecast which it reiterated in Q2), Rex has boosted its production at a compounded rate of 55% since 2009!  

What might be even more incredible is that Rex Energy is only trading at 16 times forward earnings despite its phenomenal growth rate. Some investors clearly haven't been willing to place much value on Rex considering its $490 million in debt and its history of high capital expenditures, but with the company now healthfully profitable and poised to continue expanding production I see no reason why it couldn't head higher over the long run.

This could get "interesting"
Finally, since Wall Street is forward looking in nature, perhaps it's time investors take a serious look at a wholesale brokerage and electronic execution service, GFI Group (OTC:GFIG).

GFI Group, and pretty much all brokerage and clearing companies, has traveled under investors' radar for two reasons over the past couple of years. First, volatility has hit multiyear lows, and brokerage houses will earn less when retail and commercial clients aren't executing stock and bond trades. Secondly, record-low lending rates in the U.S. and EU have reduced investors' interest in purchasing fixed income securities, further hampering GFI's ability to grow.

Source: Baer Tierkel, Flickr.

The good news is that the tide could be about the turn for GFI Group. Recently the Federal Open Market Committee's minutes revealed its intention to remove QE3 in its entirety by the end of its October meeting, which could clear the way for an interest rate hike as early as 2015. A hike in the federal funds rate would be great news for investors who prefer fixed-income securities but have been waiting for a reason to invest. It could also push corporate bond yields higher, which in turn could generate higher revenue for GFI Group.

From a valuation perspective, there's also a lot to like with GFI. The company is trading right around its book value and just 13 times forward earnings, which would appear to me to be an unreasonably low estimate considering that the U.S. interest rate tide is about to turn. And, as icing on the cake, GFI Group also pays out $0.20 per year as a dividend for a yield that currently equates to nearly 6%!