Archegos had previously told executives at LendingClub and fuboTV that it was a big shareholder, said people familiar with the matter. But without the regular disclosures that investment firms typically make after they build up a sizable stake in a stock, those executives didn’t have a way to verify the ownership claim.

It might seem surprising that a company can’t pinpoint why its stock suddenly falls, but the Archegos meltdown shows how difficult it can be for executives to determine who owns their company’s stock and for what reason.

A chorus of companies and advocacy groups are calling on regulators to revise financial-disclosure guidelines, particularly around loosely regulated family offices such as Archegos and around the use of derivatives, investor bets linked to stock prices instead of the stocks themselves.

“The U.S. has gone from a leader in timely disclosure to a laggard internationally,” said

Leo Strine Jr.,

a former chief justice of the Delaware Supreme Court who is now a corporate attorney at Wachtell, Lipton, Rosen & Katz.

“Even more embarrassingly, the U.S. fails to cover derivatives and other relevant instruments that affect target companies,” he said. “We have a 1975-era regulatory regime governing a 21st century economy, and it’s high time it was fixed.”

Family offices such as Mr. Hwang’s are lightly regulated. A law passed after the financial crisis intended to shore up financial markets, known as the Dodd-Frank Act, included an exemption for family offices from certain reporting requirements that pertain to most other investment firms managing more than $100 million.

Archegos was still subject to filing other stock-ownership disclosures required by securities laws, but the firm appeared to avoid those through its use of a type of derivative known as total return swaps—investments made by banks on behalf of clients for a fee. The swaps hid Mr. Hwang’s holdings from the companies he invested in, obscuring how much each was exposed to a single investor. Archegos declined to comment.

Archegos is just one of more than 10,000 family offices that collectively manage nearly $6 trillion in assets, said advocacy group Americans for Financial Reform in a letter calling on the Securities and Exchange Commission to take action to tighten disclosure rules around such firms.

“There is no reason why large investors whose decisions can significantly impact other investors and companies should be able to avoid the same scrutiny other investors face simply because of how they choose to structure their trade or their investment firm,” the group said in the letter.

Individual stocks move because of broader factors in the market and separate industries that wouldn’t be clear even with more aggressive disclosure requirements.

Public disclosures showed the various banks that Mr. Hwang had worked with—including

Credit Suisse Group AG

CS -3.56%

,

Nomura Holdings Inc.,

NMR 0.19%

Morgan Stanley

MS -1.21%

and

Goldman Sachs Group Inc.

GS -1.32%

—as being the major shareholders in stocks rather than Archegos. When a bank is listed as a shareholder, companies have no way of knowing if the investment is on behalf of a single investor, multiple investors or the bank itself.

Archegos had built up a large stake in ViacomCBS, so when the stock fell, Archegos and its banks sold off Archegos’s holdings to back up the trades. The banks unloaded more than $30 billion in positions that Archegos had built up in ViacomCBS, Discovery and a handful of other companies, sparking huge declines and setting in motion the family office’s meltdown.

Around the same time, shares of online lender LendingClub slumped 11% on March 26, its biggest single-day pullback since May of last year, and digital streaming service fuboTV’s stock dropped 15% that same day.

In the case of fuboTV, Archegos sought to make an investment into the sports streaming company last summer, according to a person with knowledge of the matter. Just ahead of the deal’s closure, fuboTV learned that Archegos would fund its investment through a swap with Credit Suisse, the person said. The deal culminated with a July 2 securities filing by fuboTV disclosing that Credit Suisse had bought $20 million worth of stock, which had really been for Archegos, the person said.

At the time, Credit Suisse’s involvement was more of a reassurance than a red flag, suggesting the bank had done its own due diligence on Archegos, the person said.

Mr. Hwang told associates that he had invested in LendingClub over a number of years, people familiar with the firm said.

LendingClub and fuboTV executives were stumped by the sudden pullback of their share prices until news broke of the Archegos meltdown, according to people familiar with the matter.

If Archegos continued to own either stock around the time of its meltdown, the firm might have driven down the share price by selling off its holdings. Neither company had current filings detailing whether Archegos continued to own shares or how many.

Rank-and-file employees at fuboTV who were looking for answers passed around a tweet from a pseudonymous Twitter account after its shares fell on March 26, according to a person familiar with the matter.

The tweet purported to show Archegos positions held at Nomura, including 4.7 million shares of fuboTV. The employees cross-referenced fuboTV’s largest shareholders on FactSet and saw that its largest one was Nomura, with 4.7 million shares as of the end of 2020.

One other firm on the list, Viper Energy Partners LP, a spinoff from West Texas oil producer Diamondback Energy Inc., said the buildup of stakes by banks’ prime brokerage arms was unusual and now after the incident suggests that Archegos may have been involved.

Nomura’s prime-brokerage arm is one of Viper Energy’s largest shareholders, owning a nearly 5% stake. That large of a stake by a prime broker is rare, said

Kaes Van’t Hof,

president of Viper Energy. The firm hasn’t tried to confirm whether Archegos was involved, Mr. Van’t Hof said, adding that it is “hard to impossible to find out from the prime brokers who actually owns the stock” even if they had reached out. Nomura declined to comment.

Shares of Viper Energy had mostly fallen around the time Archegos’s bets collapsed, with shares dropping nearly 10% over a three-week stretch ended April 9.

“It’s a bit one-sided how much public companies have to disclose versus investment funds,” Mr. Van’t Hof added.

LendingClub and fuboTV shares have mostly fallen since late March, with the latter’s declines drawing it down 30% for the year. Shares of Viper Energy, meanwhile, have rebounded, rising 20% so far this month.

One other stock Mr. Hwang might have been involved with is Chinese educational app maker

iHuman Inc.

IH -3.62%

Shares of the company had mostly struggled since it went public in October. But on March 29, amid Archegos’s fall, iHuman’s stock experienced its second-biggest decline ever, sliding 13%.

Like Mr. Hwang’s other bets that are now publicly known, banks such as Credit Suisse and Nomura populate iHuman’s top holdings, according to FactSet. The only other clue that the family office might have been involved is that an Archegos junior analyst had contacted iHuman for a meeting, a person with knowledge of the matter said.

A spokesman for iHuman said the company supported the call for regulators to revise disclosure guidelines for investment firms.

“I think we are in agreement with many companies in the market that there should be greater transparency around the disclosure of fund holdings,” the spokesman said in an email. “We hope the SEC will take a look at this and help increase transparency in the market.”

SEC Corporation Finance Director John Coates told an American Bar Association panel Wednesday he is personally supportive of looking at stricter disclosure requirements for reporting of derivatives trading positions, which today may not need to be disclosed in public filings.

For Archegos, Mr. Coates said disclosures were “the most natural way to respond to the biggest problem there.”

Mr. Coates, whose division oversees disclosures, said he didn’t know whether the SEC would seek to propose changes. That is up to new Chairman

Gary Gensler.

—Dave Michaels contributed to this article.

Write to Michael Wursthorn at Michael.Wursthorn@wsj.com and Peter Rudegeair at Peter.Rudegeair@wsj.com