By Juliet Chung 

The family office of Google Inc.'s Eric Schmidt bought a 20% stake in New York hedge-fund firm D.E. Shaw Group from the estate of Lehman Brothers Holdings Inc., the parties said Thursday.

It sold for roughly $500 million, a discount from the price of at least $750 million to $800 million Lehman paid, according to people familiar with the matter. Lehman, a securities firm, bought the stake in 2007 and collapsed in September 2008 during the height of the last financial crisis.

The lower price partially reflects the restrictive terms of the deal Lehman originally negotiated that the new owner was expected to assume, according to people familiar with the matter.

Lehman's 2007 deal with D.E. Shaw was part of a wave of precrisis deals from banks looking to buy their way into the hedge-fund business. Since then, banks have pulled back from the business partly because of regulatory pressures. Investment groups have stepped into the void, raising billions of dollars or using their own balance sheets to buy stakes.

Mr. Schmidt's family office, Hillspire LLC, began discussing a potential purchase of the stake about a year ago. Hillspire is run by former Treasury official and hedge fund executive Chuck Chai, and manages more than $5 billion of Mr. Schmidt's and his family's wealth. It has been a D.E. Shaw investor for at least five years, according to a person familiar with the matter.

The stake is passive, meaning Hillspire will share in the roughly $36 billion firm's profits but won't have any say in its management. The return for D.E. Shaw across its funds this year was 8.4% through March, according to a person familiar with the matter.

"As a long-standing investor in the D.E. Shaw group's funds, I have the highest regard for their team and the firm that they've built," Mr. Schmidt said in a statement Thursday.

The deal was partly attractive to D.E. Shaw because Hillspire is viewed as a longer-term investor, and doesn't have the regulatory disclosure requirements that public companies do. Meanwhile, the stake, which has been a profitable investment for the Lehman estate, is expected to generate steady income for Hillspire.

The Lehman estate had been looking to sell its D.E. Shaw stake since late 2013, but the passive role that Lehman had originally negotiated, among other restrictions, diminished the interest of some prospective buyers, according to people familiar with the matter.

The drawn-out sales process, run by Goldman Sachs Group Inc., showed the complexities that can arise when a stake is being resold rather than negotiated directly between a hedge fund and a buyer, said people familiar with the matter.

Firms that looked at buying the stake included Blackstone Group LP, KKR & Co., Neuberger Bergman's Dyal Capital Partners, The Wall Street Journal previously reported.

Affiliated Managers Group Inc. had been close to buying the stake but those talks stalled last year as AMG sought to change the terms.

Write to Juliet Chung at juliet.chung@wsj.com

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