It's the time of year when brokers are likely to offer you their top stock recommendations for the new year.

"These are the stocks to own in 2011," they'll say. "They're the ones our analysts recommend most strongly right now." Then they'll tell you all sorts of compelling reasons their analysts love the stocks, possibly coupled with impressive "price targets" for the year.

AIG is one of the least recommended stocks for 2011, according to Thomson Reuters, but Brett Arends says that makes it a better bet than any of the stocks on the most-recommended list. Brett explains why.

Should you take their advice?

Before you do, take a look at how their recommendations fared last year. And the years before that.

I thought I'd do just that.

So I contacted Thomson Reuters, which tracks the recommendations of Wall Street analysts.

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Apple is among the top analyst picks for 2011. That doesn't bode well for its shareholders.

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I asked them for the 10 stocks that analysts rated most highly a year ago. That meant the stocks in the Standard & Poor's 500 index with the most "buy" and "strong buy" recommendations, the fewest "sells" (let alone "strong sells") and the best average rating overall.

These stocks were the cool kids on the Street. The ones everyone wanted to hang with. The stocks that fund managers brag about owning when they're at the squash club.

The names ranged from chemical company FMC and printer R.R. Donnelley & Sons to tobacco company Lorillard.

How did they do?

Not bad. If you'd invested $1,000 in each one a year ago, your $10,000 stake would have grown to nearly $12,400 today—an impressive 24% return. By contrast, the S&P 500 overall gained just 13%.

So far, so good, right?

I also asked Thomson Reuters to send me the names of the 10 stocks that Wall Street analysts liked the least a year ago.

If the top 10 were the cool kids, these were the dorks. The nerds, the geeks, the losers. The stocks no one wanted to be seen dead with. The ones eating alone in the cafeteria every day and walking around the hallways with "Kick Me" signs stuck to their backs. The ones the analysts thought would do the worst.

How did they do?

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Their gain: 32%. No kidding. They knocked the stuffing out of the stock-market index overall as well as the cool kids.

Last year's dorks included bailout baby American International Group (up 92%), real-estate investment trust Apartment Investment & Management (up 65%) and Jack Daniel's distiller Brown-Forman (up 35%).

So much for the year's "hot" stock tips.

OK, so these were the results from just one year. Then I took a look at the results for the previous year, 2009. Again, Thomson Reuters gave me the 10 stocks that analysts recommended most highly at the start of that year, and the 10 they rated the lowest.

If you'd bought the analysts' favorite stocks at the start of the year, you'd have made a 22% profit.

Not bad.

But if you'd just invested in the S&P 500 index instead you'd have made 26%—four percentage points more.

And what about if you had gone completely against the grain, and had invested in the stocks that the analysts hated the most?

You'd have made an incredible 70% profit.

No, really. Sears Holdings, the most-hated stock of all, more than doubled. Ford Motor, which was the fourth most hated, quadrupled.

OK, so that's only two years' results. And both were up years for the stock market. But what about in a slump? You'd expect that analysts' top picks would protect you in a crash, right? After all, they've really kicked the tires on these babies.

So I had a look at the favorite picks of January 2008, and how they fared over the following 12 months, when everything fell apart.

That year, the S&P 500 plummeted 39%. For anyone trusting the index, it was a total disaster.

But if you'd stuck to the analysts' 10 favorite stocks instead, you'd have only lost, er, 48%.

In other words, you'd have done nine percentage points worse.

I also had a look at how the most-unpopular stocks did that year. A word of caution: As we go further back in time, the results for the lowest-rated stocks run the risk of "survivorship bias." Thomson Reuters data relates to the current S&P 500, so a stock that collapses so completely it vanishes from the index will be omitted. (This is a widespread problem that affects most stock-market indices as well.)

With that caveat, the most-hated stocks that are still in the S&P 500 today fell 51% in 2008—just three percentage points worse than the top picks.

I also checked some of that year's more-spectacular blowups.

Which stocks might reward investors most in 2011? Barron's identifies 10 big-caps worth buying now.

Lehman Brothers? At the start of 2008, 17 analysts covered the stock. Of them nine had it as a "hold," five as a "buy" and two—amazingly—had it as a "strong buy." Given that one of the smartest things anyone could have done with their money, ever, was to sell Lehman stock at the start of 2008, how many analysts actually issued that recommendation?

One. Out of 17.

Bank of America and Citigroup both cratered in 2008. But if you think the analysts would have warned you away from them at the start of the year, think again. Both started the year pretty popular with analysts. They had plenty of "buy" recommendations and few "sells." At least Washington Mutual, which collapsed into bankruptcy later that year, started 2008 unpopular.

How would you do longer term if you followed Wall Street's top recommendations each year? The future, of course, is unknowable. But I looked back over the past five years. I asked how you would have done if you bought the analysts' top 10 favorite stocks at the start of each year, held on for 12 months, and then sold and spent the money buying the new year's picks.

If you had started with $10,000 at the start of 2006, invested $1,000 in each stock and reinvested any dividends, today you'd have $10,950. That's before trading costs and taxes.

But if you had just ignored Wall Street analysts, put that money in the SPDR S&P 500 exchange-traded fund—which tracks the entire Standard & Poor's 500—and left it alone, you'd have $11,190: slightly more. And you'd have saved a lot on trading costs and capital-gains taxes as well. Overall, you'd have ended up considerably better off.

As for the unpopular stocks? Thanks to survivorship bias, we can't be completely certain. But if you'd just bought the most-hated 10 stocks (in today's S&P) each year you'd have an astonishing $16,430 today.

That's in just five years.

That beats the most-popular list, and the index, hands down.

Even allowing for the few (like Washington Mutual) that don't get counted because they went bankrupt, the results are eye-opening.

Yes, we're only looking at a small sample, a handful of years. One can't draw universal conclusions. But these findings are no accident either.

Investors frequently forget that stock-market predictions aren't like, say, weather predictions, because in the case of the stock market the predictions actually change the weather. If everyone on Wall Street already likes a stock, they probably already own it. And if that's the case, they've probably already driven up the price higher than it should be. Meanwhile, if everyone hates a stock—and especially if its reputation has fallen so low that professional fund managers are actually afraid to own it—there's a good chance it has already fallen too far.

Low-rated stocks find it pretty easy to beat expectations. The favorite stocks, meanwhile, have to jump higher and higher hurdles.

What about this year? Thomson Reuters says the most-popular stocks are scientific equipment makers Thermo Fisher Scientific and Agilent Technologies, Apple, Halliburton and IT company Compuware. The least-popular include Sears, insurer Cincinnati Financial, Warren Buffett's Berkshire Hathaway, natural-gas distributor Nicor and pharma company Eli Lilly. The full lists can be seen above. Make of them what you will.

When your broker calls to offer you his analysts' "top picks" for 2011, maybe you'd be better off asking him which stocks his analyst hates. Or you could just let the phone ring.

Write to Brett Arends at brett.arends@wsj.com

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About R.O.I.

Brett Arends writes ROI, or Return on Investment, offering analysis on what the latest news means for you and your money. The column covers investments, spending and broader personal-finance issues. Brett writes from a value-oriented and generally contrarian perspective. He has been writing about finance, in Europe and in the U.S., since the 1990s. Before that he worked as an analyst at McKinsey & Co., the strategy consultancy.

Neither this nor any other column should be taken as the sole basis for investment decisions, and investors should consider their own finances carefully before making any commitments.