The Bloomberg headline was reassuring, announcing that “Home Prices in U.S. Rise, Led by 21.7 Percent Jump in Phoenix.” It could have been written to be equally alarming and read, “Phoenix Home Prices Remain 46.2 Percent Below Peak.”

Homeowners in Phoenix undoubtedly grasp the significance of the rewritten headline. A gain of more than 20 percent does little to reverse the pain of a 56 percent decline. Nationally, home prices are more than 30 percent off the highs reached in the summer of 2006.

Large losses hurt wealth much more than most investors realize. If prices drop by half, you need them to double just to get back to the starting point. The national average of home prices is probably at least 10 years away from setting new all-time highs.

Brandes Investment Partners has found that over the very long term, from 1900 to 2002, real estate prices went up an average of 0.8 percent a year. At that rate, a full recovery will take nearly 50 years.

There is room for optimism because price gains tend to be rapid after a bear market. If home prices duplicate the performance seen in the 1940s, when they recovered from the losses of the Great Depression, they could increase an average of 7 percent a year and reach old highs by 2022.

Losses in home prices will take time to recover and even headline grabbing double-digit gains will do little to rebuild homeowner equity quickly.