This article is part of our Rising Star Portfolios series.

The headline of this article may surprise you.

Especially if you've read some of my previous articles throughout the banking meltdown and recovery. I've repeatedly warned against the big banks because their balance sheets are utterly inscrutable.

The financial shenanigans they've engaged in have brought us heretofore unheard-of time bombs like collateralized debt obligations, structured investment vehicles, auction-rate securities, Repo 105s, e-minis, and on and on. If you think this scary financial engineering ends with financial reform, you don't know Wall Street very well. 

That's why I've preferred to look at smaller banks that do what banks were intended to do -- make money on interest spreads by taking in deposits and making loans to creditworthy borrowers.

But today, despite the foreclosure mess, I see some opportunity in the big banks -- specifically Bank of America (NYSE: BAC) and JPMorgan Chase (NYSE: JPM).

From great uncertainty comes an opportunity
Bank of America and JPMorgan are neck-deep in the foreclosure mess. If you haven't been keeping up, the banking industry has been rocked by stories of mortgage servicers being less than diligent in their foreclosure procedures via robo-signers and poor paper trails.

The upshot includes investigations by all 50 state attorneys general, and there's a heavyweight consortium of BlackRock, Pimco, and the New York Fed that are targeting Bank of America specifically.

Everyone cares because of the large percentage of individual mortgages that get securitized into bonds -- scattering (and muddling) the ownership of each mortgage. Unraveling an individual botched foreclosure can thus be a nightmare.

In the worst-case scenario, banks like Bank of America and JPMorgan face the repurchase of innumerable mortgages, expensive private litigation, and regulatory scrutiny. We're talking billions and billions of dollars of risk.

All this uncertainty and fear has pushed bank shares down. And here's where the opportunity kicks in.

The opportunity
So far, I haven't made much of a case for buying shares of Bank of America and JPMorgan. Their businesses are opaque, they've proven in the past to be untrustworthy, and they've been in the headlines big-time because of the foreclosure fiasco.

Here's where the story gets good.

Since mid-April, shares of Bank of America are down about 40%, and JPMorgan's down about 20%.

I get interested in bank stocks that have price-to-tangible-book values below 1.5. Bank of America sits at 0.9, and JPMorgan sits at 1.3. That's cheap both on an absolute basis and on a relative basis versus competitors like US Bancorp (NYSE: USB) (2.8) and Wells Fargo (NYSE: WFC) (1.5). Of the largest commercial banks, only the most troubled one, Citigroup (NYSE: C), is similarly cheap (0.9).  

In addition, both B of A and JPMorgan (as well as Wells) scooped up competitors during the crisis. Bank of America swallowed up Merrill Lynch and Countrywide; JPMorgan took in Bear Stearns and Washington Mutual. And they've provisioned aggressively for bad loans. B of A has $1.21 provisioned for every dollar of bad loans, while JPMorgan is up at $2.20.

The combination of these factors means there's a lot of upside if the situation isn't as dire as the market is portraying. During the financial crisis, the government has shown a great will to ensure the prosperity of too-big-to-fail banks. My bet is that however this foreclosure mess ends up, it won't be catastrophic for the big banks. The government won't let it get that far.

Time to be a contrarian
Buying the big banks isn't a popular move right now. Perhaps that's rightfully so. This is a very risky play.

I've advocated in the past for unloved tobacco producers Altria (NYSE: MO) and Philip Morris International (NYSE: PM) (here and here). Those two face large risks (litigation, a declining market, tax increases), but their business models are transparent. Basically, they sell Marlboros all over the world (Altria in the U.S., Philip Morris International everywhere else), they make a ton of profit, and they then use that profit to make their debt payments and pay hefty dividends to their shareholders.

Those two stocks have run up a bit, so my favorite grossly unloved opportunity right now lies in these two big banks.

Despite the who-the-hell-knows-what's-going-on-inside-them factor and the foreclosure doomsday scenarios, Bank of America and JPMorgan's low valuations, their hefty coverage of bad loans, and the likelihood of stealthy government protection has me willing to roll the dice on both these banks.

Putting some money where my mouth is
And I'm putting real money behind these calls. As part of our Rising Stars feature, the Motley Fool is giving me $5,000 to start a real-money portfolio for all the world to see. They'll then add $1,000 to my portfolio each month. To invest this money, I'll be focusing mainly on the banking and financial sectors.  

To kick things off, I'm buying $750 in Bank of America stock and $750 in JPMorgan stock.  

You can follow all my buys and sells on my analyst page.

I look forward to us all learning together from my victories and defeats. I'm coming after you, Mr. Market!

This article is part of our Rising Star Portfolios series, where we give some of our most promising stock analysts cold, hard cash to manage on the Fool's behalf. We'd like you to track our performance and benefit from these real-money, real-time free stock picks. Click here to see all of our Rising Star analysts (and their portfolios).

Anand Chokkavelu owns shares of Philip Morris International, Altria, and Citigroup. Philip Morris International is a Motley Fool Global Gains selection. The Fool owns shares of Altria Group and Philip Morris International. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.