SACRAMENTO, Calif. — The pension system for California’s teachers has $56 billion less than it needs to cover the benefits promised to its 852,000 members and their families, the fund reported today, as big investment losses in 2008 continue to reverberate.

The drop in value was enough to trigger an automatic increase in the amount the state must pay into the California State Teachers’ Retirement System, which is the nation’s second largest public pension fund. That will boost the payment from California’s already strained general fund by 20 percent — from $573 million to $688 million — in the fiscal year starting July 1.

The pension shortfall as of June 30, 2010, was $15.5 billion greater than it had been a year earlier, CalSTRS officials said. The fund had expected the shortfall to be even greater, but educators received smaller raises than projected, reducing the ultimate amount of their retirement benefits, and the fund’s investments performed better than expected in the 2009-10 fiscal year.

The pension fund’s assets at the end of June were enough to cover 71 percent of its accrued liabilities during the next 30 years, down from 78 percent a year earlier.