If federal investigators are able to make a case that California misled investors about the risk in its pension fund, it would send a powerful signal to other public funds, which almost without exception base their financial reporting on average annual investment returns of about 8 percent a year, something hard to defend in today’s markets, no matter what the investment mix.

The S.E.C.’s goal is to force public pension funds to be more open, not just about their investments but about how their risk may affect the finances of the state. It is unlikely that the S.E.C. would impose any penalty because that would force taxpayers to pay for wrongs they knew nothing about. In the New Jersey case, the S.E.C. imposed no penalty but publicized the case in hopes it would be a deterrent.

Any accusation of securities fraud could take years because public finance is a new area for the S.E.C. and any case would rely on novel legal theories. It would be a blow to Calpers, which has used its institutional clout for years to promote good corporate governance and truth in accounting. Calpers has recently pushed for boardroom reforms at JPMorgan Chase, Goldman Sachs, Apple, and BP, among others. And it has sued Moody’s, Fitch and Standard & Poor’s, accusing them of giving “untrue, inaccurate and unjustifiably high” ratings to structured investment vehicles that failed in the mortgage collapse.

Its activism has served as a role model for smaller public pension funds that have also had losses, but might not have been able to challenge corporate governance practices on their own. But now the tables have turned, because S.E.C. investigators hope to use Calpers as an example in a case about of how misleading pension disclosures can amount to securities fraud, according to the person with knowledge of the investigation. Like most public plans, Calpers has maintained that its accounting methods are appropriate and that it is in full compliance.

Calpers has lately been under fire for a big benefit increase in 1999. At that time the fund ran various assumptions on how its investments might do. It discussed them in a public meeting but the state did not put them into its bond prospectus, which was the responsibility of the state treasurer, then Phil Angelides, who also sat on the board of Calpers.

In the years after that, Calpers stepped up its investments in real estate, riding the market up and then crashing when the housing bubble burst. The worst case, created by Calpers’ staff, turned out to be oddly prescient. It said the state might have to come up with $3.95 billion a year in fresh money for the pension fund by the end of 2010. In fact, the state has to contribute $3.88 billion.

Mr. Angelides, now chairman of the Financial Crisis Inquiry Commission, was not available to comment Thursday because the commission was finishing its report.