March 31 (Reuters) - The chair of the U.S. Securities and Exchange Commission took on "unicorns," tech startups and other privately held companies on Thursday, admonishing Silicon Valley firms to be fair and honest with their investors.

"Being a private company comes with serious obligations to investors and the markets," Mary Jo White said in a speech at Stanford University on Thursday, according to an advance copy of her remarks. "For the new and evolving markets to be successful, all investors need confidence that they are being treated fairly and that the full range of risks are transparently disclosed."

Stanford is at the heart of Silicon Valley, the California home of tech companies including Apple Inc, Google Inc and Facebook Inc.

In recent years "unicorns," or privately held companies valued at $1 billion or more, have sprung up all over the area.

White questioned some of these companies' "eye-popping valuations," and the ability of their investors and employees to understand their worth.

"The concern is whether the prestige associated with reaching a sky-high valuation fast drives companies to try to appear more valuable than they actually are," she said.

The SEC, the top securities regulator in the United States, has little authority over privately held companies, which unlike publicly traded companies do not have to register or file financial information with the agency regularly. Still, its mission includes protecting investors and facilitating capital formation.

White said that more small, retail investors are now able to put money into startups due to recent changes in the law and that the SEC is closely monitoring new crowdfunding portals where those investors buy stakes in companies.

The commission is also focused on the secondary market developing around pre-IPO companies, she said, referring to privately held businesses on their way to making initial public offerings that will transform them into publicly traded companies.

The secondary market is "structured largely around derivative contracts and other novel ways to capture the economic interest in a pre-IPO company without actually transacting in its stock," she said.

"Depending on the structure of these derivative deals, errors or misconceptions in valuation could be amplified - whether through leverage or simply contracts built on faulty valuations."

White also touched upon what happens after startups go public, noting that these companies should be prepared to protect investors with "enhanced structures and controls for conducting their operations."

(Reporting by Lisa Lambert in Washington; Editing by Matthew Lewis)