S&P profits have careened from great, to horrible, to starting a modest comeback. Can liftoff from here set stocks on a fantastic run, or will future earnings fall short of Wall Street's great expectations, leaving equities overpriced and due for a sharp selloff?

Earnings season kicks off this week with eagerly-awaited reports from J.P. Morgan, P&G, Johnson & Johnson, UnitedHealth, and Delta Air Lines among two dozen pillars of the S&P 500. Investors are counting heavily on a strong showing in Q3. A succession of "beats" in the days ahead would demonstrate that momentum is building to propel big cap profits well above their all-time peak set just last year. How else could Wall Street justify, in defiance of the COVID-wracked economy, pushing today's valuations into this golden zone, and claiming that the super-rich prices awarded a Tesla, PayPal or Apple make perfect sense?

It's pretty clear that in 2019, profits were inflated and unsustainable. On the other hand, it's also obvious that the pandemic has sent them into a basement where they won't stay for long. For investors understandably confused about whether equities are a good buy or outrageously expensive, here's the overarching question: When the economy rebounds, where are profits likely to settle?

At the close of last year, the S&P 500's earnings per share, based on four trailing quarters of GAAP net profits, stood at $139.47, an all-time record. Its operating income as a share of sales averaged 11.1%, far above the 9% benchmark from December of 2010 to the start of 2017. Put simply, the 500 benefited from a confluence of tradewinds that set earnings on a far more rapid course than in past decades. Chief among them: an economy running hot at around 3% over many quarters, and wages that lagged the strong expansion in sales.

At the same time, what investors paid for each dollar of earnings also sprinted. At the end of 2019, the 500's price-to-earnings multiple stood at 23.2. That doesn't sound dangerously high versus history. But keep in mind that the lofty valuation came on top of super-high EPS, achieved at the top of the profit cycle.

The pandemic took profits from handsome to horrible. The 500's EPS sank from $35.52 in Q4 of 2019 to a paltry $11.88 in Q1 and $17.83 in Q2. The crisis pushed profitability way below the normal range, and valuations far above the long-term mark. On average, operating margins dropped over those six months to 7.8%, as return on sales swung from great to less-than-mediocre. At the same time earnings shrank, the S&P 500 bridged March's deep valley to gain 10% over last year's close. The combination drove the P/E to 37 based on the past three quarters and analysts' forecasts for Q3. That's number that over the past three decades, was only exceeded in the 2001-2002 bubble, and late 2009, when the financial crisis flattened earnings.

What matters is where profits settle when the economy returns to normal in 2021 or 2022, and the P/E investors award those profits. For EPS, an excellent guide is the CAPE, or cyclically adjusted price-earnings ratio, a measure invented by Yale economist Robert Shiller. The CAPE provides a normalized, durable earnings figure by using a 10-year average of inflation-adjusted profits that eliminates the peaks and troughs, such as the summit in 2019 and the COVID-canyon of Q2 and Q3 of this year. The CAPE puts "normalized" EPS at $108. The CAPE has a downward bias because it uses a decade-long average that doesn't adjust earnings for any growth beyond increases in the CPI. Since EPS on average rises by a couple of points a year above inflation, it's best to raise CAPE earnings by 10% to get a "sustainable" figure for 2020.

Bumping the $108 by 10% renders earnings-per-share of $120. That's the best estimate of where profits will stabilize when GDP returns to its previous trajectory of 2%, say in late 2021 or early 2022. If indeed earnings slow to an annual rate of $120, the S&P would be booking $30 a quarter. That's 14% below the $35 rate in 2019.

It's remarkable that the analysts polled by S&P are forecasting EPS of $28 in Q3. That's a $112 at an annual rate, only 7% below our "up-to-date" number of $120. Indeed, according to the S&P data, earnings of $28 a quarter would generate operating margins of 9.8%, closer to the numbers from 2010 to 2016, before the huge spike in profitability. Hence, the best bet is that profits rise from the Q3 mark of $28 by less than 10% to around $30 (or $120 annualized). In other words, the pandemic has taken the air out of profits in mere months that might have taken far longer, but was still inevitable. By this analysis, we won't see anything even close to the rampaging earnings rebound Wall Steet expects.

Imagine the 500 as S&P 500 Co., an enterprise that earns $120 for each share outstanding. What should the share price be? At the close on Monday, October 13, the S&P hit 3534, just 1.4% off its all-time high reached in early September. So by our reckoning, the S&P is putting a 29.5 multiple on its most probable future profits. Since 1990, its P/E has averaged 21.8; over the past 60 years, the norm is a much slimmer 16.9.

Let's assume a sunny scenario where the multiple drifts back to the 30-year benchmark of around 22. In that case, an S&P 500 index would stand at 2616 ($120 multiplied by 21.8), or each share of our S&P 500 Co. would be worth $2616. That's 26% below its value today, though 17% higher than the nadir of March 20.

Investors may be capricious, but the market's math is a stubborn thing.