But more broadly, Wall Street consensus expects little profit growth in S&P 500 companies for the second quarter.
(Read More: Why Bullish BofA Thinks Market Gains Might Be Over)
That could be bad news for stocks, considering that earnings per share collectively has closely mirrored the 140 percent growth in the stock market index since the March 2009 lows.
All the market talk about what the Federal Reserve has in store, Levkovich said, has come "almost without spending any time looking at earnings estimates or trends less than a month before second-quarter results are released."
"Such a thought process seems ill-founded since earnings matter the most for equities, in our opinion, and there is relatively robust statistical evidence to back up that contention," he said. "In this respect, we have been a tad shocked by the surge in negative-to-positive pre-announcement trends that make 2009's surge appear less worrisome in retrospect."
Indeed, a flat earnings outlook suggests a flat market or worse, particularly after the sour reaction following last week's pronouncement from Fed Chairman Ben Bernanke that the central bank's $85 billion a month liquidity program could wrap up in 2014.
(Read More: Taper Tipoff? Bernanke Hints Easing End Is Nearing)
For his part, Levkovich is no alarmist. His team espouses what it calls a "Raging Bull" theory that sees a strongly positive long-term market outlook.
But his words do fit with an increasingly likely outlook in which the market will be at the least hard-pressed to match the 11.6 percent year-to-date gains on the S&P 500.
Bullish investors have been counting on growth to fuel the next leg of the rally.
Profit outlooks, though, seem too rosy.
S&P Capital IQ projects the third quarter to show 6.7 percent gains and the fourth quarter to register 11.6 percent. Levkovich calls the expectations "a bit too optimistic," which seems like an understatement considering that most economic indicators outside of housing are showing signs of a slowdown.
(Read More: Here's Who Wins and Who Loses From Fed Taper Talk)
He sees the future entailing a healthy pulling back of earnings estimates, which investors should watch closely.
"We suspect that such trimming may come about over the next six months, rather than in one fell swoop," Levkovich said. "Thus, future estimate cuts could be a drag on equity prices and investors need to shift their attention away from just watching every wiggle out of the Fed."
—By CNBC's Jeff Cox. Follow him
@JeffCoxCNBCcom on Twitter.