Calpers, the largest U.S. pension, has faced pressure to hit its 6.8% return target.
The alleged affair is the latest in a string of revelations about Musk's personal life.
The subpoenas relate to an inquiry last year from the SEC, the company said.
U.S. equity holdings at the billionaire's investment firm dropped by $205 million in the third quarter.
Laurene Powell Jobs used GRATS to give $500 million to family and friends, the report said.
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