SAN FRANCISCO — California luxury home prices rose at a slower rate in the second quarter than they had in the first, according to the First Republic Prestige Home Index.

The index is compiled by First Republic Bank, a publicly traded commercial bank with assets of $3.9 billion.

San Diego’s quarterly gain was 2.8%, and the San Francisco Bay Area and Los Angeles had increases of less than 1%. The average price of a Bay Area luxury home in the second quarter was $2,394,901 — an increase of 0.8% from the first quarter.

San Francisco area luxury home prices have risen 3.4% since Jan. 1 and 23.3% from a year earlier, the bank said. In Los Angeles, the average price of luxury homes rose 0.8% in the second quarter, to $1,284,517, and prices were up 8.3% since Jan. 1 and 13.6% from a year earlier. In San Diego, prices rose 2.8% in the second quarter, to $1,310,633, up 6.2% since January and 19.1% from a year earlier.

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