THE house-price boom that preceded the financial crisis was remarkable for its scope and scale. With a very few exceptions, there seemed only one way for prices to go: up. Things have been more diverse since, and our latest review of house prices is a picture with dramatic chiaroscuro. A brightening outlook for America stands out against the darkening tones of the beleaguered economies on the periphery of the euro area.

In the countries we track, house prices are rising and falling in equal numbers. Over the past year prices have jumped most in Hong Kong (see table), prompting further government efforts to cool the market. They have dropped by 9.3% in Spain, the heaviest faller. The overall trend is down, however, since in three of the countries where prices are rising they are doing so at a slower pace than a year ago—in Canada, for example, they are up by 3.3% compared with 7.1% 12 months ago.

A similar diversity characterises valuations. To gauge whether homes are cheap or expensive we use two measures, both of which compare current estimates with a long-run average (in most countries, going back to 1975). This average is our benchmark for “fair value”.

The first gauge is a price-to-rents ratio. This is analogous to the price-earnings ratio used for equities, with the rents going to property investors (or saved by homeowners) equivalent to corporate profits. The measure displays a massive range, from a whopping 78% overvaluation in Canada to an undervaluation of 37% in Japan. The other measure, the ratio of prices to disposable income per person, stretches from a 35% overvaluation in France to a 36% undervaluation, again in Japan.

America’s housing-market revival looks sustainable in part because the sharp correction in house prices over the past few years has made homes cheap by historical standards. A year ago house prices were still falling, by 3.6%. There has been a turnaround since: the latest data show prices rising by 4.3%. But based on the ratio of prices to rents, houses are still 7% undervalued; judged by the price-to-income ratio, they are 20% below fair value. It also helps that mortgage rates are at historic lows and are likely to stay that way, since the Federal Reserve has promised to keep an extremely loose monetary stance for the next couple of years.

Homeowners may be coming up for air in America, but their plight is deepening across much of Europe. The agony is most acute in Spain, where declines have gathered momentum (the 9.3% fall in our latest round-up follows a drop of 5.5% the previous year). Other big euro-zone economies are also heading in the wrong direction. In Italy and the Netherlands the pace of decline has quickened; in France prices are now edging down after a brief recovery. European valuations are most stretched in France, by as much as 50% judging by rents and by 35% on the basis of incomes. This compares with around 20% overvaluation on both counts in Spain, despite the price falls to date. But any house-price collapse in France is likely to be modest compared with Spain’s. Spain’s bust reflects a massive oversupply of housing built in the construction boom, and an unemployment rate that rose to 26.6% in November, the highest in Europe. France’s unemployment rate has edged up to 10.5% but that is in a different league to Spain’s; its banks are in better shape than Spanish ones, too. The anomaly among Europe’s big economies is Germany, where house prices are rising by a restrained 2.7%, the same pace as a year earlier. Thanks to their good fortune in missing the housing party before the financial crisis, German homeowners have a decent chance of making further gains. Homes there are 17% undervalued compared with historical averages on both our measures. German purchasers can benefit from rock-bottom borrowing costs, unlike their counterparts in peripheral Europe. One of the lowest rates of unemployment (5.4%) in Europe further underpins the housing market.

Explore and compare global housing data over time with our interactive house-price tool

British house prices have posted only modest overall declines over the past five years (although rising rents and incomes have also helped bring things closer to fair value). But the British market may do rather better than still-stretched valuations suggest. For one thing, it does not suffer from the glut of empty homes that has created ghost towns in Ireland and Spain. And according to the Bank of England’s latest credit-conditions survey lenders are more willing to make mortgage finance available than at any time since the financial crisis. The number of mortgage approvals for new purchases is at its highest for almost a year.

Overvaluation is especially marked in Canada, particularly with respect to rents (78%) but also in relation to income (34%). Mark Carney, the country’s central-bank governor, who is soon to jump ship to join the Bank of England, where he takes over from Sir Mervyn King in July, may have shown good market timing with his move to London as well as a deft hand in negotiating his lavish remuneration. Singapore and Hong Kong also look vulnerable to a correction, given the overvaluation on their price-to-rents ratios.

Misalignments with our gauges of fair value can persist for a long time, of course. That may spare countries where house prices have clearly overshot from a painful bust, but it may also mean that some markets end up mimicking Japan’s long descent and badly undershoot. At some point, central banks will have to take away the balm of easy money. If housing markets remain so fragile when they are getting so much help, they may break when it is removed.