NEW YORK (Reuters) - For now, William Ackman is getting the better of Carl Icahn in a well-publicized grudge match between the billionaire investors over Herbalife Ltd (>> Herbalife Ltd.).

Shares of the nutritional supplement company are down 20 percent since the hedge fund managers duked it out by telephone on cable television station CNBC on Jan 25., exchanging barbs about Ackman's bold $1 billion bet that Herbalife is an unsustainable pyramid scheme destined to collapse.

But a big concern for investors in Ackman's $12 billion Pershing Square Capital Management is whether Icahn, who boldly predicted Ackman will get caught in the "mother of all short squeezes," will have the last laugh in this battle of hedge fund titans.

A short squeeze is a trading scenario that occurs from time to time in heavily shorted stocks, when bearish traders are forced to buy shares to avoid big losses - something that ends up pushing the stock only higher.

A short squeeze could be particularly punishing for Ackman's Pershing Square, which has shorted some 20 million shares of Herbalife. That accounts for roughly 56 percent of the shares sold short, according to January 15 data released by Nasdaq.

Short squeezes can quickly wash out bearish traders with weak stomachs who used a loan to borrow shares from a broker. And in a worst case scenario the losses can be unlimited if a stock keeps rising and a trader waits too long to buy shares to close out the short position.

But Pershing Square may be better positioned than other short sellers in Herbalife. A person familiar with the hedge fund said Pershing Square largely used cash on hand to build its short position last year.

Paul Irvine, a finance professor at the University of Georgia who has done research on short squeezes, said because Ackman did not use borrowed money, he does not face the additional risk of a margin call and is less likely to be forced out of his position.

Ackman then may be better able to stand by his conviction that Herbalife is a pyramid scheme that generates most of its revenues from sales to its network of distributors and not from outside consumers. But it could take years for his view to pan out, if ever, setting the stage for a protracted battle with Herbalife's more bullish investors.

Herbalife has denied Ackman's claim it is pyramid scheme and said the company is "financially strong and successful" and operates in 88 markets around the world after 32 years in business.

Pershing Square already weathered an initial short squeeze in Herbalife that began a week after Ackman went public with his criticisms of the company on December 20. That first squeeze began before the January 9 disclosure by Daniel Loeb's Third Point hedge fund that it had amassed an 8 percent equity stake in Herbalife.

Loeb has told his investors Herbalife is a strong financial performer that could see its stock trade up to $55 to $68 a share.

Icahn won't confirm whether he owns Herbalife shares but the Wall Street Journal reported he acquired a small position around the same time as Loeb.

"Less than a week after Ackman's announcement on December 20th, we saw a sharp increase in traders covering their short positions, seemingly resulting in a squeeze," said Karl Loomes, market analyst at SunGard's Astec Analytics, a provider of data on securities lending.

Shares of Herbalife, which initially plunged 40 percent after Ackman's presentation, surged 76 percent during the height of that initial short squeeze, which took place approximately from December 24 to January 15.

During the period Herbalife shares were roaring back from $26.06 to $46.19, the cost of borrowing Herbalife shares from a broker surged from 1 percent to a peak of over 7 percent on an annualized basis, according to data from Astec Analytics.

Since the squeeze ended, the cost of borrowing Herbalife shares has fallen to around 2 percent annually.

Ackman's Pershing Square, according to sources familiar with the fund, has not covered any of its short positions in Herbalife. It ended January up roughly 4 percent, compared to a roughly 1.74 percent gain for the average hedge fund, according to a Bank of America/Merrill Lynch research analyst.

It's not known at what price Ackman began shorting shares of Herbalife but he has said he began doing so last May when the stock was trading around $45 a share. The stock closed trading on Tuesday at $35.75 a share.

Pershing Square's better than average performance came mainly from the performance of other stocks in its portfolio such as Canadian Pacific Railway (>> Canadian Pacific Railway Limited) and Procter & Gamble (>> The Procter & Gamble Company), which both rose sharply in January.

Meanwhile, Loeb's flagship Third Point Offshore fund was up 4.8 percent in January.

Still, there are some indications that another short squeeze could be in the offing, which raises the question of just how much pain and volatility Ackman and his investors can withstand.

Thomson Reuters StarMine compiles an indicator using a stock's volatility over the past 3 and 12 months and the level of short interest to predict the likelihood of a short squeeze over the next 30 days. On a scale of 1 to 100, with 100 meaning a short squeeze is very likely, Herbalife scores a 95.

Another way in which Ackman's big short could go against him is if Herbalife bought back a number of its outstanding shares, or if another company decided to make an offer for Herbalife.

"Companies often increase share repurchases when short selling increases," said Edward Swanson, a professor at the Mays Business School at Texas A&M University.

Herbalife already did exactly that when it increased a share buyback program in May after short-seller David Einhorn questioned the company's disclosures about its network of distributors .

Einhorn recently told his Greenlight Capital investors he is no longer short the stock. It's not known when he began shorting the company's shares.

(Reporting By Peter Rudegeair and Svea Herbst-Bayliss; Editing by Matthew Goldstein and Claudia Parsons)

By Peter Rudegeair and Svea Herbst-Bayliss