Luxury home values rose to an all-time high in Los Angeles in 2005 on the strength of double-digit gains, but appreciation slowed significantly in the fourth quarter, according to a quarterly report released Wednesday by First Republic Bank.

The San Francisco-based bank’s Prestige Home Index, which has tracked luxury homes since 1985, found that Los Angeles values rose 0.7 percent in the fourth quarter of 2005 from the third quarter and jumped 16 percent for the year. The average luxury home in Los Angeles is now a record $2.3 million, up $316,000 from a year ago.

In L.A., the 16 percent increase in 2005 followed a gain of 27.7 percent in 2004, 14.9 percent in 2003 and 3.6 percent in 2002. Since December 2002, the average luxury home in Los Angeles has increased more than $945,000.

Agents interviewed by First Republic said that the market is off to a vigorous start in 2006 after a slow fourth quarter, fueled by a lack of inventory and a large pool of buyers who stayed on the sidelines toward the end of the year. One of the agents surveyed in the report, David Offer of Prudential California Realty in Brentwood, said L.A. on course to see 10 percent or higher appreciation in 2006.

“Continuing demand and limited inventory in some markets may result in increased luxury home prices in 2006, but at a very modest level compared to the past two years,” said Katherine August-deWilde, chief operating officer of First Republic Bank. “In markets where inventories spike, values will be impacted.”

First Republic’s index defines luxury homes as having 3,000 to 6,000 square feet, three to six bedrooms and three to six bathrooms. Properties considered in Los Angeles represent a cross-section of luxury homes in Arcadia, Beverly Hills, Calabasas, La Canada-Flintridge, Encino, L.A., Malibu, Marina del Rey, North Hollywood, Pacific Palisades, Pasadena, Playa del Rey, Santa Monica, Studio City and the West Los Angeles enclaves of Bel Air, Brentwood and Westwood.