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Why you’re right to be obsessed with Apple stock

FORTUNE — Just thinking about Terry and Jeanne Gregory’s portfolio can be a little scary. Retirees now living in Honolulu, the Gregorys have basically their entire life savings — about $2.5 million — invested in just one stock: Apple Inc.

The Gregorys’ love affair with Apple (AAPL) flouts every bit of investment advice doled out by magazines like this one and by mainstream investment strategists. No investor — especially a retiree whose portfolio should be geared toward income and wealth preservation, not growth and risk taking — should have all his money invested in just one stock. Right?

Well, before you dismiss the Gregorys as fools, ask yourself these questions. Do you live in a $650,000 luxury condo a stone’s throw from Waikiki Beach? And did you have the smarts, conviction, and stick-to-itiveness to turn a $200,000 investment in 2004 — in a seemingly past-its-prime computer stock with a mere 3% market share — into a nearly $3 million windfall that financed a dream early retirement? “All the advice was to diversify, but in our experience, diversification didn’t really work,” says Jeanne Gregory, 62, who, like her husband, Terry, 58, is retired from the advertising industry. “Diversification,” adds Terry, “may be good for preserving your wealth, but we needed our wealth to grow.”

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The Gregorys are not alone. Online message boards like the boards, Proboards’ Apple Finance Board, and the investor forums on the Braeburn Group website are filled with Apple obsessives who proudly admit to having all or most of their money in Apple.

For many of these folks, investing in the stock — and keeping tabs on the company (often for hours a day) — isn’t just a financial pursuit. It’s a higher calling. “Apple is not just a maker of widgets or digital devices,” says all-Apple investor Robert Paul Leitao, director of operations for a Catholic church in Burbank, Calif., and also the founder of the Braeburn Group of independent Apple analysts (a website Leitao named after an apple variety with “smart and complex flavor”). “I believe the design and functionality of Apple products speak to the dignity of the human experience.”

Ten years ago there wasn’t a single mutual fund that counted Apple as its largest holding, according to Morningstar. Today there are 683 — or one out of every eight funds. Some of the funds are just about as all-in on Apple as the IRS rules for mutual fund diversification allow. There are 12 funds with 20% or more of their assets in Apple. There’s now an Apple-only hedge fund — Bullish Cross Asset Management, which trades both AAPL shares and options — run by Andy Zaky, an independent Apple analyst and a contributor.

Why such fervor? “It’s an emotional stock,” explains Bernstein analyst Toni Sacconaghi. “People get excited about the new product. The news flow about how well the new products are selling intensifies that excitement, which affects the buying behavior.” Professional money managers get caught up just as easily as individual investors do. “They have iPhones and iPads,” says Sacconaghi. “They go to the stores and see the massive lines. You can’t really do that with, say, enterprise software.”

For those with the fortitude to put all their apples in this basket, the stock has been a fabulous wealth creator. At one point this year, Apple was responsible for 17% of the gains of the entire Standard & Poor’s 500 (SPX), according to Sacconaghi. Over the past 10 years, the stock has soared some 7,800%, vs. 54% for the S&P 500. A $50,000 investment in Apple in December 2002 would be worth $3.9 million today.

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Apple’s shorter-term gains have been almost as impressive because they’ve come at a time when the overall market has declined. Whereas a $50,000 investment in the S&P 500 in December 2007 has shrunk to $46,000 (excluding dividends), the same investment in Apple would be worth $144,000 today.

Of course, that last number would have been even bigger — closer to $180,000 — a few months ago, before Apple’s nosedive from $702 to $560 a share. The recent selloff is definitely a turning point for the stock. The question is, Turning to where? Skeptics see it as the beginning of the end of Apple’s amazing run: “The pie is almost baked,” declares Nomura analyst Stuart Jeffrey. For the true believers, however, it’s an early Christmas present — the ultimate door-buster for Wall Street bargain hunters. Apple’s price/earnings ratio of 13 is near a 10-year low, and Apple now has a lower valuation than large-cap peers with far inferior earnings growth such as Wal-Mart (14 P/E) (WMT), Coca-Cola (20) (KO), Pfizer (19) (PFE), and Qualcomm (18) (QCOM).

The stock is so cheap that Mark Mulholland, portfolio manager of the Matthew 25 fund (MXXVX), has been adding to his Apple position even though he already had an 18% position in the stock before the decline. “It’s unbelievable,” Mulholland said when the stock dipped below $550. “I am so psyched to be able to get shares of Apple at this level.”

Terry and Jeanne Gregory retired early to Honolulu after putting essentially all their money into Apple stock.

Terry and Jeanne Gregory are sticking with Apple too. They and other Apple-centric investors we interviewed say the media have made too much of Apple’s recent missteps, which include the iPhone 5 map snafu, an earnings miss in October, and the ousters of iOS software chief Scott Forstall and Apple Store head John Browett.

“Apple doing good is not news. Only Apple doing bad is news,” says Terry, adding that he actually prefers the new Apple Maps app to Google Maps.

If the Gregorys seem skeptical of the financial press, perhaps that’s because bucking the establishment is how they got rich on Apple in the first place. In 2004 they inherited about $200,000 after the death of Jeanne’s parents. At the time, both Terry and Jeanne worked in a niche of the advertising industry — typesetting and print production — that was threatened with obsolescence in the world of digital printing and online advertising. They knew they didn’t have much job security, and the returns they had been earning on mutual funds in their 401(k)s were underwhelming. “My feeling was that we would be better off putting it all in one stock that we thought would perform well rather than spreading it out,” says Jeanne. “We weren’t exactly kids at the time, and it was clear that we weren’t going to have this much money to invest again. We had to make it count.”

