The largest public pension in America recently loaded up on some volatile stocks, invested more in Warren Buffett's firm, and trimmed a position in a slipping software stock.

In the fourth quarter, California Public Employees' Retirement System more than quadrupled investments in AMC Entertainment and GameStop, two high-profile "meme stocks," and dramatically lifted its holdings in Berkshire Hathaway, Buffett's investment firm, and probably the polar opposite of a meme stock. Calpers, as the pension is known, also sliced off nearly 11% from its stake in Palantir Technologies, a provider of data-analytics software.