Even the Nasdaq Composite Index (COMP) — long a nattering nabob of optimism — got caught up in the selling frenzy, sliding 110 points, or 2.7%, by 4 p.m. on Jan. 24 from its close two days earlier. For many tech investors, this had to feel like a seismic jolt. Still, many true believers will brush off the rattle and keep on believing. Of all the glories of the bull market, nothing has matched the astounding comeback in the Nasdaq. A few years ago, a common riff among middle-aged Wall Streeters was that “we won’t see the Nasdaq back at 5000 in our lifetimes.” Now, even with the two-day selloff last week, the tech-laden index hovers at 4128, just 18% below its record close of 5039 on March 10, 2000, at the peak of the dotcom craze. In 2013, the Nasdaq Composite surged 38.3%, waxing the S&P 500 by around 10 points, and it had, until Friday, even managed a small gain this year in a generally falling market.

If you believe the champions of the Apples (AAPL), Googles (GOOG), and Facebooks (FB), the Nasdaq will soon get past whatever nastiness caused last week’s temblors, then bust through the 5000 barrier, and keep on going from there.

(For one perspective on what’s driving the rising valuations of some newer tech issues, for instance, see the recent commentary in Fortune.com by Andreessen Horowitz managing partner Scott Kupor: “Don’t believe the tech bubble hype: 3 reasons why tech valuations aren’t as outrageous as some think.”)

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But my math leads to me to a very different conclusion: The Nasdaq’s prices are severely stretched. Whether such calculations will ultimately lead to a correction in the tech index, of course, depends on whether investors care about linking share prices to such antiquated notions like profits. (I won’t wager on that one …)

That said, here’s a quick analysis of the 30 stocks with the largest market caps trading on the Nasdaq, a group that runs from Apple ($496 billion) to Kraft Foods (KRFT) ($32 billion). Today, the combined value of these 30 companies is $3.37 trillion, or around two-thirds of the Nasdaq 100 total. All together, they posted $156 billion in GAAP earnings over the past four quarters in which each company reported.

The current price/earnings ratio of the Top 30 is 21.6. While that’s pretty high, it doesn’t approach the staggering 42 P/E in the year 2000, around the apex of the dotcom bubble. The 30 stocks pay just over $50 billion a year in dividends; Apple, Microsoft (MSFT), and Intel (INTC) are all big payers. That’s a dividend yield of 1.5%, well below the S&P average of around 1.9%, which is itself paltry by historical standards.

Given this low yield, the 30 companies would presumably need to generate big capital gains to satisfy investors. But what gains are investors currently demanding? Judging from the great expectations of pension fund managers, Wall Street equity strategists, and analysts, a reasonable estimate is around 8%. (Note — when one includes in that reckoning an inflation rate of, say, 2%, the investors’ expected “real return” is just 6%.)

Keep in mind that one quarter of that 6% real return (about 1.5 percentage points) will flow from dividends. So the remainder needs to come from growth in earnings — and therein lies the rub. How fast do total profits need to expand, you might ask, to generate a real capital gain of 4.5% a year — or a 6.5% capital gain including inflation? The answer is a lot faster than 6.5%.

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Here’s why. First, it’s likely that the combined P/E will fall over time as the younger companies mature and their growth rates wane. A reasonable estimate is a fall of 0.5% a year, so that the overall price-to-earnings multiple declines to around 17 in a decade’s time.

Second, what matters here isn’t the company’s growth in profits overall. Rather, it’s the company’s earnings-per-share growth. On average, S&P companies dilute shareholders by 2% a year by issuing new shares. They need the proceeds from those offerings to fund growth.

In our group, Microsoft and Intel are clearly cash cows that repurchase shares. But most of the companies are relatively young and thirsty for capital. “In general, the Nasdaq is skewed to younger, more rapidly growing companies,” says Chris Brightman, head of investment management at Research Affiliates, a firm that oversees strategies for $156 billion in investment assets. “Those companies tend to dilute far more than the average.”

Still, let’s assume that our group issues 2% more shares than it repurchases each year, on average. Now the performance bar is getting high. To generate a 6.5% increase in share prices — which, as I said above, is necessary to reward investors enough so that they keep their money in the stocks and continue buying shares — the 30 stocks must generate earnings-per-share growth of 9%­­ — that 6.5% goal, plus 0.5% to compensate for the annual decline in the multiple, plus another two points to offset dilution.

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Growing total earnings by 9% a year would indeed achieve the goal of an 8% total return (6.5% capital gain plus the 1.5% dividend yield). And to get there, the 30 stocks would need to lift overall profits by 54%, to $240 billion from their current $156 billion or so.

It won’t happen. The reason is that earnings — to say nothing of profit margins — are already at all-time highs. So far — and give these cool tech companies their due — they’ve repressed the gravitational force that yanks down on margins in most industries over time. But it’s nothing less than a leap of faith to assume this sort of earnings growth can continue much longer. “The big issue is that today’s earnings are not sustainable,” says Brightman. “Periods of five to 10 years of declining real EPS are a normal part of markets. People get accustomed to thinking recent history is normal. They have a hard time understanding that this isn’t a new normal, that things will be different.”

Brightman adds that Nasdaq earnings are far more volatile than S&P profits. When earnings fall everywhere, they tend to drop far more swiftly for the high-flyers, and our group is loaded with them.

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Indeed, neither of the two components of earnings growth — expanding margins and expanding sales — is likely to materialize. Right now, the average operating margin for the six largest market cap players in our group of 30­­ — Apple, Microsoft, Google, Qualcomm (QCOM), Intel, and Cisco (CSCO) — is a lofty 29%. That’s three times the average for all S&P 500 companies. “You’d expect margins to get competed down from these levels, not get even better,” says Brightman. Even if margins somehow remain constant at these elevated levels, revenues would need to grow extremely rapidly to satisfy investors.

How fast would sales need to grow? The answer is at the same 9% rate as profits, or far faster than that if margins drop. After inflation, that’s a growth rate of roughly 7% — or two to three times GDP growth, which is estimated to be in the 2.5% to 3.5% range in the near future.

If margins shrink — and count on the fact that they will — that growth rate would need to stretch well into the double-digits. Suspend what you want to believe, and ask yourself if that’s possible.

To be sure, Google, Apple, and many others have been formidable growers over the past few years. But recent history shows that it’s unlikely their spectacular expansion will persist. Over the last four quarters for which they reported, Google grew revenues by 3.3%, and Apple suffered a severe decline in sales.

True, the Nasdaq’s ascension is a near miracle that almost no one foresaw. The best bet is that the age of miracles, Nasdaq and otherwise, is over.