Since 1974, federal judges have been prohibited by federal law from hearing cases involving companies in which they hold even a single share of stock.

The law, signed by former President Gerald Ford about four months after the resignation of Richard Nixon, created a black-and-white rule: If judges, their spouses or minor children own a “legal or equitable interest, however small,” in a plaintiff or a defendant in their court, they must disqualify themselves from the case.

Before...

Since 1974, federal judges have been prohibited by federal law from hearing cases involving companies in which they hold even a single share of stock.

The law, signed by former President Gerald Ford about four months after the resignation of Richard Nixon, created a black-and-white rule: If judges, their spouses or minor children own a “legal or equitable interest, however small,” in a plaintiff or a defendant in their court, they must disqualify themselves from the case.

Before then, federal law relied on judges’ discretion to decide whether a financial conflict of interest was substantial enough to warrant recusal.

The 1974 law requires judges to inform themselves about their own financial interests and to make a reasonable effort to do the same regarding spouses and minor children.

Placing stock in trusts or letting financial advisers manage or control the investment accounts doesn’t excuse judges from their obligations to step aside.

Federal judges must certify that their annual disclosure forms are accurate and complete. They could face civil and criminal sanctions for “knowingly and willingly” falsifying their reports.

The law provides some exceptions: Judges have no duty to disqualify themselves from cases involving parties whose stock is held by a mutual fund in which the judges or family members are invested.

And if judges belatedly discover they hold stock in a party “after substantial judicial time has been devoted to the matter,” they can divest themselves of it and stay on the case, the law says.

In the later Ethics in Government Act of 1978, Congress required that judges file a financial disclosure statement, the primary way the public or a party can determine whether a judge had an ownership interest that required recusal.

Federal law and ethics rules for federal judges are more stringent in parts than the American Bar Association’s Model Code of Judicial Conduct, which most states have adopted. The ABA in 1990 gave judges a reprieve from disqualification if their interest in a party was “insignificant.”

If plaintiffs or defendants learn that a judge on their case has a financial interest that may require a recusal, they can move for a disqualification. In general, it often falls to the judge with the potential conflict to make the call.

In rare instances, federal appeals courts have vacated rulings by judges who declined to disqualify themselves, legal scholars said.

In the 685 violations uncovered by the Journal’s investigation, 56 judges have since directed court clerks to notify parties in 328 lawsuits that they violated the stock-ownership rule and should have recused themselves.

A recusal violation in isolation could be viewed as an oversight, but the Journal’s investigation “raises a more systemic problem of judges chronically neglecting their duty to disqualify in such cases,” said Charles Geyh, a law professor at Indiana University, who has written extensively on judicial disqualification.

In several of the cases, parties have requested that courts hear their cases with new judges. New judges were assigned to consider these requests. In one case, the new judge declined to undo the result. The other requests are pending.

The 1974 law on judicial disqualification provides no penalties for judges who violate it, and judges are rarely sanctioned by the federal judiciary’s ethics watchdogs.

“I know of no public discipline of a judge for failure to recuse,” said Stephen Gillers, a legal ethics expert at New York University School of Law. “But there is rarely public discipline of federal judges for anything.”

Judges have lifetime appointments and can be removed from the bench only through the same impeachment process in the Constitution that applies to presidents.

Write to James V. Grimaldi a tjames.grimaldi@wsj.com, Joe Palazzolo at joe.palazzolo@wsj.com and Coulter Jonesat coulter.jones@wsj.com