SAN FRANCISCO — Home prices in the San Francisco Bay Area reached a new peak for the third time this year.

The research firm CoreLogic says the median sale price of a home in the nine counties last month was $787,000. Half the homes sold for more and half for less.

The price was up 12.6 percent from a year ago. In fact, year-over-year hikes have hit double digits for the past four months.

Peak prices also were reached in June and October.

CoreLogic says the soaring price reflects demand in some of the region’s costliest counties. Expensive homes sold even as the overall number of homes fell.

Southern California home prices also surged last month, tying September’s all-time high of $505,000. The price reflects a super-tight housing market in the six counties.

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