After nearly five years of punishing paper losses and mockery on Wall Street, Bill Ackman has finally given up his $1 billion short bet against Herbalife.

The embattled hedge-fund tycoon still insists that the giant supplements distributor is a “pyramid scheme,” and has spent heavily on a new batch of put options that will pay off if Herbalife’s stock falls.

But Ackman also admitted Wednesday that the big, bold short bet his hedge fund Pershing Square Capital made against Herbalife in 2012 now looks too risky to stomach any longer.

Herbalife shares are up more than 50 percent this year, due in part to a stock buyback completed last month by the company, which vehemently denies Ackman’s allegations that it practices a predatory business model.

The rally has likewise been driven by investors anticipating a “short-squeeze,” in which short sellers would have quickly buy back the stock they’ve sold to make their bearish bets — a move that also drives up the price.

Among those who have bet directly against Ackman on Herbalife is his nemesis, billionaire Carl Icahn, who now owns nearly a quarter of Herbalife shares.

“There is no longer an opportunity to squeeze Pershing Square,” Ackman said in a Wednesday interview with CNBC.

Instead of shorting Herbalife, Ackman is now shelling out cash for put options, which will pay off if Herbalife shares drop but which don’t pose the risk of a short squeeze.

Unlike holding shares short, where Pershing Square’s losses could be unlimited, Ackman said losses would now be capped at 3 percent of capital — what he called “modest investment.”

Nevertheless, “They’re going to charge Ackman a premium … for the privilege of him owning a put,” Ihor Dusaniwsky, head of predictive analytics at financial analytics firm S3 Partners told The Post.

Ackman’s dealer — who sold the put option — now holds the short position, according to Dusaniwksy.

“Ackman has increased his expenses but he has increased his safety,” Dusaniwsky said, estimating that this year alone Ackman has faced an estimated $455 million paper loss on Herbalife.

Pershing Square declined to comment on its Herbalife paper losses, or the premiums it has paid to drop its short bet, or the terms on the new put options it has purchased.

But that didn’t stop Ackman on Wednesday from continuing to defend his costly war against the company.

“We’ve been entirely right on our Herbalife investment in terms of the fundamentals of the business. We’ve been wrong on the share price,” Ackman told CNBC.

Herbalife’s stock has more than doubled since Ackman announced his short position. An investigation by the Federal Trade Commission that concluded last year tore into Herbalife’s business practices but stopped short of calling it a pyramid scheme and shutting it down.

Pershing Square is down 5.8 percent through the end of September.

Reps from Herbalife did not respond to requests to comment.

Herbalife shares were down 2.4 percent at $70.85 Wednesday.