Short sellers are betting against a cryptocurrency whose price shouldn’t move.

A few investment firms, including Fir Tree Partners and Viceroy Research LLC, have placed substantial bets in recent months that the price of tether will fall, according to people familiar with the matter. Tether is the most popular currency for trading bitcoin and is supposed to have a fixed value pegged to the U.S. dollar.

Some hedge funds arranged short sales of tether with Genesis Global Trading Inc., one of the larger crypto brokerages for professional investors, said Matt Ballensweig, Genesis’s co-head of trading and lending. About a dozen funds discussed doing the same with Genesis, but many didn’t move forward, Mr. Ballensweig said.

With about $82 billion tether in circulation, tether is the largest so-called stablecoin, a digital asset linked to the dollar and backed by reserves of cash or other financial instruments.

The short sellers follow a pack of regulators, lawmakers, prosecutors, plaintiffs attorneys and amateur sleuths who have spent months, or years, in some cases, attempting to unearth details about a cryptocurrency whose usage has far outpaced its transparency.

Tether isn’t a household name, but it is a cornerstone to the crypto ecosystem. Traders on big exchanges often use tether as an easier way to buy crypto than through bank accounts or wire transfers.

A Tether spokesperson said that the short sellers seem to be involved in a “clever scheme to raise capital from those less knowledgeable, by leveraging on disinformation with the end goal of collecting a management fee.”

“Tether has been stress tested time and time again and passed with flying colors. During such events, its peg remained solid, all redemptions were honored and even the price on exchanges remained stable,” the spokesperson added.

That price stability—tether hasn’t traded lower than 0.999 cents against the U.S. dollar in the past year—means that short sellers’ bets have yet to pay off. And most of Genesis’s initial clients have since exited the initial trade, Genesis said, though some investors have wanted to discuss ways to short tether in recent weeks. Fir Tree’s shorting of tether was earlier reported by Bloomberg News.

Short sellers are betting that the $82 billion portfolio that underpins tether’s value, now the size of a big money-market fund, is at risk of losses that the parent company hasn’t disclosed, according to some of the people familiar with the short positions.

Tether releases new tether tokens when it receives a corresponding amount of dollars from customers. It then invests those proceeds into reserves that back the tokens, a portfolio that includes both safe investments, such as cash and short-term U.S. government securities, and riskier ones, including short-term IOUs known as commercial paper, secured loans to companies and other cryptocurrencies.

Tether’s opacity, combined with its rapid growth, also has made it a frequent topic of conversation in Washington. The Commodity Futures Trading Commission found last year that Tether only held equivalent dollar reserves in its accounts on a little more than a quarter of the days during a roughly two-year period, leading Tether to reach a $41 million settlement with the regulatory agency. Tether neither admitted nor denied wrongdoing as part of its settlement with the CFTC.