By Allan Sloan
June 1, 2011

FORTUNE — Welcome to the second day of summer. Yes, I know that today’s June 1st, not June 22nd. But we’re talking Wall Street seasons here, not calendar seasons.

By the Street’s calendar, summer runs from Memorial Day to Labor Day, which is vacation season for many of us. It also happens to be the time of year that Wall Street incessantly promotes the concept of a summer rally. As in, “Buy now, you don’t want to miss the summer rally.”

But guess what? The “summer rally” hasn’t existed for at least 40 years. I’m not saying this just because I’m a professional skeptic, but because I got actual facts from Jeff Hirsch, editor in chief of the Stock Trader’s Almanac, a delightful publication whose motto is, “profit from history.”

One way to profit from history, Hirsch says, is to ignore the drumbeats touting a summer rally. “That’s an old retail brokers’ line,” Hirsch told me. “Things tend to be slow in the summer, and this is a way for brokers to round up business.”

But don’t stock prices tend to rise during the summer? Well, yes. But they also tend to rise during the three other seasons. That’s because Wall Street has more up years than down years. So the odds are roughly two in three that stocks will end any given Wall Street season higher than they started it.

Now, to the math. The last 40 Wall Street summers have produced an average gain of just 1% in the S&P 500 index, Hirsch says, compared with 3.6% for spring, and 3% for winter. The only season summer has beaten is fall, which has risen an average of only 0.2%. Summer also comes in third if you measure the Nasdaq stock market or the Russell 2000. That’s not exactly a great summer record, is it?

For those of you trying to do these numbers at home, please remember that we’re talking Wall Street seasons, not normal calendar seasons. In addition to the Memorial Day-Labor Day summer, Hirsch says, Wall Street seasons are Labor Day to Thanksgiving for fall, Thanksgiving to President’s Day for winter, and President’s Day to Memorial Day for spring.

Even though Hirsch doesn’t believe in the summer rally, he is predicting for a big rise in stock prices over the next 14 plus years. He says the Dow Jones Industrial Average will hit 38,820 by the end of 2025, though he expects a lot of sharp drops and assorted nastiness along the way.

That wonderfully precise 38,820 prediction is based on the Dow rising 500% from its intra-day low of 6470 on Mar. 6, 2009, a low-to-high jump that Hirsch says has been the case in the three previous stock market cycles.

This prediction (Is he right? Who knows? Ask me in 14 ½ years) shows how astute Hirsch is with numbers. He’s talking a huge increase, what he calls a “super bull” market, a prediction that got him a lot of publicity. But as he’ll be the first to tell you, it would take a rise of only about 8.5% a year, compounded, from current levels for the Dow to hit Hirsch’s magic number by the end of 2025. At the time he made the prediction, in September of 2010, the Dow was considerably lower than it is now—but a compounded rise of less than 9% a year from that point would have done the trick.

So tune out the talk of a summer rally. Let’s just hope for a good Wall Street summer. And a good calendar summer, too.

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