By Jason Zweig

If you think individual investors can’t move the stock market anymore, think again.

At the beginning of next month, a few tiny stocks may suddenly jump in price and trading volume. Behind the moves: the American Association of Individual Investors. This Chicago-based organization, founded in 1978, is the largest nonprofit devoted to teaching ordinary people how to invest. Its 171,000 members gather in some 50 chapters nationwide to learn about taxes, mutual funds, diversification and financial software — a social club for folks who get their kicks talking about stock picks.

Since 1993, AAII has tracked what it calls the Model Shadow Stock Portfolio. What happens to these two or three dozen stocks is fascinating — and holds lessons for all investors.

Three to five companies could be added to the portfolio around Dec. 1, says AAII’s founder and chairman, James Cloonan. He launched the model (which has no outside clients and holds just $610,000) to capitalize on research published by academics in the early 1980s suggesting that cheap stocks too small for institutional investors to buy — but theoretically ideal for individuals to hold — have tended to outperform. In the 1970s, the great financial analyst Benjamin Graham had also urged individual investors to choose their holdings from among stocks institutions couldn’t buy.

Since 1993, the Shadow Stocks have returned an average of 15.6% annually, versus 8.7% for the S&P 500, according to AAII. But not all its followers have matched that return — because most don’t learn about the portfolio’s latest trades until well after it makes them.

To be eligible, a company must be profitable, cheap and itsy-bitsy (with a total market value between $30 million and $300 million, such stocks lurk in the shadows of the multi-billion-dollar behemoths in the S&P 500).

Look at CDI Corp.CDI -3.31%, a Philadelphia-based provider of staffing, engineering and technology services. Between June 4 and June 10, CDI’s shares rose 3%. Then, on June 16, CDI surged 9.8% on trading of nearly 160,000 shares, triple its recent average volume.

“Of course we noticed it,” says Vincent Webb, CDI’s head of investor relations. “We were puzzled, because we hadn’t issued any earnings release or disclosed any news around that timeframe.”

Salem Media Group SALM +0.64%, a Camarillo, Calif.-based radio and publishing company, was deleted from the Russell 2000 Index, a leading measure of small stocks, at the end of June. That usually makes stocks drop, not rise.

Yet, between June 4 and June 15, Salem gained 15%. Then, on June 16, it climbed another 8.5%. There was no material news around that time, says Evan Masyr, head of investor relations.

On June 4, AAII’s Shadow Stock portfolio bought $24,900 worth of CDI, a new holding, and added about $8,700 to the position it already held in Salem. After the close of trading on June 15, AAII updated the list of holdings on its website. That appears to have unleashed a buying frenzy by individual investors on June 16.

In nine trading days, the total market value of CDI had shot to $265 million from $243 million; Salem, to $153 million from $122 million. In conjunction with less than $34,000 in purchases in the AAII portfolio, the two companies gained about $55 million in market value.

Analyzing 169 stocks bought by the Shadow Stock portfolio, my colleague Tom McGinty found that trading volume in these stocks consistently peaked in the first four days after AAII disclosed they had been added.

Some AAII members, especially those who pay $198 a year for its premium software, appear to be using their computers to predict which stocks on the candidate list will go into the Shadow Stock portfolio next. “I know there’s some of that going on,” says Mr. Cloonan. That gives some people an edge of almost two weeks.

There’s nothing illegal or even unethical about this, say securities lawyers, although Mr. Cloonan says AAII might consider changing how it discloses the trades in order to minimize the potential for a few to get out ahead of others.

Unless you traded exactly when AAII does, you couldn’t have matched the astounding performance of the Shadow Stock portfolio. “Because we [trade] before we tell everyone what we did,” says Mr. Cloonan, “the people trying to emulate us create an upward bias.” The portfolio gets to buy earlier than most people who follow it, giving its holdings a boost as soon as hordes of eager investors mimic the latest trade.

Much the same thing happens when Warren Buffett buys a stock, a newsletter editor touts a trade or the top managers of a company buy its own shares. Following them makes what they have already done even more profitable — for them. Those who follow, however, shouldn’t expect to match the returns they are seeking to copy.

— Write to Jason Zweig at intelligentinvestor@wsj.com, and follow him on Twitter at @jasonzweigwsj.

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