Jessica Rinaldi/Reuters
The stake was previously owned by the estate of Lehman Brothers Holdings.
DE Shaw manages about $32 billion in assets.
Schmidt bought the stake through his family office, Hillspire.
Terms of the deal were not disclosed in a press release.
Last year, the WSJ reported that Boston investment firm Affiliated Managers Group was in talks to buy the same 20% stake for $500 million.
When Lehman bought the stake in 2007, it reportedly paid between $750 million and $800 million.
Schmidt is worth $8 billion or $9 billion, according to most estimates.
We reached out to DE Shaw for comment and will update this story if the firm gets back to us.