The California Public Employees’ Retirement System is making a $1 billion wager that small private equity firms without the heft of the biggest buyout institutions can boost the pension giant’s returns and clout.

Blackstone Inc., the world’s largest alternative-asset manager, cashed out of big deals in the second quarter, mitigating the sting from writedowns on investments and the tumult rippling through markets.

The California Public Employees’ Retirement System sold about $6 billion of its stakes in private equity funds to second-hand buyers, severing ties with a slew of past managers and freeing up cash for new wagers.