I'm about to give you the best reason to buy into today's stock market. When I tell you, you're going to say I'm nuts or that I don't appreciate the dire situation facing the global economy. But to be one of the few investors who beats the market, you have to do what most other investors aren't doing. That's the very definition of beating the market.

In other words, if you follow the herd, you'll do average -- at best! And at The Motley Fool, we don't want to settle for average returns. We want blockbuster returns.

And that means we have to be contrarian.

So below I'm going to tell you the best reason to buy into the market and give you five stocks to play it.

The top reason to buy
The best time to be a buyer is when everyone else is selling. And massive waves of selling are exactly what we've seen since 2007. From then until early October of this year, investors have pulled $4.1 trillion from domestic stock mutual funds! Americans are running out of the market when they should be charging in.

So far this year, investors have removed $84 billion from domestic mutual funds, on top of $83 billion last year. If the trend continues for the rest of 2011, it will be the fifth straight year of outflows.

There are a variety of reasons for the exodus. Some investors have been spooked by market volatility, while others are rightly concerned about the worsening economic situation in Europe.

And to be fair, not all of those billions are completely leaving the market. Domestic ETFs have seen net inflows of nearly $23 billion this year. Meanwhile, bond funds are having a string of good years, with $111 billion in new money so far this year, on top of $246 billion and $376 billion in 2010 and 2009, respectively.

And then there are the baby boomers, who are taking cash out of the market to fund their retirements.

Whatever the reason, the time to buy is when investors are selling en masse. While fearful investors wait for the situation to become "safe," opportunistic investors are scooping up great deals on solid companies -- just like what happened immediately after the financial crisis, before the S&P went on to rally 84% since March 2009.

With so much money pouring out of U.S. stocks, it's a perfect time to find cheap companies. In other words, be contrarian, even when your friends and colleagues say you're crazy for putting money back into the market. (We've all got those stories...)

5 for the road
With that in mind, I've selected five stocks with low or moderate P/Es that can appeal to the contrarian streak of opportunistic investors like us. Most even sport solid dividends, so you can get paid while you wait for other investors to spot these great deals (and your own foresight).

Company

P/E

Dividend Yield

Contrarian Because...

Bridgepoint Education (NYSE: BPI) 8.2 0% The for-profit education sector is under regulatory scrutiny.
National Grid (NYSE: NGG) 9.8 5.9% A high-yield utility with low growth.
Philip Morris International (NYSE: PM) 14.8 4.5% Company derives 40% of revenue from the EU, which is in dire straits.
Ultra Petroleum (NYSE: UPL) 13.2 0% Natural gas at multiyear lows, so no one loves gas players.
Brookfield Infrastructure (NYSE: BIP) 6.6 5.0% Who likes infrastructure stocks?

Source: S&P's Capital IQ.

Bridgepoint is as contrarian a stock as you could find. The entire for-profit education industry is suffering from Congressional scrutiny and new regulations. But this company is one of the best operators and already meets the regulatory standards, unlike some peers. It trades at a bargain basement P/E but new student enrollment and total enrollment are estimated to pick up next year. Oh, and the company has been aggressively buying back shares in recent quarters -- a good sign.

I'll lump National Grid and Brookfield Infrastructure into the same category. They're the "boring" investments that keep pushing out growing dividends year after year. But that's exactly the right kind of boring for dividend investors. They're both infrastructure plays. National Grid owns and operates gas and power transmission assets in the U.S. and U.K., while Brookfield owns stakes in a wider and more global variety of infrastructure, including ports, railroad terminals, utilities, and timberlands.

National Grid and Brookfield own irreplaceable assets that generate rising cash streams year after year and that's why they're a cornerstone in my World's Best Dividend Portfolio.

Philip Morris is a behemoth, earning better than 40% operating margins on $30 billion in sales. It's growing profits at a nice clip, but its P/E stands at around 15. The likely explanation? Its huge exposure to Europe. But the company has been rapidly diversifying its business, especially in Asia, where profitability has grown 50% in just the last year or so. Former parent Altria (NYSE: MO), which spun off Philip Morris in 2008, can't boast growth rates anything like that, though it doesn't have exposure to Europe either. Philip Morris gives both dividend investors and growth investors something to love for decades to come.

Ultra Petroleum just looks ridiculously cheap compared to recent buyouts in the space, as my Foolish colleague Mike Olsen explains. Natural gas prices are low, hurting high-cost players. Those low prices have led some rivals such as Sandridge Energy (NYSE: SD) to move production away from gas and toward higher-priced oil. But Ultra is the low-cost producer in the industry, exactly what you want to buy before gas prices turn up. It's got a management team with a great reputation and trades around its financial crisis levels.

Foolish bottom line
So those are five cheap contrarian stocks that I think are poised for solid long-term gains, and dividends only add to their appeal. Looking for other great dividends? Consider the 11 names from a brand new free report from The Motley Fool's expert analysts called "Secure Your Future With 11 Rock-Solid Dividend Stocks." Today I invite you to download it at no cost to you. Get instant access to the names of these 11 high yielders -- click here.