Investors are using a new tactic to pressure some of the country’s biggest companies. And the firms are fighting back.

The bets, called total return swaps, excite activists but terrify corporate managers. Hedge funds have used them in high-profile campaigns against the management of companies like CSX and Target, and they have quietly grown into a $1 trillion market. What makes swaps alarming (to firms) and alluring (to activists) is the possibility that they can be used to exert pressure on companies, in spite of the fact that they’re unregulated, carry no disclosure requirements, and are nearly impossible to track.

Think of them as private wagers on a firm’s stock price: A bank pays you if the price of a stock goes up; you pay the bank if the price goes down. The more the price changes, the more money changes hands. It’s like betting on a sporting event, except that in the case of swaps, you win more if your team scores more points and lose more if it scores fewer.

Who does this? Activists Carl Icahn and Nelson Peltz have bet on companies without buying their shares outright. Last Christmas Eve, investor Bill Ackman disclosed that he had used private contracts to gain “economic exposure” to more than 80 million shares of Target, or more than 12 percent of the company. He did so without buying Target shares. Instead, the exposure came from side bets placed on Target’s share price. Most recently, two hedge funds have bought swaps and pressured the management of the 180-year-old railroad CSX, landing both sides—and me—in court.

There are various reasons to purchase swaps. Some investors use them to buy into otherwise inaccessible markets, for example firms listed on foreign exchanges. Others use them to limit taxes on dividends or capital gains. Another benefit is leverage. For a swap based on $100 worth of stock, a bank might require that the investor pay just $10 up front.

But the reason swaps have become controversial is that they’re done in secret. Investors can use swaps to gain economic exposure to a company without disclosing their positions. Whereas shareholders trade in real-life stock markets, where it’s relatively easy to track their moves, swapholders are hidden in a virtual reality where disclosure rules don’t apply. Actual ownership of swap-related stock is negotiated privately between swapholders and banks, and neither side is obligated to buy actual shares or tell anyone about their swaps. Managers despise this secrecy; they want to know who has bet on their companies.

Swaps have been in the headlines recently as a result of a legal dispute between CSX and two hedge funds. The railroad firm sued the funds, claiming in court that they had illegally used swaps to pressure CSX, even though they initially didn’t own any of its stock.

Before the CSX dispute, investors had assumed that a rule requiring disclosure of share positions of 5 percent or more didn’t apply to swaps. After all, a swap was just a side bet, and swap­holders didn’t own shares. Nor did they enjoy the advantages of stock ownership, such as receiving dividends from the company or a right to vote. Although the Securities and Exchange Commission had not released a formal regulation for swaps, investors followed a related ruling that 5 percent positions in security futures, which resemble swaps, could remain secret. Even after the hedge funds in the CSX case had accumulated swaps amounting to side bets on 12 percent of CSX shares, they didn’t disclose their positions.

The absence of an S.E.C. rule left just enough room for CSX’s lawyers to combine two arguments into a claim that the swaps amounted to ownership and therefore should have been disclosed. CSX’s expert witness testified, first, that banks offering swaps “had to” buy actual CSX shares as hedges and, second, that the hedge funds had power over how the banks voted and sold those shares. CSX lawyers said that this power amounted to ownership and that ownership had to be disclosed.

It’s easy to demonize the hedge funds here. Secret use of swaps can appear unseemly, and it no doubt rattles management. But in this case, the hedge funds—the Children’s Investment Fund and 3G Capital Partners—are right, which is why I agreed to testify as a paid expert witness for them in the CSX case. (I’m a law professor at the University of San Diego.)

The response to CSX was straightforward: The swap contracts didn’t give the hedge funds any power over how banks voted any of the shares they bought as hedges. Although banks frequently hedged swaps by buying shares, they didn’t have to; they were free to hedge in other ways or not to hedge at all. Betting on CSX shares wouldn’t make a hedge fund an owner of shares any more than betting on the San Diego Padres would make me an owner of the team.

The judge in the case expressed skepticism about the hedge funds’ motives and ability to influence the banks and asked the S.E.C. to weigh in. After the S.E.C.’s Division of Corporation Finance took the hedge funds’ side, the judge waffled. He found that the hedge funds should have disclosed their swaps but didn’t restrict the voting of any CSX shares. The result was a win for the funds; though votes were still being counted at press time, it appeared that CSX shareholders would elect most, if not all, of the fund-backed directors.

The central question—whether a swapholder should be treated as a shareholder—remains tricky, and this is where the upcoming battle will be fought. Although swaps gave the hedge funds no real claim on CSX, their economic incentives were exactly the same as an actual shareholder’s. Which party was the true CSX “owner”: the indifferent banks with voting shares but no economic exposure (since the banks both owned shares and bet on them through the swaps)? Or the hedge funds with side bets tied to the share price but no actual shares?

The strange thing about swaps is that actual shareholders with power (banks) have little incentive to act in a company’s best interest, while those with side bets but no votes (hedge funds) do. Indeed, as the hedge funds boosted their exposure to CSX, the company’s share price rose 80 percent during a time when the markets were flat.

For more than a decade, I have been a critic of various aspects of the market, including swaps. But in my view, the real problem here arises from banks buying shares as hedges, not from activists purchasing swaps. Banks that hold shares but do not have the same economic interests as shareholders are corporate noncitizens, like those who leave their country and renounce their citizenship. They should not have the right to vote in a corporate election.

The only true solution to the swaps quandary would be to ensure that banks cannot and do not vote any shares they purchase as hedges. The secrecy of swaps would then be of less consequence to managers. When hedge funds actually decide to challenge managers—to go activist—they would need to leave the secretive world of swaps and buy actual shares. Indeed, this is precisely what the hedge funds in the CSX case ultimately did. By the time the CSX vote came about, the hedge funds owned more than 8 percent of CSX’s actual shares, in addition to their swaps.

Regulators, or perhaps companies, could implement reform by barring votes from shareholders who lack an economic interest. Meanwhile, managers will be left wondering whether someone is secretly buying swaps and putting them at risk.