Stocks could fall 15 to 20 percent after the Federal Reserve completes its quantitative easing (QE), says Peter Boockvar, chief market analyst at The Lindsey Group.

The Fed already has cut its bond purchases to $45 billion a month from $85 billion last year and is expected to finish its tapering in October or December.

This is the Fed's third round of QE, and stocks dropped sharply at the end of QE1 and QE2, Boockvar tells CNBC. "I think we're going to see a repeat of that," he predicts.

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"I think we've already seen the rumblings of that in the Russell 2000 [and] a lot of high-flying Nasdaq stocks. And I do think it's going to sprinkle into the bigger cap S&P and the Dow names that people have been hiding in."

The Russell 2000 index of small-cap stocks has slid 9.3 percent from its March 4 record high. The S&P 500 stood at 1,872.83 Wednesday morning. A 20 percent drop would put the index at about 1,500.

"The Fed has been driving markets up," Boockvar explains. "And when they pull back, they're going to drive markets down."

Meanwhile, Alan Blinder, former vice chairman of the Fed, says the central bank will fall into conflict when QE finishes and the question of when to further withdraw easing arises.

As the tapering nears an end, "financial markets will fixate completely on the Federal Reserve's eventual exit from its current extraordinarily easy monetary policy," he writes in The Wall Street Journal.

"And it will probably be accompanied by a revival — likely a loud revival — of the hawk-dove wars at the central bank."

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