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If you're one of those calm, rational investors who believes that earnings, not wild shifts in momentum, drive stock prices, you'll probably draw the logical conclusion from the phenomenal rally in stocks: The markets are unhinged from reality.

Indeed, the view that stocks are defying gravity and will fall to earth is probably the right one. But a slim chance exists that equities are entering a new era of super-high valuations, and not just for a couple of years—a trademark of past bubbles—but as an enduring new normal. The reason: Interest rates on risk-free Treasuries that compete with stocks for investors' dollars will remain far below historic norms for many years to come.

On June 5, the S&P 500 closed at 3194, a 43% jump since the March lows that marks the biggest short-term rally ever. The index now sits just 1% below its near-record close last year. The reason for the jump looks crazy: It's hard to envisage a scenario in which profits rebound fast enough to remotely support prices that since February have careened from rich to reasonable to rich again.

To be sure, the surprise surge in new jobs that ignited June 5’s 2.7% breakout was great news. But what matters most is where profits are headed, and on that front the news remains dismal even as the market parties on. At the close of 2019, the S&P posted net earnings, based on the trailing four quarters, of $139.47, an all-time high. Where would those profits need to settle once we get past the shutdown and tumult from the coronavirus pandemic for shareholders to make a decent return from here?

The intrepid folks buying stocks at these heights are taking big risks, so they'll want a pretty good return. Let's be conservative and say they're looking for 5% capital gains (that's a modest total return of 6.8% including the dividend yield). In that case, the S&P would need to hit 3522 by early June 2022, when it's safe to predict the hurricane has passed. Now, we need to choose a reasonable price/earnings ratio, what investors are willing to pay for each dollar of profits, two years hence. That's a tricky job, since multiples have varied widely in past decades. For example, the median P/E since 1990 was 21.8, far higher than the 60-year benchmark of 17.4.

I choose a P/E of 20 because it's around halfway between the two readings—higher than the long-term number but below the extremely elevated levels of recent years. Dividing the current S&P index by 20 to get a measure on where earnings must go to justify price is the test I call "the Tully 20 rule."

At a 20 multiple, the Tully 20 rule says earnings would need to hit $176 a share by mid-2022. That's a 26.3% increase from the end of 2019. Getting there would require a Rip Van Winkle fantasy. You fell asleep in February, never knew about COVID-19, and woke up to see earnings rise over 9% a year in mid-2022. You'd be pleasantly surprised in any case and dumbfounded once you learned about the pandemic.

Right now, earnings are headed in the opposite direction, in a big way. The analysts polled by S&P predict profits will drop 34% to $92 at the end of this year. And those ever-cheery prognosticators see profits only reaching $146 by the end of 2021, a long way from the $176 needed to justify a 20 P/E. In fact, if Wall Street is right about this year, profits would need to soar from $92 to $176 in just under 18 months from the start of 2021 to early June 2022 in order to catch the explosion in valuations, and expectations of what's to come.

The sober numbers person can say with virtual certainty that profits will go nowhere near $176 by mid-2022. That outcome borders on the mathematically impossible. A better predictor is Robert Shiller's cyclically adjusted P/E multiple of CAPE, which adjusts earnings based on a 10-year average. Smart money managers I know bump up the Shiller number by between 7.5% and 10% to get a reading on where profits stand on a normalized basis. That formula would put today's EPS at $120.

But let's make the optimistic forecast that profits climb back to their fourth-quarter 2019 level of $139. At least that outcome is conceivable, while $179 is not. If that happens, an S&P at 3572, 10% higher than today, is a possibility. It could happen if the P/E multiple goes to around 25.6 (3572 divided by $139). That's almost 18% higher than the 20-year average and more than 40% above the norm since 1960.

Of course, investors want a margin over risk-free Treasury yields in exchange for the rough ride of owning stocks. So the total gains they demand are the sum of the risk-free rate and that margin, known as the equity risk premium, or ERP. A reasonable estimate of that extra cushion over long periods is 3.5 points. So if the "real" inflation-adjusted rate is 0.5% (meaning the 10-year Treasury is at 2%, and inflation is running at 1.5%), then the ERP plus the real rate is 4%. That's the "real" return investors would be expecting. Hence, they'd settle for $4 in earnings for every $100 they pay, for a P/E of 25 ($100 stock price divided by $4 in profits).

Today that outcome looks feasible, since the 10-year yield now sits at 0.92%. That could explain why the market is factoring in a huge P/E a couple of years out. Keep in mind, however, that these are extraordinary times, when rates are depressed by gigantic flows from foreign investors seeking safety.

Real rates have been dropping in recent years and will probably stay well below the long-term average—which, by the way, is over 5%. But if the U.S. economy grows at 2% or more, it's hard to see how the real rate could be much lower than that, since GDP growth is closely correlated with demand for capital and real rates.

If the right P/E is 20, not 25.5, stocks are now extremely pricey and probably overvalued. If earnings do get back to $139 by mid-2021, the S&P would be 2780, 13% below its level today, and that's optimistic.

In sum, you can invent a plotline that gets the market to today's heady valuation and makes room for gains from here. But that's like watching one of those cinema thrillers where you can't imagine how the hero can escape, yet he ducks the gunfire and somehow manages to declare victory. It happens in the movies. It's still unlikely to happen in the markets.