Both Terry and Jeanne had used Apple computers at ad agencies. “Apple changed our whole industry,” Terry says, noting how every year the computers seemed to get smaller and more innovative. The Gregorys were already Apple fans when the iPod Mini came out in 2004, convincing Terry in particular that Apple’s emphasis on miniaturization would be a strategic advantage.

Jeanne printed up some information on the newest iteration of the iPod and then paid a visit to their local brokerage office, hoping to get some expert advice on whether Apple was the right investment for them. No such luck. Her broker just wanted to talk about new funds and account services the brokerage was selling.

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They wound up buying Apple stock at $30 a share, and have stuck with it ever since, selling shares only to pay for their Honolulu condo and for vacations. They spend an hour or two every morning reading and discussing the latest Apple headlines, but nothing they’ve read to date has shaken their faith. “You know that scene in You’ve Got Mail when Maureen Stapleton confides to Meg Ryan, ‘I’m very rich — I bought Intel (INTC) at $6’?” Jeanne says. “Well, sometimes I feel like that’s us.”

Apple made Robert Paul Leitao a millionaire — almost all of his $1.5 million investment portfolio is in Apple. But Leitao seems to get almost as much satisfaction from the Apple-related windfalls of his Braeburn Group readers as he does from his own gains. “I get e-mails that are truly heartwarming,” he says, “people who just wanted to thank me for giving them the conviction to stick with it so that now they have the money to pay for their child’s college education.”

His emotional connection to the Apple story makes sense given how he came to invest in the stock. When Leitao’s father passed away 26 years ago — 25 years to the day before Steve Jobs’ death — he inherited his dad’s old MacPlus and wound up using it to write his father’s eulogy. Leitao considers that eulogy “the most stirring and most challenging” thing he’s ever written, and he credits the Macintosh itself for inspiring him.

A single parent at the time, Leitao began squirreling away money to buy shares of a company that, to many outsiders, including his own stockbroker, seemed to be circling the drain. “Right before Apple bought Next and announced that Steve Jobs was coming back, I got a call from my broker,” Leitao says. “He was trying to sell me on some other stocks, and I told him I wanted to stick with Apple. He got indignant and told me I needed to face the music and accept that the Apple story was over.”

Like the Gregorys, Leitao and his family have a multitude of Apple products in their home — iPod, iPhone, iPad, and “more Macs than people.” For him, it’s all interrelated. “I investigate all the products the same way I investigate the financials. I’m constantly checking and rechecking the logic behind my investment decision.”

But his thesis for owning the stock hinges in large part on something that is basically uncheckable. “We’re all pretty much betting on Apple’s ability to continue to innovate,” Leitao says. He thinks sales growth for the iPhone could peak in a year or so, which means Apple will have to, in Leitao’s words, “disrupt a new market in order to maintain current levels of revenue and earnings growth.” Now that Apple has nearly half a billion iTunes subscribers, he’s guessing that the new market will be video content. But that would involve challenging the cable companies’ stranglehold on mainstream television. “I don’t claim to be clairvoyant,” he says. “I simply have faith in Apple’s ability to innovate.”

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It’s a semi-blind faith shared by institutional investors who own the stock too. “They’ve updated so many products this year, the question is, What do they have planned for 2013?” says Malcolm Fobes, portfolio manager of the Berkshire Focus fund (BFOCX), which has a 23% position in Apple. (Fobes calls Apple, which he’s owned since 2004, a “holy grail” stock that offers both low valuation and high earnings growth.) “There’s a lot of talk about TV, but I think that’s a misdirection play. I think it’s going to be something we’ve never seen before.”

Oddly, the Apple-centric investor with the deepest doubts about the company’s ability to come up with the next big thing is the one with the most aggressive price target for the stock. Andy Zaky, the 33-year-old independent analyst and money manager at Bullish Cross, expects Apple to hit $2,000 a share within five years. At that price, Apple would have a market cap of nearly $2 trillion.

For Zaky, a lawyer by training, the Apple story is essentially an iPhone story. Globally, smartphones account for about 30% of handset sales, double the market share of a year ago. Given the rapid growth of the smartphone market — the penetration rate is already past 50% in the U.S. — he expects annual iPhone sales to increase from 65 million units a quarter to 200 million units within five years. The resulting earnings growth, he predicts, will drive the stock to $2,000 a share.

“That’s going to be when Apple peaks,” Zaky says. “What it comes down to is that there’s no other market Apple could operate in that could produce close to the same level of revenue as smartphones. The TV market, for instance, is a fraction of smartphones in terms of total revenue.”

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Zaky thinks it’s “obvious” Apple will hit $2,000 a share and then plateau, with the company continuing to enjoy recurring (though not substantially growing) earnings from the sale of new iPhones and iPads. Presumably, Apple $2,000 would be almost as good for Zaky’s business as his own Apple-only portfolio. Apart from his asset-management business, Zaky has 750 subscribers to his online Apple newsletter, which costs $2,400 a year.

But nothing is really obvious when it comes to the future of technology. Sacconaghi, who has an $800 12-month price target for Apple, does believe that Apple’s iCloud, iTunes, and App Store customer base reduces the risk that existing users will migrate to a competing technology: “It means more buyers will be repeat purchasers, which makes it more difficult for sales to suddenly fall.”

Clearly the biggest threat to Apple now is the Google (GOOG) Android smartphone platform. For their part, the Gregorys insist they’re not worried. “Apple is like the haute couture lines in fashion pushing the edge of design,” says Jeanne. “Android is a knockoff.”

She’s right, of course. Then again, Microsoft (MSFT) Windows was a knockoff too.

This story is from the December 24, 2012 issue of Fortune.